Aesthetics, art, beauty and mind Culture Logic and First Principles of right reason

Logic & First Principles, 14: Are beauty, truth, knowledge, goodness and justice merely matters of subjective opinions? (Preliminary thoughts.)

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We live in a Kant-haunted age, where the “ugly gulch” between our inner world of appearances and judgements and the world of things in themselves is often seen as unbridgeable. Of course, there are many other streams of thought that lead to widespread relativism and subjectivism, but the ugly gulch concept is in some ways emblematic. Such trends influence many commonly encountered views, most notably our tendency to hold that being a matter of taste, beauty lies solely in the eye of the beholder.

And yet, we find the world-famous bust of Nefertiti:

The famous bust of Nefertiti, found in Thutmose’s workshop (notice, how subtle smiles will play a role in portraits of beautiful women)

Compare, 3400 years later; notice the symmetry and focal power of key features for Guinean model, Sira Kante :


Sira Kante

And then, ponder the highly formal architecture of the Taj Mahal:

The Taj Mahal

ADDED: To help drive home the point, here is a collage of current architectural eyesores:

Current Eyesores

Added, Mar 23 — Vernal Equinox: The oddly shaped building on London’s skyline is called “Walkie-Talkie” and due to its curved surface creates a heating hazard at the height of summer on a nearby street — yet another aspect of sound design that was overlooked (this one, ethical):

Louvre as seen from inside the Pei pyramid

Since it has come up I add the Louvre’s recent addition of a Pyramid (which apparently echoes a similar temporary monument placed there c. 1839 to honour the dead in an 1830 uprising). Notice, below, how symmetric it is in the context of the museum; where triangular elements are a longstanding part of the design as may be seen from the structure below the central dome and above many windows. Observe the balance between overall framework and detailed elements that relieve the boredom of large, flat blank walls. Historically, also, as Notre Dame’s South Rose Window so aptly illustrates, windows and light have been part of the design and function of French architecture. Notice, how it fits the symmetry and is not overwhelmingly large, though of course those who objected that it is not simply aligned with the classical design of the building have a point:

Yet again, the similarly strongly patterned South Rose Window at Notre Dame (with its obvious focal point, as well as how the many portraits give delightful detail and variety amidst the symmetry) :

Notre Dame, South Rose Window

Compare, patterning, variety and focus with subtle asymmetry in part of “Seahorse Valley” for the Mandelbrot set:

Seahorse Valley zoom, Mandelbrot set

I add, let us pause to see the power of spirals as a pattern, tying in the Fibonacci sequence and thus also the Golden Ratio, Phi, 1.618 . . . (where concentric circles as in the Rose Window, have much of the same almost hypnotic effect and where we see spirals in the seahorse valley also):

Here, let us observe a least squares fit logarithmic spiral superposed on a cut Nautilus shell:

Let us also note, Da Vinci’s Vitruvian Man, as an illustration of patterns and proportions, noting the impact of the dynamic effect of the many S- and J-curve sculptural forms of the curved shapes in the human figure:

Note, a collage of “typical” human figure proportions:

Contrast the striking abstract forms (echoing and evoking human or animal figures), asymmetric patterning, colour balances, contrasts and fractal-rich cloudy details in the Eagle Nebula:

The Eagle Nebula

Also, the fractal patterning and highlighted focus shown by a partially sunlit Grand Canyon:

Grand Canyon

And then, with refreshed eyes, ponder Mona Lisa, noticing how da Vinci’s composition draws together all the above elements:

Mona Lisa — the most famous portrait
A modern reconstruction of what Mona Lisa may have looked like on completion

Let me also add, in a deliberately reduced scale, a reconstruction of what the portrait may have originally looked like. Over 400 years have passed, varnish has aged and yellowed, poplar wood has responded to its environment, some pigments have lost their colour, there have apparently been over-zealous reconstructions. Of course, the modern painter is not in Da Vinci’s class.

However, such a reconstruction helps us see the story the painting subtly weaves.

A wealthy young lady sits in a three-quarters pose . . . already a subtle asymmetry, in an ornate armchair, on an elevated balcony overlooking a civilisation-tamed landscape; she represents the upper class of the community that has tamed the land. Notice, how a serpentine, S-curved road just below her right shoulder ties her to the landscape and how a ridge line at the base of her neck acts as a secondary horizon and lead in. Also, the main horizon line (at viewer’s eye-level) is a little below her eyes; it is relieved by more ridges. She wears bright red, softened with dark green and translucent layers. Her reddish brown hair is similarly veiled. As a slight double-chin and well-fed hands show, she is not an exemplar of the extreme thinness equals beauty school of thought. The right hand is brought over to the left and superposed, covering her midriff — one almost suspects, she may be an expectant mother. Her eyes (note the restored highlights) look to her left . . . a subtle asymmetry that communicates lifelike movement so verisimilitude, as if she is smiling subtly with the painter or the viewer — this is not a smirk or sneer. And of course the presence of an invited narrative adds to the aesthetic power of the composition.

These classics (old and new alike) serve to show how stable a settled judgement of beauty can be. Which raises a question: what is beauty? Like unto that: are there principles of aesthetic judgement that give a rational framework, setting up objective knowledge of beauty? And, how do beauty, goodness, justice and truth align?

These are notoriously hard questions, probing aesthetics and ethics, the two main branches of axiology, the philosophical study of the valuable.

Where, yes, beauty is recognised to be valuable, even as ethics is clearly tied to moral value and goodness and truth are also valuable, worthy to be prized. It is unsurprising that the Taj Mahal was built as a mausoleum by a King to honour his beautiful, deeply loved wife (who had died in childbirth).

AmHD is a good place to start: beauty is “[a] quality or combination of qualities that gives pleasure to the mind or senses and is often associated with properties such as harmony of form or color, proportion, authenticity, and originality. “

Wikipedia first suggests that beauty is:

a property or characteristic of an animal, idea, object, person or place that provides a perceptual experience of pleasure or satisfaction. Beauty is studied as part of aesthetics, culture, social psychology, philosophy and sociology. An “ideal beauty” is an entity which is admired, or possesses features widely attributed to beauty in a particular culture, for perfection. Ugliness is the opposite of beauty.

The experience of “beauty” often involves an interpretation of some entity as being in balance and harmony with nature, which may lead to feelings of attraction and emotional well-being. Because this can be a subjective experience, it is often said that “beauty is in the eye of the beholder.” However, given the empirical observations of things that are considered beautiful often aligning with the aforementioned nature and health thereof, beauty has been stated to have levels of objectivity as well

It then continues (unsurprisingly) that ” [t]here is also evidence that perceptions of beauty are determined by natural selection; that things, aspects of people and landscapes considered beautiful are typically found in situations likely to give enhanced survival of the perceiving human’s genes.” Thus we find the concepts of unconscious programming and perception driven by blind evolutionary forces. The shadow of the ugly gulch lurks just beneath the surface.

Can these differences be resolved?

At one level, at least since Plato’s dialogue Hippias Major, it has been well known that beauty is notoriously hard to define or specify in terms of readily agreed principles. There definitely is subjectivity, but is there also objectivity? If one says no, why then are there classics?

Further, if no, then why could we lay out a cumulative pattern across time, art-form, nature and theme above that then appears exquisitely fused together in a portrait that just happens to be the most famous, classic portrait in the world?

If so, what are such and can they constitute a coherent framework that could justify the claim to objective knowledge of aesthetic value?

Hard questions, hard as there are no easy, simple readily agreed answers. And yet, the process of addressing a hard puzzle where our intuitions tell us something but it seems to be forever just beyond our grasp, is itself highly instructive. For, we know in part.

Dewitt H. Parker, in opening his 1920 textbook, Principles of Aesthetics, aptly captures the paradox:

Although some feeling for beauty is perhaps universal among men, the
same cannot be said of the understanding of beauty. The average man,
who may exercise considerable taste in personal adornment, in the
decoration of the home, or in the choice of poetry and painting, is
at a loss when called upon to tell what art is or to explain why he
calls one thing “beautiful” and another “ugly.” Even the artist and
the connoisseur, skilled to produce or accurate in judgment, are often
wanting in clear and consistent ideas about their own works or
appreciations. Here, as elsewhere, we meet the contrast between feeling
and doing, on the one hand, and knowing, on the other.

Of course, as we saw above, reflective (and perhaps, aided) observation of case studies can support an inductive process that tries to identify principles and design patterns of effective artistic or natural composition that reliably excite the beauty response. That can be quite suggestive, as we already saw:

  • symmetry,
  • balance,
  • pattern (including rhythms in space and/or time [e.g. percussion, dance]),
  • proportion (including the golden ratio phi, 1.618 etc)
  • unity or harmony (with tension and resolution), highlighting contrast,
    variety and detail,
  • subtle asymmetry,
  • focus or vision or theme,
  • verisimilitude (insight that shows/focusses a credible truth/reality)
  • echoing of familiar forms (including scaled, fractal self-symmetry),
  • skilled combination or composition
  • and more.

We may see this with greater richness by taking a side-light from literature, drama and cinema, by using the premise that art tells a story, drawing us into a fresh vision of the world, ourselves, possibilities:

Already, it is clear that beauty has in it organising principles and that coherence with variety in composition indicates that there is indeed organisation, which brings to bear purpose and thus a way in for reflective, critical discussion. From this, we reach to development of higher quality of works and growing knowledge that guides skill and intuition without stifling creativity or originality. So, credibly, there is artistic — or even, aesthetic — knowledge that turns on rational principles, which may rightly be deemed truths.

Where, as we are rational, responsible, significantly free , morally governed creatures, the ethical must also intersect.

Where also, art has a visionary, instructive function that can strongly shape a culture. So, nobility, purity and virtue are inextricably entangled with the artistic: the perverse, ill-advised, unjust or corrupting (consider here, pornography or the like, or literature, drama and cinema that teach propaganda or the techniques of vice) are issues to be faced.

And, after our initial journey, we are back home, but in a different way. We may — if we choose — begin to see how beauty, truth, knowledge, goodness and justice may all come together, and how beauty in particular is more than merely subjective taste or culturally induced preference or disguised population survival. Where also, art reflecting rational principles, purposes and value points to artist. END

PS: To document the impact of the beauty of ordinary things (we have got de-sensitised) here are people who thanks to filtering glasses are seeing (enough of) colour for the first time:

Similarly, here are people hearing for the first time:

This will be a bit more controversial, but observe these Korean plastic surgery outcomes:

399 Replies to “Logic & First Principles, 14: Are beauty, truth, knowledge, goodness and justice merely matters of subjective opinions? (Preliminary thoughts.)

  1. 1
    kairosfocus says:

    Logic & First Principles, 14: Are beauty, truth, knowledge, goodness and justice merely matters of subjective opinions? (Preliminary thoughts.)

  2. 2
    StephenB says:

    KF,
    Congratulations! This brilliant presentation on the objective and subjective components of beauty fulfills a desperate need. It should be required reading for all millennials.

  3. 3

    And anyone wanting to find out how subjectivity actually works, which seems to be on point for a post discussing logic and subjectivity, can just look at the rules used in common discourse, with subjective words like “beautiful”. By choice, and expressing what it is that makes a choice.

    I find the painting “beautiful” .

    By choice, and expressing what it is that makes a choice.

    Ryan is “lazy” .

    By choice, and expressing what it is that makes a choice.

    I believe in “God and the soul” .

    By choice, and expressing what it is that makes a choice.

  4. 4
    kairosfocus says:

    MNS, no one disputes that we choose, though I rather suspect that we have an intuitive reaction to many beautiful things, which delight and create wonder and attraction — something central to tourism, fashion, jewellery, visually oriented media, music, architecture (that has not simply become grotesque) and more. That aesthetic reaction is something that can be developed, refined, guided in light of discernible rational principles. A consequence of this is an evolution of technique, style, knowledge, where these go through the human soul thus are inevitably entangled: beauty, truth, knowledge, goodness, justice and more need to be in a coherent order. Where also, the artistic may awaken us to discerning traces of the principles, stylistic signature and practices of design by an artist. I find, that in part it is the undermining of the rational, responsible side of the aesthetic that is an identifiable part of the ongoing corruption of our civilisation. For instance, in absence of refined, spiritually influenced uplifting tastes, we resort to the benumbing, addictive, progressively ruinous influences of the sensual out of control. Drugs, junk food, general entertainment and more point in that same direction. KF.

  5. 5
    kairosfocus says:

    SB, why are we so lacking of a sound aesthetics education? KF

  6. 6
    daveS says:

    KF,

    are there principles of aesthetic judgement that give a rational framework, setting up objective knowledge of beauty?

    Perhaps. On the other hand, can we know we are not “simply” discussing what humans find beautiful?

    Could humans look like this and still find each other attractive (and beautiful)?

  7. 7
    kairosfocus says:

    DS, such animals are driven by instinct, stimuli and hormones not an aesthetic sense. They probably respond to what is the norm or programmed rather than to what is aesthetic, which is obviously a very high level cognitive function. We are discussing with one another as the only readily accessible population with that level of cognitive function, and find that it is not merely human identity or taste but as we see above, a clear pattern of phenomena, which do appeal to high level cognitive processes. So, would another similar creature find the chaotic, disintegrating, corrupted and evil attractive in the same way as we find the beautiful? If you think so, why? KF

  8. 8
    kairosfocus says:

    F/N: Notice, music turns on harmony, rhythm etc, which turn out to be connected to simple numerical patterns, ratios etc. Principles of beauty in music, which again is proved by classic status or dominance, is typically tied to such patterns, hence the pattern of notes, tones etc that we use. KF

  9. 9
    hazel says:

    Other cultures have music that is vastly different than Western music in these regards. I seriously doubt there is some objective standard of beauty in music.

  10. 10
    LoneCycler says:

    There may be principles of aesthetic judgement giving a rational framework for what objective beauty is, but every time we think we have that figured out along comes another world-wide movement like Art Deco that ridiculously permeates culture to include art, graphic design, architecture, furniture design, interior design, textiles, clothing, automobile and home appliances.

    It took hold in America during the 1920’s and up until WWII permeated even the public purse during FDRs New Deal spending. If a new Post Office was going to be built somewhere they had to have an Art Deco architect design it. It was SO modern. Today only a few examples remain in historically protected places like South Beach in Florida (Miami), and even in Napier, New Zealand as it was a world-wide fad.

    https://pixabay.com/photos/art-deco-miami-beach-south-3703012/

    Art Deco stated an opinion which said humanity was in a new age and it needed to cast off previous ideas about beauty. And people did. Like most such things opinions change. So while at times everyone thinks they know what beauty is as it turns out this is not entirely true. It appears to be subjective. But if you examine some examples of Art Deco many are still appealing today.

    Because some work of beauty still moves people’s thoughts and emotions even across a long period of time it’s suggestive that there might be some elemental part of it that is rational, and thus we might be able to identify what it consists of. This is a mistake materialists make in a lot of categories.

    What remains to us across the gulf in time between when something was created by Leonardo, as an example, the thing that binds thought and feeling is not the art itself but the people observing the art. Leonardo, like us, was human and felt the way about beauty that we do. Leonardo had a spirit, and so do we.

    Many mathematical proofs contain beauty. Claiming that there is artistic or aesthetic rational principles behind them is something Sabine Hossenfelder, much quoted here at UD has a thing or two to say about much more eloquently than I.

    In answer to the question of why there are classics, we have all been created in the image of the Designer, and without putting too fine a point on it, we all share similar conscious thoughts about beauty and much else besides, in the past as well as today.

    As far as the attempt to identify principles and design patterns that create beauty, like symmetry, balance and etc., this is like a quote I read here in another OP about someone soldering wires and switches together in an attempt to create Microsoft Windows 7, or something similar. The idea towards solving the problem of beauty by doing it this way isn’t even wrong.

  11. 11
    daveS says:

    KF,

    DS, such animals are driven by instinct, stimuli and hormones not an aesthetic sense. They probably respond to what is the norm or programmed rather than to what is aesthetic, which is obviously a very high level cognitive function.

    Sure, but if humans looked like that monkey, would we think we were beautiful? Nevermind what the monkeys think, if anything.

  12. 12
    Pater Kimbridge says:

    If beauty is an objective property, then build me a device to measure it.

  13. 13

    KFS, you “must” then appreciate the Eurythmics, who sought to apply mathematical principle in their music. Also Vanessa Hill, who heads up research on algae for fuel, she also does mathematically based dancing.

    But the truth is that people generally don’t comprehend subjectivity itself, as shown by the large number of materialists.

  14. 14
    StephenB says:

    KF

    SB, why are we so lacking of a sound aesthetics education? KF

    The academy, which now serves the ruling class, does not want young minds to think noble thoughts since they lead to independence of thought. Beauty, a “transcendal,” is the external manifestation of the other related transcendentals, such as goodness, truth, being and unity. All these metaphysical realities are a threat to the tyrants of thought control. A thorough study of beauty will prompt questions about the existence of the other transcendentals and lead to freedom from thought control.

  15. 15
    kairosfocus says:

    H:

    Music normally has a pattern of rhythm,numerically related tonal patterns etc, the Indians have an intermediate between western notes but the same basic patterns obtain.

    LC,

    the art deco you show shows strong patterning and use of familiar shapes, as I also recall from cases I know. No they did not wholly abandon the sort of things I pointed to. There are some Po Mo cases that do, and they are objectively both ugly and weird.

    DS,

    A pointless hypothetical, pardon. The relevant monkeys are not rational, cognitively advanced creatures. That is why I pointed to the difference above. I doubt they have a concept of beauty, which as was noted above, is quite subtle.

    PK,

    Not everything which is rational is reducible to mechanisms and devices, or computations. However, note, the Mandelbrot set is a fractal, which shows a beautiful pattern that was programmed, and we now use fractals to render clouds, rocks, etc. So, yes, we see some of the rational principles there, here scalar self-symmetry.

    MNS

    Rationality does not equal reduction to mathematical formulae or axiomatic systems. Indeed, even Mathematics is not so reducible, as we know post Godel.

    The mathematical patterns in music are readily seen in the structure of instruments and the use of harmonic ratios in musical sound [e.g. an octave is a doubling in frequency], also rhythmic patterns with music and particularly percussion instruments. I note that it is very hard to fit in all the ratios together and how say a piano is tuned compromises to get a good enough behaviour.

    KF

  16. 16
    kairosfocus says:

    SB,

    food for thought indeed.

    I fear, you have a sobering point.

    The substitution of sensualism for beauty is indeed chaotic and in the end ruinous.

    KF

  17. 17
    Pater Kimbridge says:

    @KF #15 said:
    “Not everything which is rational is reducible to mechanisms and devices, or computations. However, note, the Mandelbrot set is a fractal, which shows a beautiful pattern that was programmed, and we now use fractals to render clouds, rocks, etc. So, yes, we see some of the rational principles there, here scalar self-symmetry.”

    The math gives us scalar self-symmetry.
    Only your mind can interpret it as beauty, hence beauty is purely subjective.

  18. 18
    daveS says:

    KF,

    A pointless hypothetical, pardon. The relevant monkeys are not rational, cognitively advanced creatures. That is why I pointed to the difference above. I doubt they have a concept of beauty, which as was noted above, is quite subtle.

    The question is whether humans would find each other beautiful if they looked like those ugly-ass, *erm*, sorry, monkeys (but otherwise had the same cognitive abilities etc).

    This question has nothing to do with the monkeys’ cognitive abilities.

    Edit: In any case, take this as a rhetorical question.

  19. 19
    kairosfocus says:

    PK, it is precisely minds which can grasp objective truth or reasoning or mathematics. Subjectivity is thus not the logical complement of objectivity, they overlap considerably as we are subjects, responsibly and rationally free. If we were not, we could not reason, warrant or know. Objectivity has to do with explicit or implicit warrant that grants credibility and reliability to truth claims. KF

  20. 20
    kairosfocus says:

    DS, the creatures which are as you show, alas, are not cognitively sophisticated. What we can see is that even the horribly disfigured do have a sense of beauty, are capable of grasping the transcendent. That includes also goodness, harmony, truth, justice, etc. As we reflect together on what attracts and gives us wonder aesthetically, we find that there are patterns, patterns of composition on the part of artists, or in patterns of natural entities, e.g. there are astronomical phenomena that would be high priced works of art were they in museums etc. Thus, we find reason to believe that a rational creature would be able to understand the principles involved, and perhaps would be able to respond with appreciation. Even if not, the cognitive component would credibly be in the reach of such a creature. As to whether such a creature would perceive itself as beautiful, were it able to form the concept and respond aesthetically, that is a hypothetical. Now, too, I find it interesting that you are not disputing that the patterns I showed and pointed out are not there, or that they are connected to the aesthetic response, but are on what is a tangential point. Perhaps then, I should ask you, what is beautiful, why. KF

    PS: Let us note from the OP, AmHD:

    AmHD is a good place to start: beauty is “[a] quality or combination of qualities that gives pleasure to the mind or senses and is often associated with properties such as harmony of form or color, proportion, authenticity, and originality. “

    Do you agree or disagree, why? is it or is it not the case that the patterns are there in the Mona Lisa and other cases? Is anyone willing to argue that the Mona Lisa or the Taj Mahal or the portraits of two African women about 4,000 years apart are examples of ugliness or of beauty without the sort of characteristics identified, on what grounds?

  21. 21
    hazel says:

    Once again, commonalities that are shared by all humans does not mean that those commonalities have some transcendental existence apart from their widespread and subjective manifestation in the minds of individual human beings.

  22. 22
    kairosfocus says:

    H, these are commonalities that we can and do observe, symmetry, proportion, harmony [tied to ratios of frequencies], variety, fractal patterns, subtle asymmetries often tied to focal points, patterns (I here think of the slight sigmoid and entasis, e.g. the Parthenon is deliberately subtly curved in order to look better than what straight lines would) etc. Where, the fact that a wide diversity of humanity observes in common is itself evidence that it is credible that there is an object or entity that they are responding to. Kindly, look at the cluster of examples above, noting the significance of especially the last i/l/o the others. KF

  23. 23
    Ed George says:

    KF

    DS, such animals are driven by instinct, stimuli and hormones not an aesthetic sense.

    It is quite possible that you are correct, but is this not a conclusion based more on our sense of exceptionalism than on any true knowledge of whether animals (at least high animals) have any sense of aesthetics?

  24. 24
    Ed George says:

    PK

    The math gives us scalar self-symmetry.
    Only your mind can interpret it as beauty, hence beauty is purely subjective.

    I think you have hit the nail on the head here. I can only use myself as an example, but the women that I find attractive all have some asymmetry in their faces. A crooked smile, teeth that are not perfectly aligned, etc.

  25. 25
    Pater Kimbridge says:

    @Ed George #24
    Indeed.
    It is the flaws that tell you a gemstone is genuine and natural.
    Those asymmetries in people’s faces can be interpreted as beauty to some, ugliness to others.

  26. 26
    ET says:

    Pater K:

    If beauty is an objective property, then build me a device to measure it.

    It’s you, Pater.

  27. 27
    daveS says:

    KF,

    As to whether such a creature would perceive itself as beautiful, were it able to form the concept and respond aesthetically, that is a hypothetical.

    Yes, it is hypothetical. This question is supposed to get at whether some people (for example, Sira Kante) have beauty which objectively exists or not.

    BTW, I think the definition(s) you have posted of beauty are reasonable, but I agree with hazel in #21.

  28. 28
    kairosfocus says:

    EG, kindly, take time to ponder what AmHD and Wikipedia (quite diverse sources!) have summarised. Observe, the cluster of cases above. Tell us whether or no they are generally acknowledged as cases of beauty. Tell us whether there are indeed the sorts of patterns and themes or foci, fractals etc identified, and what in your opinion would happen were those patterns absent. Now, identify cases of generally acknowledged beauty where none of those patterns, themes etc are present. (We can readily identify cases of ugliness and chaos that follow little or no pattern etc.) Then, explain to us how, say bilateral symmetry, focal highlights, variety within a pattern, etc are not intelligible and objective (ponder especially seahorse valley) BECAUSE we, self-aware highly cognitively proficient subjects are just that, aware and minded. As for the monkeys, kindly provide a case where they exhibit higher cognitive behaviours starting with abstract language, reflective observation and concepts required for aesthetics. It is fair comment that you have no evidence but simply posed an empty what if to try to shift the burden of argument. KF

    PS: Right now, I know a fine young lady who would be astonishingly physically beautiful, but for one unfortunately ill formed feature. She more than makes up for it with a gracious warmth. Another has a very pretty face, and the scar from surgery to correct a cleft palate does not materially detract from it.

  29. 29
    kairosfocus says:

    DS, symmetry, harmony, fractal patterns, focal features, pattern, diversity amidst pattern, etc etc are all readily observable and even measurable. There is a cluster of cases on the table. To in effect sidestep that and suggest that agreement is not enough to establish the fact, is a strawman argument. There is a concrete, readily observable cluster on the table, including major wonders, which clearly demonstrate the listed patterns. Kindly, address them. Tell me, on what grounds, these patterns are not observably present in Mona Lisa, or if they are, how they do not contribute to the aesthetic impact. KF

  30. 30
    Ed George says:

    KF, I don’t find the Taj Mahal, the Rose Window or the Nefertiti bust particualarly beatiful. The former two I find to be impressive pieces of engineering but I find them gaudi and austentatious. But that is just me. I also understand that others find them beautiful. I have seen both in person and, meh.

    It is fair comment that you have no evidence but simply posed an empty what if to try to shift the burden of argument.

    This comment just proves that you have no idea why I posed this “what if”. If you want to know, just ask. Please don’t ascribe other motives when you don’t know what they are.

  31. 31
    daveS says:

    KF,

    DS, symmetry, harmony, fractal patterns, focal features, pattern, diversity amidst pattern, etc etc are all readily observable and even measurable.

    And we agree that humans find those things beautiful.

  32. 32
    kairosfocus says:

    EG,

    These are known, world class exemplars of beauty.

    The what-if stands as unsubstantiated and rhetorically serves as a distractor. Proboscis monkeys have very useful noses (which function as a signalling organ), but they do not show significant signs of higher order, abstract cognition sufficient to address aesthetics.

    DS,

    Human\s find them beautiful, and — repeat, AND — that they exhibit long known aesthetic patterns and principles, where also, those patterns contribute to the impact . . . as my two comparatives also support. That points to intelligibility, rationality and objectivity.

    KF

  33. 33
    Ed George says:

    KF

    These are known, world class exemplars of beauty.

    According to who? I’m sorry, but I decide what I perceive as beautiful, I don’t consult a public opinion poll.

    The what-if stands as unsubstantiated and rhetorically serves as a distractor. Proboscis monkeys have very useful noses (which function as a signalling organ), but they do not show significant signs of higher order, abstract cognition sufficient to address aesthetics.

    First, I never said anything about monkeys, secondly, you still have not asked why I posed my “what if”. I really have no idea what you are going on about.

  34. 34
    Pater Kimbridge says:

    @Ed George #33

    KF demonstrates the time-honored tradition of equivocating and muddling concepts so as to justify “seeing God” in the universe.
    This mindset appears to require ignoring the boundary of where one’s mind ends and the rest of the universe begins.

  35. 35
    kairosfocus says:

    EG,

    Let’s roll the tape, with a little added context:

    23
    Ed George
    March 11, 2019 at 1:47 pm (Edit)

    KF

    [KF –> DS] DS, such animals [= Proboscis Monkeys etc, per a linked picture] are driven by instinct, stimuli and hormones not an aesthetic sense.

    It is quite possible that you are correct, but is this not a conclusion based more on our sense of exceptionalism than on any true knowledge of whether animals (at least high animals) have any sense of aesthetics?

    The context was immediately a particular type of monkey and by extension others of like level. Perhaps you did not follow out the full chain of discussion.

    My general response remains:

    [KF, 28:] EG, kindly, take time to ponder what AmHD and Wikipedia (quite diverse sources!) have summarised. Observe, the cluster of cases above. Tell us whether or no they are generally acknowledged as cases of beauty. Tell us whether there are indeed the sorts of patterns and themes or foci, fractals etc identified, and what in your opinion would happen were those patterns absent. Now, identify cases of generally acknowledged beauty where none of those patterns, themes etc are present. (We can readily identify cases of ugliness and chaos that follow little or no pattern etc.) Then, explain to us how, say bilateral symmetry, focal highlights, variety within a pattern, etc are not intelligible and objective (ponder especially seahorse valley) BECAUSE we, self-aware highly cognitively proficient subjects are just that, aware and minded. As for the monkeys, kindly provide a case where they exhibit higher cognitive behaviours starting with abstract language, reflective observation and concepts required for aesthetics. It is fair comment that you have no evidence but simply posed an empty what if to try to shift the burden of argument.

    KF

  36. 36
    hazel says:

    re 34, to Pater: Yes, a good and essential point. Also, considering one’s own cultural norms as somehow representative of universal norms.

  37. 37
    kairosfocus says:

    PK, descent into sneering, kindly desist. There is a substantial issue on the table in its own right, aesthetics, with a framework of cases in point that are widely acknowledged. One of them is the number one portrait painting in the world, which so happens to also pull together the panoply of patterns identified. And BTW, note the difference between subtle asymmetry that promotes focus or variety and harmony and that which is chaotic or distractive, leading to spoiled beauty. There is a line between a “character” feature and spoiling what would have been beautiful. The cases manifestly exhibit patterns that are often identified as contributing to aesthetic effects, and we can identify cases of spoiled or repaired beauty which align with said principles. That is, on fair comment, demonstrative of being a causal factor. If you consider them irrelevant, kindly give us cases of widely acknowledged beauty that do not exhibit such patterns. KF

    PS: For Symmetry, try, lines of reflection. Subtle asymmetries in some cases show near mirror image patterns (e.g. real faces are generally not perfectly symmetrical, part of the secret of naturalness). The Rose Window is nearly radially symmetrical, with scale contributing to the framing — about 40 ft across. The stained glass panels then give detail, variety and subtle asymmetry. The window, which is on a sun-facing transept, then contributes to the way the church is lighted, augmenting its other-worldly atmosphere. This then blends with the aesthetics of worship services within.

  38. 38
    daveS says:

    KF,

    Human\s find them beautiful, and — repeat, AND — that they exhibit long known aesthetic patterns and principles, where also, those patterns contribute to the impact . . . as my two comparatives also support. That points to intelligibility, rationality and objectivity.

    In other words, given a collection of pieces of art, it is possible (to an extent) to objectively determine which pieces humans will find beautiful—using elements of your list of patterns and principles.

  39. 39
    kairosfocus says:

    H, did you notice that I deliberately chose cross-cultural cases, natural and mathematical cases? The old subjectivism and cultural relativism/ Western cultural imperialism dismissive talking points fail — but are tells on how we have been led away from aesthetics. FYI, a civilisation will either prize the aesthetic or it will falter and fail through the addictive cycle of sensualism, benumbing and ever more intense or outright bizarre thrill seeking to compensate leading to ruin . . . so, yes, aesthetics cannot be isolated from ethics and truth. As for the insinuation of a hidden theistic agenda, did you notice that I am speaking to objective patterns and am seeking intelligible principles? Where, in using faces, I have pointed to concrete cases of spoiled and repaired beauty? Cleft palate repair, for example, has dramatic impact. KF

    PPS: I pondered the rather severe beauty of the classic katana, but felt no that would be distractive — I just say, when MacArthur pondered destroying all swords he was presented with the contrast of the merely utilitarian and the works of high art; the point was made. I need not point to oriental paintings, pagodas and palaces, they will show similar aesthetic patterns amidst their own distinctive styles.

  40. 40
    hazel says:

    Google “pictures of Omo people” for some perspective.

  41. 41
    Pater Kimbridge says:

    This is like the question of whether a falling tree makes a sound if there is nobody in the forest. The reason it seems like a paradox is that we have lumped the entire idea into one word, “sound”. If we realize that the falling tree likely generates acoustic energy waves, but that these do not become “sound” until there is a person or animal there to hear it, then the paradox is no longer.

    Likewise, there are patterns in the universe that sometimes are associated with aesthetically pleasing experiences in humans. But if you remove the humans, there is no longer an experience of beauty or pleasure.

    Conflating the patterns with the experience is called a “confusion”.

  42. 42
    kairosfocus says:

    DS, repeating the already corrected will not suddenly establish what already failed. We are a community of the intelligent who recognise and enjoy many varieties of beauty. That beauty, through many cases, shows consistent, intelligible principles and compositional patterns that successfully fuse them. This has been so for thousands of years, across many arts and civilisations. Indeed, the classic cave paintings of old are among the many cases of exemplification of the principles — which have had to be preserved from the impact of the great numbers who came to admire them. I forgot, at a lower level, they did find a cave man wearing fur clothing. It turns out, they were clearly tailored (then patched by a far less expert hand — maybe our man fallen on hard times). Such is warrant for holding them objective and even as causal factors, especially as we can see cases of spoiled and restored or repaired beauty. The issue of harmony amidst diversity is of course a particularly relevant point as it speaks to a well known major philosophical challenge: the one and the many. KF

  43. 43
    Ed George says:

    KF@35, so, you still have not taken the logical next step and asks me why I posed the “what if” question. Rather, you doubled and tripled down on ascribing my motives for posing it. Obviously, there is little point in continuing to try to discuss this with you. Bye.

  44. 44
    Ed George says:

    Am I the only one who sees the Taj Mahal and the Notre Dame Rose Window as remarkable feats of design and engineering rather than objectively beautiful pieces?

    Similarly, I see rocky seascapes as being beatiful but mountain ranges as just being impressive. Admittedly, subjective distinctions, and I wouldn’t take offence at anyone who sees the opposite, but I think that just makes my point.

    From my few conversations with Hazel, I’m sure that she sees a certain beauty in mathematics. Whereas I don’t see the same beauty (no offence intended, Hazel).

    I don’t see how anyone can say that beauty is objective given the fact that we all perceive it differently. I see beauty in different combinations of color in a painting, but does a person who is color blind see the same beauty? I doubt it.

  45. 45
    kairosfocus says:

    EG, we are here and for many millennia have shown the aesthetic response, which pivots on intelligible, readily demonstrable aesthetic patterns, principles and styles. Yes, people can also do some fairly ugly things (often, to get a fearsome image that wards off the evil spirits or for sub cultures repels the rejected out-group) — no one implies that good taste or refined aesthetics are universal, even within our own communities. I find many Japanese car designs anything but attractive, especially when they get a little garish or overly buggy in appearance. But that does not mean there is no intelligible aesthetic difference between such and a real head-turner. To be concrete, I find the mid 200’s RAV4 far more aesthetically pleasing than many later models, and I thought the 1990’s models a little too cutesy. But then, I love great Celtic illustrated manuscripts and have played with calligraphy. I have already written about two young ladies of my acquaintance. And BTW, has anyone noticed the story in the Mona Lisa, which may be read from its visual composition — a subtle part of its beauty? Start from sitting in an ornate arm-chair on a balcony high above a landscape with human, technological features. And of course, Lisa has a slight bit of a double chin and noticeably well fed fingers . . . super-skinny is not equal to beauty or charm. KF

  46. 46
    StephenB says:

    Pater K

    Only your mind can interpret it as beauty, hence beauty is purely subjective.

    If beauty was purely subjective, anyone could win a beauty contest, but only a few can.
    If beauty was purely subjective, anyone could be a concert pianist, but only a few can.
    So beauty is mostly objective.

    On the other hand, beauty is partly subjective because not everyone agrees on which beautiful woman is the most beautiful of all, and not everyone agrees on which concert pianist produces the most beautiful music, though anyone can recognize a dud.

    On the whole, beauty is about 80% objective and 20% subjective.

  47. 47
    kairosfocus says:

    EG, I laid out facts of context. Please note, particular tastes of an individual or culture are not equal to beauty or sound aesthetics. Many a Mansion or Sculpture or Public building is an aesthetic disaster. That is demonstrably so for the more bizarre post-modern exercises that seek arbitrary uniqueness and end up as Emperor has no clothes absurdities. By utter sharp contrast, the Vietnam Memorial wall is tragically beautiful through using the same principles. Polished black rock carries with it an aesthetic all of its own. KF

  48. 48
    kairosfocus says:

    PS: Let me adjust:

    I don’t see how anyone can say that beauty [–> the world we live in] is objective given the fact that we all perceive it differently. I see beauty [–> the world we live in] in different combinations of color in a painting, but does a person who is color blind see the same beauty [–> the world we live in]? I doubt it.

    See the problems? Subjectivity and diversity of perspectives does not imply that there is no objective reality. Likewise, a colour-blind person recognises that he has a defect of vision. The reaction on putting on the new filtering spectacles speaks volumes. Can someone be beauty-blind? Yes. Can someone be blind to well founded principles and patterns? Yes also.

    We have subjective awareness, we have capability to inquire, reason and warrant. The result is subjective knowledge of objective truths. The two go together, they are not opposites.

  49. 49
    kairosfocus says:

    SB, there is subjectivity in experience of beauty, and there is objectivity in principles and patterns of beauty. KF

  50. 50
  51. 51
    StephenB says:

    Pater Kimbridge

    Likewise, there are patterns in the universe that sometimes are associated with aesthetically pleasing experiences in humans. But if you remove the humans, there is no longer an experience of beauty or pleasure.

    The human experience of beauty depends on the existence of the beautiful thing; the existence of the beautiful thing does not depend on the human experience of beauty.

  52. 52
    StephenB says:

    KF

    SB, there is subjectivity in experience of beauty, and there is objectivity in principles and patterns of beauty. KF

    Correct. The subject experiences the object of experience (a transcendental) which is, in this case, a beautiful pattern. The human experience of beauty depends on the existence of the beautiful thing; the existence of the beautiful thing does not depend on the human experience of beauty. The transcendental must exist (logically and chronologically) before it can be experienced.

  53. 53
  54. 54
    Pater Kimbridge says:

    @Stephen B #46
    You seem to use the word subjective to mean that different people can have different takes on an experience.
    By that usage, your statements make sense.

    I use the word subjective to mean something that does not even exist outside of human thought.
    I use the word objective to mean that something does have ontological existence outside of human thought, and would exist even if humans did not exist.

    A sunset is objectively real.
    A person’s experience of beauty in reaction to that sunset is subjective, by my usage of the word.

  55. 55
  56. 56
    kairosfocus says:

    PK, the subject-IVE is a matter of the experience of a subject. That experience may be idiosyncratic, delusional, or reflective of object-IVE reality. We have already looked at this in the context of Mathematics, and I again commend to you the exercise of cutting cylindrical paper loops and two mobius loops, the first two, around in the middle, the third, 1/3 way in from one side. The three different results will demonstrate how a seemingly mental construct is embedded in space and bodies. Coming back to beauty, we experience a beauty reaction in the face of certain things. It turns out that such things tend to reflect clusters of properties such as in the OP. To see what happens when an art (architecture) deliberately rejects coherence etc, see here: https://www.currentaffairs.org/2017/10/why-you-hate-contemporary-architecture The pictures of incoherent, eccentric, oddball, lopsided, bizarre buildings will speak volumes. KF

  57. 57
    hazel says:

    I imagine the Omo think they are beautiful when they decorate themselves, and distort (from our point of view) their lips and earlobes. Are you saying that they are “incoherent, eccentric, oddball, lopsided, [and] bizarre”, since you liken them to the buildings you linked to?

  58. 58
    Ed George says:

    Hazel@57, you only have to walk down the Main Street of any city to see the subjective nature of beauty. Variously colored hair, body piercings, tattoos, pants hanging off the ass, etc.

    These are all beautiful to some. As is country music, rap, punk, classical, blues, reggae, etc. But not beautiful to all.

    So much for objective beauty.

  59. 59
    kairosfocus says:

    H and EG:

    There is a world of difference between taste and sound aesthetics, whether individual or culturally dominant.

    Indeed, one speaks about the refining of taste, of (in the bad sense) popular or vulgar tastes, which tend to be overly sensualised and gaudy. I note here, a common feeling that the 1970’s were the decade that taste forgot. The very fact that we can see how such can be identified as inadequate and can point to how matters may be improved, speaks. We do contrast the crude and unskilled from the skilled, refined and well balanced.

    Again, the repellent impact of ever so much Modern and Post Modern architectural monstrosities speaks.

    The moderns went for overly blocky or otherwise geometrically over-simplified patterns, leading to stylistic incongruities . . . often in a context of dominance because of size. (In some cases, they went for the economic advantage of scaling laws, but missed out on the effect that would have.) The function first approach led to an industrial, ugly factory-like effect, which BTW often subtly alienates those who have to live or work with or in such things. In this context, reflective glass (which echoes the calming, mirror like qualities of undisturbed ponds or rivers) fails to have a calming effect.

    The metaphor of sexual assault has often been noted, especially for skyscrapers; one such — a Russian communications monitoring tower — has been seen as a case in point, being so dominant and incongruous that it becomes a message in itself . . . so, no, it is not just the Capitalists. The lack of rich, fractal-like detail is so unnatural and the scale so intimidating that it sends a message of uncaring domination.

    It is interesting, how plants have been used to try to soften the effect — plants are very fractal and natural.

    BTW, tanks have much the same brutal effect and are difficult to conceal because of how they stand out from the natural. Notice, here, how camouflage patterns and netting with branches etc were used to try to hide them. Camouflaged uniforms and Ghillie suits for snipers are again an interesting side-light.

    With Po Mo, the resort to the outright bizarre and utterly asymmetrical by way of claimed originality, pushed the volume knob to eleven. The effect was to demonstrate by undeniable inadvertent counter-example just how powerful the sort of aesthetic principles that were highlighted are. Again, simply look as linked. Indeed, I will add to the cluster of cases in the OP to illustrate by counter-example.

    Prince Charles had a serious point.

    KF

  60. 60
    kairosfocus says:

    F/N: I have added a collection of eyesores that show by way of absurdities that are chaotic or out of sync with surroundings just how rejection of the aesthetic principles actually (at cumulatively billion dollar cost) inadvertently demonstrates the validity of said principles. KF

    PS: Also, a modern reconstruction of Mona Lisa, with some remarks.

  61. 61
    daveS says:

    KF,

    On the “eyesores” page, I got the answer to the Barcelona hospital question wrong. At least I think I did.

    I find the “world’s most beautiful hospital” to be hideous, while at least the plain one is not offensive and *looks* like a hospital.

    I’m in agreement with most of the other examples.

  62. 62

    To say society is becoming more subjectivist in it’s sense of beauty is quite absurd. Creationism is universally rejected in academics while subjectivity is an inherently creationist concept. I tried for years trying to find anyone on internet forums who accepts the validity of subjectivity, to no avail. The whole category of the spirirtual domain is rejected for the precise reason that there is no evidence at all for the spiritual domain.

    The concept of subjectivity has become mangled to make it into a subcategory of objective fact. To say a painting is beautiful, has become to be understood as stating a FACT that a love for the way the painting looks, exists in the brain. Subjective statements therefore has become a subcategory of facts, namely facts about brainstates.

    Objective patterns relating to beauty, probably it has to do with the mathematical way in which the mind works. The beauty is at the agency of a choice. Probably the objective patterns of beauty correspond with an organization of decisionmaking processes in the mind. Also it seems that the form of the opposite sex is inherent in the mind, which makes it easier to imagine the form of the opposite sex, making the opposite sex come alive in imagination, without much effort.

  63. 63
    ET says:

    Ed George:

    you only have to walk down the Main Street of any city to see the subjective nature of beauty. Variously colored hair, body piercings, tattoos, pants hanging off the ass, etc.

    Who said those are supposed to represent beauty? Why don’t they just represent someone’s personal fare?

  64. 64
    Barry Arrington says:

    I award the Taj Mahol 100 Beaut-Ls. See here.

  65. 65
    Ed George says:

    M

    Creationism is universally rejected in academics while subjectivity is an inherently creationist concept.

    How so?

  66. 66
    ET says:

    Yes, mohammadnursyamsu, Ed, also know as “acartia, acartia bogart, William spearshake, wants to know.

    Or is it just a coincidence that every time acartia is online in another forum Ed, BB or daves is here?

  67. 67

    1.Creator, chooses, spiritual, existence of which is a matter of chosen opinion
    2. Creation, chosen, material, existence of which is a matter of fact forced by evidence

    So you see subjective opinion is validated in category 1 of creationism, while objective fact is validated in category 2.

    That is consistent with the rules that are applied with subjective words like “beautiful” in common discourse. Subjective words are used by choice, and express what it is that makes a choice.

    Choosing is the mechanism of creation, how any material thing originates.

  68. 68
    kairosfocus says:

    DS, I think that, in due proportion (and without say wrecking the Paris skyline), a modern style building can be beautiful enough to pass, especially for industrial type purposes. The sort of atrocities I collected above, do not impress me at all. They demonstrate what happens when someone knowingly violates the patterns, and it is awful. Who ever got the idea that a twisted, wrenched building or an oddly shaped die or the like would be even remotely beautiful? I find the mocking echo of a Greek column to be a sneer. They do make a statement, however: power, money and imposition whether you like it or not. And, as the site is obviously socialist, that is not just from capitalists. KF

  69. 69
    daveS says:

    Socialist? Which site?

    Edit: Oh, I guess the Current Affairs website.

  70. 70
    Ed George says:

    M@67, thanks for the explanation. I just couldn’t figure out the logic for your claim that subjectivity is an inherently creationist concept. I’m not sure that I agree but it has given me food for thought.

  71. 71
    goodusername says:

    I’m a little surprised at how many people here seem to be equating inter-subjectivity with objectivity. I’m inclined to believe that there are certain patterns and features that are universal (or nearly so) among humans in regards to what we find “beautiful”. There’s certainly a lot of disagreement (as seen above) as to what degree “nature” plays a role versus “nurture” in regards to what we find beautiful, but I think most people would agree that “nature” is a factor.

    I believe that the reason for this inter-subjectivity is that we, as fellow humans, share certain features, and thus it’s to be expected that there would be certain similarities to what we find pleasant or unpleasant.

    I have no doubt that if we encounter space-faring intelligent aliens, that they will agree that 2 + 2 equals 4, but it wouldn’t be the least bit surprising if they had very different ideas of what is beautiful – that’s even assuming that they have a concept of “beauty”.

    If the only requirement here for saying that something is objective is to show inter-subjectivity, does that also apply to other areas (e.g. morality)?

  72. 72
    hazel says:

    Good point about alien math vs alien beauty.

  73. 73
    hazel says:

    Good point about alien math vs alien beauty.

  74. 74
    Pater Kimbridge says:

    Yes, that is a good point.
    It reminds me of how some people point out similarities in near-death experiences, and use that to infer that there must be an afterlife, when in reality it just points to common culture and common brain chemistry.

  75. 75
    kairosfocus says:

    GUN (attn H and PK), there is no conflation of intersubjective agreement (limited or universal) with objectivity. There is a set of cases (now with an architectural counter example) which shows the intelligibility of rational principles of aesthetics. Notice, above I spoke of two cases where [1] reparative surgery in accordance with said principles led to much enhanced facial beauty (cleft palate surgery, FYI), and [2] where an otherwise highly beautiful face is marred by a distorted, misaligned feature. The architectural eyesores clearly demonstrate what happened when the known principles were willfully mocked and defied — to the tune of billions that simply proved the original point. Though, the willful imposition of the ugly may very well be sending a message. I add, the cases and counters point to actual causal factors being at work, the aesthetic sense is responding to something real, measurable, effective. The hypothetical aliens may or may not natively have the concept of beauty, or may not have the aesthetic sensibilities to feel much as we do when confronted by great beauty, but surely, they will grasp the mathematical relationships that are demonstrably involved in exciting our response. BTW, I was just looking at the comparison of Da Vinci’s two — yes, credibly TWO — Mona Lisa paintings (one seems younger and has the same balcony but different landscape features . . . yes that is suggestive of artistic rather than literal purpose), and they remarked on his geometrical focus at the time, showing some convincing parallels of proportion and compositional patterns. See here for starts. KF

    PS: Video: https://www.youtube.com/watch?list=PLUv9oht3hC6Q8RDzfG8H0tUHqcy_a7Zav&time_continue=45&v=IUr-5Rwy8VY

  76. 76
    Brother Brian says:

    Hazel

    Good point about alien math vs alien beauty.

    I’m not sure about this. I find the green skinned Orion women on Star Trek very beautiful. 🙂

  77. 77
    hazel says:

    But what does that say about you, Brian? What star system are you from? 🙂

  78. 78
    Brother Brian says:

    Hazel

    But what does that say about you, Brian? What star system are you from?

    I guess we would just be star-crossed lovers. 🙂

  79. 79
  80. 80
    ET says:

    What it says about Brian is that he has a fetish for actresses in green body paint. 😛

  81. 81
    hazel says:

    All kidding aside, the substantial point is that we would expect aliens to have the same math, but not the same sense of what is beautiful.

  82. 82
    kairosfocus says:

    PK, similar pose, not the same woman. It seems Da Vinci worked on this theme for years producing two paintings. That he might have done such a nude study (likely NOT with the paying client) is not unlikely. The article suggests a nude painting was done. Remember, the figure sets the foundation for the clothed figure — hence anatomical dissection studies done by the artists of that time. KF

  83. 83
    kairosfocus says:

    H, hypothetical, but we have no reason to assume such would have the concept, beauty, much less the similar aesthetic response. However, on contact with us, they could form the concept due to the objective properties, even were they unresponsive in the way we are. KF

  84. 84
    Brother Brian says:

    Hazel@81, I don’t think you even have to invoke a hypothetical alien. Different cultures have different ideas of what is beautiful. And even within a single culture, the variation is huge.

    I see a parallel in this with moral values. Beauty and moral values vary within a culture, vary even more between cultures, and change throughout time. Subjectivity informed by nurture seems to explain this much better than some I’ll-defined, unidentifiable objective nature.

  85. 85
    hazel says:

    re 83: Incredibly parochial viewpoint, I think.

  86. 86
    Brother Brian says:

    Hazel

    Incredibly parochial viewpoint, I think.

    Perhaps. What does parochial mean? 🙂

  87. 87
    ET says:

    Brother Brian:

    Beauty and moral values vary within a culture, vary even more between cultures, and change throughout time.

    And from the Old Testament the consequences of the Tower of Babel explains that.

    Again, just because we find ourselves in a chaotic time doesn’t mean there isn’t or never was an objective morality or that beauty isn’t objective.

  88. 88
    kairosfocus says:

    BB, aesthetical relativism has no better warrant than ethical relativism or Mathematical nominalism. If you look at the OP you can see in the counter-instances a billion dollar exercise in deliberately violating the sort of principles that the OP lists. Billions worth of eyesores that mar our cityscapes is the direct and blatant result. Never mind the sort of institutional, ideological and political dominance it took to push through such monstrosities and eyesores. And yes, I look towards the controlled demolitions to come. KF

  89. 89
    kairosfocus says:

    H, we are speaking of hypothetical aliens. You are using them as a foil for differing views on beauty. I pointed out that we have no warrant for thinking that an alien race would have the sort of aesthetic response we have to beauty at all, BUT that they will be able to conceptualise i/l/o the clearly mathematical import of concepts such as symmetry, harmony, simple ratio overtones, formants in voice boxes and windpipes (the human vocal tract is a wind instrument working off harmonic excitations and transients with nodes and antinodes), subtle asymmetries, diversity and detail in the midst of patterns etc. In short, because there is an objective side, even aliens who have no response as we do, would be able to form the concept. Such is patently the utter opposite of provincialism or the like. KF

  90. 90
    hazel says:

    Perhaps aliens do have as well-developed an aesthetic sense of beauty as we have, but think our noses are incredibly ugly! I can’t believe you think this is comparable to math.

    And Brian, my remark about “parochial” was addressed to kf: it means having a narrow viewpoint that just expresses the ideas of one’s own group. Thinking that having tea at 4:00 pm is the only civilized way to live is parochial.

  91. 91
    Brother Brian says:

    Hazel

    And Brian, my remark about “parochial” was addressed to kf:

    I knew that. I was just being a [SNIP — Ed]. I apologize.

    But i agree that there are some broad stroke ideas of beauty that most of us would agree on. But the bigger question is if our anscestors would agree with us. In previous ages pasty white skin was the ideal. And women who were more “pudgy”? And this is just European norms. I’m sure that African ideals of beauty, and Indian, East Indian, Australian aborigiginal, etc were completely different than our modern ideal.

    I am hoping that late middle age, beer bellied men become the epitome of male beauty. I won’t hold my breath. (ET, feel free to hold your breath).

  92. 92
    ET says:

    Thankfully clever, humorous conversation, broad shoulders and a chest that fills out the shirt, still work. 😎 😛

  93. 93
    kairosfocus says:

    H, do you notice, that I have separated the aesthetic impact we feel from the intelligible, rational principles and connected metrics and functions on structure and quantity? This is why I have pointed out that even an alien species that has no reaction of that sort, on encountering creatures such as we are, could form the concept. Precisely because it is intelligible. Which is specifically broader than having any particular taste or preference. And that has nothing to do with anything as particular as views on attractiveness vs functionality of noses etc. Recall, the OP is looking at a wide array of cases. KF

  94. 94
  95. 95
    kairosfocus says:

    F/N: Notice, on the logic of octaves in music thence the challenge of harmony and creation of scales — further drawing out the principle of coherence or harmony and the role of subtle asymmetry — here due to a problem of reconciling ratios — and the place of a focal point:

    https://en.wikipedia.org/wiki/Octave

    Explanation and definition

    For example, if one note has a frequency of 440 Hz, the note one octave above is at 880 Hz, and the note one octave below is at 220 Hz. The ratio of frequencies of two notes an octave apart is therefore 2:1. Further octaves of a note occur at 2 n {displaystyle 2^{n}} 2^{n} times the frequency of that note (where n is an integer), such as 2, 4, 8, 16, etc. and the reciprocal of that series. For example, 55 Hz and 440 Hz are one and two octaves away from 110 Hz because they are ? 1?2 (or 2 ? 1 {displaystyle 2^{-1}} 2^{{-1}}) and 4 (or 2 2 {displaystyle 2^{2}} {displaystyle 2^{2}}) times the frequency, respectively.

    The number of octaves between two frequencies is given by the formula:

    Number of octaves = log_2 ? ( f 2 /f 1 )

    The octave is defined by ANSI[4] as the unit of frequency level when the base of the logarithm is two.

    Octave equivalency

    After the unison, the octave is the simplest interval in music. The human ear tends to hear both notes as being essentially “the same”, due to closely related harmonics. Notes separated by an octave “ring” together, adding a pleasing sound to music. The interval is so natural to humans that when men and women are asked to sing in unison, they typically sing in octave.[5]

    For this reason, notes an octave apart are given the same note name in the Western system of music notation—the name of a note an octave above A is also A. This is called octave equivalency, the assumption that pitches one or more octaves apart are musically equivalent in many ways, leading to the convention “that scales are uniquely defined by specifying the intervals within an octave”.[6] The conceptualization of pitch as having two dimensions, pitch height (absolute frequency) and pitch class (relative position within the octave), inherently include octave circularity.[6] Thus all C?s, or all 1s (if C = 0), in any octave are part of the same pitch class.

    Octave equivalency is a part of most “advanced musical cultures”, but is far from universal in “primitive” and early music.[7][8] The languages in which the oldest extant written documents on tuning are written, Sumerian and Akkadian, have no known word for “octave”. However, it is believed that a set of cuneiform tablets that collectively describe the tuning of a nine-stringed instrument, believed to be a Babylonian lyre, describe tunings for seven of the strings, with indications to tune the remaining two strings an octave from two of the seven tuned strings.[9] Leon Crickmore recently proposed that “The octave may not have been thought of as a unit in its own right, but rather by analogy like the first day of a new seven-day week”.[10]

    Monkeys experience octave equivalency, and its biological basis apparently is an octave mapping of neurons in the auditory thalamus of the mammalian brain.[11] Studies have also shown the perception of octave equivalence in rats (Blackwell & Schlosberg 1943), human infants (Demany & Armand 1984),[12] and musicians (Allen 1967) but not starlings (Cynx 1993), 4–9 year old children (Sergeant 1983), or nonmusicians (Allen 1967).[6]

    A good referent, here, is to recognise that the human vocal tract is effectively a wind instrument with transients and node-antinode patterns. Like other instruments, it responds to acoustical vibrations by forming standing waves which have over a given length L, a pattern of peak and minimal vibrations termed nodes and antinodes (best seen with strings). These create a pattern of whole number numerical ratios between a fundamental vibration mode and harmonics that have more nodes and antinodes. In a typical instrument, there will be a particular pattern of such harmonics, giving rise to its timbre or quality of sound . . . essentially, wave-shape (and yes, this points to Fourier analysis). In basic quantum theory, say the particle in a box, similar standing wave patterns naturally give rise to quantum numbers.

    Let me add, 3/2 * 2 = 6/2, a third harmonic to the fundamental. Likewise, 3/2 * 3 = 9/2, 4.5:1 and 3/2 * 4 = 12/2, etc. Of course, in the physical acoustic system, higher order harmonics will normally have lower and lower amplitudes. Clipping distortion [due to hard saturation] tends to have odd number harmonics and crossover distortions, even number harmonics, which are relevant especially to electronic instruments. Note, too, conical and exponential horns are dispersive media with wavelength-dependent velocity leading to phase-shifts. Such horns serve as acoustic impedance match devices, reducing standing waves and enhancing transfer to the general atmosphere.

    The chromatic scale of notes is a cycle of twelve notes spanning an octave at an interval of the twelfth root of two. However, it is more instructive to understand the creation of a scale of notes from the attempt to fuse octaves (2:1 frequency ratios) and fifths (3:2 ratios):

    http://www.sound-physics.com/M.....ean-Comma/

    Pythagorean Comma

    Although musical notes can be calculated mathematically, doing that creates notes which are slightly off pitch.

    The Perfect Fifth is the lowest ratio harmonic you hear and is mathematically calculated by multiplying a frequency the ratio by 3/2 or 1.5. For example, in the note of C, the perfect fifth would be a G. In harmonic terms, the perfect fifth is one octave below the third harmonic [–> i.e. triple the fundamental frequency, f_0, yielding 3 * f_0, then halve that to get 1.5 * f_0].

    Pythagorous of Samos (c.582 – c.507 B.C.) discovered that you could make a musical scale by continuing through the Circle of Fifths, and dividing down harmonically with The Law of Octaves to determine the pitch for each note.

    There is a distinct problem in this procedure, however. It does not add up correctly but leaves a small residual error that has been the frustration and bane of musicians ever since.

    It works out like this. Say we start at C at 256 Hz. G would be 1.5 x C or 384. D would be 1.5 x 384 or 576. This continues as follows:

    C > G > D > A > E > B > F# > C# > G# > D# > A# > F > C.

    C 256 > G 384 > D 576 > A 864 > E 1,296 > B 1,944 > F# 2,916 > C# 4,374 > G# 6,561 > D# 9,841 > A# 14,762 > F 22,143 > C 33215

    Then utilize the Law of Octaves to divide down C at 33,215 Hz by 2 until you obtain 259.5 Hz. The difference between C at 256 Hz, and C at 259.5 Hz is known as the Pythagorean Comma. It works out to the ratio of about 74/73 or 743/733. There is another comma defined in music, the comma diesis which is equal to about 81/80 or 5.4 savarts.

    This small excess ratio means that a music scale cannot be completely harmonic with regard to octaves and with regard to the interval of a fifth since this musical error must reside somewhere in the scale. The question is- where?

    Thousands of musical scales have been invented to reduce the effects of this error . . .

    So, the physics of voicing, sounding and of hearing through in effect a mechanical fourier transform naturally emphasises whole number ratio harmonics. However, the two key harmonic ratios 2:1 (leading to octave equivalence) and 3:2 (lowest heard aesthetically pleasing blend) cannot be exactly reconciled, leading to slight asymmetries that have to be distributed across the scale somehow. And of course, the fundamental is a hidden focus in the patterns.

    We here see an example of how the aesthetic principles naturally emerge and of how say a hypothetical hearing-less alien race (say, they communicate by radio) could come to understand the aesthetic principles of our music without being able to directly appreciate it. However, if the aliens have vocalisation and auditory systems, it is likely that they will have the same frequency responsiveness with the same octave and fifth responses as these are closely tied to the physics of harmonics and reinforcing rather than clashingly an-harmonic overtones.

    Similar aesthetics extend to the visual and plastic arts. (Notice, our visual arrays will recognise the evenly spaced and what is significantly out of a pattern as a change. The Weber-Fechner law highlights that we respond to delta-x/x, to change. A natural pattern will not tend to have co-ordinated regularities, e.g. dappled colours and shadows in a forest, so a regularity or shape-pattern will highlight itself for good or ill.)

    In literature and drama, other morally governed races would readily appreciate the pattern of plotline in context with challenge and conflict interacting with motive and character towards climax and outcome.

    This further underscores the significance of the principles as were noted above.

    KF

    PS: consider, similarly, a race that say sees mostly in our IR zone. Note, visual range is connected to energy gaps between orbitals in atoms and molecules, thus chemical interactions and onward to blackbody radiation peak bands, our visual range is roughly an octave in electromagnetic vibrations. Yes, finetuning again. Such IR-sensing creatures likely would not see our paintings as we do but could use false colours to detect what we see, and again the logic of patterns, regularities and sensitivity to fractional change would bring out ability to recognise and respond. The mathematical patterns of symmetry, reflection, rotation, translation, asymmetry etc would be relevant. (Recall, the earlier discussion on how core structure and quantity are necessarily embedded in any possible world. Dismissiveness at that point will predictably lead to needless difficulties at this point. I again recommend the mobius strip cutting exercises as a way to break through controlling presuppositions that are serving as crooked yardsticks.)

  96. 96
    daveS says:

    KF,

    Does this mathematical analysis provide evidence that certain pieces of music are objectively beautiful?

    It seems to me that you have explained that many humans (those of us in the west, esp.) find music with certain mathematical properties to be beautiful. But not that the beauty we experience in, for example, a Bach cello suite exists independently of our minds.

    You have also explained that humans find architecture, paintings, and even geographical formations with certain mathematical properties to be beautiful.

    So we can conclude that humans, across cultures and time (to some extent), share similar tastes in art, and these tastes are connected to “mathematics” (using the term in a very broad sense).

    I still don’t see how you can know, based on your arguments, that there actually is such a thing as objective beauty.

  97. 97
    ET says:

    Mathematics is beautiful

  98. 98
    Brother Brian says:

    I don’t doubt that there is a mathematical underpinning to music, but to suggest that this mathematical underpinning is responsible for the beauty of the music does not follow. If this were the case, we should be able to program a computer to create beautiful music.

  99. 99
    ET says:

    I don’t doubt that there is a mathematical underpinning to music, but to suggest that this mathematical underpinning is responsible for the beauty of the music does not follow.

    Why not?

    If this were the case, we should be able to program a computer to create beautiful music.

    That doesn’t follow, unless you are using FORTRAN

  100. 100
    kairosfocus says:

    DS, aesthetic enjoyment (as opposed to sensuality) is indeed a personal experience. The point is, that it is observably directly tied to mathematical and physical phenomena which are objective, many embedded in the world. For example, the phenomenon of harmonics and fundamentals is a property of an inertial, elastic body. The octave pattern turns out to be tied to frequency, wavelength, wave velocity, reflections and standing waves. That notes in octave have a similarity because of how onward harmonics behave (waves out of such symmetric alignment will have odd interference effects), and that notes in the fifth relationship are similar and can come close enough to alignment to fit in well enough (but not perfectly) actually provides an objective basis for musical scales. Similarly, given our vocal tracts as musical instruments and given interference and the related phenomenon of Fourier summing of harmonics to yield a waveform, it is unsurprising that our auditory system uses a basilar membrane set up so frequencies cause resonant peaks at particular points along the coil of the cochlea, which then goes in like pattern to the brain. All of this comes together as objective phenomena tied to aesthetic principles that help us understand the enjoyable structure of music. Such phenomena are clearly objective, and point again to how the aesthetic principles guide creativity in making beautiful music. Where of course, tastes can be outright bizarre, not just abnormal or culture-bound. One may always stoutly resist the conclusion of a convergent pattern of evidence and argument, but it is clear enough that there are aesthetic principles that are readily intelligible, are rooted in observable structural, quantitative and physical phenomena, and contribute to the patterns and phenomena we enjoy as beautiful. When they are willfully discarded as a bloc, it is equally clear that the result is chaotic and ugly. Billions of dollars of recent architectural eyesores are literally massive evidence on the point. I repeat, the subjective is not the opposite of the objective and the presence of intelligible, objective frameworks for aesthetics demonstrates that yes, beauty is in material part an objective predictable phenomenon, amenable to controlled, insightful skill rather than a hit and miss affair — indeed the art of photography is also evident in the cases above. It is not an accident that Grand Canyon was photographed at just that moment, from that angle with settings, filters, focus etc. KF

  101. 101
    kairosfocus says:

    BB, computers are not independent creators, they are a means by which a programmer may in this case compose music. MIDI allows one to go from notes to voices of instruments [thanks to the mathematical magic of Fourier and Nyquist] to music that can be heard. There are many people with perfect pitch who by simply reading a score can hear it played perfectly in their minds, similar to how we may “hear” as we read silently . . . and BTW, a mike can pick up the sounds (yes, that is direct proof of objectivity of the process for the hyperskeptical) — the inner ear is a two-way street. KF

  102. 102
    kairosfocus says:

    F/N: IEP on objectivity:

    https://www.iep.utm.edu/objectiv/

    Objectivity

    The terms “objectivity” and “subjectivity,” in their modern usage, generally relate to a perceiving subject (normally a person) and a perceived or unperceived object. The object is something that presumably exists independent of the [I add, particular] subject’s perception of it. In other words, the object would be there, as it is, even if no subject perceived it. Hence, objectivity is typically associated with ideas such as reality, truth and reliability.

    The perceiving subject can either perceive accurately or seem to perceive features of the object that are not in the object. For example, a perceiving subject suffering from jaundice could seem to perceive an object as yellow when the object is not actually yellow. Hence, the term “subjective” typically indicates the possibility of error.

    The potential for discrepancies between features of the subject’s perceptual impressions and the real qualities of the perceived object generates philosophical questions. There are also philosophical questions regarding the nature of objective reality and the nature of our so-called subjective reality. Consequently, we have various uses of the terms “objective” and “subjective” and their cognates to express possible differences between objective reality and subjective impressions. Philosophers refer to perceptual impressions themselves as being subjective or objective. Consequent judgments are objective or subjective to varying degrees, and we divide reality into objective reality and subjective reality. Thus, it is important to distinguish the various uses of the terms “objective” and “subjective.”

    In short, the issue of objectivity is that of warrant. If there is warrant that makes it reasonable and responsible to accept that X exists or is the case, it is an objective claim.

    In the case of beauty, it is obviously an abstract phenomenon that emerges in our perceptions through our response to certain phenomena, some inner, some outer. We see there is a reasonable, responsible framework that warrants the conclusion, X is beautiful, it is not merely equal to x, per his/her unaccountable tastes, likes X or x’s culture has set up a rule and indoctrinates its members to like X. After all. x’s tastes may be defective, cultures go through eras of manifestly poor taste — see the architectural eyesores — or his or her senses may be malfunctioning. The amazed reaction of the colour-blind on being given filtering glasses speaks volumes to this — and shows the stability of the principles.

    There is warrant for holding beauty (as opposed to aesthetic or sensuality-driven or sensationalist impact on any given x) has responsible, rational warrant on intelligible and defensible principles, so it is objective. As SB points out (and as we may extend), not just anyone can win a serious beauty contest, or become a world class singer or composer or architect who actually avoids the fashionable monstrosities of today.

    KF

  103. 103
    daveS says:

    KF,
    Clipping the relevant parts of your post:

    DS, aesthetic enjoyment (as opposed to sensuality) is indeed a personal experience. The point is, that it is observably directly tied to mathematical and physical phenomena which are objective, many embedded in the world.

    Yes, works of music that humans find beautiful have the properties that you describe. And these properties can be described objectively using the language of physics and mathematics.

    All of this comes together as objective phenomena tied to aesthetic principles that help us understand the enjoyable structure of music. Such phenomena are clearly objective, and point again to how the aesthetic principles guide creativity in making beautiful music.

    “Us”, meaning humans.

    One may always stoutly resist the conclusion of a convergent pattern of evidence and argument, but it is clear enough that there are aesthetic principles that are readily intelligible, are rooted in observable structural, quantitative and physical phenomena, and contribute to the patterns and phenomena we enjoy as beautiful. When they are willfully discarded as a bloc, it is equally clear that the result is chaotic and ugly. [according to humans]

    To summarize, works of music which humans find beautiful can usually (or sometimes at least) be identified by properties which objectively exist.

    This explains in part why humans find Bach’s cello suites beautiful. It’s because we find music with the elements you have listed are present in the suites.

    This says nothing about whether the cello suites have objective beauty. How do we know our “choice” of musically beautiful elements is actually indicative of objective beauty, rather than being just one of many possible choices?

  104. 104
    daveS says:

    KF,

    As SB points out (and as we may extend), not just anyone can win a serious beauty contest, or become a world class singer or composer or architect who actually avoids the fashionable monstrosities of today.

    This could be explained by the very useful term that GUN introduced to the discussion: intersubjectivity.

  105. 105
    ET says:

    Artificial music: The computers that create melodies

    If this were the case, we should be able to program a computer to create beautiful music.

    We have. 😎

  106. 106
    kairosfocus says:

    F/N: I added three videos as a PS. They are a lesson about beauty we take for granted.

  107. 107
    kairosfocus says:

    DS, I already pointed out how intersubjective agreement fails: a consensus of bad tastes has created a billion dollar exercise of imposing the grotesque in the name of being fresh architecture. The issue is warrant, and it has long been clear that the determined will never concede warrant even in the face of the equivalent of a plumb line example. BTW, that is where I have now reached on the design inference: it is abundantly well warranted but there are those who will never concede that such could even be possible. KF

  108. 108
    daveS says:

    KF,

    DS, I already pointed out how intersubjective agreement fails: a consensus of bad tastes has created a billion dollar exercise of imposing the grotesque in the name of being fresh architecture.

    How does it “fail”? Most of us find those eyesore examples to be ugly. Architecture, just like any other art, is susceptible to trends. And most of us have little to no say in the design of large buildings in our cities.

  109. 109
    kairosfocus says:

    DS, we find them ugly not just as clashing with our tastes — I hate prunes (an acquired taste for some) — but for good reason. The architects, caught up in a rebellion against long known aesthetics principles, induced decision-makers to spend billions. They only managed to create eyesores — exactly as the canons predicted: too much asymmetry leads to incoherence, incongruity and chaos, which for good reason is repulsive save to those whose inner riot seeks an outer reinforcement. I doubt the lesson has been duly learned. Ponder the contrast between the sad man who has spent US$ 200k on trying to make himself look like a tiger, and those who sought plastic surgery to relieve deformities. Note also the impact of “ordinary” beauty we have become benumbed to, on those who see colour or hear in reasonable fidelity for the very first time. KF

  110. 110
    Brother Brian says:

    DaveS

    How does it “fail”? Most of us find those eyesore examples to be ugly. Architecture, just like any other art, is susceptible to trends. And most of us have little to no say in the design of large buildings in our cities.

    I agree. Further to the subject of architecture and its beauty, I would suggest that part of the formula we use to determine if something is beautiful is what we are have become familiar with. Thinks like the Eiffel Tower were thought to be ugly when it was built. The same can be said for the Sydney Opera House and the glass pyramids of the Louvre. Many still feel that the glass pyramids are ugly but I find that they, somehow, add to the view. Maybe my sense of taste is terrible, but isn’t that what we would expect if the concept of beauty was subjective?

  111. 111
    daveS says:

    Yes, the architects designed buildings which most humans find ugly. Because they violated design principles which humans have discovered lead to buildings which humans find beautiful. None of this entails that the buildings on that page are either objectively beautiful or objectively ugly.

    Clearly I’m repeating myself, so I’ll turn it over to others for now.

  112. 112
    daveS says:

    Brother Brian,

    Yes, I believe so. Even though I believe humans share quite a bit of our aesthetic sense in common, it must be shaped by culture to some extent.

  113. 113
    kairosfocus says:

    DS,

    Let us compare:

    Even though I believe humans share quite a bit of our aesthetic [–> Mathematical] sense in common, it must be shaped by culture to some extent.

    The issue is not intersubjective agreement, it is not culture, it is not tastes, it is warrant.

    Warrant, backed by billions of dollars worth of blunders that created eyesores because powerful and culturally influential professionals decided to upend the historic framework of well founded aesthetics principles.

    Reflecting a now all too familiar pattern of chaotic decadence in our civilisation.

    KF

  114. 114
    daveS says:

    KF,

    Would you care to explain the comparison between the two sentences explicitly? I posted one of them, but not the other.

  115. 115
    hazel says:

    I agree with Dave at 111. There is no use in repeating the obvious again and again.

  116. 116
    kairosfocus says:

    DS, I may elaborate later. Right now, I put a single word on the table: nominalism. KF

  117. 117
    Brother Brian says:

    KF

    DS, I may elaborate later. Right now, I put a single word on the table: nominalism

    I would put one word on the table, but the last time I did that, you censored it. 🙂

  118. 118
    hazel says:

    Plastics?

  119. 119
    daveS says:

    hazel,

    Is that a reference to The Graduate? 🙂

  120. 120
    hazel says:

    In order to balance my facetious comment at 118 (Dave got it!), this is an interesting paragraph from Wikipedia on conceptualism (to give kf something to do.)

    A clear motivation of contemporary conceptualism is that the kind of perception that rational creatures like humans enjoy is unique in the fact that it has conceptual character. McDowell explains his position:

    I have urged that our perceptual relation to the world is conceptual all the way out to the world’s impacts on our receptive capacities. The idea of the conceptual that I mean to be invoking is to be understood in close connection with the idea of rationality, in the sense that is in play in the traditional separation of mature human beings, as rational animals, from the rest of the animal kingdom. Conceptual capacities are capacities that belong to their subject’s rationality. So another way of putting my claim is to say that our perceptual experience is permeated with rationality. I have also suggested, in passing, that something parallel should be said about our agency.[17]

    McDowell’s conceptualism, though rather distinct (philosophically and historically) from conceptualism’s genesis, shares the view that universals are not “given” in perception from outside the sphere of reason. Particular objects are perceived, as it were, already infused with conceptuality stemming from the spontaneity of the rational subject herself.

    Just food for philosophical thought.

  121. 121
    Brother Brian says:

    Hazel

    Plastics?

    No. I think it had somstung to do with some guy named Richard, or Dick. Or something like that. 🙂

  122. 122

    The actual logic of subjective opinion.

    If a choice is made between A and B, and A is chosen, then the question “what was it that made the choice turn out A?”, can only be answered with a choice between X and Y, where either chosen answer X or Y is equally logically valid.

    Therefore to say the building is ugly, it requires the alternative possibility of saying the building is beautiful, which would be an equally logically valid opinion. And to say the building is ugly identifies a hate for the way the building looks as agency of the choice to say it is ugly.

    And to be sure, all the ugly buildings pictured were probably built by materialists who had no idea about subjectivity. It doesn’t make sense to “accuse” of a subjective conception of beauty, when most probably all those ugly buildings stem from the materialist culture around science, which science only accepts facts.

  123. 123
    kairosfocus says:

    DS & H:

    Having slept a bit, let me now follow up.

    In effect, what I think we are seeing is the effect of a subtle controlling worldview concept, nominalism — which is of course an issue in Mathematics, hence my comparative.

    Namely, the idea that, per Wiki as handy reference, can be summed up:

    In metaphysics, nominalism is a philosophical view which denies the existence of universals and abstract objects, but affirms the existence of general or abstract terms and predicates.[1] There are at least two main versions of nominalism. One version denies the existence of universals – things that can be instantiated or exemplified by many particular things (e.g., strength, humanity). The other version specifically denies the existence of abstract objects – objects that do not exist in space and time.[2]

    Most nominalists have held that only physical particulars in space and time are real, and that universals exist only post res, that is, subsequent to particular things.[3] However, some versions of nominalism hold that some particulars are abstract entities (e.g., numbers), while others are concrete entities – entities that do exist in space and time (e.g., pillars, snakes, bananas).

    Enc Brit, in discussing specifically Mathematical Nominalism (vs Mathematical Platonism), similarly summarises:

    Nominalism is the view that mathematical objects such as numbers and sets and circles do not really exist. Nominalists do admit that there are such things as piles of three eggs and ideas of the number 3 in people’s heads, but they do not think that any of these things is the number 3. Of course, when nominalists deny that the number 3 is a physical or mental object, they are in agreement with Platonists. They admit that if there were any such thing as the number 3, then it would be an abstract object; but, unlike mathematical Platonists, they do not believe in abstract objects, and so they do not believe in numbers . . . .

    [T]here are essentially five alternatives to Platonism. If one does not want to claim that mathematics is about nonphysical, nonmental, nonspatiotemporal objects, then one must to claim either (1) that mathematics is about concrete mental objects in people’s heads (psychologism); or (2) that it is about concrete physical objects (physicalism); or (3) that, contrary to first appearances, mathematical sentences do not make claims about objects at all (paraphrase nominalism); or (4) that, while mathematics does purport to be about abstract objects, there are in fact no such things, and so mathematics is not literally true (fictionalism); or (5) that mathematical sentences purport to be about abstract objects, and there are no such things as abstract objects, and yet these sentences are still literally true (neo-Meinongianism).

    On such a view, there is no such thing as a nature or an intelligible, rational principle that pervades circumstances and can be extended to predict or control reality. This, of course, includes not only abstracta such as necessarily existing, world-framing structures and quantities such as numbers (N, Z, Q, R, C etc), but even more obviously such an emotive reaction laden idea as aesthetic principles of beauty.

    In effect, laws of concrete or universal nature are dead as reality has been atomised and dispersed into only the particular concrete entities. And, apologies that language is forcing us to talk as though such things are real. Tame it by holding such to be fictions we hold, shaped by our culture. That is, we only have useful fictions, labels, simulation models that may be computable, otherwise, we are running an imaginative shadow-show drama in our heads. Similarly, abstracta are fictions, at best labels for imaginary entities in our models. All of which are of course culturally influenced, likely with the concept lurking, that Western Culture’s influence is particularly suspect and inferior or oppressive. And so forth.

    The effect of such controlling ideas is that they shape what we find plausible or obvious and what we we reject or dismiss out of hand. We are back at the problem of the crooked yardstick and the challenge of responding to a plumb-line.

    However, it is patent that Nominalism is self-referentially incoherent, as universals and abstracta are inescapable in our thinking and reasoning, including in stating the claim that roughly runs: [we know, per some warrant that] there are no universals or abstracta, only names for collectives we impose.

    In effect, it affirms what it would deny.

    It is inescapably incoherent.

    A well-known logical consequence (something nominalism suspects) of incoherence is logical explosion, loss of the power of the principle that what is true only implies what else is true. But again, truth is yet another abstractum to be suspected and tamed into in effect some sort of operationalist and/or pragmatist redefinition or the like. Yet another useful fiction, and certainly not, the accurate description of “reality” whatever that is. It all depends on what the meaning of “is” is.

    But isn’t the claim, there are no universals or abstracta, just names we impose precisely a universal, abstract truth-claim, in effect a candidate foundational and intelligible, controlling law or truth of reality?

    In short, a fail.

    Likewise, we can see that those who are locked into nominalism will suspect the notion that there can be or are, intelligible rational aesthetics principles tied to mathematically shaped properties such as symmetry, fractal self-similar scaling, subtle asymmetries, proportions of harmony,

    [–> let me add that explicitly in the OP, I forgot! Therein lieth phi 1.618 etc, with Fibonacci, spirals, Marquadt masks, the golden section, the power of pentagons, Vitruvian Man, da Vinci’s proportions and geometries and much more . . . ]

    coherence, patterns, etc. That will then extend into the specific mathematical result for music that octaves tend to have a coherent pattern of harmonics [there’s that concept of harmony again] and that fifths and octaves can be brought into fairly close but not exact match, creating a core tension that we in effect resolve by finding solutions that are good enough for government work. For example, a resonance peak is typically broadened (an effect of damping in many cases and/or of overlapping peaks) so close enough is good enough. Where, we must recall, too, that Fourier analysis shows that waveforms can be broken down as sums of suitably phased harmonics of appropriate amplitudes and transients can be seen as continuous bands of sinusoids (by way of reduction to an integral, yet another abstract Mathematical process).

    In nominalist hands, the exposition that the human vocal tract is a wind instrument with fundamentals and harmonics and that the ear uses a mechanical fourier transform in the cochlea which would draw on the just above, is predictably going to be lost in the concept that there are no abstracta and/or universals and/or intelligible, universal, discoverable patterns of nature or universals. There are only concrete instances and culturally or individually imposed patterns. We cannot bridge from our ideas to the external realities of things in themselves.

    Some form of the Kantian ugly gulch has surfaced.

    It is therefore appropriate to point out F H Bradley’s corrective:

    We may agree, perhaps, to understand by metaphysics an attempt to know reality as against mere appearance, or the study of first principles or ultimate truths, or again the effort to comprehend the universe, not simply piecemeal or by fragments, but somehow as a whole [–> i.e. the focus of Metaphysics is critical studies of worldviews] . . . .

    The man who is ready to prove that metaphysical knowledge is wholly impossible . . . himself has, perhaps unknowingly, entered the arena . . . To say the reality is such that our knowledge cannot reach it, is a claim to know reality ; to urge that our knowledge is of a kind which must fail to transcend appearance, itself implies that transcendence. For, if we had no idea of a beyond, we should assuredly not know how to talk about failure or success. And the test, by which we distinguish them, must obviously be some acquaintance with the nature of the goal. Nay, the would-be sceptic, who presses on us the contradictions of our thoughts, himself asserts dogmatically. For these contradictions might be ultimate and absolute truth, if the nature of the reality were not known to be otherwise . . . [such] objections . . . are themselves, however unwillingly, metaphysical views, and . . . a little acquaintance with the subject commonly serves to dispel [them]. [Appearance and Reality, 2nd Edn, 1897 (1916 printing), pp. 1 – 2; INTRODUCTION. At Web Archive.]

    Go back above and we see why there is that claim, oh, just because you can find a pattern of appearance to us does not mean you have found an objective principle. And of course, logical-mathematical and physical warrant on such a view cannot bridge to reality. There is no abstract reality to be bridged to, or at least of the kind you are interested in, here, aesthetic reality.

    I think it is far more sensible to conclude that nominalism fails, that the ugly gulch fails, that there are patterns that serve as archetypes of particular cases, some of them being embedded in the framework of any possible world (such as first principles of reason, structure and quantity stemming from distinct identity). In that context, it is unsurprising that intelligent, rational and responsible creatures can and do detect with some degree of reliable warrant, such patterns, archetypes, principles. And, that we find the coherence of harmony, proportion, symmetry, fractal, scaling self-symmetry, variety, subtle asymmetry and focus that relieve the boredom of mechanically repeated exact symmetry will be pleasant and satisfying, beautiful, then makes a lot of sense.

    So, beauty is connected to truth, warrant, knowledge and the like.

    Consequently in a day where truth etc are under assault, we can see why beauty and associated aesthetics principles will be deeply and unjustly suspect. Indeed, will be subjected to selective hyperskepticism. Beauty is a threat.

    No wonder the powerful have been willing to spend billions to impose the ugly, through defiance of aesthetics principles. And no wonder some find in the chaotic result something that resonates with their inner turmoils. No wonder, there is a spiral of silencing objections to such eyesores and chaotic monstrosities.

    Instead, let us accept that explosion holds and that what is self referentially incoherent is self-falsified and unreliable. Specifically, nominalism.

    I stand by my remark at 100 above:

    of course, tastes can be outright bizarre, not just abnormal or culture-bound. One may always stoutly resist the conclusion of a convergent pattern of evidence and argument, but it is clear enough that there are aesthetic principles that are readily intelligible, are rooted in observable structural, quantitative and physical phenomena, and contribute to the patterns and phenomena we enjoy as beautiful. When they are willfully discarded as a bloc, it is equally clear that the result is chaotic and ugly. Billions of dollars of recent architectural eyesores are literally massive evidence on the point. I repeat, the subjective is not the opposite of the objective and the presence of intelligible, objective frameworks for aesthetics demonstrates that yes, beauty is in material part an objective predictable phenomenon, amenable to controlled, insightful skill rather than a hit and miss affair — indeed the art of photography is also evident in the cases above. It is not an accident that Grand Canyon was photographed at just that moment, from that angle with settings, filters, focus etc.

    KF

  124. 124
    kairosfocus says:

    F/N: I added to the OP on proportions, also putting in spirals and linked phenomena in the sequence of cases, including now Da Vinci’s Vitruvian Man. KF

  125. 125
    daveS says:

    KF,

    For my part, I am not denying that beauty could be at least partially objective. Rather, I don’t find your argument persuasive. As I’ve said several times, I find your argument completely consistent with the proposition “beauty is (merely) intersubjective”.

  126. 126
    kairosfocus says:

    DS, I have pointed out that the issue on objectivity is not intersubjective agreement or subjectivity (only subjects can know) but warrant. In this case we have a widely recognised (across time and culture, styles differ but these sorts of patterns are consistent), named phenomenon — not typical marks of delusions or ill-founded ideological claims. It is associated with certain aesthetics principles which are in many cases mathematically addressable (e.g. symmetry, harmony) and we can see the effects on for instance faces or buildings as such principles are fulfilled or not fulfilled. In this case, with billion dollar investments in proof. Observable, in significant part mathematically accessible, go/no go demonstrations seen. If after this you still will not accept that there is significant objective warrant that aesthetic principles are objectively warranted and give us an objective understanding of beauty commonly used by painters, decorators, architects, etc, then I do not think the issue is on the side of adequate warrant, it is that there is an underlying implicit influence by nominalistic views in this regard. There are a lot of other things that are warranted in much the same way that we routinely accept. I suggest a good cross check would be does evil have reality beyond subjective opinion and agreement in some community or other? Likewise, do numbers have reality beyond our labels, operations on imagined collections, etc, are they embedded in the framework for a world to exist? What would it mean for a scientific theory to have objective status? Is there an objective shared world that we participate in (as opposed to say some sort of Matrix-like simulation world), on what grounds? What accessible evidence or argument would lead you to accept that there is a reality to beauty beyond agreement within a subject or between some circle of subjects or other, e.g. would the eyesore buildings be beautiful if somehow a significant circle were to say so? Or have you reduced beauty to, in accord with the tastes of some reference group or other. Etc. KF

  127. 127
  128. 128
    daveS says:

    KF,

    Likewise, do numbers have reality beyond our labels, operations on imagined collections, etc, are they embedded in the framework for a world to exist?

    I do believe that numbers are real and exist independently of their minds. For example, any theorem in Peano arithmetic which we can prove could be proved in every possible world. In that sense mathematics is 100% objective. I also think I might have a very hard time convincing anyone of that.

    Is there an objective shared world that we participate in (as opposed to say some sort of Matrix-like simulation world), on what grounds?

    Another very tough question. I provisionally assume there is, based on Occam’s Razor. It does seem more parsimonious to assume the existence of an objective shared world rather than a Matrix-like simulation.

    What accessible evidence or argument would lead you to accept that there is a reality to beauty beyond agreement within a subject or between some circle of subjects or other

    That’s a good question. I don’t know that there is such a thing. It’s a difficult task you have chosen, IMHO.

  129. 129
    daveS says:

    KF,

    On Phi and attractive human faces

    Clearly humans find faces with certain proportions to be beautiful. I’m not sure I believe those proportions have much to do with the golden ratio, however. There is a lot of humbug around phi you know.

    I suspect if humans’ heads looked like hammerhead sharks we would believe ourselves to be the most beautiful creatures around, just the same.

  130. 130
    kairosfocus says:

    DS,

    The work is there to be inspected. There is no doubt that human body proportions (as opposed to primates etc) are real, and that for some unfortunate people, surgical intervention is life-transforming. It is demonstrable that structures based on phi are present in a great many bodily features including faces that are highly attractive. Despite humbug, that is readily seen.

    I again suggest: http://www.colyvan.com/papers/Musgrave.pdf

    Next, the diagnostic is that your skepticism on warrant of objective Mathematical truth is a key indicator.

    In answer, I ask that you do the Mobius strip exercise. This will empirically demonstrate mind-independent reality of deeply embedded logic of structure and quantity better than any argument. That is a plumb-line exercise. After that, we can work forward.

    Our being in a real, shared world is best understood on a reductio: any scheme of thought that entails grand delusion is fatally self undermining (and infinitely regressive in the delusions). It can be set aside as absurd.

    The onward problem flows from that spring.

    KF

    PS: Some food for thought on data compression in algorithms for face building etc:

    The work of Dr. Stephen Wolfram provides an insight into how individual cells are programmed to create the trillions of cells that comprise a living organism. Cellular automata proposes that a collection of cells creates a shape or design through a number of discrete time steps according to a set of rules based on the states of neighboring cells.

    Consider the multitude of steps that must be required for embryonic cells to create the face of a human being through its entire growth cycle. Each cell must contain a set of rules which tells it what type of cell to become and the exact position on the face for it to appear.

    Now consider that the unique mathematical properties of the golden ratio make it inherent in so many mathematical formulas and limits, as well as in many geometric constructions.

    Imagine that YOU were the programmer who had to come up the rules to create the dimensions and proportions of the human face. Imagine that YOU have to choose ratios to create a facial design structure with complexity in concept, yet simplicity and harmony in execution. Would you choose a ratio like the golden ratio, with its unique mathematical ability to create a variety of different geometries? Or would you go about this by choosing a different ratio for every aspect of your design? Beauty may exist for its own sake or as an evolutionary adaptation to indicate a healthy partner for procreation. Either way, which approach do you think would result in the most aesthetically pleasing result, the use of a single ratio or different ratios for each element in the design of a face?

  131. 131
    daveS says:

    KF,

    Next, the diagnostic is that your skepticism on warrant of objective Mathematical truth is a key indicator.

    In answer, I ask that you do the Mobius strip exercise. This will empirically demonstrate mind-independent reality of deeply embedded logic of structure and quantity better than any argument. That is a plumb-line exercise. After that, we can work forward.

    A while back I made a similar argument. I made the claim that any theorem in mathematics we have a proof for could be proved with a mechanical device (such as a Turing machine) in principle. I don’t know whether that will convince anyone, frankly, but I find it persuasive.

    Our being in a real, shared world is best understood on a reductio: any scheme of thought that entails grand delusion is fatally self undermining (and infinitely regressive in the delusions). It can be set aside as absurd.

    The proposition that we are in a Matrix-like simulation is literally unfalsifiable. We can claim it is “””absurd”””, but we cannot know it is false.

  132. 132
    hazel says:

    Hi Dave. You wrote,

    I do believe that numbers are real and exist independently of their minds. For example, any theorem in Peano arithmetic which we can prove could be proved in every possible world. In that sense mathematics is 100% objective. I also think I might have a very hard time convincing anyone of that.

    As I think I’ve mentioned, we had a long discussion about this last fall, during which I made some arguments to myself that moved me away from a Platonic view while still maintaining that mathematical truths were “objectively” true within the logical systems in which they could be expressed. Maybe I’ll try to dig up the most relevant points, and share.

  133. 133
    kairosfocus says:

    DS,

    The exercise of making three paper loops and cutting them around is not a Turing machine type proof, but an empirical exercise and experience, a Physics experiment actually. Make an ordinary cylindrical loop and two 1/2 (180 degree) twist Mobius loops (“strips”). Cut the cylinder around in the middle. Cut the first M-loop around in the middle. Cut the remaining loop around 1/3 way across. Observe the three different results: 1 — two narrower cylinders, 2 — a single longer loop with more twists in it, 3 — a smaller version of the M-loop interlocked with a longer loop.

    This demonstrates how certain structures and quantities are embedded in physical bodies (tied to number of edges and surfaces) which are independent of our views, thoughts, understandings, level of Mathematics etc. Such should serve as a plumb-line for reconsidering our understanding of abstract realities and how they are present in reality.

    Next, a clear issue is the understanding of what knowledge is and its requisite, credible rationality. Knowledge in the weaker and more generally applicable sense is warranted, credibly true (so, reliable) belief. Thus, it is corrigible, i.e. if warrant fails something we thought we knew will be reclassified. Warrant is a reasonable, responsible process that requires credibility of our cognitive faculties. Faculties, which are under duties to truth, right reason, prudence, fairness etc. Yes, that’s inextricably entangled rational and moral government of our thought lives. Wherever that leads, let the chips lie where they fly.

    When a world-concept is put up, it implicitly assumes the credibility of rationality. So, any such scheme reduces to a Plato’s Cave or Matrix style grand delusion, it fatally self-refutes. One way, is that the level 1 GD undermines rational faculties, so is this in turn subject to a level 2 GD, then level 3 etc? Such an infinite regress utterly undermines rationality and is absurd, self-falsifying. We can take it as a principle of right reason that any claimed scheme that entails grand delusion is absurd, undermining even the faculties that led to it being put forward.

    Yes, such is an exercise in reasonable, responsible faith. That is what we are capable of and we need to accept that as a part of the first fact of conscious rational reality: we must live by faith and not by utter certainty. Not even Mathematics, post Godel, can deliver utter certainty. And, Scientific theories don’t even rise to moral certainty.

    In such a context, the question is which core first plausibles will we believe, not whether we have such. And like unto it, why. Thus thirdly, we see the central importance of comparative difficulties analysis.

    KF

    PS: No-one is arguing that humans are the most beautiful of creatures, actual or possible. Indeed the Renaissance artists discovered that idealised human figures that we hardly ever see in living people are more attractive than even quite beautiful but more realistically proportioned people. One of the subtleties of Mona Lisa is, she is pretty realistic, complete with a slight double chin. Until overzealous cleaning swept it away, veins in her neck were visible, lending to the subtle sense of liveliness. That said, the reaction of people seeing colours and hearing voices accurately for the first time tells us how much beauty in “ordinary” things we take for granted. Likewise, ponder the people with unfortunate deformities or proportions who underwent plastic surgery with results that are obviously potentially transformational. One takeaway from this discussion for me is to resolve to enjoy the beauty in ordinary, commonplace things more.

  134. 134
    kairosfocus says:

    H, have you done the Mobius strip exercise yet? What are your findings, why? KF

  135. 135
    kairosfocus says:

    F/N: I added verisimilitude to the explicit list of principles. I think here about how contemporary observers spoke to visible veins in Mona Lisa’s neck that contributed to a sense of lifelikeness. KF

  136. 136
    daveS says:

    hazel,

    As I think I’ve mentioned, we had a long discussion about this last fall, during which I made some arguments to myself that moved me away from a Platonic view while still maintaining that mathematical truths were “objectively” true within the logical systems in which they could be expressed. Maybe I’ll try to dig up the most relevant points, and share.

    Those would be interesting to read. I’ve always considered myself to be a neoplatonist of some sort, but it has its downsides.

  137. 137
    daveS says:

    KF,

    When a world-concept is put up, it implicitly assumes the credibility of rationality. So, any such scheme reduces to a Plato’s Cave or Matrix style grand delusion, it fatally self-refutes. One way, is that the level 1 GD undermines rational faculties, so is this in turn subject to a level 2 GD, then level 3 etc? Such an infinite regress utterly undermines rationality and is absurd, self-falsifying. We can take it as a principle of right reason that any claimed scheme that entails grand delusion is absurd, undermining even the faculties that led to it being put forward.

    I don’t believe a Matrix-type simulation necessarily undermines our rational faculties. Rather, it just means our sensory apparatus have been taken over so that even though we may be lying in a chair motionless, we sense that we are in some other environment, performing activities such as swimming the English Channel. We may very well respond to our simulated perceptions rationally.

    I don’t think we are in such a simulation, but that’s not because it’s somehow self-falsifying.

  138. 138
    kairosfocus says:

    DS, the point is, systematic, pervasive delusion that leads us away from truth — an accurate grasp of reality. That is enough to lead to the destructive spiral of undercutting the credibility of mind. KF

  139. 139
    hazel says:

    ks writes, “H, have you done the Mobius strip exercise yet? What are your findings, why? KF”

    That is a silly question, kf. I know very well how Mobius strips work, and I’ve told you that. I used to teach about them in geometry class. You seem to think they make some big point that other examples of how geometry works in the real world don’t, but I don’t know why.

  140. 140
    kairosfocus says:

    H, the Mobius strips and cylindrical loops, precisely because they tend to be unfamiliar, allow us to see with fresh eyes how structure and quantity are embedded in the world independent of our concepts or ideas or beliefs. Notice, the exercise is a physical, not a mental one. Beyond, I agree, much the same message comes from how a 12-segment rope effects a right angle triangle, or how a triangle based on the diameter of a circle with its third vertex on the circumference MUST be a right angle triangle with the diameter its hypotenuse. Such examples show that there is a world of mathematical facts that are antecedent to our axiomatisations and are so independent of what we may think. That is a fairly serious point and it should constrain our speculations on the nature of Mathematics or the reality of key abstracta. Indeed, on the logic of being, which then indicates how logic has ontological import. Coming back to the focus of this OP, certain abstract and even mathematical principles have a significant aesthetic impact, for good or ill. We need to recognise that such principles are not arbitrary figments but are indeed canons of beauty. If next tuesday, Parliament were to pass a law that certain eyesores such as in the OP above were to be called beautiful, it would have about as much effect as calling the tail of a sheep its fifth leg. KF

  141. 141
    hazel says:

    My point is that you don’t have to ask me ever again whether I’ve “done the Mobius strip exercise.” They are not unfamiliar to me. I am not trying to open up our philosophical issues again: I am just asking you to understand that pointing them out to me is pointless repetition. Your philosophical point is not going to be suddenly illuminated if I get a strip of paper, twist it, and cut it down the middle, as I have done many times in the past when introducing my geometry students to some simple topics in topology.

  142. 142
    kairosfocus says:

    H, with all respect, you here confirm that you have done at least a part of the exercise and therefore have likely seen part of the result. (I am not sure if you have done the 1/3 way across exercise, likely you have done the second cut in the middle exercise.) That is enough to establish that you have seen it demonstrated that certain structures and quantities are as a matter of observable readily reproduced fact embedded in space and in bodies in space independent of our conceptualisation, axiomatisation etc. Therefore, you are a witness that there are world-embedded mathematical facts which are intelligible and observable accurately. Abstract entities with real world consequences, laws of nature if you will. (After all, my perspective will be that of a physicist, phusis being Greek for “nature.”) It should not be a surprise to you to see that there will be intelligible, rational principles that have observable real-world consequences that happen to be aesthetic. And so forth. KF

  143. 143
    hazel says:

    I have also drawn circles with a compass, kf. 🙂

    And shown the proof that an angle inscribed in a semicircle is a right angle.

    I live in the real world!!!

  144. 144
    daveS says:

    Therefore, you are a witness that there are world-embedded mathematical facts which are intelligible and observable accurately.

    I think people who have taught math for decades generally pick up on these things.

  145. 145
    Brother Brian says:

    If the typical human face was rather amorphous and asymmetrical rather than symmetrical, I suspect that we would, in general, find beauty in faces that are amorphous and asymmetrical. The alternative would be that we see everyone as being ugly.

    https://www.youtube.com/watch?v=gEp7yunwVF8

  146. 146
    kairosfocus says:

    BB, I am by no means so sure, as many people with faces that are problematic, perceive the difference and in the sort of cases in the OP, set about doing something. I suspect that in some cases it makes a difference to life outcomes, more power to them. Shapeless blobs or the like, would not be symmetric, proportioned, harmonious, have well located focal points and highlights, etc etc. But note, I am by no means fixated on faces, musical cacophony and architectural eyesores are very much in view. Where, we must note the sharp distinction between tastes and aesthetics. KF

  147. 147
    Brother Brian says:

    I think what is at issue here is that we do not have a common framework or definition of what beauty even is. For example, I suspect that Hazel finds beauty in mathematics. I, on the other hand, see mathematics as a powerful and functional tool. Some people find beauty in order (e.g., fractals and the Notre Dame Rose Window) whereas others see beauty in disorder (e.g., a thunder storm or a storm tossed sea). Even a couple of the buildings that KF has classified as eyesores, I find rather compelling and interesting. Maybe not beautiful, but also not an eyesore.

    Trying to argue that there is some objective measure of what is beautiful simply is not warranted.

  148. 148
    kairosfocus says:

    H, thank you. I think the point is made. Its force, though seemingly trivial, is relevant and powerful. There are intelligible rational principles and entities of structure and quantity embedded in our world independent of our own views, preferences, concepts etc. Moreover, as was shown, some of them are demonstrably necessary, framework entities in any distinct possible world. Relevant to this thread, some of those embedded things have to do with symmetry and the like, which just happen to have observable aesthetic impact-promoting effects. (Meisner’s discussion on faces and their proportions etc should be interesting.) KF

  149. 149
    kairosfocus says:

    BB, kindly see the OP on what beauty is, and on aesthetics principles that have a demonstrable track record. Cumulatively, thanks to recent architecture, in the billion dollar class. Somebody should have been fined for wrecking a skyline like that, for one. Tourism demonstrably is associated with aesthetics, with big money at stake. KF

  150. 150
    Brother Brian says:

    KF

    Cumulatively, thanks to recent architecture, in the billion dollar class. Somebody should have been fined for wrecking a skyline like that, for one. Tourism demonstrably is associated with aesthetics, with big money at stake.

    When the Eiffel Tower was built, the majority of Parisian considered it an eyesore. Today it attracts millions of tourists every year.

  151. 151
    hazel says:

    Kf you wrote,

    H, thank you. I think the point is made. Its force, though seemingly trivial, is relevant and powerful. There are intelligible rational principles and entities of structure and quantity embedded in our world independent of our own views, preferences, concepts etc. Moreover, as was shown, some of them are demonstrably necessary, framework entities in any distinct possible world.?

    I don’t think I know what you are thanking me for, or what point is made. I don’t agree with one central part of the stuff you continually write, as you wrote starting with “There are …”, so if you are thanking me for agreeing with that point I think you are confused about what I do and don’t believe, or the significance of what I wrote in 143.

  152. 152
    kairosfocus says:

    BB, kindly look at the collection of eyesores. The Eiffel Tower adheres to principles of aesthetics, what we see above does not. KF

  153. 153
    kairosfocus says:

    H, your agreement or disagreement is immaterial. The empirical evidence you yourself saw is sufficient to make the point. KF

  154. 154
    hazel says:

    Makes the point for you, as you have made many times before, but doesn’t say anything different about how I don’t completely agree with your points. I’ve certainly said nothing today that I haven’t already said countless times before, about numerous examples you have offered.

  155. 155
    Brother Brian says:

    KF

    BB, kindly look at the collection of eyesores.

    I did. And I find a couple of those aesthetically pleasing. We obviously disagree. Testament to the subjective nature of beauty.

    The Eiffel Tower adheres to principles of aesthetics, what we see above does not. KF

    When it was built it did not adhere to the principles of aesthetics of the day. Further testament to the subjective nature of beauty.

  156. 156
    kairosfocus says:

    BB, no. It was new, a new type of monument. Look at the tower: symmetrical, two converging J-curves [part of a spiral), focus the sweep to the sky, variety and detail, announces a new technological era. The current eyesores are simply and by deliberate choice in disregard. KF

  157. 157
    Brother Brian says:

    KF@156, I understand that you don’t like architecture that does not obey your desire for symmetry and flow. And, in your mind, they are eyesores. But that is subjective opinion, not objective . What do you think of the glass pyramids at the Louvre? Or this?
    https://dynaimage.cdn.cnn.com/cnn/q_auto,w_343,c_fill,g_auto,h_193,ar_16:9/http%3A%2F%2Fcdn.cnn.com%2Fcnnnext%2Fdam%2Fassets%2F131008143227-blob-buildings—golden-terraces.jpg

  158. 158
    math guy says:

    KF @ 123
    Sometimes your arguments are excessively complicated (albeit correct IMHO), but the following is a succinct jewel:

    “However, it is patent that Nominalism is self-referentially incoherent, as universals and abstracta are inescapable in our thinking and reasoning, including in stating the claim that roughly runs: [we know, per some warrant that] there are no universals or abstracta, only names for collectives we impose.
    In effect, it affirms what it would deny.
    It is inescapably incoherent.”

  159. 159
    math guy says:

    Since Hazel claims that mathematics is true but exists only inside minds, evidently Hazel’s nominalist viewpoint fits
    this category:

    (1) that mathematics is about concrete mental objects in people’s heads (psychologism)

    How does Hazel reconcile that viewpoint with the inconsistency expressed by KF in 123 and summarized in post 158?

  160. 160
    daveS says:

    I’ve always found the Eiffel Tower to be a bit homely. Except when it’s lit up, then it can be quite beautiful.

  161. 161
    hazel says:

    MG, as I have explained, I am not advocate for nor identify with any label in philosophy. In one discussion a while back I mentioned an aspect of nominalism, which I read about in Wikipedia, as appealing to me. Kf took that and made me a “champion” of nominalism, and now he keeps bringing it up. Among other things, I read on Wikipedia (which is about the extent of my education on this subject) that there is a long history and many philosophical variants related to nominalism, and I am certainly not going to try to become an academic philosopher and sort them all out and figure out what I agree with and what I don’t.

    So, following William J Murray, I have declared my philosophy to be “hazelism”. I’m quite willing to discuss my own ideas (at appropriate times, with appropriate people, about appropriate topics), but I’m not responsible for someone else’s idea about what they think my philosophy is based on some label.

    Also, you write that you think my viewpoint is,

    that mathematics is about concrete mental objects in people’s heads

    That sentence doesn’t apply to me, or make sense to me. I’m not sure what a “concrete” mental object could even be. Also, even though of course there is a connection, albeit of an unknown nature, between brain and mind, my position (somewhat speculative and tentative as it is) is that math, as a formal and logical system, exists as abstract concepts in our minds, and that written and verbal symbol systems are the way we express, and share, those concepts in the physical world.

  162. 162
    hazel says:

    P.S. Small point: I note that MG said “heads” in the quote above, so I guess I should assume he meant “minds”.

  163. 163
    kairosfocus says:

    BB, there are many examples of architectural chaos created by deliberately flouting long known aesthetic principles, cumulatively a billion dollar eyesore imposed on the public as a manifestation of an ideology. (BTW, students of Architecture study them in school, and study many, many cases, sometimes even reverse-engineering drawings based on measurements.) In pointing to this, I am not automatically condemning any and all skyscrapers or modern buildings, though sometimes there is the ruining of a cityscape by clashing with its centuries old environment. Of course, many of the worst examples are not skyscrapers and even follow natural forms (one of the examples above looks suspiciously like a bacterium on steroids.) KF

    PS: The glass pyramid at the Louvre, as I remember from when it was built, was controversial when constructed. However it seems to reasonably fit its environment, echoes a famous monument at Giza (appropriate to a world heritage museum that houses inter alia the world’s most famous portrait and painting) and is obviously in accord with symmetry principles. I note that at Giza there is a larger architectural plan, whereby the pyramids and the Nile together echo Orion’s belt and the Milky way band in the sky. And no, Dan Brown did not write a well instructed novel and I don’t buy the “the Pyramids hold the secrets of the universe and bases of measurement units” stories. Though obviously from them we can learn a good deal about ancient Egyptian measurement systems etc.

  164. 164
    kairosfocus says:

    DS, light is often a part of the effect of a design. KF

  165. 165
    kairosfocus says:

    H, I spoke to how you championed aspects of nominalism. As MG has again noted, you are exhibiting conceptualist or psychologist influences; the observation came first, the references to schools of thought were and remain, descriptive in that light. And championing is a fair comment description of roles taken up and arguments made in a long engagement. A core part of the exchange was a dual character definition of Mathematics as involving a culturally influenced study on one part and a partly reality embedded substance on the other part: the [study of the] logic of structure and quantity; where, “logic” points to intelligible, rational, structuring patterns. Consistent with psychologism or conceptualism, you have consistently pulled focus to the study aspect and to in effect agreements, disagreements and framing on clusters of axioms etc. I have pointed out that there are evident, intelligible core, world-embedded mathematical facts in quantity that are antecedent to axiomatisation conceptually and chronologically. That is, they factually constrain and audit the plausibility of axiomatic schemes. So, it is inappropriate to suggest that mathematical truths and/or facts can be reduced to conformity to or derivation from the playing out of axiomatic schemes or similar abstract logic model worlds — including say being spun out from a suitably programmed Turing Machine etc. Note here Godel’s incompleteness results etc. Truth is still best understood as accurate description of reality: saying of what is that it is and of what is not that it is not. We can add, also of what is [im]possible that it is [im]possible. My basic concern on nominalism in Math and elsewhere is that it is self-referentially incoherent thus self-falsifying. KF

    PS: If you want to place me, a good slice of my thought on Math, Sci and general education comes from Richard Skremp and what could be called moderate constructivism. We naturally infer patterns from concrete experiences, building up conceptual schemes from abstraction that in effect is suggesting or inferring archetypes. Latterly, I intersect this with the significance of the principle of distinct identity and associated logic of being. I find this fruitful in exploring not only inductive reasoning (which is where this series started) but also in understanding how explorations of abstract logic model worlds can identify necessary entities that are part of the fabric of any possible world and can also allow us to use close analogues to this world to explore plausible features. In that context, exploration of key case studies is a powerful exercise, one best done with eyes and hands. Were I to teach elementary physics again, i/l/o what I am seeing, I would insist on experiments that explore properties of space considered as a part of the fabric of physics. For example, not just Mobius strips but making semicircles and exploring how we get right angle triangles by pinning taut string to the relevant points. Twelve segment ropes might help. Making ellipses with strings and pins too. Maybe some bubble explorations. Hyperbolas from capillarity between glass blocks brought together in a narrow V too.

  166. 166
    kairosfocus says:

    F/N: I have added the case of the Louvre Pyramid to the OP, to illustrate the tension of old and new and the significance of symmetry and subtle asymmetry. KF

  167. 167
    daveS says:

    KF,

    I notice you spend a fair amount of time throwing around prejorative (in this context) labels: “fellow traveler”, “agit-prop”, “Darwinist rhetorical tactics”, and now “nominalist”. Even if someone is not a proponent of a particular idea and has said so explicitly, nevermind, they are adherents of some “fellow traveler” ideology.

    Here’s a question: Does hazel do the same to you?

  168. 168
    Brother Brian says:

    DaveS

    Here’s a question: Does hazel do the same to you?

    Nobody who disagrees with his opinion do the same thing to him. In my mind, it is a testament to the patience and restraint of those he applies these labels to.

  169. 169
    kairosfocus says:

    DS,

    First, SEP on Nominalism in Mathematics:

    Nominalism about mathematics (or mathematical nominalism) is the view according to which either mathematical objects, relations, and structures do not exist at all, or they do not exist as abstract objects (they are neither located in space-time nor do they have causal powers). In the latter case, some suitable concrete replacement for mathematical objects is provided. Broadly speaking, there are two forms of mathematical nominalism: those views that require the reformulation of mathematical (or scientific) theories in order to avoid the commitment to mathematical objects (e.g., Field 1980; Hellman 1989), and those views that do not reformulate mathematical or scientific theories and offer instead an account of how no commitment to mathematical objects is involved when these theories are used (e.g., Azzouni 2004) . . . .

    In ontological discussions about mathematics, two views are prominent. According to platonism, mathematical objects (as well as mathematical relations and structures) exist and are abstract; that is, they are not located in space and time and have no causal connection with us. Although this characterization of abstract objects is purely negative—indicating what such objects are not—in the context of mathematics it captures the crucial features the objects in questions are supposed to have. According to nominalism, mathematical objects (including, henceforth, mathematical relations and structures) do not exist, or at least they need not be taken to exist for us to make sense of mathematics. So, it is the nominalist’s burden to show how to interpret mathematics without the commitment to the existence of mathematical objects. This is, in fact, a key feature of nominalism: those who defend the view need to show that it is possible to yield at least as much explanatory work as the platonist obtains, but invoking a meager ontology. To achieve that, nominalists in the philosophy of mathematics forge interconnections with metaphysics (whether mathematical objects do exist), epistemology (what kind of knowledge of these entities we have), and philosophy of science (how to make sense of the successful application of mathematics in science without being committed to the existence of mathematical entities). These interconnections are one of the sources of the variety of nominalist views.

    The name itself highlights what is thought: a label for a concept.

    Nominalist is thus not a pejorative label, it is a viewpoint (as opposed to a school of thought with proverbially card-carrying members) which is fairly common but is arguably an error — that being fair comment.

    One may indeed take offence at an accurate term, but the term in itself provides a summary of a description.

    The premise of your claim fails.

    KF

    PS: Darwinism is also a description and there are darwinists who resort to common rhetorical tactics which are fallacious as has been explored in fair detail here at UD, years ago now. In addition, given its ideological function, there are those who are not full adherents but go along with it sufficiently that fellow travellers is an appropriate term.

  170. 170
    kairosfocus says:

    BB, kindly note the response to DS just above. A well known, commonly accepted descriptive label is simply not the same sort of thing as pejorative namecalling by way of belittling or dismissal. Especially, when the main focus is on the substantial issues and logic. In this case, also, direct empirical experimentation which demonstrates the point at stake in the end: there are observable, intelligible phenomena which show that there is substance of structure and quantity embedded in the world so that a good slice of relevant mathematical facts are discovered rather than invented. Even complex numbers, which were an invention in the historical first instance, turned out to have a very natural interpretation or understanding or even re-foundation i/l/o rotating vectors. KF

  171. 171
    hazel says:

    And yet kf adds a PS that does exactly what Dave pointed out.

    I’ll also point out that in previous posts kf’s has said that nominalism is connected to materialism and scientism, even though I have no idea how. I am absolutely not an advocate of scientism, but somehow, he implied, I am nevertheless a “fellow traveler.”

  172. 172
    daveS says:

    KF,

    We all know that “nominalist” is not prejorative in the wider world, but in the context of your threads it obviously is. Just like “fellow travelers” is. Do you not see the difference between your behavior and hazel’s?

  173. 173
    kairosfocus says:

    DS, no, that is simply wrong. I have disagreed with nominalism, on specific grounds. If those grounds are in error, simply show it. That would be more than enough to settle the matter. And, disagreement is not belittling etc. even when it uses an appropriate descriptive term. KF

  174. 174
    kairosfocus says:

    H, no. I have pointed out that nominalism is a descriptive label for a philosophical position on mathematical entities; one that I and many others — often termed mathematical platonists (which I accept though by no means do I buy into platonism etc); that is, I accept that there are abstracta of structure and quantity that have sufficient reality to be independent of our thoughts or inventions of thought, and in some cases are framework to any possible world, thus have import for the logic of being. I do not view being termed such a Platonist as namecalling or as a way to belittle and dismiss without addressing substance. By contrast, the Neo-Darwinian Synthesis is a still fairly dominant school of thought that has been demonstrably associated with ideological commitments and agendas, where some things have been done that can reasonably be described as fallacious rhetorical tactics. In addition there are many who do go along with the core committed sufficiently that fellow traveller is a fair comment description. That’s not — repeat, not — what is going on on discussion of a fairly abstruse issue in ontology: are there core mathematical entities which are necessary aspects of the fabric for any distinct possible world? To which, on the principle of Identity — W = {A|~A}, A being some aspect of W that distinguishes it from near neighbours — and its implication of nullity, unity, duality and extensions therefrom, I point to N, Z, Q, R and C, with associated phenomena. Where, I am both a Mathematical Platonist AND a moderate constructivist in regards to mathematical learning; which likely affects why I tend to look to empirical demonstrations and likely influences why I took an inductive, case study approach to drawing out principles of aesthetics. Which is still the principal focus of this thread. KF

  175. 175
    Brother Brian says:

    KF, it is possible that you don’t notice the fact that your use of these labels are perceived as pejorative by those you apply them to. But now that this has been pointed out to you by more than one person, can we expect an attempt by you to restrain your use of these labels?

  176. 176
    kairosfocus says:

    BB, anyone can perceive just about anything as pejorative. I have focussed on the substantial issues as may readily be seen. I suggest, that if you or others think I am in error, simply warrant that claim. KF

  177. 177
    Brother Brian says:

    KF@176, I take that as a no. I didn’t expect any different but I was giving you the benefit of the doubt, hoping that you would realize that your use of these terms is counterproductive of any serious discussion. This will be the last time I bring it up.

  178. 178
    ET says:

    LoL! BB is not interested in a serious discussion. BB’s sock is on record saying it comes here only to poke and muddy the waters.

  179. 179
    kairosfocus says:

    F/N: As it is perhaps lost in the onward stream of comments, perhaps this pair of comments from the Mathematician, MG, may be helpful:

    158
    math guy
    March 15, 2019 at 7:56 pm (Edit)

    KF @ 123
    Sometimes your arguments are excessively complicated (albeit correct IMHO), but the following is a succinct jewel:

    “However, it is patent that Nominalism is self-referentially incoherent, as universals and abstracta are inescapable in our thinking and reasoning, including in stating the claim that roughly runs: [we know, per some warrant that] there are no universals or abstracta, only names for collectives we impose.
    In effect, it affirms what it would deny.
    It is inescapably incoherent.”

    159
    math guy
    March 15, 2019 at 7:59 pm (Edit)

    Since Hazel claims that mathematics is true but exists only inside minds, evidently Hazel’s nominalist viewpoint fits
    this category:

    (1) that mathematics is about concrete mental objects in people’s heads (psychologism)

    How does Hazel reconcile that viewpoint with the inconsistency expressed by KF in 123 and summarized in post 158?

    That is the substantial issue that was put on the table in the thread (which is about the objective reality of aesthetic principles).

    On fair comment, it has not been answered cogently on the merits.

    KF

  180. 180
    Silver Asiatic says:

    KF

    To which, on the principle of Identity — W = {A|~A}, A being some aspect of W that distinguishes it from near neighbours — and its implication of nullity, unity, duality and extensions therefrom, I point to N, Z, Q, R and C, with associated phenomena.

    That being can be distinguished from non-being is the basis of the Law of Identity and since all mathematical structures follow from that there is good reason to see that principle, logic and math as having an independent, abstract existence.

  181. 181
    hazel says:

    kf, did you read my reply to MG at 161? What he said about/to me was inaccurate, or not very applicable.

    Also, kf, you wrote at 176.

    BB, anyone can perceive just about anything as pejorative. I have focussed on the substantial issues as may readily be seen.

    However, at 123, (and this is somewhat typical of remarks you make), you wrote

    Consequently in a day where truth etc are under assault, we can see why beauty and associated aesthetics principles will be deeply and unjustly suspect. Indeed, will be subjected to selective hyperskepticism. Beauty is a threat.

    No wonder the powerful have been willing to spend billions to impose the ugly, through defiance of aesthetics principles. And no wonder some find in the chaotic result something that resonates with their inner turmoils. No wonder, there is a spiral of silencing objections to such eyesores and chaotic monstrosities.

    Instead, let us accept that explosion holds and that what is self referentially incoherent is self-falsified and unreliable. Specifically, nominalism.

    I don’t see how you can write things like that, and also claim you are merely “focussing on substantial issues” without making pejorative comments or name calling.

  182. 182
    kairosfocus says:

    H,

    I have seen 161. In 161, you speak in favour of your own opinion vs identifying with philosophical schools of thought. Identifying is key: nominalism describes a range of views so it is very possible to hold a view X and seek to justify that belief without being aware of where it falls in a taxonomy of views. I was a constructivist before I learned the name, likely before it was widely identified by that label. MG and I have spoken to the substance and have used the name for such a view. We have pointed to reasons why we have held this view to be in error. That is not namecalling with intent to denigrate or dismiss.

    Next, notice how you went on to shift subjects to a different focus, Aesthetics (which is the focus for this thread)?

    This is not about you nor anyone else in the discussion, it is about major trends in aesthetics, especially the aesthetics we cannot avoid, the dominant built environment of significant communities across the world. Again, it is not mere namecalling, though compressed it is about substance including the issue of power that is associated with architecture on the scale in view.

    In the clip you cite, I am responding to what is a definite school of thought which has exerted power sufficient to put down billions worth of investment in buildings that are widely and for excellent reason regarded as blatant eyesores rather than exemplars of beauty. In some cases, they have effectively damaged the skylines of cities. To do that, power had to come to bear, reflecting ideology and agendas, here modernism and its extension commonly known as post modernism. Here, architects and financiers knowingly set aside long understood principles of aesthetics and got planning department approvals to violate cultural environments and/or erect buildings that are obviously chaotic.

    There are well known reasons for this sort of deliberate rejection. Where, the aesthetic effect was easily predictable. Those reasons are tied to the rise of modernism and post modernism, which indeed rejects objectivity and relativises viewpoints it does not accept. A classic illustration is how the old story of the blind men and the elephant is used to relativise perspectives while implying projection beyond the warranted. Meanwhile, implicitly (and often without self-awareness), the po mo narrator is in the position of the seeing onlooker who recognises how the blind go astray. However, that implicitly privileges his own view and becomes in fact self-referentially incoherent.

    In that context, the truth that flouting longstanding, objectively well supported aesthetics principles predictably led to less than happy consequences on the billion dollar scale is an unhappy and likely unwelcome sign. One, per fair comment, of power, imposition and over-reach. Thus of ideological failure on the aesthetic dimension; where, there have been similar failures on economics, geostrategy, education, law and society, often reflecting the dynamic, reflexive nature of individuality and social systems with the implications of unintended consequences. Where also, it is fairly well known that inner turmoil and conflicts will reflect into outer expressions. There has to be a psychological dimension and a social power dimension in the prolonging of a trend as we see over now a fair number of decades. And yes, I here reflect what I think are some valid points Marx and successors have had.

    Let me clip an article from current affairs:

    British author Douglas Adams had this to say about airports: “Airports are ugly. Some are very ugly. Some attain a degree of ugliness that can only be the result of special effort.” Sadly, this truth is not applicable merely to airports: it can also be said of most contemporary architecture.

    Take the Tour Montparnasse, a black, slickly glass-panelled skyscraper, looming over the beautiful Paris cityscape like a giant domino waiting to fall. Parisians hated it so much that the city was subsequently forced to enact an ordinance forbidding any further skyscrapers higher than 36 meters. [–> Paris being a city of the arts]

    Or take Boston’s City Hall Plaza. Downtown Boston is generally an attractive place, with old buildings and a waterfront and a beautiful public garden. But Boston’s City Hall is a hideous concrete edifice of mind-bogglingly inscrutable shape, like an ominous component found left over after you’ve painstakingly assembled a complicated household appliance. In the 1960s, before the first batch of concrete had even dried in the mold, people were already begging preemptively for the damn thing to be torn down. There’s a whole additional complex of equally unpleasant federal buildings attached to the same plaza, designed by Walter Gropius, an architect whose chuckle-inducing surname belies the utter cheerlessness of his designs. The John F. Kennedy Building, for example—featurelessly grim on the outside, infuriatingly unnavigable on the inside—is where, among other things, terrified immigrants attend their deportation hearings, and where traumatized veterans come to apply for benefits. Such an inhospitable building sends a very clear message, which is: the government wants its lowly supplicants to feel confused, alienated, and afraid [–> when sustained across decades, such has to be deliberate] . . . .

    [A] brief glance at any structure designed in the last 50 years [–> overstates the case but has a point] should be enough to persuade anyone that something has gone deeply, terribly wrong with us. Some unseen person or force seems committed to replacing literally every attractive and appealing thing with an ugly and unpleasant thing. The architecture produced by contemporary global capitalism [–> this reflects the politics of the authors, there is a strong statist and elitist element across the political spectrum and similar blunders were made behind the Iron curtain, with similar disregard for the heritage of the past] is possibly the most obvious visible evidence that it has some kind of perverse effect on the human soul. [–> right, regarding modernism and its extensions] Of course, there is no accounting for taste, and there may be some among us who are naturally are deeply disposed to appreciate blobs and blocks. [–> taste vs objective aesthetics principles] But polling suggests that devotees of contemporary architecture are overwhelmingly in the minority: aside from monuments, few of the public’s favorite structures are from the postwar period. (When the results of the poll were released, architects harrumphed that it didn’t “reflect expert judgment” but merely people’s “emotions,” a distinction that rather proves the entire point.) And when it comes to architecture, as distinct from most other forms of art, it isn’t enough to simply shrug and say that personal preferences differ: where public buildings are concerned, or public spaces which have an existing character and historic resonances for the people who live there, to impose an architect’s eccentric will on the masses, and force them to spend their days in spaces they find ugly and unsettling, is actually oppressive and cruel.

    In short, architecture is a profession with stewardship over the aesthetics of the built environment, particularly the public built environment. Indeed, that’s why we don’t just hand design of buildings and their surroundings over to engineers and economists. When significant public money is involved and/or the ambiance of a community, or the social experience of especially the vulnerable, such responsibility is redoubled. There is a reason why people speak of concrete jungles or rust belts and oppressive industrial and institutional spaces, etc.

    It is fair comment that for generations now, that stewardship has in too many instances been poorly handled, to the tune of billions. Some of it private, much of it public, all of it damaging a key commons through the classic economic problem of externalities — parties external to transactions suffer consequences. Which also directly implies that responsible regulators have failed in their duties to the public.

    I don’t endorse the fairly obvious political leanings there, but the concern over breakdown of architecture for significant buildings is a serious point. Something has had to enforce the unresponsiveness to general public feelings and response, and to sustain the message of imposition implicit in that sustained pattern. Those are substantial, policy linked issues, and they do point to serious questions regarding the stewardship of our power classes for generations.

    Something which should be familiar and which extends far beyond aesthetics. Though, this is one of the ways the problem comes out. From my angle, I would point to issues on major spheres of influence such as family, education, government, sci-tech, finance, law, arts and culture, business, worldview and linked cultural agendas. There is a consistent pattern and it does not point in a happy direction.

    Rennix and Robinson went on to pose something which is a tell as it cuts across the popular self-narrative of progressivism:

    how do we explain why, in the aftermath of the Grenfell Tower tragedy in London, more conservative commentators were calling for more comfortable and home-like public housing, while left-wing writers staunchly defended the populist spirit of the high-rise apartment building, despite ample evidence that the majority of people would prefer not to be forced to live in or among such places? Conservatives who critique public housing may have easily-proven ulterior motives, but why so many on the left are wedded to defending unpopular schools of architectural and urban design is less immediately obvious . . . . Why does there seem to be such an obvious break between the thousands of years before World War II and the postwar period? And why does this seem to hold true everywhere?

    They highlight:

    A contempt for ornament imbued the imagination of those architects who saw themselves as dedicated to social engineering rather than the mere creation of beautiful trifles. This mindset is best exemplified by the French architect Le Corbusier, who famously characterized the house as a “machine for living.” Corbusier’s ideas about planning and design were still taken seriously even when he proposed his “Plan Voisin” for Paris, which would have involved demolishing half of the city north of the Seine and replacing it with about a dozen enormous uniform skyscrapers. (Thankfully, nobody took him quite seriously enough to let him do it.) Corbusier may have done more than anyone to convince architects that they were no longer allowed to decorate their creations, issuing unquestionable pronouncements, like “the desire to decorate everything about one is a false spirit and an abominable small perversion” and “the more a people are cultivated, the more decor disappears.” He condemned “precious and useless objects that accumulated on the shelves,” and decried the “rustling silks, the marbles which twist and turn, the vermilion whiplashes, the silver blades of Byzantium and the Orient… Let’s be done with it!”

    This paranoid revulsion against classical aesthetics was not so much a school of thought as a command: from now on, the architect had to be concerned solely with the large-scale form of the structure, not with silly trivialities such as gargoyles and grillwork, no matter how much pleasure such things may have given viewers. It’s somewhat stunning just how uniform the rejection of “ornament” became. Since the eclipse of Art Deco at the end of the 1930s, the intricate designs that characterized centuries of building, across civilizations, from India to Persia to the Mayans, have vanished from architecture. With only a few exceptions, such as New Classical architecture’s mixed successes in reviving Greco-Roman forms, and Postmodern architecture’s irritating attempts to parody them, no modern buildings include the kind of highly complex painting, woodwork, ironwork, and sculpture that characterized the most strikingly beautiful structures of prior eras . . . .

    The anti-decorative consensus also accorded with the artistic consensus about what kind of “spirit” 20th century architecture ought to express. The idea of transcendently “beautiful” architecture began to seem faintly ludicrous in a postwar world of chaos, conflict, and alienation. Life was violent, discordant, and uninterpretable. Art should not aspire to futile goals like transcendence, but should try to express the often ugly, brutal, and difficult facts of human beings’ material existence. To call a building “ugly” was therefore no longer an insult: for one thing, the concept of ugliness had no meaning. But to the extent that it did, art could and should be ugly, because life is ugly, and the highest duty of art is to be honest about who we are rather than deluding us with comforting fables.

    This idea, that architecture should try to be “honest” rather than “beautiful,” is well expressed in an infamously heated 1982 debate at the Harvard School of Design between two architects, Peter Eisenman and Christopher Alexander. Eisenman is a well-known “starchitect” whose projects are inspired by the deconstructive philosophy of Jacques Derrida, and whose forms are intentionally chaotic and grating. Eisenman took his duty to create “disharmony” seriously: one Eisenman-designed house so departed from the normal concept of a house that its owners actually wrote an entire book about the difficulties they experienced trying to live in it. For example, Eisenman split the master bedroom in two so the couple could not sleep together, installed a precarious staircase without a handrail, and initially refused to include bathrooms . . .

    Clearly, something is deeply wrong, is connected to worldviews and cultural agendas, has gained power, has contemplated much worse than has been done, but has done enough. Something, that requires a substantial examination that admittedly will be painful.

    Let me add one more clip:

    The extraordinary fact about architecture over the last century, however, is just how dominant certain tendencies have been. Aesthetic uniformity among architects is remarkably rigid. Contemporary architecture shuns the classical use of multiple symmetries, intentionally refusing to align windows or other design elements, and preferring unusual geometric forms to satisfying and orderly ones. It follows a number of strict taboos: classical domes and arches are forbidden. A column must never be fluted, symmetrical pitched roofs are an impossibility. Forget about cupolas, spires, cornices, arcades, or anything else that recalls pre-modern civilization. Nothing built today must be mistakable for anything built 100 or more years ago. The rupture between our era and those of the past is absolute, and this unbridgeable gap must be made visible and manifest through the things we build. And since things were lovely in the past, they must, of necessity, be ugly now.

    One does not need to go along with these authors on everything to see that they have struck uncomfortably close to home, raising substantial points.

    KF

    PS: I add, I found the 1982 debate: http://www.katarxis3.com/Alexa.....Debate.htm

  183. 183
    math guy says:

    H @ 161, 162
    The quote “that mathematics is about concrete mental objects in people’s heads” was pasted from post 123, which KF attributes to Enc Brit. I would paraphrase as “mathematics is about actual logical structures which only exist within minds” which seems to fit previous declarations made by H.

    Also from 123 is the wikipedia quote “nominalism is a philosophical view which denies the existence of universals and abstract objects”. The current OP concerns the existence of universals such as beauty and truth. Denial of such constitutes the philosophy of nominalism. The “hazelian” philosophy (evidenced by numerous previous posts) agrees with nominalism.

    I disagree with DS that nominalism is an emotionally loaded word. It merely describes a philosophy.

  184. 184
    math guy says:

    H @ 161 has again dodged the question.
    Does Hazel deny the existence of abstracta and/or universals? If so, how can that viewpoint avoid the logical contradiction posted in 123 (and again in 158).

    Does Hazel accept the existence of some abstract or universals? If so, which ones are accepted?

    Does Hazel reject the Law of Excluded Middle and claim some third option?

  185. 185
    hazel says:

    Math Guy,

    1. I think that it is a feature of our rational minds to be able to conceive of and understand abstract ideas, to express those ideas symbolically (which allows us also to share our understandings with others) and to use logic to think about those ideas. Those abstractions exist: minds exist, and the content of those minds exist. I, nor anyone else, as I have said multiple times, know exactly how minds exist and how they interface with our bodies, but I certainly believe in the existence of minds and thus abstract concepts.

    2. If you mean do abstract concepts exist in some form outside of minds, I certainly have no experiences that make me think that is so. We certainly can, and do, form abstract ideas and more complete models about the world we experience, and in many cases, to varying degrees, those models accurately correspond to the world. However, and this is the place where I believe kf and I disagree, I don’t believe the abstractions exist in the world: rather they are abstractions about the world.

    3. You mention “logical contradictions in 123.” Post 123 is a typical hodge-podge of points, so maybe you could be more specific about what logical contradiction you are referring to.

    4. I fully accept the laws of logic as correct and necessary rules for thinking about abstract concepts, both within formal logical and mathematical systems and in our descriptive models of the real world. I think our understanding of the laws of logic are a fundamental part of our having rational minds.

    I think these are all points I’ve made at least several times before in previous threads.

    P.S. FWIW I saw 184 from MG, but not 183, for some reason, so my reply is to 184.

  186. 186
    hazel says:

    Kf addresses me at 182:

    Next, notice how you went on to shift subjects to a different focus

    Kf, perhaps you should notice that you invited me and the subject of mathematics into this conversation at 134 when you wrote, “H, have you done the Mobius strip exercise yet?”

    So exactly who shifted the focus?

    I have gotten involved in discussing math again because you specifically addressed me and brought it up.

  187. 187
    hazel says:

    At 183, MG wrote that perhaps my position is that

    mathematics is about actual logical structures which only exist within minds

    I don’t think the adjective “only” is necessary, other than to contrast with the idea that abstract concepts have some type of Platonic existence. There is nothing “only” about the existence of our minds, I don’t think. That is where our rational understanding lies.

    What I would say is this: formal mathematics is about abstract concepts expressed in logical and precisely defined symbol systems, and applied mathematics is about building mathematical models of some aspect of the world which can be tested by comparing predictions of the model with what we actual experience in the world.

  188. 188
    kairosfocus says:

    H, the shift in subject I pointed to is significance given context. While the second issue is more closely aligned with the thread’s topic, it is irrelevant to the question as to whether nominalism is a loaded term of denigration (it isn’t) and in fact even on aesthetics, the discussion was substantially based — as was further documented. It is noteworthy that this recent exchange is further tangential and as MG noted just above, there is good reason to “disagree with DS that nominalism is an emotionally loaded word. It merely describes a philosophy.” I again note that evidence has long been presented that certain types of structure and quantity are part of the fabric of the existence of any distinct possible world, as opposed to ideas and concepts etc pondered by a mind. Likewise, empirical exercises such as cutting mobius strips illlustrate that embedding in ways that are independent of our thoughts. KF

    PS: Perhaps it would be relevant to note your comment to DS at 132, earlier comments by DS etc. It was in response to 132 that I commented at 134 as there is another side to the matter. BTW, the issue is not whether abstract CONCEPTS exist independent of minds but that abstract entities of structure and quantity are embedded in the fabric of possible worlds. This goes to the two aspects view: Mathematics is a culturally influenced study and it is also a substance of structure and quantity embedded in the world that is studied.

  189. 189
    hazel says:

    Kf, you write,

    PS: Perhaps it would be relevant to note your comment to DS at 132, earlier comments by DS etc. It was in response to 132 that I commented at 134 as there is another side to the matter.

    True: for the record, I think you first introduced the topic of math at 126, to which Dave responded, when you wrote, “Likewise, do numbers have reality beyond our labels, operations on imagined collections, etc, are they embedded in the framework for a world to exist?”

    Also, you write,

    BTW, the issue is not whether abstract CONCEPTS exist independent of minds but that abstract entities of structure and quantity are embedded in the fabric of possible worlds. This goes to the two aspects view: Mathematics is a culturally influenced study and it is also a substance of structure and quantity embedded in the world that is studied.

    Yes, you explained this distinction well in another post. I’m not sure which of these, or both, MG has in mind when he asks about the existence of abstractions other than in the mind.

    Probably the key place I disagree with you philosophically is on the second point: “abstract entities of structure and quantity are embedded in the fabric of possible worlds.”

    As part of getting interested in all this philosophy, I have been reading more about quantum physics, and in particular what it says about what “reality” might really be, which is all very relevant to the subject of the nature of the relationship between mathematics and reality.

    So I’m now reading “Reality Is Not What It Seems” by the Italian physicist Carlo Rovelli, a popular account of the search for a theory of quantum gravity. At one point he mentions the Dirac equation, which made Schrodinger’s wave equation consistent with special relativity:

    See Dirac equation under Mathematical Formulation to see this. Don’t skip his step!

    There is no doubt that this equation accurately describes the world as we experience it when we investigate certain phenomena. However, does that mean that in some way this very complicated equation actually somehow exists as an abstraction embedded in every moment of every quantum interaction in the entire universe? I can’t even imagine what that might mean. How could each minute quantum moment and entity contain this abstraction?

    Better yet, why would it need to? The world doesn’t need an embedded mathematical abstraction in order to be the world, I don’t think. The world is what it is, and at the most basic level is, I think, not only incomprehensible but beyond any investigation we might devise. Given the level we can access and the investigatory approach we take, we can devise mathematical models that describe the world. That, to me, does not mean that our mathematical descriptions, or that the abstractions they represent, are actually in the world.

    I think this philosophical issue has shown up in science other times: do our mathematical descriptions reveal something real about reality, or are they “just” practically useful descriptions of something whose “real” nature is not accessible to us. I think questions like this are central to our exploration of reality through quantum physics.

  190. 190
    kairosfocus says:

    H,

    The substantial argument at 126:

    KF: >>the issue on objectivity is not intersubjective agreement or subjectivity (only subjects can know) but warrant. In this case we have a widely recognised (across time and culture, styles differ but these sorts of patterns are consistent), named phenomenon — not typical marks of delusions or ill-founded ideological claims. It is associated with certain aesthetics principles which are in many cases mathematically addressable (e.g. symmetry, harmony) and we can see the effects on for instance faces or buildings as such principles are fulfilled or not fulfilled. In this case, with billion dollar investments in proof. Observable, in significant part mathematically accessible, go/no go demonstrations seen. If after this you still will not accept that there is significant objective warrant that aesthetic principles are objectively warranted and give us an objective understanding of beauty commonly used by painters, decorators, architects, etc, then I do not think the issue is on the side of adequate warrant, it is that there is an underlying implicit influence by nominalistic views in this regard. There are a lot of other things that are warranted in much the same way that we routinely accept. I suggest a good cross check would be does evil have reality beyond subjective opinion and agreement in some community or other? Likewise, do numbers have reality beyond our labels, operations on imagined collections, etc, are they embedded in the framework for a world to exist? What would it mean for a scientific theory to have objective status? Is there an objective shared world that we participate in (as opposed to say some sort of Matrix-like simulation world), on what grounds? What accessible evidence or argument would lead you to accept that there is a reality to beauty beyond agreement within a subject or between some circle of subjects or other, e.g. would the eyesore buildings be beautiful if somehow a significant circle were to say so? Or have you reduced beauty to, in accord with the tastes of some reference group or other. Etc.>>

    At 123, I commented to you and DS jointly, starting:

    In effect, what I think we are seeing is the effect of a subtle controlling worldview concept, nominalism — which is of course an issue in Mathematics, hence my comparative

    In 113, when I compared Aesthetic sense as raised by DS to Mathematical sense, I noted: “The issue is not intersubjective agreement, it is not culture, it is not tastes, it is warrant.” Which was about nominalism, which affects both, as your comment clipping Wikipedia at 120 noted: “McDowell’s conceptualism, though rather distinct (philosophically and historically) from conceptualism’s genesis, shares the view that universals are not “given” in perception from outside the sphere of reason. Particular objects are perceived, as it were, already infused with conceptuality stemming from the spontaneity of the rational subject herself.”

    Such is of course, directly, the associated Kantian ugly gulch between our inner world of appearances and things in themselves that actually leads the OP, which falls afoul of F H Bradley’s observation (as was already noted by me at 123 but it bears repetition as reminder):

    We may agree, perhaps, to understand by metaphysics an attempt to know reality as against mere appearance, or the study of first principles or ultimate truths, or again the effort to comprehend the universe, not simply piecemeal or by fragments, but somehow as a whole [–> i.e. the focus of Metaphysics is critical studies of worldviews] . . . .

    The man who is ready to prove that metaphysical knowledge is wholly impossible . . . himself has, perhaps unknowingly, entered the arena . . . To say the reality is such that our knowledge cannot reach it, is a claim to know reality ; to urge that our knowledge is of a kind which must fail to transcend appearance, itself implies that transcendence. For, if we had no idea of a beyond, we should assuredly not know how to talk about failure or success. And the test, by which we distinguish them, must obviously be some acquaintance with the nature of the goal. Nay, the would-be sceptic, who presses on us the contradictions of our thoughts, himself asserts dogmatically. For these contradictions might be ultimate and absolute truth, if the nature of the reality were not known to be otherwise . . . [such] objections . . . are themselves, however unwillingly, metaphysical views, and . . . a little acquaintance with the subject commonly serves to dispel [them]. [Appearance and Reality, 2nd Edn, 1897 (1916 printing), pp. 1 – 2; INTRODUCTION. At Web Archive.]

    Tied to such, I earlier had commented (mainly to DS):

    KF, 100 after a description at 95 of how musical octaves and fifths arise as sufficiently harmonious patterns had been put on the table but more or less set aside with a comment in 96 beginning “Does this mathematical analysis provide evidence that certain pieces of music are objectively beautiful?”: >> aesthetic enjoyment (as opposed to sensuality) is indeed a personal experience. The point is, that it is observably directly tied to mathematical and physical phenomena which are objective, many embedded in the world. For example, the phenomenon of harmonics and fundamentals is a property of an inertial, elastic body. The octave pattern turns out to be tied to frequency, wavelength, wave velocity, reflections and standing waves. That notes in octave have a similarity because of how onward harmonics behave (waves out of such symmetric alignment will have odd interference effects), and that notes in the fifth relationship are similar and can come close enough to alignment to fit in well enough (but not perfectly) actually provides an objective basis for musical scales. Similarly, given our vocal tracts as musical instruments and given interference and the related phenomenon of Fourier summing of harmonics to yield a waveform, it is unsurprising that our auditory system uses a basilar membrane set up so frequencies cause resonant peaks at particular points along the coil of the cochlea, which then goes in like pattern to the brain. All of this comes together as objective phenomena tied to aesthetic principles that help us understand the enjoyable structure of music. Such phenomena are clearly objective, and point again to how the aesthetic principles guide creativity in making beautiful music. Where of course, tastes can be outright bizarre, not just abnormal or culture-bound. One may always stoutly resist the conclusion of a convergent pattern of evidence and argument, but it is clear enough that there are aesthetic principles that are readily intelligible, are rooted in observable structural, quantitative and physical phenomena, and contribute to the patterns and phenomena we enjoy as beautiful. When they are willfully discarded as a bloc, it is equally clear that the result is chaotic and ugly. Billions of dollars of recent architectural eyesores are literally massive evidence on the point. I repeat, the subjective is not the opposite of the objective and the presence of intelligible, objective frameworks for aesthetics demonstrates that yes, beauty is in material part an objective predictable phenomenon, amenable to controlled, insightful skill rather than a hit and miss affair — indeed the art of photography is also evident in the cases above. It is not an accident that Grand Canyon was photographed at just that moment, from that angle with settings, filters, focus etc.>>

    102, citing IEP: >>Objectivity

    The terms “objectivity” and “subjectivity,” in their modern usage, generally relate to a perceiving subject (normally a person) and a perceived or unperceived object. The object is something that presumably exists independent of the [I add, particular] subject’s perception of it. In other words, the object would be there, as it is, even if no subject perceived it. Hence, objectivity is typically associated with ideas such as reality, truth and reliability.>>

    107: >>I already pointed out how intersubjective agreement fails: a consensus of bad tastes has created a billion dollar exercise of imposing the grotesque in the name of being fresh architecture. The issue is warrant, and it has long been clear that the determined will never concede warrant even in the face of the equivalent of a plumb line example. BTW, that is where I have now reached on the design inference: it is abundantly well warranted but there are those who will never concede that such could even be possible>>

    109: >>we find them [the referred buildings, note the remarks by Rennix and Robinson cited at 182 in response to you] ugly not just as clashing with our tastes — I hate prunes (an acquired taste for some) — but for good reason. The architects, caught up in a rebellion against long known aesthetics principles, induced decision-makers to spend billions. They only managed to create eyesores — exactly as the canons predicted: too much asymmetry leads to incoherence, incongruity and chaos, which for good reason is repulsive save to those whose inner riot seeks an outer reinforcement. I doubt the lesson has been duly learned. Ponder the contrast between the sad man who has spent US$ 200k on trying to make himself look like a tiger, and those who sought plastic surgery to relieve deformities. Note also the impact of “ordinary” beauty we have become benumbed to, on those who see colour or hear in reasonable fidelity for the very first time.>>

    In short, the underlying in-common point on objectivity was that even mathematically anchored physical phenomena, principles and patterns (we used to speak of and seek out mathematically connected natural laws, rejoicing when we found such) will not be regarded as adequate evidence of objectivity and warrant, once nominalism and/or the kantian ugly gulch are in play. The problem here is not the strength of the warrant, but a prevailing mindset that imposes the notion that Mathematics and sense experiences are radically disconnected from the world of things in themselves, whatever that is — being presumably forever beyond our grasp. Such will naturally seek to redefine truth in terms of a world of concepts, labels (names, hence nominalism) and inner logic games, rather than accurate reference to reality. Which is already why F H Bradley’s point is so pivotal.

    Likewise, such thinking is in fact a reduction to grand delusion, due to the radical disconnect.

    Such brings us full circle to MG at 158 – 159:

    158
    math guy
    March 15, 2019 at 7:56 pm (Edit)

    KF @ 123
    Sometimes your arguments are excessively complicated (albeit correct IMHO), but the following is a succinct jewel:

    “However, it is patent that Nominalism is self-referentially incoherent, as universals and abstracta are inescapable in our thinking and reasoning, including in stating the claim that roughly runs: [we know, per some warrant that] there are no universals or abstracta, only names for collectives we impose.
    In effect, it affirms what it would deny.
    It is inescapably incoherent.”

    159
    math guy
    March 15, 2019 at 7:59 pm

    Since Hazel claims that mathematics is true but exists only inside minds, evidently Hazel’s nominalist viewpoint fits
    this category:

    (1) that mathematics is about concrete mental objects in people’s heads (psychologism)

    How does Hazel reconcile that viewpoint with the inconsistency expressed by KF in 123 and summarized in post 158?

    He followed up overnight, at 184:

    184
    math guy
    March 16, 2019 at 6:48 pm

    H @ 161 has again dodged the question.
    Does Hazel deny the existence of abstracta and/or universals? If so, how can that viewpoint avoid the logical contradiction posted in 123 (and again in 158).

    Does Hazel accept the existence of some abstract or universals? If so, which ones are accepted?

    Does Hazel reject the Law of Excluded Middle and claim some third option?

    So, Mathematical considerations and physical observations are closely connected to warrant for the objectivity of aesthetic principles based on symmetry, harmony and the like, but if the sort of radical disconnect we saw is imposed, such evidence will be refused its due weight. So, an underlying issue is that the grand delusion and ugly gulch issues must be resolved sufficiently to restore confidence in observations and in reason, including the logic of structure and quantity.

    KF

  191. 191
    kairosfocus says:

    PS: Further stuff, later. Let me note that for instance the famous Dirac eqn of relativistic quantum dynamics — which famously captures half of physics and all of chemistry — addresses the evident structure and quantity of the micro world through an abstract logic model on such structures and quantities. It is not this eqn or the like which are embedded (save perhaps insofar as Mathematics was part of the design of the cosmos) as structure and quantity, starting with the substance in N, Z, Q, R, C etc, all of which are embedded in the relevant Physics. Recall, those sets grow out of the import of distinct identity of a possible world W = {A|~A} involving unity, duality and nullity; where A is the unique feature of W that distinguishes it from close neighbours e.g. W’ and W”.

  192. 192
    hazel says:

    Hmmm. You quoted MG’s post where he wrote, “H @ 161 has again dodged the question. …” Sort of would have been nice to maybe have pointed out that I responded to MG at 185. Just sayin’ …, but in your frequently used phrase, telling. 🙂

  193. 193
    hazel says:

    kf, you write of Dirac’s equation “an abstract logic model on such structures and quantities. It is not this eqn or the like which are embedded.”

    Yep, that is what I am saying. The equation is “an abstract logic model” which exists in a symbol system which is understood abstractly by the cognitive, rational abilities of our mind, but is not actually embedded in the world.

    Yea, we agree! Discussion is over!!!!

  194. 194
    daveS says:

    KF,

    The problem here is not the strength of the warrant, but a prevailing mindset that imposes the notion that Mathematics and sense experiences are radically disconnected from the world of things in themselves, whatever that is — being presumably forever beyond our grasp.

    FTR, I’m definitely not saying that. (jumping in here since I was involved in the quoted exchange).

    Edit: I think this article is on-topic: TWA Hotel inside Eero Saarinen’s JFK Airport terminal open for reservations

  195. 195
    Ed George says:

    Just dropped by and saw that this thread has morphed into an extension of the previous thread on the inherent nature of mathematics. I haven’t read this thread in detail but I am sure that I can predict the issue. There are two opposing views. One is that mathematics exists in the universe and that all we do is discover it. The other is that mathematics is not inherent to the universe and that we have developed them to model the universe. One side concludes that there is adequate warrant to support their view and, therefore, the other side is being disingenuous for ignoring this warrant.

    Frankly, I don’t see the point of continuing this argument. Neither side is likely to change their minds. But not that anyone cares, my view is much closer to Hazel’s.

  196. 196
    daveS says:

    hazel,

    The equation is “an abstract logic model” which exists in a symbol system which is understood abstractly by the cognitive, rational abilities of our mind, but is not actually embedded in the world.

    Ah, that makes the issue clearer to me.

  197. 197
    hazel says:

    Dave, if you are at all interested and haven’t already, read my post at 189 for perhaps a succinct summary of the issue.

  198. 198
    daveS says:

    Thanks, hazel, I skimmed it before, but understand it better after post #193.

  199. 199
    kairosfocus says:

    EG & H (also DS), coherent structure and quantity are manifestly part of the fabric of our world — that’s a lesson hammered home by snipping mobius strips around, in the middle vs 1/3 way across. This is not equal to all of possible mathematical systems or entities are part of the fabric of any possible world or even the one we share. Just, that certain core mathematical facts will be so placed as they are connected to what is required for a distinct possible world to have its distinct identity. We may formulate abstract logic model worlds at will as possible worlds, and part of that is that certain propositions stipulating a possible world may and do often take the form of equations. In some cases, in exploring such abstract models, we discover necessary entities which will be present in any possible world. Others are contingent and obtain for some worlds but not others. Such worlds may be sufficiently analogous to our own to be useful in predicting phenomena (but such validation is provisional always). However, the study of setting up such schemes is not equal to the antecedent issue that some abstract structures and quantities, being necessary, are prior to and properly limit the construction of such models. That is, the creative study of Mathematics by which we may set up a model world is constrained by prior necessary entities, especially those that are corollaries or extensions of distinct identity — we may not set up worlds in an entirely arbitrary way, e.g. there is no coherent world in which 2 + 3 = 5 is false or where a square circle can be instantiated. Such necessary, world-framework entities are discovered, not invented and are part of the fabric for any distinct world to exist; e.g. N, Z, Q, R and C (taken as a vector-rotation structure). That is, Mathematical entities — entities exhibiting structure and/or quantity — as an overall class, are in part independent of our particular concepts, constructions, inventions, conventions and the like; that part, we discover. We are free to formulate a cosmology with novel entities to our heart’s content, and articulate it, simulating how it plays out, but in so doing we are aware that it needs not map exactly to our world and that we would be ill advised to flout core necessary structures and quantities. All of this reflects the view that Mathematics embraces two aspects: a culturally influenced study and a substance of structure and quantity that is in part made up from necessary entities which we cannot invent or dispense with at will. This is of course a partial summary of things put forward over the past few months. KF

  200. 200
    kairosfocus says:

    DS, it seems the former terminal is now a hotel. It is modernist but is in a location where that will not upset an ambiance. As may be seen, it respects canons of symmetry etc, which keeps it out of the chaos we have seen elsewhere. It may be a bit sterile for some (modernism too often eschewed the interesting variety provided by details) but it is not in the chaotic eyesore class. KF

  201. 201
    daveS says:

    KF,

    Yes, I think it’s quite beautiful.

    Edit: Note that the roof is a hyperbolic paraboloid.

  202. 202
    hazel says:

    So kf, you seem to agree (although if you don’t like my wording, please improve it) that at least some mathematics (such as the formal statement of the Dirac equation) exists as models of the physical world, in our minds and in our symbol systems, but don’t exist “embedded in the world”. Is this true?

    Question #2: does the Dirac equation exists as a Platonic ideal? That is, even if it is not embedded in the world, does it exist anywhere other than in our minds and symbol systems?

  203. 203
    kairosfocus says:

    H, I have always pointed out that only a core of structure and quantity would be necessary entities embedded in the fabric of any world; indeed, I specifically derived a cluster of such, starting from corollaries of distinct identity of a possible world. The Dirac function, Cosmology, Newtonian Dynamics, Electromagnetism and other theories and models in physics, in key respects are highly contingent (though obviously, they use a lot of that core). For that matter, there is a reason why we contrast Euclidean and alternative Geometries. These systems insofar as they are contingent are examples of abstract, logic model worlds that we can create and write down on a chalkboard, on the chalkboards in our heads or in computer programs etc; but all of such will make use of ever so many abstract entities that are necessary structures and quantities integral to the framework of any possible world. Zero is an abstract but very real entity, as are 1, 2 etc. We cannot invent them, no world is possible where they do not obtain, we cannot make them disappear: abstract but very real and relevant to the logic of being. See the difference? Where, kindly note, most supporters of intelligent design will accept that there is a strong body of evidence showing that our cosmos is fine tuned. That implies, highly contingent. Last but not least, one of the reasons I have pointed to the mobius strip exercise is because it directly demonstrates the sort of embedding that is independent of our concepts, symbols and reasoning. How many edges does such a strip have, and what happens when you cut going around in the middle? Is that result something we invent or do we not notice it as a property of a peculiarly shaped body? I add, when we measure and observe behaviours and physical constants of the world (e.g. in vacuo speed of light, Planck’s constant, Boltzmann’s constant, heat capacity of water, density of lead, 1/2 life of U-238, Hertzsprung-Russell pattern of distribution of absolute magnitude vs surface temperature of stars etc.), are those invented by us, or are they not structures and quantities that we find embedded in this world? KF

  204. 204
    kairosfocus says:

    DS, I forgot to note, the terminal turned hotel was modelled on a bird’s body form (with wings extended), which is highly symmetrical in order to better fit the requisites of flight. This is also linked to the general close symmetry of animals. There is an old saying that by and large beautiful aircraft will fly well. KF

  205. 205
    kairosfocus says:

    H,

    Let me clip from 189:

    The world doesn’t need an embedded mathematical abstraction in order to be the world, I don’t think. The world is what it is, and at the most basic level is, I think, not only incomprehensible but beyond any investigation we might devise. Given the level we can access and the investigatory approach we take, we can devise mathematical models that describe the world. That, to me, does not mean that our mathematical descriptions, or that the abstractions they represent, are actually in the world.

    This shows some of the key gaps. I have spoken primarily to structure and quantity, noting that Mathematics has two aspects. First, the intelligible, rational principles of structure and quantity which are patently manifested in the world, part being necessary to any distinct possible world, part being contingent to framing a particular world. Second, how we go about studying structure and quantity. Mathematics is a label for both; where, surely, the abstract ordering principles of the world that exhibit coherent structure and quantity are antecedent to our attempts to study such in a logically, rationally disciplined fashion.

    I should also note on some underlying logic of being.

    Nothing, properly, denotes non-being. Such, patently, can have no causal powers. Were there ever utter nothing, utter non-being (and “were” here is problematic, save as putting up a case), such would forever obtain. There would be no world, no reality.

    So, we start with, a world is and for all we know many worlds are or are possible, i.e. reality is wider than world. Where, if a world is, something of some form always was, i.e. reality in some form always was. On the alternative — utter non-being — there would be no causally effective root for a world to ever be.

    Down that line lies the distinction between contingent beings and necessary ones, contingent ones being dependent on some factor or factors that enable their existence. Necessary ones will be present in any possible world, arguably as they are part of the framework for a world to exist, inherently part of the roots of reality.

    In that context, we see that on distinct identity, a possible world W will have some particular characteristic A that marks it out from near neighbour possible worlds, allowing the partition: W = {A|~A}. Such an A is arguably connected to the causal factors/circumstances that would enable the specific world W to be.

    As we noted, by simple inspection this world has unity, duality and nullity as corollaries directly connected to the partition, showing embedded structure and quantity. A is a unit, there is nothing inside the partition, no x in W is not in A or ~A. ~A is a distinct form of unity, complex unity (which is already a structure . . . the unified many — so, ordered in some sense). Applying the von Neumann construction (which to me gives teeth to Peano’s idea of succession) we see N, and can see Z, Q, R and C as associated systems of quantities and structures. We may extend to transfinites. Such will be abstracta present in any given possible world. That is, they are inherently part of the requisites of any distinct possible world, part of the ordering principles and structures that frame it. In many cases, they may then be discerned from observing the order and structure. We may thus contemplate the rational principles as embedded and/or as abstracta in their own right.

    Possible worlds in some cases are physically actualised (this one) but may be entirely conceptual, being sufficiently complete descriptions of compossible states of affairs, i.e. structured, coherent collections of propositions specifying the possible states of affairs.

    That is the context in which I have spoken of mathematical domains as abstract logic model worlds that express structure and quantity.

    Of course, if in exploring such a world we encounter a necessary being, that entity will be present in all possible worlds.

    It is in that sense that structure and quantity are inherently in any possible world, part of its fabric. A cosmos is not an atomised, chaotic phenomenon of accidents that coincidentally happen to be there (and already, one ordering point is, we cannot have x and ~x being so in the same circumstances . . . no square circles). No, a cosmos is an ordered system of reality. The ordering is as much in the world as are whatever particular entities are there.

    Order implies rational principle, which in at least some cases will be intelligible. As opposed to “simple.” In our context, Dirac’s equation seems to aptly capture part of the relevant structural and quantitative ordering principles. BTW, the same would obtain for E = m_0*c^2, Einstein’s energy-mass relationship (key to understanding stars and atoms) and many other expressions. For example, we can contemplate c or h or Boltzmann’s k taking other values and where that would take physics and cosmology. So far as I understand, the Dirac eqn is not in itself a necessary aspect of any possible world, it is contingent.

    KF

    PS: Let me observe, that such ordering insofar as it is tied to symmetry, harmony, balance, self-similar scaling, subtle focussing or highlighting asymmetry and variety etc, gives a rational, intelligible, objective framework for what we experience and enjoy as beauty.

  206. 206
    kairosfocus says:

    F/N: One of the things that seems clear to me is that there is a cultural trend that finds the idea of intelligible, rationally ordered principles — which are inherently abstracta — that frame a cosmos to be somehow unacceptable. This seems to be part of what drives the kantian ugly gulch (which isolates the ordering to our inner cognitive world and sees us as projecting order unto the world but being inevitably unable to bridge the gap). Nominalism in its various forms runs along similar lines, here AmHD: “n. Philosophy
    The doctrine holding that abstract concepts, general terms, or universals have no independent existence but exist only as names.” Likewise, the ultramodernism commonly termed postmodernism puts up the metanarrative that suspects and eschews metanarratives — the sighted man looking on as the six blind men feel their way around an elephant implies a superior, more complete, objective perspective. As was pointed out above, such schemes consistently fall into self-referential incoherence. And of course, insofar as our experience of beauty is not merely a matter of idiosyncratic and/or culturally conditioned tastes, it would reflect rational, intelligible, harmonious and satisfying ordering — seemingly an anathema to many today despite the evidence that on billions of dollars worth of flouting canons of aesthetics, such predictably ends in chaos and ugliness. Can we point to the power of science and mathematics as at least reason to be open to the possibility that we live in a cosmos marked by embedded intelligible, rational ordering principles? Which we may at least partially elucidate through careful reflection on cases? KF

  207. 207
    daveS says:

    KF,

    One of the things that seems clear to me is that there is a cultural trend that finds the idea of intelligible, rationally ordered principles — which are inherently abstracta — that frame a cosmos to be somehow unacceptable.

    Speaking for myself, I am simply reluctant to posit the existence of things which I’m not convinced exist. I don’t find anything unacceptable about what you have described above.

    I am more or less a neoplatonist about mathematical-ish things because I believe these things exist independently of my mind in some sense (not that I have a great defense of this position).

    I am not convinced that “beauty” exists independently of our minds. For example, I don’t know that Kylie Jenner is objectively more beautiful than a proboscis monkey. Furthermore, I don’t know how to test that claim.

    Therefore I’m going to hold off on asserting that “beauty” exists objectively.

  208. 208
    Brother Brian says:

    With respect to beauty and aesthetics in architecture, I suspect that KF is reacting to our innate reluctance to accept structures that appear to be structurally unsound, rather than to any objective nature of aesthetics or beauty. For example, many of the “eyesores” that are posted in the OP appear to defy structural integrity. For whatever reason, we expect buildings to have vertical walls (for maximum strength) or to be buttressed by support structures (as seen in many cathedrals). Buildings that appear to defy this structural integrity, even though it is just an illusion, seem odd to us at first glance. But there are plenty of examples of this “oddness” that grow on people.

  209. 209
    kairosfocus says:

    BB,

    While, yes, things that seem structurally unsound will be disturbing, many manifestly structurally sound things are still patent eyesores.

    For instance in the collection in the OP, the black blob that looks like an upside-down cleated football shoe is manifestly sound but utterly ugly. If it were say an antiaircraft bunker we would not complain [such need to be structurally and militarily sound not pretty and are often deliberately brutal in appearance], but that is just what it is not.

    Similarly, in the wrecked city skyline we can see a progression from left to right: a beautiful domed cathedral once ruled the skyline with a traditional city profile. Then came the stacks of dominoes on end, then the increasingly asymmetric towers and the skyline is now spoiled.

    The others that look like random blocks and/or tornado-twisted wreckage are doubtless structurally sound, high strength alloy steel frameworks can cover a multitude of sins. But, they are blatantly chaotic eyesores that are impositions on the longsuffering public.

    In the same article I quoted earlier, we find these disturbing words which I think we should now ponder:

    The fact is, contemporary architecture gives most regular humans the heebie-jeebies. Try telling that to architects and their acolytes, though, and you’ll get an earful about why your feeling is misguided, the product of some embarrassing misconception about architectural principles. [–> translation: they KNOW they are flouting long established aesthetics principles, where they also are looking down on those who adhere to them or those who simply intuitively find the results of such avant gardism apalling] One defense, typically, is that these eyesores are, in reality, incredible feats of engineering. After all, “blobitecture”—which, we regret to say, is a real school of contemporary architecture—is created using complicated computer-driven algorithms! You may think the ensuing blob-structure looks like a tentacled turd, or a crumpled kleenex, but that’s because you don’t have an architect’s trained eye. [–> Thank God I do not have a mis-trained eye that cannot see the Emperor’s wardrobe malfunction for what it is! And when a classic story like that speaks . . . ]

    Another thing you will often hear from design-school types is that contemporary architecture is honest. It doesn’t rely on the forms and usages of the past, and it is not interested in coddling you and your dumb feelings. Wake up, sheeple! Your boss hates you, and your bloodsucking landlord too, and your government fully intends to grind you between its gears. That’s the world we live in! Get used to it! Fans of Brutalism—the blocky-industrial-concrete school of architecture—are quick to emphasize that these buildings tell it like it is, as if this somehow excused the fact that they look, at best, dreary, and, at worst, like the headquarters of some kind of post-apocalyptic totalitarian dictatorship.

    In short, power imposition on hoi polloi, the despised deplorables who actually like pretty things.

    We need to do some re-thinking.

    KF

  210. 210
    kairosfocus says:

    DS, I was not speaking of you but of a broad, generations deep, disturbing trend. However, I find it interesting to hear your doubts. Have you done or watched a vid on the mobius strip exercise? If so, do you accept that the twisted paper loop is independent of what we believe, conceive, think or understand? In which case, does it or does it not manifest quantitative structural effects reflecting rationally intelligible properties of those bodies in space? If not, could you please do the exercise, including the contrast between cutting in the middle vs 1/3 way across? Going beyond, is it possible to have a world in which oneness or twoness do not appear? If not, is that not evidence of necessary being embedded in the framework for such a world? On beauty, kindly note that I am not pointing to our experience of being impacted by beauty (and those colour blind people putting on filter glasses remind me to respect “ordinary” beauty that I have become benumbed to) but to the objectivity of aesthetics principles that allow us to objectively understand and then actually control the phenomenon of beauty. The most obvious case being the photo of Grand Canyon, which was very carefully framed just so to pick up the highlight of the sun peeking out behind clouds. Then, look at Mona Lisa and the reconstruction, and at how this number one masterpiece combines ever so many aesthetics principles to epochal result that has been a landmark for five hundred years. KF

    PS: Pardon a clip from the OP:

    a reconstruction helps us see the story the painting subtly weaves.

    A wealthy young lady sits in a three-quarters pose, in an ornate armchair, on an elevated balcony overlooking a civilisation-tamed landscape; she represents the upper class of the community that has tamed the land. Notice, how a serpentine, S-curved road just below her right shoulder ties her to the landscape and how a ridge line at the base of her neck acts as a secondary horizon and lead in. Also, the main horizon line (at viewer’s eye-level) is a little below her eyes; it is relieved by more ridges. She wears bright red, softened with dark green and translucent layers. Her reddish brown hair is similarly veiled. As a slight double-chin and well-fed hands show, she is not an exemplar of the extreme thinness equals beauty school of thought. The right hand is brought over to the left and superposed, covering her midriff — one almost suspects, she may be an expectant mother. Her eyes (note the restored highlights) look to her left, as if she is smiling subtly with the painter or the viewer — this is not a smirk or sneer. And of course the presence of an invited narrative adds to the aesthetic power of the composition.

    These classics (old and new alike) serve to show how stable a settled judgement of beauty can be. Which raises a question: what is beauty? Like unto that: are there principles of aesthetic judgement that give a rational framework, setting up objective knowledge of beauty? And, how do beauty, goodness, justice and truth align?

    These are notoriously hard questions, probing aesthetics and ethics, the two main branches of axiology, the philosophical study of the valuable.

    Where, yes, beauty is recognised to be valuable, even as ethics is clearly tied to moral value and goodness and truth are also valuable, worthy to be prized.

  211. 211
    Brother Brian says:

    KF

    Similarly, in the wrecked city skyline we can see a progression from left to right: a beautiful domed cathedral once ruled the skyline with a traditional city profile. Then came the stacks of dominoes on end, then the increasingly asymmetric towers and the skyline is now spoiled.

    Your own wording here is a little strange, and quite revealing. You found the original skyline dominated by the cathedral as being aesthetically beautiful. But rather than say that, you said traditional. This supports my opinion that much of what we accept as aesthetically beautiful has to do with what we get used to. For example, there are very few skylines in North America that are old enough to have enjoyed one of these “traditional” skylines. However, I find many of them to be aesthetically appealing. Examples would include Seattle, San Francisco, Toronto and New York.

    I think that it is important to maintain heritage buildings whenever possible, but this is more to honor history rather than to retain beauty. With regard to you saying that the skyline posted in your OP is spoiled, that is purely a subjective conclusion. I, for one, have no problem with that skyline. I think the mixture of old and new is aesthetically pleasing. I prefer that to simply tearing down the cathedral and all of the older structures and replacing them with skyscrapers and towers. Not that one is more beautiful than the other, but because I think it is important to retain history.

  212. 212
    daveS says:

    KF,

    Yes, I think everyone in this thread has done those Möbius strip exercises since primary school. I’ve already said that I consider myself a neoplatonist. I even said something about an argument similar to yours involving Turing Machines a while back, so I don’t know what we’re arguing about.

    On the other hand, I fully expect that an actual philosopher of mathematics could quickly reduce me to incoherence in a debate. I’m expressing doubts about my ability to defend my position adequately, not necessarily doubts about neoplatonism itself.

    On beauty, kindly note that I am not pointing to our experience of being impacted by beauty (and those colour blind people putting on filter glasses remind me to respect “ordinary” beauty that I have become benumbed to) but to the objectivity of aesthetics principles that allow us to objectively understand and then actually control the phenomenon of beauty.

    So am I.

    So which is more beautiful, Kylie Jenner or a proboscis monkey?

  213. 213
    kairosfocus says:

    BB, no. there are identifiable principles that were honoured but are now being flouted, to awful result. Some modern forms are lovely in themselves because they do not violate the canons, and they also respect the existing built environment. What we are seeing is very different and needlessly, heedlessly so. KF

  214. 214
    kairosfocus says:

    DS, I had to look up who Ms Jenner is, I am not part of American culture. She is a reasonably attractive young lady though it seems from time to time she has done some pretty wild things with her hair — there is a bright yellow that is a bit unnatural. The proboscis monkey’s nose is a signalling device tied to survival of the troop or whatever they may call it. Beauty is very much secondary to function. KF

  215. 215
    kairosfocus says:

    DS, second bite. I think the Mobius strip exercise gives us direct reason to see that structure and quantity are in fact embedded in the world and through logic of being affect behaviours of objects etc. Similarly, I am confident that no possible world can be such that twoness will not be present in it [note above on what the distinguishing partition presents, W = {A|~A}, thus we find embedded structure and quantity. Here, that abstract entities such as numbers have necessary existence as part of the framework for a world to be. Yes, philosophers, notoriously, are all over the map and can make cases for almost anything. But it is then a very different story when one has a pair of scissors, and has some twisted loops of paper. Empirical, direct evidence has a force all of its own.Hence the apocryphal balls falling from the leaning tower of Pisa, the pulse-timed chandelier as pendulum in the uni chapel and the apple falling from the tree as the moon swings by in orbit. Or, Young’s double slit and its quantum extension, or the dot of light in the middle of the shadow of a ball. KF

  216. 216
    ET says:

    If Aesthetics (/?s???t?ks, i?s-, æs-/) is a branch of philosophy that deals with the nature of art, beauty and taste and with the creation or appreciation of beauty, then what is “aesthetic beauty”?

  217. 217
    kairosfocus says:

    ET, beauty is the general term, aesthetics is the branch of phil that studies the principles of beauty and its value. The term you give may be emphasising the role of aesthetics in beauty, as in knowing application of such principles (see OP) is historically a part of sophisticated artistry. Da Vinci’s work on Mona Lisa is a classic in point, look at how many aesthetics factors are at work in it. KF

  218. 218
    Brother Brian says:

    KF

    BB, no. there are identifiable principles that were honoured but are now being flouted, to awful result. Some modern forms are lovely in themselves because they do not violate the canons, and they also respect the existing built environment. What we are seeing is very different and needlessly, heedlessly so. KF

    I’m afraid that we will just have to agree to disagree on the existence of objective (outside the mind) measures of aesthetic beauty.

  219. 219
    kairosfocus says:

    BB, I have not given scales and measures but examples of principles tied to case studies. For example symmetry is often measurable mathematically on its own (by way of some sort of reflection) but that by itself does not make beauty, a balance of factors is involved. What I spoke to is readily observable, the willful flouting of longstanding principles and practices leading to architectural eyesores to the cumulative direct cost in the billions. That result is not on trial, our response to it, why, is. And this thread is telling quite a story, where deterioration in the arts and of taste is one of the signs of civilisational decay. KF

  220. 220
    Brother Brian says:

    KF

    And this thread is telling quite a story, where deterioration in the arts and of taste is one of the signs of civilisational decay. KF

    I’m afraid that I can’t draw the link between buildings that you do not find aesthetically pleasing and the downfall of civilization. I see attempts to break the staid and stodgy “rules” of architecture (and other arts) as something that should be celebrated. Sometimes they will be soundly trashed but in other cases they may grow on you (or on most people, probably not you. 🙂 ).

  221. 221
    kairosfocus says:

    BB, time will tell, but it is not hard to see the progressive, chaotic breakdown of a civilisation and where it leads. The arts of our time, popular and highbrow alike, too often tell the same tale. Where, the very vision of the heroic rebel casting off “stodgy” and perceived stifling or oppressive rules speaks volumes about the inner turmoil that drives so much of what we see. To that, I suggest that there is a reason why it is futile to expect water to flow uphill, i.e. there are natural principles all across our world that one would be well advised to align with, even if one seeks to overcome natural limitations. I therefore take your heroic rebel and raise him by billions of dollars worth of grotesque, unharmonious eyesores imposed by the powerful, wealthy and influential on a public that is clearly not amused. A building that looks like a crushed sheet of paper or a blob uncannily like a cow pie actually sends yet another level of message, as does one that obviously parodies and mocks a classical column. I remember here the logo on tee shirts at the low end that read $exact$change in two telling lines — yes, there can be subtext messages in art, low brow and high brow alike. I already clipped a few remarks on the points. And last but not least we must not forget the message of demographics in all of this; which definitively points to fatal decline as fecundity plunges towards one per woman in many countries. KF

    PS: A reminder from the Current Affairs article:

    The fact is, contemporary architecture gives most regular humans the heebie-jeebies. Try telling that to architects and their acolytes, though, and you’ll get an earful about why your feeling is misguided, the product of some embarrassing misconception about architectural principles. [–> translation: they KNOW they are flouting long established aesthetics principles, where they also are looking down on those who adhere to them or those who simply intuitively find the results of such avant gardism apalling] One defense, typically, is that these eyesores are, in reality, incredible feats of engineering. After all, “blobitecture”—which, we regret to say, is a real school of contemporary architecture—is created using complicated computer-driven algorithms! You may think the ensuing blob-structure looks like a tentacled turd, or a crumpled kleenex, but that’s because you don’t have an architect’s trained eye. [–> Thank God I do not have a mis-trained eye that cannot see the Emperor’s wardrobe malfunction for what it is! And when a classic story like that speaks . . . ]

    Another thing you will often hear from design-school types is that contemporary architecture is honest. It doesn’t rely on the forms and usages of the past, and it is not interested in coddling you and your dumb feelings. Wake up, sheeple! Your boss hates you, and your bloodsucking landlord too, and your government fully intends to grind you between its gears. That’s the world we live in! Get used to it! Fans of Brutalism—the blocky-industrial-concrete school of architecture—are quick to emphasize that these buildings tell it like it is, as if this somehow excused the fact that they look, at best, dreary, and, at worst, like the headquarters of some kind of post-apocalyptic totalitarian dictatorship.

  222. 222
    daveS says:

    KF,

    DS, I had to look up who Ms Jenner is, I am not part of American culture. She is a reasonably attractive young lady though it seems from time to time she has done some pretty wild things with her hair — there is a bright yellow that is a bit unnatural.

    If you are documenting the collapse of western civilization, you should definitely familiarize yourself with her and her clan. 😛

    The proboscis monkey’s nose is a signalling device tied to survival of the troop or whatever they may call it. Beauty is very much secondary to function.

    But the question is, which is objectively more beautiful? I’m repeating myself again, so this is the last time I’ll ask.

  223. 223
    kairosfocus says:

    DS, it seems, yet another Hollywood celebrity, sad, Money, looks and fame don’t buy happiness and virtue. Our monkey’s nose is not the prettiest but is quite functional for a very significant signalling purpose, I guess like the sperm whale’s head. As I already noted, the monkey does not have the cognitive level to deal with the aesthetic. KF

  224. 224
    daveS says:

    KF,

    As I already noted, the monkey does not have the cognitive level to deal with the aesthetic.

    Neither does the Eagle Nebula.

  225. 225
    Brother Brian says:

    KF

    As I already noted, the monkey does not have the cognitive level to deal with the aesthetic.

    Is this a proven fact or simply an assumption based on our egocentric concept of human exceptionalism?

  226. 226
    hazel says:

    Good question, BB. We know that the monkey doesn’t have the abstract symbolic thinking skills we do, but do we really know if they don’t have appreciative notions of some level of aesthetic pleasure? They certainly have a range of positive and negative emotions, at least judging by their behavior.

  227. 227
    kairosfocus says:

    DS, Eagle nebula illustrates naturally occurring fractal rich patterns and abstract patterns, likewise Grand Canyon. There is natural beauty. Our monkey is an animal, but not an abstractly thinking one. It;s nose is a functional feature. likewise not everything in the human body is attractive or even pleasant to behold, e.g. we host a built in sewage system. KF

    PS: Paul touches on a relevant theme:

    1 Cor 12: 22 But quite the contrary, the parts of the body that seem to be weaker are [absolutely] necessary; 23 and as for those parts of the body which we consider less honorable, these we treat with greater honor; and our less presentable parts are treated with greater modesty, 24 while our more presentable parts do not require it. But God has combined the [whole] body, giving greater honor to that part which lacks it, 25 so that there would be no division or discord in the body [that is, lack of adaptation of the parts to each other], but that the parts may have the same concern for one another.

  228. 228
    hazel says:

    Some people think parts of the “sewage system” are beautiful!

  229. 229
    Brother Brian says:

    Hazel, and if they have some appreciation for some type of aesthetic beauty, without having the ability to think in the abstract, wouldn’t that run counter to KF’s hypothesis?

  230. 230
    kairosfocus says:

    H (& BB), the monkey is not an abstract thinker as is manifest in its lack of abstract conceptual language. It may well respond with pleasure to some aspects of its body (even as we do with some aspects of our own bodies — hence mirrors and the selfie culture) but that does not bind either it or us to hold all of our bodily features as equally attractive. We do not have our bathroom features such as water closets and tubs openly displayed in our living rooms. KF

  231. 231
    Brother Brian says:

    KF, this still does not prove that the monkey cannot have their own perception of aesthetic beauty. If this is even remotely possible, then the idea of objective measures of beauty, unless they share the same ones with us, is a non-starter.

  232. 232
    kairosfocus says:

    F/N: Vitruvius has some interesting words:

    Moral philosophy will teach the architect
    10 be above meanness in his dealings, and to avoid ar-
    rogance: and will make him just, compliant and faithful
    to his employer; and what is of the highest importance,
    it will prevent avarice gaining an ascendancy over him:
    for he should not be occupied with the thoughts of ?lling
    his co?’ers, nor with the desire of grasping every thing
    in the shape of gain, but, by the gravity of his manners,
    and a. good character, should be careful to preserve his
    dignity. In these respects we see the importance of
    moral philosophy; for such are her precepts.

    And again:

    Mu_s_i_c_assists him in the use of harmonic and
    mathematical proportion. . . . So the vessels called echeia by the Greeks, which are
    placed in certain recesses under the seats of theatres,
    are ?xed and arranged with a due regard to the laws of
    harmony and physics, their tones being fourths, ?fths,
    and octaves; so that when the voice of the actor is in
    unison with the pitch of these instruments, its power is
    increased and mellowed by impinging thereon.

    And again:

    The design of Temples depends on symmetry, the rules
    of which Architects should be most careful to observe.
    Symmetry is dependent on proportion, which the Greeks
    call analogia. Proportion is a due adjustment of the
    size of the different parts to each other and to the
    whole; on this proper adjustment symmetry depends.
    Hence no building can be said to be well designed which
    wants symmetry and proportion. In truth they are as
    necessary to the beauty of a building as to that of a well
    formed human ?gure, which nature has so fashioned,
    that in the face, from the chin to the top of the forehead,
    or to the roots of the hair, is a tenth part of the height
    of the whole body. From the chin to the crown of the
    head is an eighth part of the whole height, and from the
    nape of the “neck to the crown of the head the same.
    From the upper part of the‘ breast to the roots of the
    hair a sixth; to the crown of the head a fourth. A
    third part of the height of the face is equal to that from
    the chin to the under side of the nostrils, and thence to
    the middle of the eyebrows the same; from the last to
    the roots of the hair, where the forehead ends, the re-
    maining third part. The length of the foot is a sixth
    part ot’ me height of the body. The fore-arm a fourth
    part. The width of the breast a fourth part. Simi-
    larly have the other members their due proportions, by
    attention to which the ancient Painters and Sculptors
    obtained so much reputation. Just so the parts of Tem-
    ples should correspond with each other, and with the
    whole. The navel is naturally placed in the centre of
    the human body, and, if in a man lying with his face
    upward, and his hands and feet extended, from his
    navel as the centre, a circle be described, it will touch
    his ?ngers and toes. It is not alone by a circle, that the
    human body is thus circumscribed, as may be seen by
    placing it within a square. For measuring from the
    feet to the crown of the head, and then across the arms
    fully extended, we ?nd the latter measure equal to the
    former; so that lines at right angles to each other, en-
    closing the ?gure, will form a square. If Nature, there-
    fore, has made the human body so that the different
    members of it are measures of the whole, so the ancients
    have, with great propriety, determined that in all perfect
    works, each part should be some aliquot part of the
    whole; and since they direct, that this be observed in
    all works, it must be most strictly attended to in temples
    of the gods, wherein the faults as well as the beauties
    remain to the end of time. It is worthy of remark, that
    the measures necessarily used in all buildings and other
    works, are derived from the members of the human
    body, as the digit, the palm, the foot, the cubit, and that
    these form a perfect number, called by the Greek teleios.
    The ancients considered ten a perfect number, because
    the ?ngers are ten in number, and the palm is derived
    from them, and from the palm is derived the foot..

    This is of course the text behind Da Vinci’s famous study as is in the OP.

    KF

  233. 233
    kairosfocus says:

    BB, I have long since been confident that I should only aim to speak for record in cases such as this. If it has not registered that aesthetic thought (not mere pleasure) is a high order cognitive function involving all sorts of abstracta, for which conceptual language is a good index, then I have to simply note the fact. KF

  234. 234
    kairosfocus says:

    H, including its normal contents? KF

  235. 235
    hazel says:

    kf, some major parts of the external genitals are used for sex as well as excretion, and some people find the organs thereof beautiful.

  236. 236
    Brother Brian says:

    Hazel

    Some people think parts of the “sewage system” are beautiful!

    Having worked at a sewage plant for over a decade, I agree with this. Without the sewage system, the downstream of any moderate sized city would be a cess pool (no pun intended). Aquatic populations would be decimated. Fish caught from the river, lake or ocean would be toxic.

    But the sewage system keeps “sh__” off the streets, prevents cholera, typhoid and numerous other diseases. Allows us to use the methane generated by sewage to produce electricity, the biosolids produced to fertilize farmers field, the discharge to be “relatively” clean and safe. If that isn’t beautiful, I don’t know what is.

  237. 237
    kairosfocus says:

    BB, again, utility is not beauty, that is a categorical error. KF

  238. 238
    hazel says:

    Why can’t one see utility as beautiful?

  239. 239
    Brother Brian says:

    KF

    BB, again, utility is not beauty, that is a categorical error. KF

    Why not? A flower is beautiful yet it has a utility.

  240. 240
    kairosfocus says:

    BB (& H), the functional utility and beauty of a flower are categorically distinct. It is possible to be ugly and utilitarian, to be beautiful and otherwise non-functional and to be both functional and beautiful — think here, cars. In user interface design it has been learned that beauty confers a halo effect so the user experience is heightened and estimate of performance is also heightened. KF

  241. 241
    hazel says:

    It is also possible for someone to think that something is beautiful because it’s functionality and utility are aesthetically pleasing.

  242. 242
    Brother Brian says:

    KF, you still haven’t responded to the idea that a monkey, that doesn’t have the capability of abstract thinking like humans do, might still have the sense of aesthetic beauty. Is that impossible? And, if so, why?

  243. 243
    ET says:

    This isn’t a digital either/ or situation. People have been using scales, for example: 1-10, forever when describing other people. And it is always relative.

  244. 244
    hazel says:

    ET is right, which is another reason why, as I wrote at 21, “Once again, commonalities that are shared by all humans does not mean that those commonalities have some transcendental existence apart from their widespread and subjective manifestation in the minds of individual human beings.”

  245. 245
    math guy says:

    H @ 185 writes
    “If you mean do abstract concepts exist in some form outside of minds, I certainly have no experiences that make me think that is so. We certainly can, and do, form abstract ideas and more complete models about the world we experience, and in many cases, to varying degrees, those models accurately correspond to the world. However, and this is the place where I believe kf and I disagree, I don’t believe the abstractions exist in the world: rather they are abstractions about the world.”

    My research is in “pure math” (i.e. not applied math, not modeling anything in the physical universe). There are various well-formed logical statements that I am trying to prove or refute. I can think of several that I’m 99% convinced are true although I lack formal proofs at this point. (Let us assume that we don’t need a new axiom outside ZFC to deal with the proofs). What is the status of such a conjecture?

    The platonist says that such a conjecture is either true or false, we just don’t know at present (this seems to be an application of the Law of Excluded Middle). The second-rate philosopher A.J. Ayers dodges the issue entirely by claiming that such a well-formed logical statement has no meaning. (But after its valid proof is established, then meaning is suddenly assigned, like Athena emerging fully formed from Zeus’ head?) I am only a third-rate philosopher so I side with Plato’s viewpoint.

    How does Hazel view the truth status of an unproved conjecture?

  246. 246
    hazel says:

    Hi MG.

    I think the conjectures are either true or false, even though we haven’t figured out yet whether they are or not. In a thread last fall, I gave some examples such as the 1 billionth digit of pi, base 17, or the 1000 generation of a generation 0 of 1000 random live cells in a 50 x 50 grid in the game of Life, or the area of a triangle with sides of 2345, 78,890, and 620*pi. All of those situations have definite answers that follow logically from accepted premises, and in theory could be figured out even though they never have been.

    So your conjectures are either true or false, and maybe you’ll figure out how to prove that some of them are, or perhaps that some of them aren’t. Good luck.

  247. 247
    math guy says:

    This appears to be an issue for abstract objects that require a mind to live in because the truth or falsity of the conjecture (or septillionth decimal digit of pi) appear to be independent of any mind. In fact, Gödel’s second incompleteness theorem implies an infinite hierarchy of ever more complicated (but true) statements. Since human minds are bounded at some level and an infinite hierarchy is unbounded, there will be theorems too complicated to be comprehensible by human minds.

    Where do these theorems reside?

  248. 248
    math guy says:

    Look up Greg Chaitin’s halting constant. This is a positive real number, of which only a few decimal digits can actually be computed. The number provably exists, but cannot reside in a human mind. Where is it?

  249. 249
    kairosfocus says:

    BB, I have already pointed out from when it was first raised, the cognitive gap problem and its key index, abstract verbal language. As it was brought back up as though un-answered, I again pointed this out. Enough has been said for record: absent cognitive ability to handle high order abstracta (for which abstract verbal language is a key index) there is no basis for aesthetic reflection and conceptualisation. Monkeys simply do not have that capability, which is why they have not developed a civilisation. KF

  250. 250
    kairosfocus says:

    H, the conflation of utility and aesthetic excellence (or for that matter, ethical excellence) is a category error, as was already highlighted. Enough has been said for record and the example of cars should be enough to ponder on empirical cases. Opinion and warrant are categorically distinct. KF

  251. 251
    kairosfocus says:

    ET, that one may create ordinal, interval or even ratio scales of beauty etc and perhaps even warrant them to some degree does not alter the basic independence of utilitarian functionality and aesthetic excellence. Well engineered highly functional cars can be ugly, and fashionably attractive ones can be of such poor quality control that no one will purchase them unless s/he has little choice (I assume, sound basic engineering). That happened to American vehicles leading to the rise of Japanese imports. A similar breakdown happened with British cars. There are other cases. KF

  252. 252
    kairosfocus says:

    MG & H: a key issue is, what is truth? Once we see that it is about accurate description of reality, then it follows that if an abstract statement is true, it refers to a reality. That reality would then reside in the logic of being structure of the world. In turn, that highlights that material entities cannot exhaust reality. We have good reason to recognise that matter and resulting organised computational substrates cannot adequately account for reasoned inference, responsibility and significant freedom. So our very ability to reason mathematically points beyond the obvious world of material bodies to reality being more than this. Indeed, we have reason to see that matter is highly contingent and so cannot be the root of reality that needs to be necessary being. The concept of unknown truth is also a strong sign that there is more to mathematical reality than human conceptions. KF

    PS: Logical positivism collapsed 50 years ago. Its key claims could not pass its own verification test so were deemed meaningless. That is, it was irretrievably incoherent and self-falsifying. A familiar challenge.

  253. 253
    kairosfocus says:

    F/N: I decided to re-order the list of aesthetic design principles. Let’s refresh and update:

    reflective (and perhaps, aided) observation of case studies can support an inductive process that tries to identify principles and design patterns of effective artistic or natural composition that reliably excite the beauty response. That can be quite suggestive, as we already saw:

    symmetry,
    balance,
    pattern (including rhythms in space and/or time [e.g. percussion, dance]),
    proportion (including the golden ratio phi, 1.618 etc)
    unity or harmony (with tension and resolution), highlighting contrast,
    variety and detail,
    subtle asymmetry,
    focus or vision or theme,
    verisimilitude (insight that shows/focusses a credible truth/reality)
    echoing of familiar forms (including scaled, fractal self-symmetry),
    skilled combination or composition
    and more.

    We can of course readily see these at work in Mona Lisa and many other great or even ordinary works of art.We can also see the impact of deliberate gross violation. KF

  254. 254
    daveS says:

    Math Guy,

    Look up Greg Chaitin’s halting constant. This is a positive real number, of which only a few decimal digits can actually be computed. The number provably exists, but cannot reside in a human mind. Where is it?

    May I jump in? The definition for a particular Chaitin constant can reside in a human mind, correct? One can read and comprehend the definition without knowing all its decimal digits, for example.

    Why do you think a particular Chaitin constant “needs” to reside elsewhere?

  255. 255
    kairosfocus says:

    DS, where is likely a misnomer as it tends to suggest space. the number, let’s call it C, has a value, which gives it a reality, one that is not held in our minds, i.e. we do not know it. So, in what way is it real, KF

  256. 256
    daveS says:

    KF,

    We have a perfectly good description of the number. It’s the real number that satisfies the definition. If a LaTeX plugin were installed here, we could express the definition easily. The definition can reside in a human mind.

    Can you explain why that is not sufficient?

    Further, the complete decimal expansion of the square root of 2 cannot reside in a human mind. Does that mean the square root of 2 itself cannot reside in a human mind?

  257. 257
    daveS says:

    Math Guy, KF, hazel, et al,

    Some additional food for thought: Have you seen this paper? (link to paper included in the blog post). The authors present a 7918 state Turing Machine which:

    1. “runs forever, assuming the consistency of a large-cardinal theory called SRP (Stationary Ramsey Property)”

    2. “can’t be proved to run forever in ZFC (Zermelo-Fraenkel set theory with the Axiom of Choice, the usual foundation for mathematics), assuming that ZFC is consistent”.

  258. 258
    hazel says:

    I agree with Dave. I think the idea that these things which have not been figured out yet “reside” someplace is the mistake. They “exist” in the logical entailment of the symbol system they are part of even if no one has ever instantiated them by expressing the logical sequence that would reveal them or their truth value.

    One of my arguments against this Platonic view last fall involved Conway’s invention of the Game of Life. This cellular automaton demonstrably didn’t exist before the late 1960’s, and yet once the rules for the system were formalized, all possible generational states of all possible starting configurations all of a sudden “existed” in the sense that they were logically determined: the Nth generation of each particular generation 0, Gen0.1, Gen0. 2 … are what they are irrespective of whether anyone ever goes through the steps to find them.

    A Platonic view, as best I understand it, would posit one of two explanations, neither of which I find plausible.

    1. All possible mathematical systems, including all their logically true components, exist and have existed eternally, in some Platonic realm, irrespective of whether there is even a material world, much less beings such as us to partially express them. The Game of Life has always existed, and so has every other similar game, including ones on hexagonal grids, ones in which most or all starting generations die quickly, etc.

    2. The Game of Life was a true invention, which did not pre-exist Platonically, but as soon as it was invented, all of it’s infinite possible consequences suddenly came to exist Platonically.

    Perhaps MG believes one of these two things, or perhaps he has some other explanation of what “exists” means in a Platonic context, but I don’t find either of those options reasonable things to believe.

    I think it is more reasonable to believe what I wrote above: “Mathematical truths “exist” in the logical entailment of the symbol system they are part of even if no one has ever instantiated them by expressing the logical sequence that would reveal them or their truth value. “Exist” and “reside” are in quotes above because I think those words are inappropriate and confusing the issue.

  259. 259
  260. 260
    ET says:

    hazel:

    I think the idea that these things which have not been figured out yet “reside” someplace is the mistake.

    You are wrong.

    One of my arguments against this Platonic view last fall involved Conway’s invention of the Game of Life.

    Question-begging.

    This cellular automaton demonstrably didn’t exist before the late 1960’s,…

    That’s your unsupportable opinion, anyway.

    Again, in an Intelligent Design scenario ALL information exists outside of us. We merely tap into it and discover it. That is how and why Srinivasa Ramanujan was able to do what he did. No other explanation exists for his feats.

  261. 261
    kairosfocus says:

    DS, I would start with zero. Namely, {} –> 0. There is but one zero, and but one null set. We can severally have a concept or definition or symbol of it in mind, but that is not the same as holding the number pinned to a location. The same extends to all numbers that have a definite value. Irrationals have the added property that we cannot precisely assign a decimal value or the like, we can only represent and approximate, so we are a step further back. The number C is similar, we are not addressing it, we are not giving a decimal value, we are not doing more than symbolising and specifying what it is. We are not holding the number itself in mind. And yet, it is real, holds a definite value. This is a slice of why most working mathematicians and users of numbers simply accept them as real things that we may accurately speak of though they are abstracta. And no, there is no world of forms where we can spy out the number 0 etc on display in some sort of museum. Intangible but real, real enough that we may speak truthfully about them. KF

  262. 262
    hazel says:

    P.S to 246: There I mentioned the “area of a triangle with sides of 2345, 78,890, and 620*pi.” I just made up some numbers quickly, but actually those three numbers don’t make a possible triangle because all three combinations of a + b > c aren’t true. I’ll amend the numbers to 2345, 7889, and 2000*pi, and return to this problem later today.

  263. 263
    daveS says:

    nm, misread post.

  264. 264
    hazel says:

    At 247, MG wrote, “This appears to be an issue for abstract objects that require a mind to live in because the truth or falsity of the conjecture (or septillionth decimal digit of pi) appear to be independent of any mind.”

    The truth or falsity is independent of whether any mind, using the symbol system with which we express such things, has actually instantiated that truth or falsity. The truth is there, embedded as a logical consequence of the system, waiting, so to speak, for a mind to bring it to expression, if we chose and are able to describe the necessary logical steps.

    MG, I hope you respond to 256 about what it means for math to exist Platonically.

  265. 265
    ET says:

    daves:

    Further, the complete decimal expansion of the square root of 2 cannot reside in a human mind.

    Why not?

  266. 266
    daveS says:

    ET,

    Why not?

    That’s a good question. MG and KF appear to believe this, so I’m just going along with this assumption for the sake of argument. I’m not 100% committed to it.

  267. 267
    ET says:

    hazel:

    MG, I hope you respond to 256 about what it means for math to exist Platonically.

    What does that mean? That math exists regardless of us?

  268. 268
    Brother Brian says:

    KF

    BB, I have already pointed out from when it was first raised, the cognitive gap problem and its key index, abstract verbal language. As it was brought back up as though un-answered, I again pointed this out. Enough has been said for record: absent cognitive ability to handle high order abstracta (for which abstract verbal language is a key index) there is no basis for aesthetic reflection and conceptualisation. Monkeys simply do not have that capability, which is why they have not developed a civilisation. KF

    Your entire argument is based on the assumption that high order abstract thinking is required to appreciate aesthetic beauty, an assumption that has not been proven. And, frankly, can never be proven. As EG mentioned at 23, this assumption is based on our egocentric concept of human exceptionalism.

  269. 269
    ET says:

    When other organisms start classifying life I will gladly let go of my human exceptionalism

  270. 270
    kairosfocus says:

    ET, it is not complete in any finite number of places. KF

  271. 271
    ET says:

    Ahh, but is the human mind really finite? Or is that just an arbitrary limitation we place on it?

  272. 272
    kairosfocus says:

    BB, that is the nature of the aesthetic (as opposed to the merely pleasurable). A relevant saying goes, better a Socrates unhappy than a pig supremely happy. Socrates, he of “the unexamined life is not worth living.” KF

  273. 273
    kairosfocus says:

    ET, the point is that no particular number of decimal places, say k, will be next to transfinite such that k + 1 –> omega. For the kth place of sqrt2 there is a k+1th, k+2th etc, and the pot of gold at the end of the rainbow forever recedes. KF

  274. 274
    ET says:

    Right and we can take the journey right along with it. There isn’t anywhere it can’t go that we couldn’t go with it. That is if we are right and death does not mean the end.

  275. 275
    kairosfocus says:

    ET, there is a difference between advancing stepwise on a potentially transfinite and actualising same stepwise. The latter is a supertask that cannot be achieved. The former simply indicates onward progress without finite limit. KF

    PS: BTW, that is part of why I reject the notion of an actually traversed transfinite past of finite, causally connected stages.

  276. 276
    Brother Brian says:

    KF

    BB, that is the nature of the aesthetic (as opposed to the merely pleasurable). A relevant saying goes, better a Socrates unhappy than a pig supremely happy. Socrates, he of “the unexamined life is not worth living.” KF

    There is no consensus about what aesthetics and beauty are ( objective vs subjective), concluding that a monkey cannot have their own version of aesthetics and beauty simply is not warranted. At best, all we can say is, we don’t know.

  277. 277
    ET says:

    Seeing that aesthetics is a branch of philosophy that deals with the nature of art, beauty and taste and with the creation or appreciation of beauty, I can say with all confidence that monkeys do not have a version of it.

    That doesn’t mean they cannot find something pleasing. Some(?) birds of paradise sure do put on a display. And I don’t buy the “instinct” get out of jail free card.

    Animals aren’t the rubes we try to make them out to be.

  278. 278
    kairosfocus says:

    BB, nowadays, some toss around phrases such as “human exceptionalism” without fully realising their potentially ruinous import. A simple form is, “a rat is a pig is a boy.” This sort of thinking is part of the in-progress decay of our civilisation. KF

  279. 279
    kairosfocus says:

    H & DS, Near as I understand, Conway’s game of life creates an abstract space of possible states based on how it can be played. much like chess or draughts etc. Are those possibilities actually possible? I would think so; we thus have a case of an abstract, logic model world we can conceive of and represent. So, the possibility space is a map of realities that could be instantiated. The possibilities are obviously abstract but are real possibilities and we may speak truthfully (or make errors regarding) them. If you want to call that a platonic world, fine. Just be clear of what is being represented there: contingencies not necessary entities that are part of the framework for any possible world to be instantiated. KF

  280. 280
    Brother Brian says:

    KF <blockquote<This sort of thinking is part of the in-progress decay of our civilisation. KF
    You must be fun at parties. 🙂

  281. 281
    hazel says:

    kf writes,

    “DS , Near as I understand, Conway’s game of life creates an abstract space of possible states based on how it can be played. much like chess or draughts etc. Are those possibilities actually possible? I would think so; we thus have a case of an abstract, logic model world we can conceive of and represent. So, the possibility space is a map of realities that could be instantiated. The possibilities are obviously abstract but are real possibilities and we may speak truthfully (or make errors regarding) them.

    Much of that is correct, except it’s not actually a game like chess: once you create the original configuration, the rules create each succeeding generation in an iterative fashion.

    However, the question, which is one we return to, is what is the nature of those abstract possibilities (which is a better way of asking the question than “where do those abstractions exist?)?

    The answer I have offering is that the abstractions are elements of the logical system, and that the logical possibilities are as much elements of the system as the actual states that are instantiated at various times. A state that is instantiated (gen 3 of an original state of 9 cells with the middle cell missing, for instance, which is a common result when people explore the game) is not more or less an abstract element of the system than the 1000th generation of some complex gen 0 that no one has ever investigated.

    That is, the things we haven’t figured out yet and the things we have figured out have the same fundamental ontological status: they exist as possible elements of the logical system.

    kf adds, “If you want to call that a platonic world, fine.”

    No, I don’t think that is fine, because I don’t think what I am describing and what a “platonic world” implies are the same thing. The systems we are talking about are part of human understanding, which requires some instantiation in a symbol system, written or verbal, that includes various beginning axioms, definitions, etc. As I discussed in 258, I don’t think the idea that these exist apart from human beings in some separate Platonic realm is feasible.

  282. 282
    math guy says:

    As I have written previously, I have a job (some of which entails proving theorems!) that prevents regular posts to this forum. So my periodic absence is not necessarily a sign of throwing in the towel, so to speak.

  283. 283
    hazel says:

    Thanks, MG. I know you’ve explained your day job: FWIW: I’m enjoying my retirement. I will be interested any time you c an respond, although I hope when you do you back up a bit and look at relevant posts since the last time you were here.

  284. 284
    math guy says:

    H @ 258
    The first definition of mathematical platonism is standard and what I agree with personally (the second is silly IMHO).

    H @ 281
    “That is, the things we haven’t figured out yet and the things we have figured out have the same fundamental ontological status: they exist as possible elements of the logical system.”

    Although the above is referring specifically to cellular automata, I would opine the sentence is equally applicable to any consistent formal system, subject to the caveat that “figured out” means logically proved/derived, in which case the qualifier “possible” should be omitted.

    KF adds “If you want to call that a platonic world, fine.”

    I would call it a sub-world within the platonic realm because of my post @ 247 :

    “Gödel’s second incompleteness theorem implies an infinite hierarchy of ever more complicated (but true) statements. Since human minds are bounded at some level and an infinite hierarchy is unbounded, there will be theorems too complicated to be comprehensible by human minds.”

    The theorem cited actually shows that no single formal system encompasses all of mathematics. So all of Hazel’s logical consequences, known or unknown, comprise only a tiny sliver of mathematics, since those consequences are derived from within a single formal system.

  285. 285
    math guy says:

    KF @ 275

    “there is a difference between advancing stepwise on a potentially transfinite and actualising same stepwise. The latter is a supertask that cannot be achieved. The former simply indicates onward progress without finite limit. ”

    This appears to be Aristotle’s distinction between a potential and an actual infinity. The “supertask” of attaining the actual infinity cannot be achieved by humans in finite space and time. But to a Being not bound by such circumstances……?

  286. 286
    hazel says:

    This was written before I saw MG’s 284, but I’ll post it anyway:

    I like the way kf phrased things above: I would generalize and say any logical mathematical system has a “possibility space [that] is a map of realities that could be instantiated.” Although, as stated above, these are “realities” in that they are elements in the possibility space, not that they exist somehow outside that system.

    Consider two examples: What is the area of a triangle with sides of 917, 455, and 620 units, and what is the area of a triangle with sides of 3, 4, and 5.

    Now I am certain (and let us assume this is true) that the first question has never been asked before, and I am certain the second one has been asked.

    I’m sure we all agree that for each there is unique right answer. Each answer is in the possibility space of all questions about numerical quantities associated with triangles, the vast, vast majority of which have never been asked. They each exist as a determined, unambiguous logical consequence of our system of geometry.

    So ontologically, they have the same status: each answer is a logical consequence in the possibility space of all questions about numerical quantities associated with triangles. The fact that the second is known (A = 6 u^2) and the first is not is a fact about our knowledge within the system, but not a fact about the elements of the system itself. It is an epistemological fact, not an ontological fact.

    But wait! I know how to answer the first question! Heron’s formula gives me 126,513.18 u^2, to eight significant digits.

    Now we know the area, and moments ago we didn’t. I am the first person to ever know the answer to this question, and now I have shared it with you. Did its ontological status change? Is it any more “real” now, or “real” in a different way, than it was just because we have figured it out and expressed it within the written system that we use to instantiate these logical results?

    Which returns us to the question of in what way is formal mathematics real? Where does its reality reside? Or is that really a poor question, one which implies characteristics of math that are not true, or at least unknown.

    My answer to that question, to repeat, is that mathematical elements exist as logical possibilities within the symbol systems we use to instantiate our abstract concepts: they are potential concepts that can exist in human minds when those minds use the logical tools they haveto draw out the logical conclusions of those system. Some of them have been articulated and many have not (as my example is meant to show), but they all have the same status as a potential concept with our minds. They aren’t “residing” someplace else, waiting for us to access them, they are “residing” “inside us”, waiting for us to find them within the logical systems we have developed.

    All interesting stuff to think about!

  287. 287
    hazel says:

    So, MG, you do believe that “The Game of Life has always existed, and so has every other similar game, including ones on hexagonal grids, ones in which most or all starting generations die quickly, etc.”?

    Even if I made up some kind of system right now that had some logical rules and produced results, you would say that that system had eternally existed in a Platonic realm? I assume that is what you think.

    I have explained that I find that idea very unreasonable, so I think just trying to make it as clear as I can how I see it, rather than that way, is all I can do in this discussion.

  288. 288
    math guy says:

    Perhaps Hazel’s view of platonism existing in minds is correct, just not human minds. Johannes Kepler wrote (translated from Latin)

    “Geometry is one and eternal shining in the mind of God. That share in it accorded to humans is one of the reasons that humanity is the image of God.”

    My own opinion is that “geometry” can be replaced by much more in the above quote. On the other hand, humans are bound by finite time and space. Our mathematical deductions require formal systems like ZFC with finitely many axioms (or at most recursively many: consider the Axiom of Replacement) and proofs with finitely many steps. However as I noted previously, any such formal system that is capable of forming the set of integers is necessarily incomplete and contains true sentences that are unprovable within the system. God (by definition) is supernatural and not bound by finite processes (or countable processes, or …..) and likely can “see” the validity of such truths just as we can immediately recognize 2+2 =4 without having to count objects.

  289. 289
    kairosfocus says:

    H,

    Let us not conflate an abstract, logic model world with necessary entities that are framework to any possible world. Say, at some particular place and time as actors in our world, we create some game or model, which is thus in effect a formal system with its logic of being and of process spanning a space of possibilities . . . in what we could call a realm of ideas, perhaps even a transfinite space — e.g. a game with a token that moves on an endless tape following a program (resemblance to a Turing Machine is intended). That model spans an abstract space of possibilities we cannot exhaust already but we know that space well enough to accurately refer to it, to learn and express truths about it, maybe even profound truths that lead to a discipline we now call Computer Science.

    But that also means that several distinct individuals can work with and hold in mind truths regarding that space.

    The space is abstract, it has some sort of individual- or group- independent reality, it intersects with the real world in ways that constrain logic of physical beings, and it is significantly independent of any particular individual’s thoughts or those of the collective community working with it. After all, individuals and the community may err about it but then would be subject to the correction of more accurate reasoning.

    We thus see abstract logic model worlds with possibility spaces framed by the logic of being, which have sufficient independence of individual thinking or even intersubjective consensus to be truly objective.

    Objectivity does not entail or require concreteness nor is it dependent on individual or collective opinions. So far as I can see, to be objective we need a framework that warrants claims as credibly true and so reliable, as well as a tolerably effective means of detecting and improving on our errors. None of that requires that the domains so contemplated only comprise concrete, material entities. Or even that we have arrived at comprehensively absolute truth as a body, i.e. while we know some self evident and some other necessary plumb line truths, there is no need to assume or pretend that our system as a whole or for the most part is free of errors. Hence, the concept: improve on.

    We also see here a good reason to set aside nominalism (above and beyond its incoherence), as here we see abstract possibility spaces independent of our fallibility and shaped by the logic of being. It seems to me that we need to stretch our concept of being to include abstract entities, quantities and structures and to recognise the power of logic especially when coupled to being and possible worlds speak.

    Pardon, I now add a clip from Davies and Walker on phase or configuration or state space, an important concept in Statistical Thermodynamics and related fields . . . which BTW also brings out the significance of fine tuning and of particular start-points:

    In physics, particularly in statistical mechanics, we base many of our calculations on the assumption of metric transitivity, which asserts that a system’s trajectory will eventually [–> given “enough time and search resources”] explore the entirety of its state space – thus everything that is phys-ically possible will eventually happen. It should then be trivially true that one could choose an arbitrary “final state” (e.g., a living organism) and “explain” it by evolving the system backwards in time choosing an appropriate state at some ’start’ time t_0 (fine-tuning the initial state). In the case of a chaotic system the initial state must be specified to arbitrarily high precision. But this account amounts to no more than saying that the world is as it is because it was as it was, and our current narrative therefore scarcely constitutes an explanation in the true scientific sense.

    We are left in a bit of a conundrum with respect to the problem of specifying the initial conditions necessary to explain our world. A key point is that if we require specialness in our initial state (such that we observe the current state of the world and not any other state) metric transitivity cannot hold true, as it blurs any dependency on initial conditions – that is, it makes little sense for us to single out any particular state as special by calling it the ’initial’ state. If we instead relax the assumption of metric transitivity (which seems more realistic for many real world physical systems – including life), then our phase space will consist of isolated pocket regions and it is not necessarily possible to get to any other physically possible state (see e.g. Fig. 1 for a cellular automata example).

    [–> or, there may not be “enough” time and/or resources for the relevant exploration, i.e. we see the 500 – 1,000 bit complexity threshold at work vs 10^57 – 10^80 atoms with fast rxn rates at about 10^-13 to 10^-15 s leading to inability to explore more than a vanishingly small fraction on the gamut of Sol system or observed cosmos . . . the only actually, credibly observed cosmos]

    Thus the initial state must be tuned to be in the region of phase space in which we find ourselves [–> notice, fine tuning], and there are regions of the configuration space our physical universe would be excluded from accessing, even if those states may be equally consistent and permissible under the microscopic laws of physics (starting from a different initial state). Thus according to the standard picture, we require special initial conditions to explain the complexity of the world, but also have a sense that we should not be on a particularly special trajectory to get here (or anywhere else) as it would be a sign of fine–tuning of the initial conditions. [ –> notice, the “loading”] Stated most simply, a potential problem with the way we currently formulate physics is that you can’t necessarily get everywhere from anywhere (see Walker [31] for discussion). [“The “Hard Problem” of Life,” June 23, 2016, a discussion by Sara Imari Walker and Paul C.W. Davies at Arxiv.]

    Now, let us set one such game as the [study of the] logic of structure and quantity and call it Mathematics. Which just happens to be pivotal to the sciences and to daily affairs in general.

    Where, we know per Godel, that our contemplations can never span the possibilities on any formal set of start-points (axioms) and we cannot build such a limited set that we can guarantee as coherent.

    Mathematics is inherently transfinite and irreducibly complex, no finite mind can comprehensively span it.

    Indeed, we are forced to take it on trust that our more comprehensive thoughts and systems are coherent, i.e. to walk by faith and not by sight, though such can be reasonable and responsible. Where, for me, things like the Euler identity tell me that major domains are perfectly locked together in infinitely precise fit.

    Where also, there are many independently intelligible and known “core mathematical facts” that constrain axiomatisations.

    So, just to build our civilisation, to run it and to do science, we are forced to work with an objective abstract realm of structure and quantity that has ability to correct our errors. Reality and being are not constrained to materiality and concreteness.

    Thus also, let us posit another game, one that creates or contemplates entities that manifest beauty.

    That is, phenomena, that as contemplated by suitably cognitively capable beings will commonly excite appreciation, a sense of high worth or value tied to form, wonder, pleasure etc; responses which are in material part intelligible, being due to manifest form, proportions, symmetry, patterns, harmony, balance, subtle asymmetry, focus, verisimilitude, dynamism, etc. and so too due to their overall structure and/or composition and creativity. Or, as AmHD put it: “[a] quality or combination of qualities that gives pleasure to the mind or senses and is often associated with properties such as harmony of form or color, proportion, authenticity, and originality.” Where, several of these aspects are direct manifestations of structure and quantity, so are intelligible and amenable to derivations and calculations — as say Vitruvius and Da Vinci showed. Where, yes, mathematical objects can and do fit this conception of beauty, e.g. famously,

    0 = 1 + e^i*pi.

    Or even:

    i^i = e^-pi/2 = 0.20787956 . . .

    Let us call this new game, Aesthetics.

    Why should we suppose that there is no more to this logically governed game than essentially arbitrary individual or intersubjective tastes and opinions, any more than with Mathematics or Physics etc?

    I can see no good reason to so confine Aesthetics.

    Aesthetics is thus both a significantly objective study and that study addresses an equally objective substance.

    Beauty is more than the eye and peculiar tastes of the beholder.

    KF

  290. 290
    kairosfocus says:

    PS: Let us now also contemplate infinite, trans spatial, trans temporal necessary being Mind. Could not such a Mind know all possibilities and whatever is knowable? Let me add, including any particular decimal digit of sqrt2 or pi etc. Would not that Mind constitute, instantly, a domain — as opposed to a concrete location that is only contingently present in some space and time etc — a realm that transtemporally knows all possibility spaces, actualised or not? Would that not then fill the bill on being a Platonic domain? One, that is eternal such that discoveries, calculations or creations/inventions we make at particular times and places are automatically trans-temporally, trans-spatially present to such a Mind . . . we can even see that an extradimensional being could fill this bill just as for one y, any x is available in the plane. Is such a Mind inherently silly, incoherent, impossible of being? (Where, serious candidate necessary beings are either impossible of being or else actual; such actual beings are part of the fabric for any world to exist.)

  291. 291
    kairosfocus says:

    MG:

    I see your:

    Johannes Kepler wrote (translated from Latin)

    “Geometry is one and eternal shining in the mind of God. That share in it accorded to humans is one of the reasons that humanity is the image of God.”

    My own opinion is that “geometry” can be replaced by much more in the above quote. On the other hand, humans are bound by finite time and space. Our mathematical deductions require formal systems like ZFC with finitely many axioms (or at most recursively many: consider the Axiom of Replacement) and proofs with finitely many steps. However as I noted previously, any such formal system that is capable of forming the set of integers is necessarily incomplete and contains true sentences that are unprovable within the system. God (by definition) is supernatural and not bound by finite processes (or countable processes, or …..) and likely can “see” the validity of such truths just as we can immediately recognize 2+2 =4 without having to count objects.

    I think that fits with my remarks just above. What do you think?

    KF

  292. 292
    daveS says:

    hazel, Math Guy, KF,

    From post #288,

    Perhaps Hazel’s view of platonism existing in minds is correct, just not human minds.

    Is it necessary to posit another “participant” (God in particular) in our mathematical activities? What evidence is there which supports this?

    As Math Guy stated earlier:

    Gödel’s second incompleteness theorem implies an infinite hierarchy of ever more complicated (but true) statements. Since human minds are bounded at some level and an infinite hierarchy is unbounded, there will be theorems too complicated to be comprehensible by human minds.

    Yes, but we do what we can, and it turns out to be rewarding as well as practically useful.

    The theorem cited actually shows that no single formal system encompasses all of mathematics. So all of Hazel’s logical consequences, known or unknown, comprise only a tiny sliver of mathematics, since those consequences are derived from within a single formal system.

    I’m not sure that hazel means that we must choose a single formal system and stick with it forever. We can explore various systems around the hierarchy MG described, within our abilities (which is what mathematicians actually do, as far as I know). One can prove theorems in Peano Arithmetic before lunch, and then switch to some stronger, large cardinal theory after lunch.

  293. 293
    kairosfocus says:

    F/N: Guardian on London (the spoiled skyline city) and new year’s resolutions for architects: https://www.theguardian.com/artanddesign/architecture-design-blog/2014/dec/31/new-years-resolution-architects-2015-smart-cities-poor-doors And, concerns on skylines: https://www.theguardian.com/uk-news/2016/aug/27/londoners-back-skyscraper-limit-skyline Concerns on skyscrapers: https://www.theguardian.com/artanddesign/2014/apr/29/top-10-worst-london-skyscrapers-quill-odalisk-walkie-talkie KF

    PS: Money clip from the last:

    Sprouting over every corner of the city, most are of an architectural quality that recalls the outskirts of Dubai or Shenzhen. The overall impression is of an unplanned free-for-all, a steroidal frenzy of building tall, with little attention to individual design quality, or the cumulative effect that these scattered hulks might have on the city.

    The Planning Decisions Unit of the Greater London Authority, the body responsible for greenlighting these schemes, begs to differ. “It is simply not true to say these towers haven’t been planned,” says director Colin Wilson. “They have been very carefully planned. But we prefer to use a flexible framework, rather than a rigid masterplan. This liberty is what makes London successful.”

    The London Plan, the mayor’s rulebook for development across the capital, supports tall buildings where they “create attractive landmarks enhancing London’s character”. It states that such developments “should be of the highest design quality … attractive to look at and, where appropriate, inspire, excite and delight”. [–> as in should reflect sound aesthetics individually and in context]

    So how are these rules shaping up in reality?

  294. 294
    hazel says:

    Yes, Dave. There are those that think all this math can and does exists in the Mind of God, or some other Being, and thus ground the “Platonic nature” of math there. But there is nothing in my own experience that leads to that hypothesis, so I ground my understanding in human beings, human minds, and human symbol systems. This difference is probably the background source of most of the disagreements on this subject that go on here.

  295. 295
    daveS says:

    hazel,

    This difference is probably the background source of most of the disagreements on this subject that go on here.

    Amen to that.

  296. 296
    Brother Brian says:

    Hazel

    This difference is probably the background source of most of the disagreements on this subject that go on here.

    I don’t think there is any “probably” about it. One side believes that math exists somewhere outside the human mind and others don’t find the arguments or evidence for this compelling.

  297. 297
    ET says:

    hazel:

    As I discussed in 258, I don’t think the idea that these exist apart from human beings in some separate Platonic realm is feasible.

    Well, they do. All information exists regardless of us. That is just the way it is in this Intelligently Designed universe.

  298. 298
    ET says:

    Brother Bogart:

    One side believes that math exists somewhere outside the human mind and others don’t find the arguments or evidence for this compelling.

    Those “others” don’t have an argument or any evidence. So who cares if they want to live in denial?

    Srinivasa Ramanujan is evidence enough that math exists somewhere outside the human mind. Ignorance of Srinivasa Ramanujan is not an argument.

  299. 299
    ET says:

    hazel:

    But there is nothing in my own experience that leads to that hypothesis, so I ground my understanding in human beings, human minds, and human symbol systems.

    Then your experience is very, very limited and you have clearly never read of the exploits of Srinivasa Ramanujan and how he came about his knowledge

  300. 300
    kairosfocus says:

    BB, does mathematical truth exist? If so, what do you mean by truth. If not, why not. And, why do we see the uncanny effectiveness of math in the real world. Where, I again point to the mobius strip as a direct, mind-independent manifestation of structure and quantity embedded in real world bodies. The responses to this case and similar ones actually tell us far more on the roots of disagreements than any metaphysical skepticism on your part. For, the case in hand is a direct, empirical, readily replicable demonstration. KF

  301. 301
    kairosfocus says:

    H & DS, I again point to the mobius strip as a direct empirical demonstration of structure and quantity embedded in the world. I have long since pointed out how the requisites of a distinct possible world lead directly to numbers as necessary but obviously abstract entities antecedent to creatures such as ourselves. Most recently, I have discussed the issue that a possibility space is not nothing, KF

  302. 302
    Brother Brian says:

    KF

    BB, does mathematical truth exist?

    I’m not sure what you mean by this. Do mathematical proofs exist? Yes. That is what makes mathematics different than the rest of science. But that still doesn’t mean that mathematics exists outside and independent of the human mind.

  303. 303
    kairosfocus says:

    BB, let’s start simply. Is it true that || + ||| –> ||||| ? Is or is that not a mathematical truth? Does it need to be pinned in an axiomatic system and derived from theorems to be true — or more exactly, proved i.e. a result from a game? If your concept of Mathematics cannot stand up to joining two sticks to three more to obtain five, and if that fiveness is just a mental game to you, I would advise a pause to re-think. KF

    PS: And BTW, Mathematics is not science.

  304. 304
    kairosfocus says:

    F/N: Guardian on the Walkie Talkie building:

    https://www.theguardian.com/artanddesign/architecture-design-blog/2015/sep/02/walkie-talkie-london-wins-carbuncle-cup-worst-building-of-year

    It has singed shopfronts, melted cars and caused great gusts of wind to sweep pedestrians off their feet. Now the Walkie Talkie tower, the bulbous comedy villain of London’s skyline, has been bestowed with the Carbuncle Cup by Building Design (BD) magazine for the worst building of the year.

    Responsible for a catalogue of catastrophes, it is hard to imagine a building causing more damage if it tried. It stands at 20 Fenchurch Street, way outside the city’s planned “cluster” of high-rise towers, on a site never intended for a tall building. It looms thuggishly over its low-rise neighbours like a broad-shouldered banker in a cheap pinstriped suit. And it gets fatter as it rises, to make bigger floors at the more lucrative upper levels, forming a literal diagram of greed . . . . The headquarters of the Royal Institute of Town Planners stands two streets away. “It’s a daily reminder,” sighs one employee, “never to let such a planning disaster ever happen again.”

    Just a reminder,

    KF

  305. 305
    hazel says:

    I don’t think dismissing logical mathematical systems as “just a mental game” is justified.

  306. 306
    kairosfocus says:

    H, if Mathematics does not in the end accurately and substantially refer to anything outside the human mind then it is just a mental game. KF

  307. 307
    Brother Brian says:

    KF

    H, if Mathematics does not in the end accurately and substantially refer to anything outside the human mind then it is just a mental game. KF

    I think you are misrepresenting what Hazel is saying. Mathematics is a powerful tool that we use to model the universe around us. To categorize it as a “mental game” is disingenuous at best. But the fact that it is powerful doesn’t mean that it somehow exists outside the human mind. This is a testament to the human mind, not to some ill-defined necessary being.

  308. 308
    kairosfocus says:

    BB, Only if Mathematics is able to accurately address reality. Which means, what we say and conceive is objectively true in material part. Again, I point to an extremely simple case: is it true that 3 + 2 = 5? Or, that ||| + || –> ||||| ? In short, do our mental exercises and studies regarding structure and quantity in material part accurately describe the substantial reality of structure and quantity in the extra-mental world? If we are locked into an inner world of appearances and concepts, we are dealing with mental games and have surrendered the claim to truth regarding reality, much less warranted truth. (And yes, I suspect, here, the long shadow of the kantian ugly gulch; which is self-referentially incoherent.) KF

  309. 309
    Brother Brian says:

    KF@308, and what happens if I break one of the sticks in half? 🙂

    The fact that we can devise a system to accurately model the real world doesn’t mean that this system existed before us. It is an indication that we are good at seeing patterns.

  310. 310
    hazel says:

    kf writes,

    H, if Mathematics does not in the end accurately and substantially refer to anything outside the human mind then it is just a mental game. KF

    There are a whole bunch of very hard-working theoretical mathematicians that would take exception and offense at that, I think.

    There are two kinds of truth here, as we have discussed before, propositions which can be proven as necessarily true within a logical symbol system, on the one hand, and provisional truths about the physical world, some of which are described with mathematics, on the other.

    I think we (MG, Dave, BB, me) have, for the last few days, been discussing pure mathematics. To say math has value “only if [it] is able to accurately address reality” is wrong.

    Among other things, pure mathematics has value because it has, dare I say the word, beauty. Utility in describing the world is good, but, as I recall from earlier in the thread, utility is not the same as beauty!

  311. 311
    Brother Brian says:

    Hazel@310, I agree. There are two types of math. The first type is the math that we use to send ships into orbit, to build buildings, to make an MRI function. All very practical and useful tools. And then there is the mathematics that just make us think hmmm. That math that we engage in just for the pure joy and intellectual fun of it. With no expectation of practical benefit. In the science field, we would call that the “pure science”. But the amazing thing about this is the unintentional benefits that can come from these ventures.

  312. 312
    math guy says:

    KF @ 289, 290, 291
    Well said, and I agree. “Mind” such as you describe, containing all the relationships, structures, patterns, and information that humans can conceive of (and much more) seems to be a necessary component for a universe such as ours, and must certainly precede human minds. The opposite a-mat direction implies incredibly precise order arising spontaneously from chaos. As is repeatedly pointed out on this website, no such example of complex, specified information has ever been observed emerging from chaos.

    WJM had some lovely ideas in a previous thread: the closer we examine physical matter, the more elusive it becomes. At the quantum level, elementary “particles” appear to exist only when we try to “look” at them (measurement). When we’re not looking, they are waveforms that obey a Schrödinger equation. Like the characters in Toy Story, that only behave like inert toys when humans are watching but are off doing completely different things when nobody is watching, elementary “particles” don’t even exist unless measured (since BA77 can cite to us how hidden variable theories have all been disproven).

    On the other hand the unwatched (complex valued!!!) wave functions are modeled by a sophisticated differential equation, with extreme precision. WJM , like Pythagoras before him, believes that the model IS the reality (along with some free-will thrown into the mix).

    Now consider the extremely unlikely order-from-chaos alternative favored by a-mats. A consequence is that mathematics can only exist via (human) minds. These minds invent complex numbers, Hilbert spaces, and then QM. All matter obeys the rules of QM, including the matter comprising brains (since incorporeal minds are impossible in a-mat philosophy). This leads to a chicken-egg paradox regarding the origin of QM.

  313. 313
    kairosfocus says:

    BB, notice your distractive evasion? That is evidence that you have no cogent answer to what is a self-evident mathematical fact and truth: ||| + || –> |||||. Here, we see that intelligible rational principles, structures and quantities are inextricably embedded in reality starting with self-evident truths such as 3 + 2 = 5. This is a plumb line test, and it was failed. Where, I am sure you also learned in primary school that fractions exist as parts of a unit, so that 1 = 1/2 + 1/2 or if the fraction is some odd value f, from first steps in Algebra you know that 1 = f + (1 – f), etc. By breaking a unit into fractions, one has not eliminated the unit. The distraction fails and the embedded intelligible rational principles and facts of structure and quantity that are part of reality AND the corresponding rational contemplation of structure and quantity can and very often does accurately reflect that reality — i.e. are true — are telling us something. Namely, they point to the rationality of the roots of reality, thus the intelligible order of the world. If your worldview is uncomfortable with an intelligible rational order of the world without and our minds within from the roots up, that is a sign that it is inherently anti-rational and thus chaotic. Where, in fact, that rationality premise lies at the root of science as well as mathematics (historically as well as in principle), not to mention common good sense. Which last is increasingly manifestly getting scarce. Something that is plainly manifest in the Walkie Talkie tower in London, as was noted earlier . . . I cannot believe that the planners and regulators failed to figure out that curved reflective surfaces will concentrate sunlight even if they are not full focussing curves. There are many other similar signs of suicidal disintegration across our civilisation, but the breakdown of the rationality premise is one of the most disturbing. In short, artistic and functional principles are sending much the same message. Last but not least, the unresponsiveness to the message of mobius strips cut around in the middle vs 1/3 way across is sending the same message of embedded intelligible rational principles of structure and quantity that are antecedent to and independent of our thoughts and mind games. KF

    PS: I would think that we would have picked up the echo of Wittgenstein’s Language Games, which are also mind games. Let me clip SEP as food for thought:

    Throughout the Philosophical Investigations, Wittgenstein returns, again and again, to the concept of language-games to make clear his lines of thought concerning language. Primitive language-games are scrutinized for the insights they afford on this or that characteristic of language. Thus, the builders’ language-game (PI 2), in which a builder and his assistant use exactly four terms (block, pillar, slab, beam), is utilized to illustrate that part of the Augustinian picture of language which might be correct but which is, nevertheless, strictly limited. ‘Regular’ language-games, such as the astonishing list provided in PI 23 (which includes, e.g., reporting an event, speculating about an event, forming and testing a hypothesis, making up a story, reading it, play-acting, singing catches, guessing riddles, making a joke, translating, asking, thanking, and so on), bring out the openness of our possibilities in using language and in describing it.

    Language-games are, first, a part of a broader context termed by Wittgenstein a form of life (see below). Secondly, the concept of language-games points at the rule-governed character of language. This does not entail strict and definite systems of rules for each and every language-game, but points to the conventional nature of this sort of human activity. Still, just as we cannot give a final, essential definition of ‘game’, so we cannot find “what is common to all these activities and what makes them into language or parts of language” (PI 65).

    It is here that Wittgenstein’s rejection of general explanations, and definitions based on sufficient and necessary conditions, is best pronounced. Instead of these symptoms of the philosopher’s “craving for generality”, he points to ‘family resemblance’ as the more suitable analogy for the means of connecting particular uses of the same word . . .

  314. 314
    kairosfocus says:

    H, kindly note the just above to BB, especially the PS. KF

    PS: I sometimes think family resemblance operates like multiple overlapping fuzzy sets.

  315. 315
    kairosfocus says:

    MG, I tend to be cautious in making pronouncements on QM, but it is clear that this level of reality is an alien world to us, one we struggle to form an intuitive consciousness on. That said, QM is not all of reality, indeed it rests on the premise of rational ordering that is at least partly intelligible. As in, I here nod to Heisenberg and Einstein uncertainty. But even uncertainty is ordered, forcing a tradeoff between position and momentum and energy vs time. This echoes Godel’s incompleteness results and resulting uncertainty by a distant family resemblance. And yes, wave functions are complex . . . but then C is a superset of R. Something like taking powers of a number is then tantamount to vector rotation and expansion/compression using the z = r*e^i*wt result, spanning the space. Where, too, it becomes increasingly obvious that Wigner’s astonishment at the “unreasonable effectiveness of Mathematics” reflects the discomfort of blind watchmaker evolutionary materialistic scientism with the rationality principle. Even as it is increasingly clear that deep structure and quantity are inextricably woven into the fabric of our world, utterly antecedent to us and our mathematical studies. (I keep on giving the case of cutting around Mobius strips in the middle vs 1/3 way in from the edge; utterly independent of our thoughts, demonstrating spatially embedded structure and quantity.) Where of course the DNA code in our bodies highlights that this includes algorithms and so to symbolic machine code language. In that context is should not be surprising to see that structure, quantity and intelligible rational order seem to be at the root of reality, reflected in cosmological fine tuning. Even beauty turns out to pivot on intelligible rational and even mathematical principles (I especially think of symmetry, fractal self-similar scaling and subtle asymmetries — the case of octaves and fifths in music with harmonics and the challenge of fitting together is a good example). The more I ponder the more sensible it seems to put reason at the root of reality. KF

  316. 316
    hazel says:

    MG, I am not an “a-mat”, in case you were including me at 312. And my philosophical speculations about the base level of the reality of matter and mind involves QM, which I’ve read a lot about recently.

    Question: does the proboscis monkey know that II + III = IIIII? Why or why not?

  317. 317
    daveS says:

    hazel,

    does the proboscis monkey know that II + III = IIIII?

    Yes. proof

    I believe some animals can do basic addition, but presumably they wouldn’t understand the meaning of “II + III = IIIII”. At least not without intensive tuition.

  318. 318
    hazel says:

    Nice picture, Dave. I’m a monkey and apes fan: took a neat course way back in college just for fun, and have kept up a bit on research about their skills over the years.

  319. 319
    ET says:

    How is that proof of anything beyond a primate looking at its fingers?

  320. 320
    daveS says:

    These are jokes, ET.

  321. 321
    ET says:

    So there isn’t any evidence that we invented mathematics nor any part that goes with it. All our opponents have is a denial that mathematics exists regardless of us.

    Why bother arguing with the willfully ignorant?

  322. 322
    hazel says:

    Yes, Dave’s picture was a good joke.

    This question, however, is serious:”Question: does the proboscis monkey know that II + III = IIIII? Why or why not?

  323. 323
    daveS says:

    I think it’s possible. Many people insist that animals (other than humans) are incapable of abstract thought, but I don’t find the arguments very persuasive. Unfortunately we can’t ask the monkeys. Perhaps they are capable of enough abstract thought to understand what we call the positive integers as well as a young human child does.

    The second part of my post was actually serious—I don’t know how to represent the abstract statement “2 + 3 = 5” in a form that a monkey could potentially understand.

  324. 324
    kairosfocus says:

    DS, absence of complex abstract verbal language is a strong sign of absence of the required level of cognition. I am not talking about ability to make more or less concrete connexions, but the sort of language we have. That has been pivotal to creating civilisation. KF

  325. 325
    ET says:

    Question: does the proboscis monkey know that II + III = IIIII?

    Who cares? If someone does then it is up to them to find out or forget about it.

    Starlings, raised without their parents, know what to do when the seasons and sky change. They were never taught to stir and migrate. But they do.

  326. 326
    kairosfocus says:

    H & DS, what is a number? Would you expect a monkey to understand the concept, much less be able to use it? Why? KF

  327. 327
    daveS says:

    KF,

    I don’t know. In fact, I don’t know how it is that humans understand and use numbers.

    Edit: I will say that I believe addition of small positive integers is much simpler than speaking a natural human language such as English. Some animals do have a sort of number sense and are able to distinguish between 4 things and 5 things. Therefore I think it’s conceivable that monkeys are capable of abstract thought.

    Ultimately we don’t have direct access to animals’ minds however.

  328. 328
    hazel says:

    I am pretty sure there are experiments that show that some primates, and some birds, can recognize some small number of objects irrespective of the object (star, heart, picture of grape, etc) and of the arrangement, as long as they are in the same visual space. This is done by something like having a reward behind the door with five objects on it, and showing that the animal learns to pick the correct door.

    This says to me that there is some primitive, incipient creation and use of an abstract concept of a specific small number (distinguishing five from four or six) that is not dependent on symbolic understanding.

    This does not address the issue of addition, which is harder, but it does address the concept of abstracting the concept of a specific quantity from examples involving different objects with the same quantity.

  329. 329
    kairosfocus says:

    H, yes, there is a primitive number sense and at about 4 – 5 animals max out. The case I know is send 5 men into a tower, 4 come out, a bird thinks it is empty, nab it. But that is not counting much less addition and subtraction much less the concept, number. KF

  330. 330
    daveS says:

    To muddy the waters a bit, I’ll throw this out: TensorFlow Object Counting API

    The TensorFlow Object Counting API is an open source framework built on top of TensorFlow that makes it easy to develop object counting systems.

  331. 331
    kairosfocus says:

    DS, digital counter technology is very old stuff now. KF

  332. 332
    daveS says:

    KF,

    Can you provide an example?

    Edit: This example simply shows that “counting” objects of various types can be done purely mechanically, without the ability to think abstractly.

  333. 333
    kairosfocus says:

    DS, I cut my eyeteeth on 7490 decade counters. Feed outputs to 7-segment LEDs and you are good to go. KF

    PS: These chips of course were simply electronic entities, they neither were aware of nor cared what they were doing, e.g. working with a VCO and temp sensitive resistance sensor to measure temperature (actual precision about 1/100 degree C).

  334. 334
    daveS says:

    KF,

    Pardon, but that’s not at all comparable to what I linked to. Did you look at the github page?

    Back to hazel’s question, I suspect these object recognition systems could be trained to simulate understanding of symbolic expressions such as “II + III = IIIII”, at least. Time will tell, anyway.

    And hypothetically, if they can simulate this sort of understanding, will they become indistinguishable at some point from beings capable of abstract thought?

  335. 335
    kairosfocus says:

    DS, counting is counting, in the mechanical sense of incrementing registers. What you are looking at is object detection in a field and then counting by category. That, again, is programming. We can set that up and can imagine a simulation which some may say is good enough. However, this leaves off self aware responsibly and rationally free agency. Likely, i/l/o worldviews influences. KF

  336. 336
    daveS says:

    KF,

    What you are looking at is object detection in a field and then counting by category. That, again, is programming. We can set that up and can imagine a simulation which some may say is good enough. However, this leaves off self aware responsibly and rationally free agency.

    Of course, but I am talking about the ability to do rudimentary arithmetic here (the type that animals do). To distinguish between 4 and 5 objects, for example. To recognize that 2 bananas plus 3 bananas equals 5 bananas.

  337. 337
    hazel says:

    Looking at this from a different angle:

    I think it is correct to say that the animals in question have an abstract concept of small numbers, like 5, because they can identify five objects irrespective of shape, color, position, etc. I think it is correct to say they don’t have an abstract concept of addition, equals, or quantity or number in general.

    With that in mind, let’s look at kf’s example of I I + I I I = I I I I I. Let’s assume that the objects represented by each “I” don’t have to be exactly identical, because we understand the abstract idea of quantity irrespective of other properties the items might not have in common. All that is necessary is that the objects be grouped together enough: perhaps two pebbles of different sizes and shapes are sitting at one end of a rock and three similarly different pebbles are sitting at the other end of the rock.

    Does the monkey look at that and think “2 + 3 = 5”. Of course not. He doesn’t have the ability to have those abstract concepts.

    But when we look at the pebbles, we do see that 2 + 3 = 5, because not only do we have the capacity to form those concepts, we have in fact acquired them at some early point in our cognitive development, about age four or five.

    So where does the abstraction 2 + 3 = 5 reside? In the world, or in our minds?

    It seems clear to me that even though individual objects exist in the physical world, the abstract ideas of quantity, addition, and equality arise in the minds of beings with rational, abstract cognitive abilities such as we have. If the world were just monkeys, 2 + 3 = 5 would not exist as an abstract fact, which is of course different than saying the pebbles wouldn’t be sitting on the rock.

    I think one reason it seems compelling to say 2 + 3 = 5 exists outside of our minds is because we can’t think of what the world is like without using the the concepts already present in our minds. We have to use our minds to describe the world, so how can we describe what it is like when it is not being described by a mind?

    It seems to us that the abstraction is a necessary part of the world, and in the world, but that is just a projection of our understanding overlaid on the world we observe. We can’t think about the world without using the abstract concepts we have in our minds

    This difference has been made clearer to me by thinking about the difference between the world as it appears to the monkey and the way the world appears to us.

  338. 338
    math guy says:

    H @ 316
    My post @ 312 was directed at KF. I was not insinuating that any particular UD characters were a-mats, rather that their position entails yet another logical absurdity.

    From 337: “So where does the abstraction 2 + 3 = 5 reside? In the world, or in our minds?”
    You have asked me (and other readers) an opinion question. My opinion is both: abstraction is embedded into the fabric of the universe itself, as KF has demonstrated with his Möbius band example. However it takes a certain amount of intelligence (and attention) to observe such abstract relationships. As I have remarked @ 247, (some) humans have known since at least 1931 that there exist levels of abstraction too deep to be discovered by human minds. Whether those abstractions are also embedded into our universe or not (i.e. form a branch of applied math) cannot be determined by us.

  339. 339
    kairosfocus says:

    DS, what we have is two distinct things. First, a “mechanical” counter. Second, a system designed to detect objects and categorise them in a pixel field (perhaps, converted into a 3-d world model) and store in some sort of database record. The counter is applied and it seems a boxing and labelling layer is imposed on a display of the pixel field. None of this reflects autonomous, conscious self awareness or the level of cognition required to understand the nature of objects, what numbers are, what operations on same are, thus functions and relationships, etc. Animals by contrast do in some cases have a number sense, being able to detect differences of discrete quantity up to maybe 4 or 5. This is, again, not the same as counting, adding, recognising number as a concept or having the cognitive level to form the abstractions of Mathematics.If you have clear evidence to the contrary, kindly provide it. Likewise, that animals exert aesthetic judgements. Linked, ethical judgements — where, our life of reasoning is inextricably governed by known duties to truth, right reason, prudence, fairness etc, i.e. a vast array of sophisticated abstract concepts and constraints are entangled in the seemingly simplest acts of rational cognition, including basic arithmetic. I again note that want of abstract, conceptual language (as opposed to responses to concrete entities) is a key index of the gaps in question. There is utterly no evidence that computation on a substrate can pull itself up by its own bootstraps into a self aware, conscious, contemplative entity with the cognitive capacity to form the abstract concepts and schemes of thought required to actually understand mathematical concepts. Despite a lot of speculation to the contrary, despite an expectation from evolutionary materialistic scientism (which is self-refuting) computation is simply not a process of rational inference and wider cognition. We have direct awareness of the latter and routinely design and build systems that do the former, we should not unduly conflate the two. KF

  340. 340
    kairosfocus says:

    H:

    where does the abstraction 2 + 3 = 5 reside? In the world, or in our minds?

    It seems clear to me that even though individual objects exist in the physical world, the abstract ideas of quantity, addition, and equality arise in the minds of beings with rational, abstract cognitive abilities such as we have. If the world were just monkeys, 2 + 3 = 5 would not exist as an abstract fact, which is of course different than saying the pebbles wouldn’t be sitting on the rock.

    I note, again, that we must distinguish the study of the logic of structure and quantity from the structure of structure and quantity that are evidently embedded in the world as part of a pattern of intelligible rational principles it manifests; often through the logic of being. I have pointed to the behaviour of a Mobius strip when cut around 1/3 way in from its edge vs in its middle. Those are embedded structural, quantitative properties in action, utterly independent of and antecedent to our cognition and conception.

    Likewise, if by some chance two pebbles fall on a rock shelf and later three more, by force of the logic of structure and quantity, there will now be five pebbles there, regardless of whether we have come along to contemplate it. These sorts of events exhibit the logic of being. At another level, such phenomena are pivotal to the ability of our cosmos to support the sort of life we enjoy. Again, antecedent to our existence.

    Indeed, the ideas of number, structure, wider quantities etc are mental phenomena. The disciplined, logical study of same is also mental. Just as ability to recognise and infer principles of aesthetics is a mental process. Likewise, the underlying inextricably entangled ethical process of moral government of our cognition by known duties to truth, right reason, prudence, fairness etc is inevitably mental as well. Moreover, I find the three are inextricably intertwined.

    I suggest, yet again, that while monkeys or birds etc evidently do not have the cognitive ability to develop mathematics, aesthetics and ethics as disciplines, there is significant evidence that such considerations are embedded in the world of life and in the prior ordering of an observed cosmos fine tuned in a multitude of ways that support such life. For the first, I point to D/RNA, the involved code and complex algorithms with associated molecular nanotech execution machinery found in metabolic automata with integrated von Neumann kinematic self replication facilities. For the latter I point to our discoveries of just how fine tuned our cosmos’ physics is on key structures and quantities — which are obviously embedded in the world — that enable C-chemistry, aqueous medium, terrestrial planet in stellar and galactic habitable zone life.

    In short, there is significant but often overlooked evidence that points to a mathematically framed design of the world of life and the cosmos that hosts it.

    Such points onward to cognitive function and capacity to carry out such contemplations, i.e. to a cosmos-enabling, mathematically sophisticated designer as the locus of evident design.

    KF

  341. 341
    kairosfocus says:

    MG,

    338: >> I was not insinuating that any particular UD characters were a-mats, rather that their position entails yet another logical absurdity.

    From [H,] 337: “So where does the abstraction 2 + 3 = 5 reside? In the world, or in our minds?”
    You have asked me (and other readers) an opinion question.>>

    1: indeed. A necessary distinction.

    >> My opinion is both: abstraction is embedded into the fabric of the universe itself, as KF has demonstrated with his Möbius band example.>>

    2: Thank you for this recognition of a striking manifest phenomenon that shows something that does not seem to have fully registered with many people in our civilisation.

    3: In the context of this and linked exchanges at UD, a key point has been the definition of Mathematics I put on the table: the [study of the] logic of structure and quantity.

    4: This points to both a discipline and to a reality-embedded intelligible substance that is there to be explored and teased out in terms of its rational principles, elements and organisation.

    >> However it takes a certain amount of intelligence (and attention) to observe such abstract relationships.>>

    5: Yes, absent certain cognitive capabilities that manifest in abstract language, reasoning and ability to recognise the ability of truth — accurate description of reality — to span the gap between our inner world and the outer one of things in themselves, Mathematics is impossible as a disciplined study carried out by individuals in community.

    6: I point to the central importance and sign of abstract, concept-rich language, including its extension into Mathematical exposition and computing science.

    >>As I have remarked @ 247, (some) humans have known since at least 1931 that there exist levels of abstraction too deep to be discovered by human minds. Whether those abstractions are also embedded into our universe or not (i.e. form a branch of applied math) cannot be determined by us.>>

    7: A humbling, significant recognition. Let’s pull back up 247, as comments get buried under the onward exchange:

    MG, 247: >>This appears to be an issue for abstract objects that require a mind to live in because the truth or falsity of the conjecture (or septillionth decimal digit of pi) appear to be independent of any mind. In fact, Gödel’s second incompleteness theorem implies an infinite hierarchy of ever more complicated (but true) statements. Since human minds are bounded at some level and an infinite hierarchy is unbounded, there will be theorems too complicated to be comprehensible by human minds.

    Where do these theorems reside?>>

    8: Objective truth rests in credible, reliable, warranted accuracy of description of reality.

    9: It is subjects who can recognise, warrant and state truth, and such subjects in our case are inherently, inescapably limited.

    10: Where Mathematics is irreducibly complex and cannot be spanned by a coherent, known to be coherent, constructed axiomatic system.

    11: So, there are structural and quantitative realities we cannot warrant on our schemes of thought, but perhaps we may state some of them as conjectures that turn out to be undecidable on particular axiomatic schemes such as ZFC. Which is itself an adjusted system ultimately deriving from the problems of naive set theory.

    KF

    PS: Aren’t there procedures that give arbitrary position digits of pi, or are those in binary form, which does not simply translate to decimal digit form under place value notation. I confess to using tables of pi as random number tables, and to finding telephone numbers there etc. (My argument for sufficient randomness is want of correlation between two determined systems, the value of pi and the place value decimal system of counting on powers of 10.)

  342. 342
    daveS says:

    KF,

    Despite a lot of speculation to the contrary, despite an expectation from evolutionary materialistic scientism (which is self-refuting) computation is simply not a process of rational inference and wider cognition.

    I’m 99% sure you’re correct. 😛

  343. 343
    daveS says:

    KF,

    Aren’t there procedures that give arbitrary position digits of pi, or are those in binary form, which does not simply translate to decimal digit form under place value notation.

    In case this is not a rhetorical question, yes:

    The Bailey–Borwein–Plouffe formula (BBP formula) is a spigot algorithm for computing the nth binary digit of the mathematical constant π using base-16 representation. The formula can directly calculate the value of any given digit of π without calculating the preceding digits.

  344. 344
    kairosfocus says:

    DS, thanks, I had only seen some reference and vaguely remembered it. Four suitably framed binary digits in succession would give a hexadecimal digit but that would not readily translate into decimal digits. KF

    PS: Pi hex: 3.243F6 A8885 A308D 31319 8A2E0 37073 44A4 . . .

  345. 345
    daveS says:

    KF,

    You’re welcome. (Edit: Interesting, I’ve never seen pi in hex before).

    Going back to some points raised earlier about Möbius strips, formal systems, hazel’s take on platonism, here’s a related question. It sounds trivial, but there is a point.

    Suppose we have an arbitrary Turing machine and a particular input for that Turing machine (i.e., a paper strip containing a finite string of symbols from its alphabet).

    Is it true that the Turing machine either will halt or not halt given this input, and that this behavior is independent of our minds?
    And further, that this behavior is the same in every possible world?

  346. 346
    kairosfocus says:

    DS, a Turing machine is a highly contingent entity so by definition it will not exist in every possible world, and it is dependent on antecedent causal factors. Once it exists — that is a part specification of a contingent state of affairs, and it is fed an input it will halt or else it will not halt, but that is often undecidable a priori. That behaviour is the result of its having been set up and having particular rules and structures of operation, perhaps as a model on some computer as we do not usually actually set up a physical instantiation or model, which given the infinite tape is in principle impossible.Likewise, we can see that a set of activities proceeds and for all we know seems to be set to go on endlessly but that is something we cannot observe: a stepwise set of causally connected finite stages spanning an actual infinity is a supertask; we can observe a halt but not a no-halt, though we may properly infer that. That said, once set up and functional, it seems the case that its onward behaviour on an input is independent of what we may think assuming we do not interfere further. The Mobius strip is a clear case of this. KF

  347. 347
    daveS says:

    KF,

    I think I mostly agree, particularly with this:

    Once it exists — that is a part specification of a contingent state of affairs, and it is fed an input it will halt or else it will not halt…

    There is a single objectively true answer to the question of whether it halts or not (according to platonists anyway).

  348. 348
    hazel says:

    kf writes,

    There is a single objectively true answer to the question of whether it halts or not (according to platonists anyway).

    To me, too. I don’t see what this has to do with Platonism. As I have explained, once a logical system is started, the logical consequences are determined.

  349. 349
    daveS says:

    hazel,

    Thanks, you are correct. It is actually a separate question after all. I should be talking about truth-value realism apparently:

    Truth-value realism is the view that every well-formed mathematical statement has a unique and objective truth-value that is independent of whether it can be known by us and whether it follows logically from our current mathematical theories. The view also holds that most mathematical statements that are deemed to be true are in fact true. So truth-value realism is clearly a metaphysical view. But unlike platonism it is not an ontological view. For although truth-value realism claims that mathematical statements have unique and objective truth-values, it is not committed to the distinctively platonist idea that these truth-values are to be explained in terms of an ontology of mathematical objects.

    Mathematical platonism clearly motivates truth-value realism by providing an account of how mathematical statements get their truth-values. But the former view does not entail the latter unless further premises are added. For even if there are mathematical objects, referential and quantificational indeterminacy may deprive mathematical statements of a unique and objective truth-value. Conversely, truth-value realism does not by itself entail Existence and thus implies neither object realism nor platonism. For there are various accounts of how mathematical statements can come to possess unique and objective truth-values which do not posit a realm of mathematical objects.

    (from the SEP entry on platonism in the philosophy of mathematics)

  350. 350
    hazel says:

    Thanks Dave – that’s very interesting, and I appreciate your finding it.

    I have already been burned once, so to speak, by expressing an attraction to a philosophical label, but I like the phrase and description, for the most part, of truth-value realism, which is a term I have never heard before.

  351. 351
    hazel says:

    Dave quotes the SEP as saying,

    For there are various accounts of how mathematical statements can come to possess unique and objective truth-values which do not posit a realm of mathematical objects.

    I wonder if there is a nice layman’s description someplace of what some of those accounts are?

  352. 352
    kairosfocus says:

    DS & H:

    I note, given a running TM, the options per logic of process are that that state continues [does not halt] or changes [halts]. The former in principle is infinite so cannot be directly observed but can be inferred similar to say the cycling of a long division exercise . . . our first imposed halt on an algorithm. The two alternatives, in context, are mutually exclusive and exhaustive — they dichotomise possibilities.If no halt, then continue.(If you dispute such, kindly explain why.)

    The remarks on truth-value realism are a discussion on the nature of propositions: AmHD: “5. Logic a. A statement that affirms or denies something. b. The meaning expressed in such a statement, as opposed to the way it is expressed.” Collins: “2. (Philosophy) philosophy a. the content of a sentence that affirms or denies something and is capable of being true or false b. the meaning of such a sentence: I am warm always expresses the same proposition whoever the speaker is.” RHK Webster’s: ” 6. Logic. a statement in which something is affirmed or denied, so that it can therefore be significantly characterized as either true or false.”

    These document the standard understanding: A proposition is an assertion about reality, internal or external, that X is so or else that ~X is so, which may be accurate or inaccurate, beyond whatever we may happen to know at a given point on whatever degree of warrant we may have. In a Kantian ugly gulch haunted world, it is unsurprising that some would seek an alternative (but notice the subtle self-reference — whether a proposition refers to what is the case or not is itself a proposition.)

    The key issue is that we must distinguish accuracy of reference from adequacy of warrant.

    That something refers to what may or may not be the case in reality is one thing, that we have a belief or perception that it is or is not so is a second, that we may be in doubt is a third, that we have warrant sufficient to responsibly accept it as so is a fourth. But the second through the fourth do not alter the first, they pivot on it. Nor does resorting to the Language Game model escape this issue: A language of Mathematicians L-M in which X is true/~true and a different one for Philosophers L_P where such is not the case, becomes obscure and self-referentially incoherent as this discussion is itself a discussion of what is or is not the case. The infinite regress problem opens up.

    Note, how SEP continues:

    many nominalists endorse truth-value realism, at least about more basic branches of mathematics, such as arithmetic. Nominalists of this type are committed to the slightly odd-sounding view that, although the ordinary mathematical statement

    (1) There are primes numbers between 10 and 20.

    is true, there are in fact no mathematical objects and thus in particular no numbers. But there is no contradiction here. We must distinguish between the language LM in which mathematicians make their claims and the language LP in which nominalists and other philosophers make theirs. The statement (1) is made in LM. But the nominalist’s assertion that (1) is true but that there are no abstract objects is made in LP. The nominalist’s assertion is thus perfectly coherent provided that (1) is translated non-homophonically from LM into LP. And indeed, when the nominalist claims that the truth-values of sentences of LM are fixed in a way which doesn’t appeal to mathematical objects, it is precisely this sort of non-homophonic translation she has in mind. The view mentioned in the previous note provides an example.

    This shows that for the claim Existence to have its intended effect, it must be expressed in the language LP used by us philosophers. If the claim was expressed in the language LM used by mathematicians, then nominalists could accept the claim while still denying that there are mathematical objects, contrary to the purpose of the claim.

    See the regress beginning to gather speed?

    The very obvious solution is to acknowledge that we may ponder abstracta, which manifest themselves in part by being embodied in reality. As we can directly observe with the peculiar properties of the Mobius strip. We do an operation and see the paper model convincingly has ONE side and ONE edge, by contrast with an ordinary untwisted cylindrical loop of paper. This requires reference to what an operation is, what a loop is, what an edge is, what a side is, even what orientability is, etc. All of these are abstract, we cannot evade abstracta, universals, propositions, numbers, structures, information, energy, time, frequency, states of affairs and much more. Socrates is a name, an abstract entity. A certain bearer [abstract[ of this name is [abstract] a man [abstract]. Men [abstract] are [abstract] mortal [abstract]. Socrates is [abstract] mortal.

    We cannot get away from abstracta, and the nominalist’s denial of same begins the self-referential spiral.

    The issue is indeed ontological, it pivots on the logic of being, what does it mean for a concrete [an abstract category] entity to exist, and to exist as an example or case of a class? What does it mean for such a universal to exist or be real, given its abstract nature? Ditto for the existence of a proposition. Ditto for a number, starting with one, two, zero.

    So far as I can see, we can make a simple observation: for some x to be, it is AS an instance of some distinct kind of thing, X-class, X_C. That is, there are in-common core properties that place x in X_C, and to hold distinct identity x, there is some unique aspect of x, A. We are back to law of distinct identity. Where, that x is concrete typically means that it is tangible, directly observable. In observing it, however, we are instantly forced to refer to and frame it in terms of abstracta. x is distinct from the rest of actualised or potential reality ~x, by virtue of some characteristic A, but it already belongs to classes, an actual or potential entity in reality for instance.

    We therefore must acknowledge that in-common aspect of being, which means that classes are real, exist in a different sense, intangible and abstract. First, obviously in our minds — another intangible but directly experienced reality that is pivotal in grounding warrant for ever so much more. But, did our particular minds [dubiously . . . ] impose and project X_C unto x? No, down that road lies utter confusion, we recognised that x is or may be and that it therefore has a property of actual or potential existence along with many other things such as ourselves. So, too, we recognised X_C implicitly, the relevant class of x.

    Let x for the moment be say Earth in the solar system.

    Absent our planet, we would not exist, absent the Sol system, it could not harbour life including ours. The categories and members are antecedent to us, we recognise the realities we do not invent them.

    So, abstracta must have existence in some sense, a sense that must include cases antecedent to our existence.

    Classes hold reality by being natural or invented categories that reflect the in-common aspects of being. A proposition involving classes has existence not just as an utterance or thought but as a thought that asserts something to be true to reality, and may succeed or fail. A number has reality by expressing a particular sort of quantitative property of the world or wider reality and possible worlds within structures that tie such together: N, Z, Q, R, C. Such are aspects of reality, which is antecedent to our existence and independent of our success or failure in attempts to attain knowledge.

    Prime numbers have properties in common that we happen to find interesting. Between 10 and 20, 11, 13, 17, 19 are prime, 15 is odd but not prime. They are numbers with additional, restrictive properties. Where each is distinct, 11 is not 13 etc. We discover those properties, we did not invent them. Indeed, likely our remote ancestors saw this by noting how pebbles or sheep or fruit could not be evenly shared as intact units among a smaller number of persons, reflecting how concrete circumstances exhibit the in-common properties. (This then, doubtless led to fractions thus rationals, then onward irrationals etc as recognised real classes.)

    So, wisdom is to swallow the unpalatable but effectively undeniable reality of abstracta. Contemplated by minds, yet antecedent to our own. Real, as connected to any x holding distinct identity. And insofar as one may desire a world of forms that eternally recognises such, a logical candidate — again peculiarly repugnant to many — would be a mind at world-root. ut that is an onward debate.

    KF

  353. 353
    kairosfocus says:

    PS: Such abstracta then extend very naturally to aesthetics and ethics too. Namely, are there true principles of value/worth, aesthetical or ethical? Where if something gives us pleasure to contemplate, can that be grounded on objective principles? Yes, tracing to symmetry, balance, harmony, variety, etc. — many of which pivot on the embedding of structure and quantity in the world of objects. Are such contemplations autonomous? No, all aspects of human reality and cognition are morally and rationally governed. Some aesthetics pleasures begin to drift into the oppressive — the castrata singers of the past being a case in point. We forgo certain aesthetical experiences on moral grounds, for cause . . . castrata being a capital example, the last such having been laid to rest many years ago. Rumours regarding certain pop stars notwithstanding. Likewise, pornography can be aesthetically attractive as the notorious case of D H Lawrence demonstrated. But, again, moral considerations are at stake. Anatomy textbooks contain images that could be used in a pornographic manner — for prurient purposes, but have a very important and legitimate use. A katana of traditional manufacture is indubitably highly refined and beautiful, but may be used to murder. The state of Japan finds it an important contribution to culture to support as living treasures, the expert artisans who to this day produce such swords. Even so strapped a country as Jamaica finds it a vital contribution to national progress to provide support to writers. By contrast, London has clearly done significant damage to its aesthetic worth by granting permission to erect the Walkie Talkie building and the like — something that can have measurable impact on tourism and on degradation of environment that supports various social pathologies with even criminal manifestations. Ironically, in other contexts, even such marred entities may be an aesthetic improvement. And more.

  354. 354
    hazel says:

    kf, what is this “Kantian ugly gulch” of which you speak so often?

  355. 355
    hazel says:

    kf writes, “We cannot get away from abstracta.”

    I agree, and said this at 337:

    It seems clear to me that even though individual objects exist in the physical world, the abstract ideas of quantity, addition, and equality arise in the minds of beings with rational, abstract cognitive abilities such as we have. If the world were just monkeys, 2 + 3 = 5 would not exist as an abstract fact, which is of course different than saying the pebbles wouldn’t be sitting on the rock.

    I think one reason it seems compelling to say 2 + 3 = 5 exists outside of our minds is because we can’t think of what the world is like without using the the concepts already present in our minds. We have to use our minds to describe the world, so how can we describe what it is like when it is not being described by a mind?

    It seems to us that the abstraction is a necessary part of the world, and in the world, but that is just a projection of our understanding overlaid on the world we observe. We can’t think about the world without using the abstract concepts we have in our minds.

  356. 356
    kairosfocus says:

    H, the gap between the inner phenomenal world (appearances) and the noumenal (things in themselves), the phrase is by no means original to me. I think it is from Kantians, not Kant himself. KF

    PS: F H Bradley — a noted British philosopher — on the issue:

    We may agree, perhaps, to understand by metaphysics an attempt to know reality as against mere appearance, or the study of first principles or ultimate truths, or again the effort to comprehend the universe, not simply piecemeal or by fragments, but somehow as a whole [–> i.e. the focus of Metaphysics is critical studies of worldviews] . . . .

    The man who is ready to prove that metaphysical knowledge is wholly impossible . . . himself has, perhaps unknowingly, entered the arena . . . To say the reality is such that our knowledge cannot reach it, is a claim to know reality ; to urge that our knowledge is of a kind which must fail to transcend appearance, itself implies that transcendence. For, if we had no idea of a beyond, we should assuredly not know how to talk about failure or success. And the test, by which we distinguish them, must obviously be some acquaintance with the nature of the goal. Nay, the would-be sceptic, who presses on us the contradictions of our thoughts, himself asserts dogmatically. For these contradictions might be ultimate and absolute truth, if the nature of the reality were not known to be otherwise . . . [such] objections . . . are themselves, however unwillingly, metaphysical views, and . . . a little acquaintance with the subject commonly serves to dispel [them]. [Appearance and Reality, 2nd Edn, 1897 (1916 printing), pp. 1 – 2; INTRODUCTION. At Web Archive.]

  357. 357
    hazel says:

    I thought that might be what you referring to. I accept that external reality exists, and that our perceptions of it, at the macroscopic level that they exist, are in general accurate. I understand the argument that we can’t really know the thing-in-itself, but I don’t find that a useful idea to attach myself to, even though, technically, it is true.

  358. 358
    kairosfocus says:

    F/N: Walkie Talkie melting car parts and shop front stuff, scorching carpets etc: https://www.bbc.com/news/uk-england-london-23930675 (see egg frying demo: https://www.youtube.com/watch?v=XBPq6B_soAw ) and no, I don’t buy the excuse this was not foreseen. The seasonal motion of the sun in the sky (part of the seasons due to the tilt between our plane of orbit and axis of rotation which precesses) has been well known for thousands of years, as is the concentrating effect of a curved reflecting surface. Vitruvius, in discussing what an Architect should know, speaks to that sort of astronomical knowledge, c what 30 BC? This red flags the quality of regulatory review on the building. KF

  359. 359
    kairosfocus says:

    H, we cannot know completely and perfectly, but as F H Bradley highlighted, the very act of denying any knowledge of actual reality is by implication such a knowledge claim. It refutes itself. I would argue that knowledge of certain key structures and quantities is knowledge of aspects of reality. And BTW, knowledge is yet another abstract entity. KF

  360. 360
    daveS says:

    Bradley shows that one cannot claim that metaphysical knowledge is impossible without contradicting oneself.

    Robert Marks states that we can know that things exist which are unknowable.

    Luckily most of us agree with these two statements.

  361. 361
    kairosfocus says:

    F/N: I updated the OP to include a picture on Walkie-Talkie’s street scorcher problem. KF

  362. 362
    kairosfocus says:

    DS, both are true and are so regardless of who is or is not willing to agree. Marks’ point is a case of known unknowns, the Heisenberg-Einstein uncertainty issues are other known unknowns. A big problem is Rumsfeld’s unknown unknowns. KF

  363. 363
    hazel says:

    kf writes,

    And BTW, knowledge is yet another abstract entity

    Yes, another abstract entity in the minds of human beings.

    I’m pretty sure you don’t get the point I’ve made in 337 and repeated in 355. I don’t mean “agree with it”, I mean “get it.” I don’t deny the abstract entities exist. It is where and how they exist that our differences lie.

  364. 364
    daveS says:

    KF,

    both are true and are so regardless of who is or is not willing to agree.

    Indeed.

  365. 365
    kairosfocus says:

    H, I actually think it is clear that the difference is about the distinct identity, nature and being of entities which we interact with and form concepts about. The mobius strip is a key test, as its behaviour when cut around is radically different if you cut at the middle (1/2 way across) or 1/3 way across. This is strictly independent of our thoughts, concepts, opinions, beliefs, agreement or disagreement, and it directly demonstrates that key aspects of structure and quantity are embedded in the world independent of our thoughts. KF

  366. 366
    hazel says:

    Of course what happens in the world is independent of what we think about it. Who said otherwise? It is the abstractions we make about what happens that I am talking about.

    To quote myself above avove

    It seems clear to me that even though individual objects exist in the physical world, the abstract ideas of quantity, addition, and equality arise in the minds of beings with rational, abstract cognitive abilities such as we have. If the world were just monkeys, 2 + 3 = 5 would not exist as an abstract fact, which is of course different than saying the pebbles wouldn’t be sitting on the rock.

  367. 367
    bornagain77 says:

    as to:

    Of course what happens in the world is independent of what we think about it. Who said otherwise?

    Hazel, did you even read the reference that you yourself gave me the other day?

    More Than One Reality Exists (in Quantum Physics)
    By Mindy Weisberger – March 20, 2019
    Excerpt: “measurement results,, must be understood relative to the observer who performed the measurement”.
    https://www.livescience.com/65029-dueling-reality-photons.html

    Yet Hazel, regardless of how he (Weinberg) and other atheists may prefer the world to behave, and as the present experiment that you yourself referenced further verifies, quantum mechanics itself could care less how atheists prefer the world to behave. As your referenced article itself stated, “measurement results,, must be understood relative to the observer who performed the measurement”.
    https://uncommondescent.com/intelligent-design/viruses-devolve/#comment-674639

  368. 368
    hazel says:

    ba, I was talking about everyday experiences, such as the Mobius strip that kf has now mentioned 27 times.

    I understand that there are other issues when you think about this at the quantum level.

  369. 369
    kairosfocus says:

    H, the structure and quantity manifested in the Mobius strip are demonstrably independent of our concepts and abstractions. Cut it around in the middle vs 1/3 way across and dramatically different results obtain, because of its structural and quantitative properties, which can properly be said to be embedded in space and in the body. Further to this, by contrasting an ordinary cylindrical loop we can readily demonstrate one side in a 3-d object vs two, and one edge vs two. We use terms and form concepts about unity and duality but those concepts reflect a real albeit abstract property. Our thoughts are not controlling or inventing the behaviour, they are responding to the behaviour.In the case of the Mobius strip there is documentation of such a strip in Roman times, though there are no records of certain astonishing properties. Cutting around would likely have been harder to do, though spring shears existed and pivoted scissors seem to have been invented by the Romans c 100 AD, they were also known in the far east. KF

  370. 370
    hazel says:

    28 times.

    And, yes, “Our thoughts are not controlling or inventing the behaviour, they are responding to the behaviour.” Absolutely. The world does what the world does. No arguments there. No one ever said that our thoughts are “controlling or inventing” the world.

  371. 371
    Brother Brian says:

    Hazel

    28 times.

    It reminds me of Dr. Evil saying “magma”.

  372. 372
    kairosfocus says:

    H & BB: I will continue to cite a clear, plumb-line test case as many times as are necessary to finally hammer home the point that the world embeds intelligible structure and quantity, exhibiting numbers, geometric features, topological properties and many other things that we recognise or discover rather than invent or conceive — the mobius strip is utterly different from Conway’s game of life. Further to this, that certain abstract properties reflecting said structure and quantity are part of the nature and distinct identity of entities up to and including all possible worlds. KF

  373. 373
    hazel says:

    But do you acknowledge that I (and probably everyone else involved in his conversation) agree that “our thoughts are not controlling or inventing the behaviour, they are responding to the behaviour.” What happens in the world is independent of our thoughts about it.

    We agree on these two points – true?

  374. 374
    kairosfocus says:

    H,

    I will respond to your proposed points, but think it advisable to first, again, highlight the core point demonstrated empirically in key part by the Mobius strip, a point which you do not directly address just above in suggesting two matters that you think are not in contention:

    the world embeds intelligible structure and quantity, exhibiting numbers, geometric features, topological properties and many other things that we recognise or discover rather than invent or conceive — the mobius strip is utterly different from Conway’s game of life. Further to this, that certain abstract properties reflecting said structure and quantity are part of the nature and distinct identity of entities up to and including all possible worlds.

    The strip behaves differently from a cylindrical loop, because of the half-twist used to create a single-surface, single edged entity. When it is cut around in the middle, it does not separate into two items. When cut around at 1/3 of the way across, it separates into two interlocked loops with different characteristics. These are structurally embedded, quantitative phenomena, embedded in a body and in space. Such phenomena historically contributed to the rise of Topology, a significant branch of Mathematics.

    We here see how our world embeds structural and quantitative, intelligible properties exhibiting mathematical facts — a substance of structure and quantity. These properties express abstracta such as number (of edges, of surfaces) that affect behaviour. The difference between the ways we cut around show further similar embedding. These manifest themselves through the logic of being of the looped strips, by which structural and quantitative characteristics influence behaviour. We explore, recognise or discover, analyse using active logical reasoning, conclude. Here, the substance precedes and constrains the study, as happened historically — we would not accept as valid a framing of mathematics that failed to account for the observed facts.

    So, in that context, it is manifest that “our thoughts are not controlling or inventing the behaviour, they are responding to the behaviour.” So, I would rephrase, “What happens in the world is independent of [–> antecedent to and insofar as it is intelligible, influences] our thoughts about it [which thoughts in many cases may and do accurately describe reality, concrete and abstract.”

    KF

  375. 375
    kairosfocus says:

    PS: Now that ‘net is back, let me point to a more central case, for the record. One, where we can show that key abstract elements of structure and quantity are necessary aspects of the logic of being a distinct possible world.

    Consider a distinct possible world, W which is distinct from near neighbours (say W’, W’) by having some aspect of core characteristics A, unique to itself. Were there no A, the world would be indistinguishable from near neighbours and we would recognise that distinct labels have been attached to the same underlying possible world. Such allows us to view W as a structured set:

    W = {A|~A}

    Now, nothing is in W that is not in A or else ~A, the dichotomy is empty and there is no x in W but not in A or else ~A. This is the quantitative property, nullity; thus zero is present, {} –> 0. Likewise, A is a distinct thing, a unit. Unity is present, so one. Following von Neumann, {0} –> 1, where also A manifests unity. In a different sense, ~A is a complex unity, collecting many other things, pointing to collectives, to systems, to organisation, to function based on organisation etc. For our purposes, ~A is a unit but one different from A, so we need to recognise duality, two-ness, thus two: {0,1} –> 2. Obviously, such succession continues without limit and manifests the naturals, also implying the transfinite ordinals on the premise of order type {0,1,2 . . . } –> w (omega).

    Likewise, we may contemplate an inverse such that -x + x –> 0, which is a vector of one dimension. We now have integers. Ratios of integers gives rise to rationals and convergent sums yield the rest of the reals. This gives us continuum. From this, the vector rotation operator i*x repeated twice to give – x allows us to have 2-d vectors in a continuum, a plane. An abstract plane that we may contemplate but which pervades any possible world. Where such a world is sufficiently spatially extended and actualised, we may observe continua, dimensions, vectors, rotations, trajectories etc.

    So, we see where any possible world, simply on being distinct, manifests directly 0,1,2 and by extension on the logic of being, N, Z, Q, R, C. The vector phenomenon captured from Z on, allows us to extend the abstract continuum to arbitrarily many dimensions. (Notice the distinction between world manifestations and our extension to n-dimensional entities, n arbitrarily high.In physics we speak of 10^22 degrees of freedom routinely, for statistical thermodynamics, just for a reasonably accessible case.)

    Our world manifests three spatial dimensions on the macro scale, and we can observe things like Mobius strips etc.

    The underlying point is, that we see intelligible, abstract, necessary, structural and quantitative entities as part of the fabric of any distinct world, part of its framework, part of the logic of its being as a distinct possible world.

    In that context, we may identify certain facts of structure and quantity that necessarily obtain.

    For instance consider five distinct units and how they may be partitioned into a pair and a triple: ||||| –> || + |||. Obviously, this can be reversed, || + ||| –> |||||. Addition and subtraction have a natural sense of partitioning and combining units. Multiplication and division are extensions as are many onward operations, relations and functions. And so forth.

    The point is, that there are abstract, structural and quantitative entities that are intelligible on logic of being which are necessary corollaries of any distinct possible world. These abstracta, we recognise and observe through the effects of the logic of being, we do not invent. They are not merely concepts and constructs we invent and project to a world of things in themselves. That, being in reality just an inner game on the appearances we have and imagine as reflecting the outer world. No, the Kantian ugly gulch fails and we have no good reason to imagine the behaviour of a Mobius strip is some sort of contemplative inner dream. Such dreams we could modify at will, the logic of being is far less yielding than that.

    So, we need to frame an understanding of Mathematics that recognises that we may study the logic of structure and quantity, but this is not isolated from the intelligible substance of structure and quantity manifest in the world. Yes, our sense of being and of cause needs to adapt to the logic of being that involves necessary albeit abstract entities. For instance, nullity, the empty set, zero are manifest in a myriad circumstances, indeed in any possible, distinct world. But as {} is indistinguishable from {} there is good reason to see that it is one and the same common entity. Which is a characteristic shown by many abstract entities.

  376. 376
    kairosfocus says:

    F/N: Back on focal topic, observe the reaction of London’s residents to skyscraper blight:

    https://www.theguardian.com/uk-news/2016/aug/27/londoners-back-skyscraper-limit-skyline

    Londoners want curbs placed on the number of new high-rise buildings in the capital, amid concerns that a wave of monolithic skyscrapers is transforming the skyline.

    Six out of 10 support a limit on the height of new skyscrapers, with the same proportion backing restrictions on the number of buildings with more than 50 floors.

    The unprecedented survey, by Ipsos Mori, found that many Londoners, particularly those who live in the most affected areas, think the trend towards ever taller, bolder skyscrapers has gone too far. More than 400 buildings of more than 20 floors are in the pipeline in London, according to a recent report by New London Architecture and property consultant GL Hearn, which is twice as many as two years ago.

    The volume of projects in the offing has led to flashpoints as developers meet opposition from local communities. Architect Renzo Piano was forced to withdraw plans for a 72-storey tower in west London, dubbed the Paddington Pole, following outrage from campaigners. The heritage group Historic England recently lodged an objection to a proposed 25-storey tower of luxury flats in Somers Town, north London, citing its effect on views from Regent’s Park.

    Barbara Weiss, architect and co-founder of the pressure group Skyline Campaign, said the glut of skyscrapers was down to a combination of borough councils trying to raise money and the desire by former mayor Boris Johnson to boost London’s international profile.

    “It’s partly austerity because boroughs are strapped for cash and can’t run normal services. They need money; developers provide money,” said Weiss. “On the other side was Boris with crazy ideas about London needing to be put on the map. He was encouraging these excesses and Londoners didn’t know they were happening.”

    In short, harmony with context and harmony in itself are clearly important aesthetics values.

    A linked issue is, why all of that glass?

    https://www.bbc.com/news/magazine-27501938

    One of the best-known glass building mishaps took place last summer, when the Walkie-Talkie at 20 Fenchurch Street in London was accused of melting cars. The 37-storey building reflected light in its glass facade and shone powerful rays at its surroundings. Cars parked underneath were damaged, and passers-by even managed to fry eggs using only sunlight.

    In the end the developers, Land Securities, had to apply for planning permission to obscure architect Rafael Vinoly’s £200m design with a permanent “brise soleil” or sunshade.

    And yet despite this, Land Securities recently revealed that the widely reported calamity “did nothing to deter lettings”.

    Glass buildings are popular – not just because of their striking appearance but for the views they boast, and the increased light they let in.

    When German architect Ludwig Mies Van Der Rohe designed what is said to be the world’s first glass skyscraper in 1921, he associated the glass facade with purity and renewal. Later in the century, British architect Richard Rogers praised glass buildings because of their social worth. Glass walls enabled even employees working in the basement to benefit from reflected natural light and dissolved barriers between a cramped indoor office space and the greenery outside.

    Companies like to give the impression of a democratic working environment – open-plan and with floor-to-ceiling windows, so that all employees, not just the boss, benefit from the view.

    However, as concerns over global warming have become more widespread, so the glass structure has come under scrutiny.

    Since leaving Foster and Partners in 2006, Shuttleworth has become a key voice in the fight against glass. Despite his background working on giant glazed buildings, he has founded an architectural practice in which floor-to-ceiling windows are considered an archaic luxury.

    “Everything I’ve done for the last 40 years I’m rethinking now,” he says. “If you were designing [the Gherkin] today… it wouldn’t be the same product all the way around the building.

    “We need to be much more responsible in terms of the way we shade our buildings and the way we thermally think about our buildings.”

    Glass and steel are of course symbols of modernity, and will draw the avant garde. Yes, green issues are now on the table, raising ultimately ethical questions. But there is also an aesthetical one: fairly smooth reflective surfaces are similar enough to calm water surfaces to evoke a sense of tranquility, faceted reflecting surfaces are jewel-like and also from the days of grand cathedral windows with stained glass have contributed to atmosphere.

    So, glass may make more acceptable what would seem particularly ugly, hulking, brutally imposing otherwise.

    We are back to balance and moderation.

    KF

  377. 377
    hazel says:

    kf writes,

    What happens in the world is independent of [–> antecedent to and insofar as it is intelligible, influences] our thoughts about it [which thoughts in many cases may and do accurately describe reality, concrete and abstract.”

    I’ll agree that the world is antecedent to our thoughts: we experience the world and then form thoughts about.

    I’ll agree that “insofar as it is intelligible, [the world] influences our thoughts about it, which thoughts in many cases may and do accurately describe reality, concrete and abstract

  378. 378
    kairosfocus says:

    H, that apparent rejection of the reality of certain abstracta, if so, is fatally self-referential for much the same reason as nominalism (which is a form of such rejection) fails. KF

  379. 379
    hazel says:

    I’ve explained my position, and see nothing “fatally self-referential” in it. The world is intelligible, and we are intelligent, so our understandings provide reasonably accurate maps of the world. We use abstractions to describe the world, but the world itself is “concrete” in the sense that it is its behavior which we observe that is the source of the material for our abstractions.

    Probably no need for you (or me) to repeat ourselves again (although I do have a new thought on the matter that I may share later in the day when I have some time.)

  380. 380
    kairosfocus says:

    H, when an objective matter is on the table, agreement or disagreement is immaterial. Just to make statements you have had to repeatedly rely on abstracta being the case not just perceptions. Indeed, truth is an abstract relationship of statements to what is the case, belief or disbelief, agreement or disagreement too. The reality of core abstracta is inescapable. KF

  381. 381
    hazel says:

    kf, I have clearly said that we use abstractions – we have to – just to talk about the world, so of course I agree with you when you write, “Just to make statements you have had to repeatedly rely on abstracta being the case not just perceptions.” Perceptions of the world bring in the data from which we create our abstractions, but abstractions are a necessary, central aspect of our ability, as rational, logical creatures, to understand the world.

    Is this the point upon which you think my position is “fatally self-referential”?, because if so it misrepresents me. Perhaps you could explain more about your “fatally self-referential” statement.

  382. 382
    kairosfocus says:

    H, this begins to approach the inescapability of the laws of thought, which embed cases in point. To attempt to deny one is forced to accept implicitly. For instance, you are affirming or implying that somethings are true, are accurate descriptions of reality, which is itself an abstract relationship, indeed the words and what they represent involve abstract relations. That is telling us something — we are at a start-point. KF

  383. 383
    hazel says:

    Yes, I have continually said that we use abstract concepts to make statement about reality that are, to various degrees, accurate descriptions.

  384. 384
    daveS says:

    KF and hazel,

    What do you think of this statement:

    “If there is a greatest perfect number x, then x is at least 191561942608236107294793378084303638130997321548169216.”

    This statement is no doubt true, yet it might be the case that there is no greatest perfect number. In that case, this is a true statement about a nonexistent entity.

  385. 385
    kairosfocus says:

    DS, a hypothetical. If false then implication loses ability to discriminate truth from falsity. Here, all you are saying is there is a large perfect number and if there is a biggest it will exceed such. This does not require or entail that there is such a greatest number. KF

  386. 386
    kairosfocus says:

    H, we cannot escape core abstracta and they are inescapably true or real as appropriate. KF

  387. 387
    daveS says:

    This does not require or entail that there is such a greatest number.

    Obviously not.

    It does show that we can make true statements about entities that might not (or do not) exist.

  388. 388
    kairosfocus says:

    DS, yes we can draw out a valid implication that may lead to a true consequent on a hypothesis that is or may be false. That is how modelling works. However, as the principle of explosion obtains on such a case, we must be particularly careful to validate and calibrate as such hypotheses are inherently unreliable. This is also the root of the pessimistic induction regarding scientific theories. You will note that I have emphasised empirical reliability and have pointed out that such theories do not amount to even moral certainty. Empirical reliability in a validated domain does, but that is because it is a tested observation backed by the uniformity principle. Disproof by contradiction also works on consequences of a hypothesis, and is used in Mathematics to establish the denial of what reduces to absurdity. KF

  389. 389
    hazel says:

    kf writes “that apparent rejection of the reality of certain abstracta, if so, is fatally self-referential.” I accept the reality of the abstract concepts we create that describe the reality we experience. How is that “fatally self-referential”? I don’t see how you have explained that.

  390. 390
    kairosfocus says:

    H, Let’s roll the tape a bit:

    H, 377: >>kf writes,

    What happens in the world is independent of [–> antecedent to and insofar as it is intelligible, influences] our thoughts about it [which thoughts in many cases may and do accurately describe reality, concrete and abstract.”

    I’ll agree that the world is antecedent to our thoughts: we experience the world and then form thoughts about.

    I’ll agree that “insofar as it is intelligible, [the world] influences our thoughts about it, which thoughts in many cases may and do accurately describe reality, concrete and abstract”>>

    KF, 378: >>H, that apparent rejection of the reality of certain abstracta, if so, is fatally self-referential for much the same reason as nominalism (which is a form of such rejection) fails.>>

    H, 379: >>I’ve explained my position, and see nothing “fatally self-referential” in it. The world is intelligible, and we are intelligent, so our understandings provide reasonably accurate maps of the world. We use abstractions to describe the world, but the world itself is “concrete” in the sense that it is its behavior which we observe that is the source of the material for our abstractions.

    Probably no need for you (or me) to repeat ourselves again (although I do have a new thought on the matter that I may share later in the day when I have some time.)>>

    KF, 380: >>when an objective matter is on the table, agreement or disagreement is immaterial. Just to make statements you have had to repeatedly rely on abstracta being the case not just perceptions. Indeed, truth is an abstract relationship of statements to what is the case, belief or disbelief, agreement or disagreement too. The reality of core abstracta is inescapable.>>

    H, 381: >> I have clearly said that we use abstractions – we have to – just to talk about the world, so of course I agree with you when you write, “Just to make statements you have had to repeatedly rely on abstracta being the case not just perceptions.” Perceptions of the world bring in the data from which we create our abstractions, but abstractions are a necessary, central aspect of our ability, as rational, logical creatures, to understand the world.

    Is this the point upon which you think my position is “fatally self-referential”?, because if so it misrepresents me. Perhaps you could explain more about your “fatally self-referential” statement.>>

    KF, 382: >>this begins to approach the inescapability of the laws of thought, which embed cases in point. To attempt to deny one is forced to accept implicitly. For instance, you are affirming or implying that somethings are true, are accurate descriptions of reality, which is itself an abstract relationship, indeed the words and what they represent involve abstract relations. That is telling us something — we are at a start-point.>>

    H, 383: >>Yes, I have continually said that we use abstract concepts to make statement about reality that are, to various degrees, accurate descriptions.>>

    KF, 386: >>we cannot escape core abstracta and they are inescapably true or real as appropriate.>>

    H, 389: >>kf writes “that apparent rejection of the reality of certain abstracta, if so, is fatally self-referential.” I accept the reality of the abstract concepts we create that describe the reality we experience. How is that “fatally self-referential”? I don’t see how you have explained that.>>

    Notice, how you repeatedly affirm certain things to be true, i.e. to actually accurately describe real states of affairs? That is itself an abstract relationship, which must be real albeit abstract or discussion collapses. Likewise, the Mobius strip’s behaviour pivots on how it has ONE edge, ONE surface, etc. So if by cutting we introduce one or two further edges, it will form a longer loop or two interlocked loops. One-ness, two-ness, three-ness and consequences on the logic of being are abstract but take effect in space and bodies. It does so independent of our thoughts, concepts, expectations, as the relevant abstract properties are part of its core characteristics.

    Above, at 375, I again laid out a demonstration as to why numbers are necessary entities that will manifest in any possible world, antecedent to our thoughts about a world. We are contingent beings within an already formed world.

    Going back to the self-reference, to assert that in effect conceptualism about abstracta is true, one relies on abstracta being in reality, e.g. here that a description or assertion can hold a relationship of accurate description with things as they are. Absent the reality of such a relationship independent of our individual or collective concepts, truth is meaningless. If only the concrete exists in reality, truth, an abstract relationship using symbolic representation (other abstracta!) is a case of non-being, illusion. Actually, illusion is another abstract relationship. Meaninglessness is next up, but this too is an abstract state of affairs. The infinite regress of abstracta begging to be acknowledged as real yawns open.

    The reality of core abstracta is inescapably the case, i.e. it is necessarily true on pain of not being able to think, communicate conceptually, reason [implication is abstract], speak truth, demonstrate, warrant, know etc.

    The serious issue then follows: in what way are such things real?

    The best I can answer for now is that such abstracta are connected to the logic of being for worlds or things in the world. They are logically relevant characteristics of being, which in many cases are shared across beings as archetypes that are in-common, or even are in-common across possible worlds. In some cases such as numbers they are in common to all possible worlds as part of the fabric of any distinct possible world.

    We may recognise or discover them and try to identify what they precisely are, but in many cases they defy particular definition in words.

    Where do they come from, where are they? They come from the logic of being and are embedded as constraints on being. For instance, no entity E is such that it has two core characteristics x and y where y = ~x.

    That is why square circles are impossible of being. Regardless of how we may form a fuzzy imagination that oscillates between the shapes or may try to superpose and blend the two.

    Thus, abstracta are part of the distinct identity, nature and being of any particular entity. That is, the principle of distinct identity has ontological, not just conceptual, significance. That’s why we recognise it as a first principle of right reason.

    So, not a spooky, mysterious, metaphysical world of forms, just the architecture of — rational principles or “logic” of — being or possible being (and of impossibility of being). Where of course a considerable part of that embedded architecture of being is structural and quantitative. That is, Mathematical. Mathematics has in key part ontological import. Hence, Wigner’s point on its astonishing power. The music of the spheres is written in the language of mathematics, with — I daresay — Fourier leading the charge.

    Speaking of architecture, that does point to architect. But that is an onward discussion tied to the necessary being root of reality.

    KF

  391. 391
  392. 392
    hazel says:

    kf, I understand your position. However, I see nothing where you actually try to explain why my position is “fatally self-referential”.

    at 379, I wrote,

    I’ve explained my position, and see nothing “fatally self-referential” in it. The world is intelligible, and we are intelligent, so our understandings provide reasonably accurate maps of the world. We use abstractions to describe the world, but the world itself is “concrete” in the sense that it is its behavior which we observe that is the source of the material for our abstractions.

    I accept that we have a difference philosophical position, and I appreciate the way you have distinguished your view from a Platonic one, “a spooky, mysterious, metaphysical world of forms”, but rather “the architecture of — rational principles or “logic” of — being.” That’s a ood distinction.
    This paragraph might illuminate the difference:

    Going back to the self-reference, to assert that in effect conceptualism about abstracta is true, one relies on abstracta being in reality, e.g. here that a description or assertion can hold a relationship of accurate description with things as they are. Absent the reality of such a relationship independent of our individual or collective concepts, truth is meaningless.

    Perhaps the issue here is truth. Perhaps this is an accurate paraphrase of your view: that if there is to be true truth about the world, the abstract concepts in our minds must have a valid and complete relationship with corresponding abstractions in the world. To me, however, truth is always provisional and partial, because the abstractions only exist in our minds, and can never correspond to reality completely. Even if our abstractions seem to correspond exactly, that is only because they are abstractions which leave out the huge multiplicity of details which are not being abstracted.

    So perhaps you think my position is “fatally self-referential” because it can’t lead to Truth, with a capital T, and if so, I stand guilty as charged. However, I don’t see that as “fatal”: I see it as realistic about the nature of human knowledge.

  393. 393
    kairosfocus says:

    H, I have taken up the matter in a new thread, this is now long and problematic with loading etc, also, it has a natural focus that is something else. I will answer you there in a bit, RW lurks. KF

  394. 394
    hazel says:

    Your new post is way too long, and repeats all sorts of issues, too many of them, which aren’t at the heart of the present state of the discussion, so I replied here. If the size of this thread is a problem (it’s not for me but I have good internet access on a good computer), then just the last part of your 390, starting with “Notice …” and my reply at 392, would carry the discussion forward. I don’t intend to reply to your new post: we have reached some focus and perhaps clarity here, and your new post is quite a few steps backwards in that regard, I think.

  395. 395
    kairosfocus says:

    I responded in the new thread, where this matter is focal. KF

  396. 396
    kairosfocus says:

    F/N: An interesting read:

    https://clinicalarchitecture.com/three-principles-of-good-architecture/

    >>The Roman architect Vitruvius in his treatise on architecture, De Architectura, asserted that there were three principles of good architecture:

    Firmatis (Durability) – It should stand up robustly and remain in good condition.
    Utilitas (Utility) – It should be useful and function well for the people using it.
    Venustatis (Beauty) – It should delight people and raise their spirits.

    The question on the table is: do these principles, meant to apply to physical architecture, apply to system architecture and more specifically clinical architecture? . . . . Most technologists can easily believe that the first two principles are our responsibility and the third is optional. I would argue that the third principle, venustatis, is at as important as the first two.

    Why is Beauty important?

    Let’s go back to Vitruvius and the translation of the first two paragraphs in book one of De Architectura titled “On the training of Architects”:

    “The science of the architect depends upon many disciplines and various apprenticeships which are carried out in other arts. His personal service consists in craftsmanship and technology. Craftsmanship is continued and familiar practice, which is carried out by the hands in such material as is necessary for the purpose of a design. Technology sets forth and explains things wrought in accordance with technical skill and method

    So architects who without culture, aim at manual skill cannot gain a prestige corresponding to their labors, while those who trust to theory and literature obviously follow a shadow and not a reality. But those who have mastered both, like men equipped in full armor, soon acquire influence and attain their purpose”

    What Vitruvius is saying is that architecture is about craftsmanship and technology. Also, in the second paragraph, if you interpret culture as an appreciation for the sensibilities and behaviors of your target audience this, drives directly to the point I am going to make.

    The difference between a good application architect and a great application architect is the ability to craft an elegant solution in a way so as to delight the user. >>

    Food for thought.

    KF

  397. 397
    kairosfocus says:

    F/N2: Wiki summarises Hogarth’s Principles of beauty:

    >>In The Analysis of Beauty Hogarth implements six principles that independently affect beauty. Although he concurs that those principles have an effect, he is not determinate on their specific influence. The first principle of beauty Hogarth describes is fitness, which is not in itself a source of beauty, but can be described as a material cause of it. Though the account of fitness on the total beauty of an object is only moderate, it is a necessary cause. Fitness does not necessarily imply purpose. However, improperly implied forms cannot be the source of beauty. It is in this that the necessity of fitness must be seen: if not accounted for, a form cannot readily be assumed beautiful.

    The second major principle of beauty is variety. It is the source of beauty, which Hogarth shows us by the contrary notion of “sameness”: “sameness”, a lack of variety, offends the senses. “The ear is as much offended with one even continued note, as the eye is with being fix’d to a point, or to the view of a dead wall.”[3] In contrast, our senses find relief in discovering a certain amount of “sameness” within a varietal experience.

    The third notion of regularity is understood as a form of “composed variety”: it only pleases us when it is suggestive to fitness. Similar to this notion in effect is simplicity, which enhances the pleasure of variety in that it pleases the eye. The variety which causes a beautiful experience should, so to speak, be tempered by simplicity. On the other hand: simplicity without variety at best does only not displease.

    Intricacy is a strange principle in that it does not directly follow from the formal behaviour of a beautiful object. Hogarth means by this the habit which causes us to end up in the whirling game of pursuit, when bit by bit discovering the beauty of an object. Intricacy arises from the love of this pursuit. Every difficulty in understanding or grasping the object enhances the pleasure of overcoming it, to continue the pursuit. There is a direct connection here to the Line of Beauty Hogarth dictates, along which every image is built up. Though the movement of our eye is discrete in itself, the movement of our “Mind’s eye” follows a duplicate course of the line, a principal ray of light moving along with the line of sight. The continuous movement of our “Mind’s eye” triggers the notion of intricacy.

    Quantity, finally, is associated with the notion of the sublime, which, when Hogarth’s book appeared, was not yet entirely distinguished from the apprehension of beauty. Hogarth thus does not speak of sublimity, but of greatness. He recognises a great quantity to have an aesthetic effect on the beholder without the necessity of a varietal or fitting form. This should not be exaggerated, as that might lead to absurdities. >>

    More food for thought.

    I should note, he champions the serpentine, S-shaped curve as a dynamic element in beauty. I see it as two J-curves joined, and that J curves are part spirals, which have extraordinary focal power. I think that is because the progressive curve draws the eye in a literally hypnotic effect.

    Further food for thought.

    KF

  398. 398
    kairosfocus says:

    F/N3: A very good discussion with diagrams is here:

    http://learn.leighcotnoir.com/artspeak/principles/

    I clip: >>Principles of Art
    Next, the “Principles of Design”

    The “principles of design” are mechanisms of arrangement and organization for the various elements of design in artwork. Please note that different sources might list slightly different versions of the “Principles of Design,” but the core fundamentals are essentially the same.

    Harmony
    Balance
    Proportion
    Dominance/Emphasis
    Variety
    Movement
    Rhythm

    Harmony

    Harmony in art and design is the visually satisfying effect of combining similar, related elements. For instance: adjacent colors on the color wheel, similar shapes etc.
    harmony
    Harmony

    Balance

    A feeling of equality in weight, attention, or attraction of the various visual elements within the pictorial field as a means of accomplishing organic unity.

    There are a few types of balance:

    Symmetry: A form of balance achieved by the use of identical balance compositional units on either side of a vertical axis within the picture plane.
    Approximate Symmetry: A form of balance achieved by the use of similarly balanced compositional units on either side of a vertical axis within the picture plane.
    Radial Symmetry: A form of balance than is even, radiating out from a central points to all four quadrants of the shape’s constraining plane.
    Asymmetry: A form of balance attained when the visual units on balance either side of a vertical axis are not identical but are placed in positions within the picture plane so as to create a “felt” equilibrium of the total form concept.

    symmetry
    Horizontal Symmetry
    Approximate Symmetry
    Approximate Symmetry
    Radial Symmetry
    Radial Symmetry
    Asymmetry
    Asymmetry

    Proportion

    Proportion is the comparison of dimensions or distribution of forms. It is the relationship in scale between one element and another, or between a whole object and one of its parts. Differing proportions within a composition can relate to different kinds of balance or symmetry, and can help establish visual weight and depth.
    Proportion
    Proportion (ratio)
    Proportion (scale)
    Proportion (scale)

    Dominance/Emphasis

    The principle of visual organization that suggests that certain elements should assume more importance than others in the same composition. It contributes to organic unity by emphasizing the fact that there is one main feature and that other elements are subordinate to it. In the below examples, notice how the smaller elements seem to recede into the background while the larger elements come to the front. Pay attention to both scale and value of the objects that recede and advance.
    Dominance
    Dominance / Emphasis

    Variety

    Variety is the complement to unity and harmony, and is needed to create visual interest. Without unity and harmony, an image is chaotic and “unreadable;” without variety it is dull and uninteresting. Good design is achieved through the balance of unity and variety; the elements need to be alike enough so we perceive them as belonging together and different enough to be interesting.
    Variety
    Variety

    Movement

    Movement is the path our eyes follow when we look at a work of art, and it is generally very important to keep a viewer’s eyes engaged in the work. Without movement, artwork becomes stagnant. A few good strategies to evoke a sense of movement (among many others) are using diagonal lines, placing shapes so that the extend beyond the boundaries of the picture plane, and using changing values.
    Movement
    Movement

    Rhythm

    A continuance, a flow, or a feeling of movement achieved by the repetition of regulated visual information.>>

    KF

  399. 399
    kairosfocus says:

    F/N4: Parker on Principles of Aesthetics:

    http://www.authorama.com/princ.....ics-9.html

    >>As we appreciate it to-day, music lends itself readily to our definition of art. It is a personal expression–who, when listening to music which he enjoys, does not feel himself poured forth in the tones? It is social and public–what brings us together under the sway of a common emotion more effectively than concert or opera? It is a fixed and permanent expression, for we can renew it so long as men preserve the score where it is written; and, finally, it is free–who can find any practical or moral or scientific purpose in an etude of Chopin or a symphony of Mozart? Music is the most signal example of a mode of expression that has attained to a complete and pure aesthetic character, an unmixed beauty. Yet this was not true of music in its earlier forms, and a long process of development was necessary before freedom was realized. For we must look for the beginning of music in any and all sounds through which primitive men sought to express and communicate themselves. These were, first of all, the cries of the human voice, expressive of fear and need and joy–at once direct outpourings of basic emotions and signals to one’s fellows, to help, to satisfy, and to sympathize. In the voice nature provided man with a direct and immediate instrument for the expression and communication of himself through sound. Then, perhaps by accident, man discovered that he could make sounds in other ways, through materials separate from his body, and so he constructed drums and cymbals and gongs; and by means of these, too, he communicated his needs and stimulated himself to rage and excitement–and his enemy to fear–in war dance and battle rush. And in doing this he was imitating nature, whose noises, exciting and terrifying, he had long known: the clap of thunder, the whistle of the wind, the roar of the waves, the crackling of burning wood, the crash of fallen and breaking things.

    Out of unbeautiful noise sprang beautiful music. Men discovered that through the voice they could make not only expressive noises, but also pleasant tones; they found, perhaps by accident, that they could do much the same thing with reeds and strings; they observed that when they beat their drums at regular intervals to mark the motion of the dance, they not only danced together more easily, but also experienced joy in the very sounds they made; or that when they threshed the corn with rhythmic strokes or rowed a boat in rhythmic unison, their task was lightened and their wearied attention distracted to the pleasure of their noise. Hence at their dances of love or war or religion, they sang instead of shouted; and their instruments of irregular and expressive noise became instruments of rhythmical and melodious tones. Eventually, having experienced the pleasure there is in tones and rhythmical sounds, they made them for their own sake, apart from any connection with tribal festivals, and the free art of music was born. And yet, as we shall see, the significance of music depends largely upon the fact that tones are akin to noises; music could not take such a hold of the emotions of men did they not overhear in the tones the meaningful and poignant noises of voice and nature; to understand music, we must think of it against its background of expressive noise. In music we still seem to hear a voice that breaks the silence and speaks, the thunder that terrifies.

    The material of music consists of tones, the conscious counterparts of periodic, longitudinal vibrations of the air. Tones differ among themselves in many attributes, of which the following are of chief importance for music: pitch, determined by rate of vibration, through which tones differ as higher and lower; color, determined by the complexity of the vibration wave, the presence of overtones of different pitch along with the fundamental tone in the total sound; intensity, dependent upon the amplitude of the vibration, through which tones of the same pitch differ as soft or loud; and finally, quality, that specific character of a tone, by reason of which middle C, for example, is more like the C of the octave below or above than like its nearer neighbors, B or D, whence the series of tones, although in pitch linear and one-dimensional, is in quality periodic, returning again and again upon itself, as we go up or down the scale. [Footnote: “See Geza Revesz: Tonpsychologie.”]

    The number of qualities in use in music–twelve in our scale of equal temperament–is, of course, not all there are in the world of tones; they are a human and arbitrary selection, governed by technical and historical motives, into which we shall not enter. Peoples with a different culture have made a different selection. But we are not concerned with the music of angels or of orientals, but with our own. With these twelve, with their possible variations in pitch, loudness, and tone-color, the musician has a rich and adequate material.

    All the elements of an aesthetic experience are present in striking simplicity even in the single musical tone. There is the sensuous medium, the sound; there is a life expressed, a feeling aroused in us, yet so completely objectified in the sound that it seems to belong to the latter on equal terms with color or quality or loudness; there is a unity and variety and orderly structure in the dominance of the fundamental among the overtones and the fusion of all in the total clang. Thus every note is a complete little aesthetic organism. Yet the beauty of single tones is very slight,–less, I think, than that of single colors; they need the contrast or the agreement in consonance with other tones in order to awaken much feeling; they must be members of a wider whole; observe how, when sounded after other tones, they become enriched through the contrasting or consonant memory of those tones. Nevertheless, the single tone has its feeling, however slight, and to understand this is to go a long way toward understanding the more complex structures of music.

    In the first place, tones, unlike noises, are all pleasant. Although we cannot be sure why this is true, there can be little doubt, I think, that the regularity of the vibrations of the former, in contrast with the irregularity of the latter, is largely responsible. The clang, with its ordered complexity, is a stimulus that incites the sense organ and connected motor tracts to a unified and definite response, unlike noise, which creates confusion. The pleasure in the single tone is similar, in its causes, to the pleasure in the consonance of two tones. As we should expect from this analogy, the pleasure is greater in rich tones, which contain many partials, than in thin tones, which are relatively uninteresting. But the feeling of tones is something more than mere pleasantness; it is also a mood. Now this mood of tones is partly due to associations,–some superficial in character, like the pastoral quality of flute tones or the martial character of bugle tones, others more fundamental; but it has also a still deeper-lying root. For a sound stimulus awakens not only a sensory process in the ear, the correlative of which is a sensation, but also incipient motor reactions, which, if carried out, would be an emotion, but which, being too slight and diffuse, produce only what we call a mood. Every sensation has a meaning for the organism in an environment where it has constantly to be on its guard for danger or assistance; every sensation is therefore connected with the mechanism of reaction, with its attendant emotions. In ordinary experience, there are objects present to which the organism may actually respond, but in the aesthetic experience there are no real objects towards which a significant reaction can take place; in music, the source of the sound is obviously of no practical importance, while in such arts as painting and sculpture where interesting objects are represented, the objects themselves are absent; hence the reaction is never carried out, but remains incipient, a vague feeling which, finding no object upon which it may work itself off, is suffused upon the sensation. These sense feelings are the subtle, but basal, material of all beauty.>>

    KF

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