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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:

Comments
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?math guy
March 15, 2019
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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."math guy
March 15, 2019
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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.jpgBrother Brian
March 15, 2019
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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. KFkairosfocus
March 15, 2019
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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.Brother Brian
March 15, 2019
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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.hazel
March 15, 2019
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H, your agreement or disagreement is immaterial. The empirical evidence you yourself saw is sufficient to make the point. KFkairosfocus
March 15, 2019
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BB, kindly look at the collection of eyesores. The Eiffel Tower adheres to principles of aesthetics, what we see above does not. KFkairosfocus
March 15, 2019
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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.hazel
March 15, 2019
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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.Brother Brian
March 15, 2019
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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. KFkairosfocus
March 15, 2019
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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.) KFkairosfocus
March 15, 2019
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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.Brother Brian
March 15, 2019
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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. KFkairosfocus
March 15, 2019
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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=gEp7yunwVF8Brother Brian
March 15, 2019
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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.daveS
March 15, 2019
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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!!!hazel
March 15, 2019
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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. KFkairosfocus
March 15, 2019
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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.hazel
March 15, 2019
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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. KFkairosfocus
March 15, 2019
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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.hazel
March 15, 2019
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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. KFkairosfocus
March 15, 2019
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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.daveS
March 15, 2019
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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.daveS
March 15, 2019
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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. KFkairosfocus
March 15, 2019
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H, have you done the Mobius strip exercise yet? What are your findings, why? KFkairosfocus
March 15, 2019
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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.kairosfocus
March 15, 2019
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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.hazel
March 14, 2019
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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.daveS
March 14, 2019
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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?
kairosfocus
March 14, 2019
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