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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
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. KFkairosfocus
March 22, 2019
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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.math guy
March 21, 2019
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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.hazel
March 21, 2019
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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.daveS
March 21, 2019
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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. KFkairosfocus
March 21, 2019
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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?daveS
March 21, 2019
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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).kairosfocus
March 21, 2019
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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.daveS
March 21, 2019
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DS, digital counter technology is very old stuff now. KFkairosfocus
March 21, 2019
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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.
daveS
March 21, 2019
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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. KFkairosfocus
March 21, 2019
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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.hazel
March 21, 2019
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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.daveS
March 21, 2019
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H & DS, what is a number? Would you expect a monkey to understand the concept, much less be able to use it? Why? KFkairosfocus
March 21, 2019
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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.ET
March 21, 2019
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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. KFkairosfocus
March 21, 2019
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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.daveS
March 21, 2019
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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?"hazel
March 21, 2019
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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?ET
March 21, 2019
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These are jokes, ET.daveS
March 21, 2019
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How is that proof of anything beyond a primate looking at its fingers?ET
March 21, 2019
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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.hazel
March 21, 2019
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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.daveS
March 21, 2019
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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?hazel
March 21, 2019
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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. KFkairosfocus
March 20, 2019
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H, kindly note the just above to BB, especially the PS. KF PS: I sometimes think family resemblance operates like multiple overlapping fuzzy sets.kairosfocus
March 20, 2019
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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 . . .
kairosfocus
March 20, 2019
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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.math guy
March 20, 2019
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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.Brother Brian
March 20, 2019
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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!hazel
March 20, 2019
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