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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
F/N4: Parker on Principles of Aesthetics: http://www.authorama.com/principles-of-aesthetics-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.>> KFkairosfocus
March 25, 2019
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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.>> KFkairosfocus
March 25, 2019
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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. KFkairosfocus
March 25, 2019
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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. KFkairosfocus
March 25, 2019
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I responded in the new thread, where this matter is focal. KFkairosfocus
March 25, 2019
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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.hazel
March 25, 2019
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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. KFkairosfocus
March 25, 2019
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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.hazel
March 25, 2019
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I have headlined 390: https://uncommondescent.com/philosophy/logic-and-first-principles-15-on-the-architecture-of-being-or-are-certain-abstract-entities-abstracta-such-as-numbers-natures-truth-etc-real-if-so-how-and-where/kairosfocus
March 25, 2019
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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. KFkairosfocus
March 25, 2019
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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.hazel
March 24, 2019
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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. KFkairosfocus
March 24, 2019
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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.daveS
March 24, 2019
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H, we cannot escape core abstracta and they are inescapably true or real as appropriate. KFkairosfocus
March 24, 2019
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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. KFkairosfocus
March 24, 2019
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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.daveS
March 24, 2019
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Yes, I have continually said that we use abstract concepts to make statement about reality that are, to various degrees, accurate descriptions.hazel
March 24, 2019
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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. KFkairosfocus
March 24, 2019
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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.hazel
March 24, 2019
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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. KFkairosfocus
March 24, 2019
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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.)hazel
March 24, 2019
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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. KFkairosfocus
March 24, 2019
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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 abstracthazel
March 24, 2019
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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. KFkairosfocus
March 24, 2019
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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.kairosfocus
March 24, 2019
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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." KFkairosfocus
March 24, 2019
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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?hazel
March 23, 2019
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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. KFkairosfocus
March 23, 2019
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Hazel
28 times.
It reminds me of Dr. Evil saying “magma”.Brother Brian
March 23, 2019
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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.hazel
March 23, 2019
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