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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
H & DS, Near as I understand, Conway's game of life creates an abstract space of possible states based on how it can be played. much like chess or draughts etc. Are those possibilities actually possible? I would think so; we thus have a case of an abstract, logic model world we can conceive of and represent. So, the possibility space is a map of realities that could be instantiated. The possibilities are obviously abstract but are real possibilities and we may speak truthfully (or make errors regarding) them. If you want to call that a platonic world, fine. Just be clear of what is being represented there: contingencies not necessary entities that are part of the framework for any possible world to be instantiated. KFkairosfocus
March 19, 2019
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BB, nowadays, some toss around phrases such as "human exceptionalism" without fully realising their potentially ruinous import. A simple form is, "a rat is a pig is a boy." This sort of thinking is part of the in-progress decay of our civilisation. KFkairosfocus
March 19, 2019
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Seeing that aesthetics is a branch of philosophy that deals with the nature of art, beauty and taste and with the creation or appreciation of beauty, I can say with all confidence that monkeys do not have a version of it. That doesn't mean they cannot find something pleasing. Some(?) birds of paradise sure do put on a display. And I don't buy the "instinct" get out of jail free card. Animals aren't the rubes we try to make them out to be.ET
March 19, 2019
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KF
BB, that is the nature of the aesthetic (as opposed to the merely pleasurable). A relevant saying goes, better a Socrates unhappy than a pig supremely happy. Socrates, he of “the unexamined life is not worth living.” KF
There is no consensus about what aesthetics and beauty are ( objective vs subjective), concluding that a monkey cannot have their own version of aesthetics and beauty simply is not warranted. At best, all we can say is, we don't know.Brother Brian
March 19, 2019
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ET, there is a difference between advancing stepwise on a potentially transfinite and actualising same stepwise. The latter is a supertask that cannot be achieved. The former simply indicates onward progress without finite limit. KF PS: BTW, that is part of why I reject the notion of an actually traversed transfinite past of finite, causally connected stages.kairosfocus
March 19, 2019
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Right and we can take the journey right along with it. There isn't anywhere it can't go that we couldn't go with it. That is if we are right and death does not mean the end.ET
March 19, 2019
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ET, the point is that no particular number of decimal places, say k, will be next to transfinite such that k + 1 --> omega. For the kth place of sqrt2 there is a k+1th, k+2th etc, and the pot of gold at the end of the rainbow forever recedes. KFkairosfocus
March 19, 2019
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BB, that is the nature of the aesthetic (as opposed to the merely pleasurable). A relevant saying goes, better a Socrates unhappy than a pig supremely happy. Socrates, he of "the unexamined life is not worth living." KFkairosfocus
March 19, 2019
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Ahh, but is the human mind really finite? Or is that just an arbitrary limitation we place on it?ET
March 19, 2019
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ET, it is not complete in any finite number of places. KFkairosfocus
March 19, 2019
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When other organisms start classifying life I will gladly let go of my human exceptionalismET
March 19, 2019
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KF
BB, I have already pointed out from when it was first raised, the cognitive gap problem and its key index, abstract verbal language. As it was brought back up as though un-answered, I again pointed this out. Enough has been said for record: absent cognitive ability to handle high order abstracta (for which abstract verbal language is a key index) there is no basis for aesthetic reflection and conceptualisation. Monkeys simply do not have that capability, which is why they have not developed a civilisation. KF
Your entire argument is based on the assumption that high order abstract thinking is required to appreciate aesthetic beauty, an assumption that has not been proven. And, frankly, can never be proven. As EG mentioned at 23, this assumption is based on our egocentric concept of human exceptionalism.Brother Brian
March 19, 2019
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hazel:
MG, I hope you respond to 256 about what it means for math to exist Platonically.
What does that mean? That math exists regardless of us?ET
March 19, 2019
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ET,
Why not?
That's a good question. MG and KF appear to believe this, so I'm just going along with this assumption for the sake of argument. I'm not 100% committed to it.daveS
March 19, 2019
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daves:
Further, the complete decimal expansion of the square root of 2 cannot reside in a human mind.
Why not?ET
March 19, 2019
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At 247, MG wrote, “This appears to be an issue for abstract objects that require a mind to live in because the truth or falsity of the conjecture (or septillionth decimal digit of pi) appear to be independent of any mind.” The truth or falsity is independent of whether any mind, using the symbol system with which we express such things, has actually instantiated that truth or falsity. The truth is there, embedded as a logical consequence of the system, waiting, so to speak, for a mind to bring it to expression, if we chose and are able to describe the necessary logical steps. MG, I hope you respond to 256 about what it means for math to exist Platonically.hazel
March 19, 2019
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nm, misread post.daveS
March 19, 2019
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P.S to 246: There I mentioned the "area of a triangle with sides of 2345, 78,890, and 620*pi." I just made up some numbers quickly, but actually those three numbers don't make a possible triangle because all three combinations of a + b > c aren't true. I'll amend the numbers to 2345, 7889, and 2000*pi, and return to this problem later today.hazel
March 19, 2019
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DS, I would start with zero. Namely, {} --> 0. There is but one zero, and but one null set. We can severally have a concept or definition or symbol of it in mind, but that is not the same as holding the number pinned to a location. The same extends to all numbers that have a definite value. Irrationals have the added property that we cannot precisely assign a decimal value or the like, we can only represent and approximate, so we are a step further back. The number C is similar, we are not addressing it, we are not giving a decimal value, we are not doing more than symbolising and specifying what it is. We are not holding the number itself in mind. And yet, it is real, holds a definite value. This is a slice of why most working mathematicians and users of numbers simply accept them as real things that we may accurately speak of though they are abstracta. And no, there is no world of forms where we can spy out the number 0 etc on display in some sort of museum. Intangible but real, real enough that we may speak truthfully about them. KFkairosfocus
March 19, 2019
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hazel:
I think the idea that these things which have not been figured out yet “reside” someplace is the mistake.
You are wrong.
One of my arguments against this Platonic view last fall involved Conway’s invention of the Game of Life.
Question-begging.
This cellular automaton demonstrably didn’t exist before the late 1960’s,...
That's your unsupportable opinion, anyway. Again, in an Intelligent Design scenario ALL information exists outside of us. We merely tap into it and discover it. That is how and why Srinivasa Ramanujan was able to do what he did. No other explanation exists for his feats.ET
March 19, 2019
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Just FYI for math lovers: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prizehazel
March 19, 2019
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I agree with Dave. I think the idea that these things which have not been figured out yet "reside" someplace is the mistake. They "exist" in the logical entailment of the symbol system they are part of even if no one has ever instantiated them by expressing the logical sequence that would reveal them or their truth value. One of my arguments against this Platonic view last fall involved Conway's invention of the Game of Life. This cellular automaton demonstrably didn’t exist before the late 1960’s, and yet once the rules for the system were formalized, all possible generational states of all possible starting configurations all of a sudden “existed” in the sense that they were logically determined: the Nth generation of each particular generation 0, Gen0.1, Gen0. 2 … are what they are irrespective of whether anyone ever goes through the steps to find them. A Platonic view, as best I understand it, would posit one of two explanations, neither of which I find plausible. 1. All possible mathematical systems, including all their logically true components, exist and have existed eternally, in some Platonic realm, irrespective of whether there is even a material world, much less beings such as us to partially express them. The Game of Life has always existed, and so has every other similar game, including ones on hexagonal grids, ones in which most or all starting generations die quickly, etc. 2. The Game of Life was a true invention, which did not pre-exist Platonically, but as soon as it was invented, all of it’s infinite possible consequences suddenly came to exist Platonically. Perhaps MG believes one of these two things, or perhaps he has some other explanation of what “exists” means in a Platonic context, but I don’t find either of those options reasonable things to believe. I think it is more reasonable to believe what I wrote above: “Mathematical truths "exist" in the logical entailment of the symbol system they are part of even if no one has ever instantiated them by expressing the logical sequence that would reveal them or their truth value. “Exist” and “reside” are in quotes above because I think those words are inappropriate and confusing the issue.hazel
March 19, 2019
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Math Guy, KF, hazel, et al, Some additional food for thought: Have you seen this paper? (link to paper included in the blog post). The authors present a 7918 state Turing Machine which: 1. "runs forever, assuming the consistency of a large-cardinal theory called SRP (Stationary Ramsey Property)" 2. "can’t be proved to run forever in ZFC (Zermelo-Fraenkel set theory with the Axiom of Choice, the usual foundation for mathematics), assuming that ZFC is consistent".daveS
March 19, 2019
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KF, We have a perfectly good description of the number. It's the real number that satisfies the definition. If a LaTeX plugin were installed here, we could express the definition easily. The definition can reside in a human mind. Can you explain why that is not sufficient? Further, the complete decimal expansion of the square root of 2 cannot reside in a human mind. Does that mean the square root of 2 itself cannot reside in a human mind?daveS
March 19, 2019
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DS, where is likely a misnomer as it tends to suggest space. the number, let's call it C, has a value, which gives it a reality, one that is not held in our minds, i.e. we do not know it. So, in what way is it real, KFkairosfocus
March 19, 2019
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Math Guy,
Look up Greg Chaitin’s halting constant. This is a positive real number, of which only a few decimal digits can actually be computed. The number provably exists, but cannot reside in a human mind. Where is it?
May I jump in? The definition for a particular Chaitin constant can reside in a human mind, correct? One can read and comprehend the definition without knowing all its decimal digits, for example. Why do you think a particular Chaitin constant "needs" to reside elsewhere?daveS
March 19, 2019
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F/N: I decided to re-order the list of aesthetic design principles. Let's refresh and update:
reflective (and perhaps, aided) observation of case studies can support an inductive process that tries to identify principles and design patterns of effective artistic or natural composition that reliably excite the beauty response. That can be quite suggestive, as we already saw: symmetry, balance, pattern (including rhythms in space and/or time [e.g. percussion, dance]), proportion (including the golden ratio phi, 1.618 etc) unity or harmony (with tension and resolution), highlighting contrast, variety and detail, subtle asymmetry, focus or vision or theme, verisimilitude (insight that shows/focusses a credible truth/reality) echoing of familiar forms (including scaled, fractal self-symmetry), skilled combination or composition and more.
We can of course readily see these at work in Mona Lisa and many other great or even ordinary works of art.We can also see the impact of deliberate gross violation. KFkairosfocus
March 19, 2019
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MG & H: a key issue is, what is truth? Once we see that it is about accurate description of reality, then it follows that if an abstract statement is true, it refers to a reality. That reality would then reside in the logic of being structure of the world. In turn, that highlights that material entities cannot exhaust reality. We have good reason to recognise that matter and resulting organised computational substrates cannot adequately account for reasoned inference, responsibility and significant freedom. So our very ability to reason mathematically points beyond the obvious world of material bodies to reality being more than this. Indeed, we have reason to see that matter is highly contingent and so cannot be the root of reality that needs to be necessary being. The concept of unknown truth is also a strong sign that there is more to mathematical reality than human conceptions. KF PS: Logical positivism collapsed 50 years ago. Its key claims could not pass its own verification test so were deemed meaningless. That is, it was irretrievably incoherent and self-falsifying. A familiar challenge.kairosfocus
March 19, 2019
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ET, that one may create ordinal, interval or even ratio scales of beauty etc and perhaps even warrant them to some degree does not alter the basic independence of utilitarian functionality and aesthetic excellence. Well engineered highly functional cars can be ugly, and fashionably attractive ones can be of such poor quality control that no one will purchase them unless s/he has little choice (I assume, sound basic engineering). That happened to American vehicles leading to the rise of Japanese imports. A similar breakdown happened with British cars. There are other cases. KFkairosfocus
March 19, 2019
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H, the conflation of utility and aesthetic excellence (or for that matter, ethical excellence) is a category error, as was already highlighted. Enough has been said for record and the example of cars should be enough to ponder on empirical cases. Opinion and warrant are categorically distinct. KFkairosfocus
March 19, 2019
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