SAE Judgment and Aesthetics — In Tribute to Kant
SAE 判断力与美学 · 致敬康德
This paper sets out the general framework of SAE aesthetics. A personal aesthetic is each person's own; aesthetics is the part that subjects with judgment cannot not acknowledge together, which this paper calls the overlap. The overlap is large; what does not overlap is larger. The ground of this shared acknowledgment is the full unfolding of a construct at a given dimension: whoever looks cannot not see it, and whoever has seen it cannot not acknowledge that it is beautiful. The ground precedes the subject; aesthetics does not. The construct does not wait for anyone; aesthetics waits for subjects. The paper states three propositions of aesthetics (cannot not be beautiful, cannot not develop, cannot not be questioned) and names two hinges in their derivation, the Remainder Overflow Principle and the subject's own cannot-not: the remainder gives a direction and pushes no one; the drive is inside the subject. The central corollary is that there is no supreme beauty. Six core theorems (the Chisel-Construct Identity, the Internality of Context, the Anti-Correlation of Beauty with Alien Control, Dimensional Irreducibility, the Conservation of Locus, and Thickening) make up the mechanics of SAE aesthetics. Beauty is not correctness, not usefulness, not importance, not understanding; from perception on, one more thing has to be said: beauty is not pleasure, and pleasure is not beauty. The chain of subject conditions (cannot not see, cannot not pursue, cannot not be questioned) closes into a loop through its three conditions. The paper separates aesthetics from personal aesthetics, distinguishes the overlap from Rawls's overlapping consensus, and traces where the overlap comes from: Shi Bo, Yan Ying, Confucius, Mencius, Bharata and Abhinavagupta; Shaftesbury, Vico, Hutcheson, Hume and Kant; Arendt, Bourdieu and the debate on aesthetic testimony. The SAE dimensional sequence (0DD to 16DD) generates thirteen beauties, a chisel-construct chain with a phase transition between 12DD and 13DD. A ray is a direction of judgment, not a classification of objects, and the order of the rays is the order of asking. The paper gives the reading that all thirteen rays share and a one-line definition of each, and offers four non-trivial predictions with falsification conditions. It is the prescription for "The Artist Is Dead."
Keywords: SAE aesthetics, aesthetics, personal aesthetic, overlap, beauty, chisel-construct cycle, dimensional sequence, Remainder Overflow Principle, thirteen beauties, subject conditions, Kant, Hegel
1. The Problem: Why Begin at 0DD
1.1 Where SAE Aesthetics Stands in the System
Kant needed three Critiques to complete his system. The Critique of Pure Reason answers "What can I know?" and deals with the theory of knowledge; the Critique of Practical Reason answers "What ought I to do?" and deals with ethics; the Critique of the Power of Judgment builds a bridge between nature and freedom. The three Critiques correspond to the true, the good and the beautiful, or more precisely to understanding, reason and judgment.
The SAE system has a parallel structure but starts elsewhere. The three SAE methodology papers (the overview, the epistemological map, and how to find remainders with AI) answer "how to chisel, how to construct, how to identify a remainder," and deal with method.[^1] SAE ethics (One's Own Law) answers "how a subject gives itself law," and deals with ethics.[^2] Now SAE Judgment and Aesthetics answers a more basic question: what is beauty?
SAE answers this question differently from Kant. Kant starts from the subject who judges beauty: he asks by what right a judgment of taste may demand the agreement of others, and his aesthetics is anchored in the subject's power of judgment. SAE starts from the construct: when a construct fully unfolds at a given dimension, the subject who sees it cannot not acknowledge that it is beautiful. Full unfolding is the ground. The ground is there before any subject appears; aesthetics waits for subjects with judgment. The construct does not wait for anyone; aesthetics waits for subjects.
That is where this paper stands in the SAE system. It does not extend the theory of knowledge (that is the work of the methodology papers) or supplement ethics (that is the work of One's Own Law). It goes back to the bottom and asks a question more basic than "how to chisel" or "how to legislate": when a construct fully unfolds, what is it that the subject who sees it cannot not acknowledge? The answer is: beauty.
1.2 A History of Narrowing
The history of aesthetics is a history of narrowing. What narrowed was not whether beauty needs a subject; it was the range of things that were seriously asked about as beautiful. Understanding this narrowing is the way to understand why the question has to be asked again from 0DD.
For Plato, beauty stands beside the good and the true. Beauty itself is independent of every beautiful thing; bodies, souls, institutions and kinds of knowledge are all on the way toward it.[^3] This is the widest starting point. Aristotle pulled beauty back from the separate Form to the order, symmetry and definiteness of things themselves, and said that mathematics shows these most of all.[^4] The place where the question was asked changed; the range did not shrink.
In the eighteenth century Baumgarten gave the discipline its name. It was the science of sensible cognition, and beauty was the perfection of sensible cognition as such.[^5] Hume looked for a standard of taste: the joint verdict of true judges, while leaving room for blameless differences of preference.[^6] Kant went deepest. To call a thing beautiful is not to say that I like it; it is to demand the agreement of everyone. No concept can prove this demand; it speaks with a universal voice, and that voice is only an idea.[^7] From here on, to ask about beauty was first to ask about the one who judges it. Here too the first step of narrowing was taken: the beauty of mathematics was set outside. Kant would not allow the name "intellectual beauty"; he would only grant that a demonstration may be called beautiful.[^8]
The real narrowing came in the nineteenth century. Schelling called his aesthetics a philosophy of art.[^9] Hegel says at the outset that the proper name of the discipline is the philosophy of fine art, and that the beauty of art stands higher than the beauty of nature.[^10] He placed the ground of beauty in spirit, which is wider than Kant's; but what he asked about was far narrower: from then on aesthetics made its home in art. He called beauty the sensuous appearance of the Idea, a formula that comes from the lectures as edited by Hotho.[^11] Hegel also said that, in its highest vocation, art is for us a thing of the past. This does not mean that people stop painting; it means that art is no longer the highest way in which spirit knows itself.[^12] Read in terms of the remainder (this is the reading of this paper, not Hegel's vocabulary), absolute spirit wants to leave no remainder. Without a remainder there is nothing left to chisel; without anything to chisel there is no new construct; without a new construct there is no new beauty. Aesthetics was already dead in Hegel: not killed, but "completed" to death.
For the next two hundred years many worked under that verdict. Heidegger said that the decision on Hegel's verdict has not yet been reached.[^13] Mainstream analytic aesthetics moved the question from "what is beauty?" to "what is art?": Goodman asked when something is art, Danto spoke of the artworld, Dickie of the institution of art.[^14] Adorno observed that after Schelling aesthetic interest centered on the work of art, and that natural beauty had all but ceased to be a topic of theory.[^15] Bourdieu asked where taste comes from, Rancière how the sensible is distributed; neither took beauty as his subject.[^16] In the art of the twentieth century, beauty almost left the stage.
In the last forty years or so, beauty has come back into philosophy.[^17] But it has come back mostly as a value in art and in life. Those who ask about it starting from chaos, number or causation are still few.
1.3 Diagnosis and Prescription
"The Artist Is Dead" diagnosed the end point of this narrowing: when beauty is wholly identified with the creative act of the artist, aesthetics dies.[^18] The artist becomes the only source of beauty, the audience becomes a passive receiver, and the beauty in nature, mathematics and physics is treated as a "metaphor," not as "real" beauty. Mathematicians call a proof "elegant" and physicists call an equation "beautiful," but in the mainstream framework of contemporary aesthetics they are only borrowing the word; they are not really talking about beauty.
This paper starts from the view that the diagnosis needs a prescription. The prescription is not to repair existing aesthetics, not to say "we need a better theory of aesthetics," and not to say "everyone is an artist." It is to answer "what is beauty?" again, from the ground up.
SAE provides that ground. The SAE dimensional sequence begins at 0DD (chaos) and runs through philosophy, mathematics, physics, causation, biology, reproduction, perception, cognition, self, purpose and non-doubt to 16DD (mutual non-doubt). Each level of the sequence has its own construct, and the construct of each level can fully unfold. When a construct fully unfolds at a dimension, the subject who sees it cannot not acknowledge that it is beautiful. The prescription has a second half: separating aesthetics from personal aesthetics. A personal aesthetic is each person's own; aesthetics is the part that subjects with judgment cannot not acknowledge together, which this paper calls the overlap (Section 4).
1.4 Why We Must Begin at 0DD
So aesthetics need not begin by asking about perception (9DD+10DD), or cognition (11DD+12DD), or the subject (13DD). Aesthetics begins by asking at 0DD.
A subject who looks back at chaos cannot not see, and having seen cannot not acknowledge, one thing: no distinction that has been made has the right to pass final judgment on the whole. Chaos is the undivided whole. Nothing has yet been divided off; it lacks nothing, because there is not yet a standard by which to judge what it lacks.
So too with the distribution of the primes. That structure unfolds into that shape, and whoever can follow it cannot not see why the part already proved can only be as it is, and what the part not yet proved is missing. This is not because mathematicians find it elegant; it is because the construct has fully unfolded there.
So too with what has already happened. A subject who looks back cannot not see that what has happened cannot be undone and that it remains in what comes after. The patina on an old object, the broken edge of a ruin, fallen petals covering the ground: these are the shape that what has happened leaves on things. What the subject who sees them cannot not acknowledge is that shape; the sadness they stir is each person's own.
These are not metaphors, not "like beauty." They are beauty, each at its own dimension. When a mathematician calls a proof "elegant" and a physicist calls an equation "beautiful," they are not borrowing the word; they are reporting what they have seen: the full unfolding of a construct at its dimension.
That is why the question must be asked from 0DD. The ground is older than the subject, older than life, older than consciousness, older than judgment. Aesthetics is not older than the subject; it waits for people. But once someone looks, what he sees does not begin with him. Kant began his inquiry with judgment: his common sense is directed at aesthetics itself, while the pleasure and purposiveness he describes in detail fall in the stretch of perception (9DD+10DD). Hegel began with spirit, and looked mostly at how spirit knows itself. SAE begins with the construct and asks all the way down to 0DD.
Kant's critique of judgment built a bridge between nature and freedom. SAE Judgment and Aesthetics does not build a bridge between two domains. What it has to say is that beauty from 0DD to 16DD is different stretches of one river. The bridge is not built between two separated things. The bridge is the river itself.
2. Three Propositions of Aesthetics
In the "Analytic of the Beautiful" of the Critique of the Power of Judgment, Kant characterizes the judgment of taste through four moments: quality (disinterested satisfaction), quantity (subjective universality), relation (purposiveness without a purpose) and modality (necessity). The four moments form a framework of analysis, tightening step by step until they fix the a priori conditions of the judgment of taste.
SAE aesthetics uses propositions, not moments. It does not analyze the conditions of judging beauty; it starts from the full unfolding of the construct and writes out three cannot-nots: in acknowledgment, in development and in questioning. The three propositions form a chain of derivation: the first leads into the second, the second into the third. Only the first needs a defense of its own; getting from the first to the second needs two hinges, set out in 2.2. Each step has its own antecedent, and each rests on SAE's postulates, as 2.4 makes clear.
2.1 Proposition One: Cannot Not Be Beautiful
A subject who sees a fully unfolded construct cannot not acknowledge that it is beautiful. This is not a choice, not a preference, and not a personal aesthetic.
What this means is: a construct has fully unfolded at a given dimension; a subject looks at it, not in order to use it for something else, and has the power of judgment for this dimension; then he cannot not see it, and having seen it he cannot not acknowledge that it is beautiful. To say "I see that this construct has fully unfolded, but it is not beautiful" does not, on this paper's view, make sense: whoever has really seen it cannot get around it. This is not a contradiction derived from a definition. It is a claim that can be wrong, and the next paragraphs say how it could be. Beauty is not a reward the construct receives after it unfolds, and not a label an observer attaches afterward; it is the place that those who have seen it cannot not acknowledge.
Two misreadings must be headed off here.
The first: someone will say that I have simply redefined beauty as the full unfolding of a construct and then declared beauty necessary; this is a tautology and tells us nothing new. The reply is that the first step of Proposition One is indeed a decision: it places the ground of acknowledgment in the construct, not in feeling, concept or authority. The force of the decision lies not in whether it is "right" or "wrong" but in what follows from it. If, starting from it, one can derive a framework with more explanatory power than existing theories of aesthetics, it is worth adopting; the six theorems and thirteen rays that follow do exactly this. But after the decision Proposition One says more than a definition: it states a cannot-not, and that cannot-not can be wrong. Suppose someone really saw a fully unfolded construct and did not acknowledge it; or suppose that where people acknowledge beauty, examination after examination finds, broadly and not in one or two people's occasional mistakes, no construct there. If either held, Proposition One would be false. "Really seen" means something different at each dimension, and the ray papers treat this one by one (5.1); so acknowledgment is not being used here to define seeing.
The second: Proposition One does not say that everyone will acknowledge, still less that everyone ought to. Whether those who look are few or many does not change this cannot-not; those who do not look, and those without the power of judgment for this dimension, are not included. So this paper does not say "every subject cannot not"; it says only "the subject who has seen it cannot not." The part that subjects with judgment cannot not acknowledge together, this paper calls the overlap, and aesthetics is the overlap; which beauty moves a given person, and where he stops, is his personal aesthetic (Section 4 goes into this).
This is Proposition One's answer to whether beauty needs a subject: the construct does not wait for anyone; aesthetics waits for subjects. Chaos was the undivided whole before anyone looked at it; the distribution of the primes unfolded as it does before any mathematician. These are the ground, and the ground precedes the subject. But acknowledgment can only be made by a subject; without subjects there is no one who cannot not acknowledge anything.
Kant could say half of this sentence. He said that a judgment of taste demands the agreement of everyone, and this comes very close to the overlap. The points of difference are more than one, and Section 4 and "To Kant" take them up; two may be named here. He says that everyone ought to agree; this paper says only that whoever looks cannot not see, and whoever has seen cannot not acknowledge. He places the common ground in the free play of the faculties;[^19] this paper places it in the construct and its dimension. Plato said something close as well: beauty itself is independent of beautiful things. This paper does not say that. The ground is independent of the subject; aesthetics is not. And the ground needs no realm of Forms, only "construct" and "full unfolding." Both concepts are already defined in the SAE dimensional sequence: from 0DD to 16DD each level has its own construct, and each level's construct has its own way of fully unfolding.
2.2 Proposition Two: Cannot Not Develop
The subject who has seen cannot not acknowledge (Proposition One); but aesthetics does not reach its end in one step.
Getting from Proposition One to Proposition Two needs explicit hinges. Proposition One says only that when a construct fully unfolds, those who have seen it cannot not acknowledge it; it does not say that things go further. Full unfolding could also mean that things stop here: the construct has unfolded completely and nothing new remains. If so, aesthetics would be static and Proposition Two would fail.
There are two hinges, and they do different work. The first is the Remainder Overflow Principle: the full unfolding of each level exposes a remainder that the level cannot contain.
This is one of SAE's central insights, and it is not limited to aesthetics. The full unfolding of a construct is not closure. On the contrary: the more fully it unfolds, the more definite the exposed remainder. The full unfolding of philosophy exposes the question of form, which philosophy cannot contain; that remainder becomes the place where mathematics begins to ask. The full unfolding of mathematics exposes the question of reality, which mathematics cannot contain; that remainder becomes the place where physics begins to ask. The full unfolding of physics exposes the question of irreversibility, which physics cannot contain; that remainder becomes the place where the beauty of causation begins to ask.
The Remainder Overflow Principle is structural; it needs no subject and no intention. But it only marks where one could go on, and in what direction; it pushes no one. Since SAE: The First Critique, the remainder is no longer the drive.[^20] What the remainder gives is a direction: a direction of development, a direction of cultivation. The drive is the second hinge: the subject's own cannot-not. Whether to go, and by which opening, depends on his being unable to stop, not on being forced by the remainder.
Two misreadings must be prevented here. One is to take the remainder as "the unbeautiful": the dregs of beauty, its opposite, raw material waiting to be constructed. The reverse is true. Without a remainder the construct stops: without a remainder there is nowhere to go on. Generative beauty is a chiseling in progress, and where it chisels is often the remainder exposed by the level before. To eliminate every remainder is not the completion of beauty; it is a halt. On this paper's reading, that is exactly the mistake of Hegel's absolute spirit. The other misreading is to think that the remainder pushes the subject along. It does not. From the same remainder one person begins to ask and another does not; the movement happens inside the person.
On three rays, mathematics, physics and causation, the remainder sometimes has a shape of its own, drawn by what already stands; seeing that shape is also a kind of beauty, called the beauty of the remainder. It is how Proposition Two is seen from inside the subject, and it does not push anyone to fill the gap. The other rays are not forced to have this face.
So the derivation of Proposition Two has the same form as Proposition One. The Remainder Overflow Principle is the ground: every full unfolding exposes a remainder its level cannot contain, and this level does not wait for anyone. The subject who has seen the remainder cannot not acknowledge that things are not finished here: he may choose not to go there, but he cannot say that the place has been closed. This is overlap, not something each person chooses. Aesthetics therefore cannot be closed; no place in it can be declared complete. Whether to go there, and through which opening, comes, like where one looks, from each person's own cannot-not; the development of aesthetics takes place in those who cannot not go. This paper does not guarantee that every patch of remainder will find someone who goes there, and it does not write the history of aesthetics as an engine.
The chisel-construct chain is not pushed along by an outside force, nor by the remainder. The thirteen beauties are not a list of equals but an ordered chain; the order is the order of asking, not the order of the universe, and not a ladder that lifts people up. One ray leaves a question behind; the next begins to ask from there. Whether anyone asks depends on a person's cannot-not.
Corollary: There Is No Supreme Beauty
From Proposition Two it follows that there is no supreme beauty. This paper does not deny that, among a set of things, one may pick out the finest, nor that each person has his own favorite: that is comparison, and personal aesthetic. What this paper denies is a supreme beauty within aesthetics: any beauty that, on the strength of its present construct and present context, gains a standing that no future context and no ray could ever question again.
The corollary has two supports, and there is one boundary to draw.
The first support comes from Proposition Two. A subject who sees a construct fully unfolded also sees the remainder it cannot contain, and cannot not acknowledge that things are not finished here. "This is the most beautiful; there is nothing left to ask" is a sentence of aesthetics, and it would have to fall within the overlap. But the more fully someone sees, the less he can say it. So it cannot fall within the overlap.
The second support comes from the internality of context (Theorem Two, developed in Section 3): context is a component of beauty, and when the context changes, the beauty is rewritten. This paper does not predict how contexts will change. But for a beauty to become the supreme beauty of aesthetics, someone would have to vouch for it against every future context, and no one can give that guarantee.
The boundary comes from the overlap itself: the overlap is large; what does not overlap is larger. Each person may have his own most beautiful thing; that is his personal aesthetic, and it is not a mistake. No one's personal aesthetic covers the whole overlap; only when someone presents his own most beautiful as the most beautiful that everyone cannot not acknowledge can he be wrong.
"There is no supreme beauty" therefore does not depend on whether there is a 17DD. It is a corollary within SAE's postulates (2.4), not an empirical guess, and it can be wrong: if there were a beauty such that all who saw it cannot not acknowledge that nothing about it is left to ask, the corollary would fall.
This is also SAE's direct reply to Hegel. Read in terms of the remainder (this is the reading of this paper, not Hegel's vocabulary), absolute spirit wants to eliminate every remainder: spirit knows itself completely, and there is no more overflow, no more development. Within the postulate that the remainder cannot be eliminated, this cannot be done. The Remainder Overflow Principle says that full unfolding always exposes a remainder; "all remainders eliminated" and "the construct has fully unfolded" cannot both hold. If absolute spirit really had eliminated every remainder, it would not have fully unfolded, because the mark of full unfolding is precisely the exposure of a new remainder.
Any theory, artist or civilization that declares its own most beautiful to be the supreme beauty of aesthetics makes, at that moment, the same mistake: it takes the elimination of the remainder for full unfolding, which is exactly the opposite of full unfolding.
The last ray is no exception. The beauty of mutual non-doubt (16DD) is the last of the thirteen rays, not the highest: rays are directions, not a ladder, and the last is only the last. Two people each stand on their own law, each recognizes the other as an end too, each has chiseled the other, and neither has fallen: this can be seen. Widen it: three people, a group, many strangers, who recognize and chisel one another in the same way, and no one falls: this is heading toward the kingdom of ends. Between two people a first form of it can already be seen; among many it is still a direction. When it will come, how, and whether it will come at all, this level cannot contain; whether it deserves the name of a kingdom, this paper does not decide; whether many people who recognize and question one another can grow into a common legislation is, as SAE: The First Critique says, left to SAE: The Second Critique.[^21] There is no supreme beauty: not the beauty of mutual non-doubt, and not the kingdom of ends.
2.3 Proposition Three: What Beauty Is Cannot Not Be Questioned
Since there is no supreme beauty (the corollary of Proposition Two), the question "what is beauty?" can never be closed.
But Proposition Three has a trigger condition: it has not been there since the beginning of the universe. Aesthetics is conditioned on subjects from the start; in a pre-subjective universe the construct unfolds, but no one looks and no one asks. Proposition Three says only this: once a present subject appears who can reflect on beauty, the questioning cannot be closed.
"Present" is the key word. Being questioned by future subjects does not count as questioning: the questioning must come from a present subject and take place in the present context. Future questioning has a future context; that is another questioning of another beauty.
Beauty cannot not be questioned, not because people are curious, but because, since there is no supreme beauty, every answer about beauty is provisional. Every answer is one unfolding in the present context, and the context changes, the construct goes on unfolding, and the remainder goes on being exposed; so every answer stays open and leaves a place where the next round can chisel it.
This is the dynamics of the history of aesthetics. Plato asked; Aristotle chiseled Plato, pulling beauty back from the separate Form to the order of things themselves. Kant asked; Hegel chiseled Kant, pushing beauty from judgment into the historical unfolding of spirit. Mainstream analytic aesthetics chiseled Hegel, moving the question from "what is beauty?" to "what is art?" SAE now chisels all of them: it asks again from 0DD, returns the ground of acknowledgment to the construct, and separates aesthetics from personal aesthetics.
And SAE itself cannot not be questioned. Since there is no supreme beauty, SAE is not an end point either. Here SAE admits its own remainder: not only the remainder of aesthetics but the remainder of the SAE system itself. A framework about remainders must admit that it has remainders too; otherwise it contradicts itself.
2.4 The Overall Structure of the Chain
The three propositions are not three separate declarations; they are three links in one chain of derivation.
Proposition One (ground): a subject who sees a fully unfolded construct cannot not acknowledge that it is beautiful.
Proposition One, together with the Remainder Overflow Principle and the subject's own cannot-not, yields Proposition Two (dynamics): aesthetics cannot not develop. The remainder gives the direction; the cannot-not is the drive.
Proposition Two yields a corollary: there is no supreme beauty. It has two supports: whoever sees the remainder cannot not acknowledge that things are not finished, and no one can vouch for every future context. There is also one boundary: each person's most beautiful is a matter of personal aesthetic, not the supreme beauty of aesthetics.
The corollary, together with the appearance of a reflecting subject, yields Proposition Three (reflexivity): once reflection appears, beauty cannot not be questioned, because there is no supreme beauty and the question cannot be closed.
The chain rests on SAE's postulates. The Remainder Overflow Principle rests on the postulate that the remainder cannot be eliminated. The hierarchy of dimensions from 0DD to 16DD is likewise a postulate SAE takes on, not a derived necessity; the hierarchy adds layers and does not replace them, so the appearance of a new layer does not presuppose the erasure of the old (Theorem Five). SAE: The First Critique has already examined this: apart from one performative axiom, SAE's foundational claims are all postulates, taken on actively, answered for, and open to replacement; whether each step in the dimensional sequence is necessary is examined separately and graded, not grounded.[^22] So the "cannot not" of the three propositions is always a cannot-not within these postulates. Each step has its own antecedent: Proposition One requires that someone see; Proposition Two requires that someone see the remainder, and development further requires that someone cannot not go; Proposition Three requires that a reflecting subject appear. When the antecedent is met, that step cannot be escaped; when it is not met, this paper does not supply it; if a postulate is broken, the step that rests on it falls with it.
This is not a retreat into personal aesthetics. That whoever sees the remainder cannot not acknowledge that things are not finished is still overlap. What this paper puts forward is an aesthetics that can stand and can also be wrong, and it welcomes falsification: the four predictions of Section 6 are the doors left open for it.
This structure differs at root from Kant's four moments. Kant's moments analyze four aspects of one phenomenon (the judgment of taste); they are parallel, and from any one of them one reaches the same core. SAE's three propositions are not parallel; they have a direction: one leads into two, two into three. This direction is the direction of the chisel-construct chain, from ground to development to reflection, and it matches the order of the dimensional sequence from 0DD to 16DD; that order, as said above, is the order of asking.
2.5 The Complete Sequence of Thirteen Beauties
The three propositions state the cannot-not of acknowledgment, the development of aesthetics and the questionability of beauty. But beauty is not one undifferentiated thing: it takes different forms at different dimensions. The SAE dimensional sequence (0DD to 16DD) generates thirteen beauties. Each is a threefold unity: a chiseling of the level before, a construct at its own level, and something chiseled open by the level after (chaos has no level before; at the last, what cannot be contained stays where it is).
The chain undergoes a phase transition between 12DD and 13DD. Up to 12DD, the unfolding of beauty needs the structural space of a double DD level (5DD+6DD for biology, 7DD+8DD for reproduction, 9DD+10DD for perception, 11DD+12DD for cognition) or a single DD level (0DD to 4DD). The two DDs of a double level are two halves of one beauty, not a composite of two beauties. From 13DD on, the appearance of subjectivity makes each DD level thick enough to be a beauty on its own. The cause of the transition is the appearance of subjectivity: in dimensions without a subject the construct needs more structural space to fully unfold; in dimensions with a subject, the subject itself gives the construct density. What changes is the object acknowledged, not whether a subject is needed: up to 12DD the construct acknowledged is not a subject; from 13DD on, the construct acknowledged is itself a subject. Aesthetics always waits for subjects.
The complete sequence of the thirteen beauties follows. The one-line definition of each is the anchor of one of the thirteen ray papers, where it is developed in full.
| Dimension | Form of beauty | One-line definition |
|---|---|---|
| 0DD | Beauty of chaos | The undivided whole: nothing has yet been divided off; it lacks nothing, because there is not yet a standard by which to judge a lack |
| 1DD | Beauty of philosophy | The first distinction: something that could not be put clearly can, for the first time, be asked |
| 2DD | Beauty of mathematics | Pure form, after structure has come away from matter |
| 3DD | Beauty of physics | Form meets the world: the world answers it at the point where the form is necessary |
| 4DD | Beauty of causation | What has happened cannot be undone: things have a history, and that history is itself construct |
| 5DD+6DD | Beauty of biology | Still itself while its material is exchanged, its offspring carrying on its pattern: one pattern continues through changed material, and outside conditions cannot account for it completely |
| 7DD+8DD | Beauty of reproduction | Difference becomes role, and offspring grow their complex selves again: generation anew in a world of rising entropy |
| 9DD+10DD | Beauty of perception | The world comes to matter to a living thing, and appears to it |
| 11DD+12DD | Beauty of cognition | The absent is still there, the not-yet-come arrives first: for the first time the construct goes beyond the present |
| 13DD | Beauty of the self | The construct becomes itself: an I appears, and judgment has an owner; the I is finite, and the direction is not yet its own |
| 14DD | Beauty of purpose | One's own cannot-not: a direction has come, not pushed by others, not set on a whim, but one I cannot not follow |
| 15DD | Beauty of non-doubt | Inwardly, self-legislation; outwardly, acknowledging others as ends too: I do not need your confirmation, I do not forbid your questioning, and I do not confirm on your behalf |
| 16DD | Beauty of mutual non-doubt | The bridge between two selves: I recognize you as an end, and you recognize me as an end; after chiseling each other, neither has fallen |
This table is a general outline, not a final text, and it keeps two things apart. Concrete beauties, the shape a construct takes in a particular context, are inexhaustible: contexts change and old beauties thicken (Theorems Two and Six), and beauties not written in this table will certainly be seen; but each of these is a new place on one of the thirteen rays, not something outside the table. The rays themselves are another matter. The hierarchy of dimensions from 0DD to 16DD is an SAE postulate (2.4), and within that postulate this paper claims that the thirteen rays are a complete table of types. This paper does not say the table will never need changing. It says that changing it can only come by falsification, not by patching: find a beauty that falls on none of the rays, and the table is wrong; if a new DD had to be set up to hold it, then the postulate of the DD hierarchy has been broken, this edition falls with it, and a revision takes its place (Prediction Four). Each definition is examined and refined more strictly in the ray papers, and the ray papers themselves are only one unfolding in the present context, not final answers.
3. Core Theorems
The three propositions give the ground, the development and the reflexivity of aesthetics. But the propositions answer "what is beauty?"; the theorems answer "how does beauty work?" The six theorems are the mechanics of SAE aesthetics: they state the structural regularities a construct follows as it unfolds, changes, persists and grows, that is, how the place that those who have seen cannot not acknowledge comes about and how it changes.
The theorems are not a flat list of six. They depend on one another: Theorem One is the base; Theorem Four gives the layering; Theorem Five rests on the postulate that the dimensions add layers, and joins Theorem Four; Theorem Two gives the mechanism of concretion; Theorem Six follows from Theorems Two and Five together; Theorem Three cuts across all dimensions. The reader need not memorize this dependency map, but should know that the six are not independent axioms; they form a system with an internal structure.
Six theorems, no more and no fewer. The fewer the theorems, the fewer the constructs, and the more room there is for beauty.
Beyond the six theorems there is one sentence that holds for every ray: beauty is not correctness, not usefulness, not importance, not understanding. From perception on, one more has to be added: beauty is not pleasure, and pleasure is not beauty (see 5.1).
3.1 Theorem One: The Chisel-Construct Identity
In the occurrence of beauty, chiseling and constructing are two faces of a single event.
Chiseling the level before is constructing at this level. When mathematics chisels philosophy, forcing philosophy's questions in natural language into formal structure, that is the unfolding of the mathematical construct. When physics chisels mathematics, forcing pure form toward the test of reality, that is the unfolding of the physical construct. There is no temporal sequence of "first chisel, then construct"; chiseling and constructing happen at once.
This theorem is the most basic of the six. What those who have seen cannot not acknowledge is not the finished product of the construct after the chiseling is over; it is the event in which chiseling and constructing happen together. To take beauty as a static object is to look in the wrong place: what you see is a cross-section of the chisel-construct event; when the cross-section is complete, that is how the event looks when it is complete.
Does this contradict Proposition One? Proposition One speaks of a construct that "has fully unfolded," which sounds like a state. Theorem One says that what is acknowledged is the event in which chiseling and constructing happen together, which sounds like a process. The key to resolving the tension is that full unfolding can present itself either as a process still unfolding (the generative state) or as a state that has come fully into place (the completive state). Both are beauty, with different textures.
Corollary: Generative Beauty and Completive Beauty
The Chisel-Construct Identity means that each beauty has two faces: generative beauty and completive beauty.
Generative beauty is the face of the chisel: the process in which the construct is chiseled out of the level before. It is happening, tense, in motion. Watching a mathematical proof being worked out, watching the bridge between two subjects being built, watching a poem emerge from the chaos of language: these are generative beauty. Its texture is tension, anticipation, uncertainty.
Completive beauty is the face of the construct: the state in which the construct has fully unfolded at its level. It has come into place; it is full and quiet. Looking at an elegant proof already complete, at two people for whom chiseling each other has become ordinary and who each stand where they stand, at a poem in its final form: these are completive beauty. Its texture is satisfaction, wholeness, calm.
Generative and completive beauty are not two different beauties but two faces of one beauty. The Chisel-Construct Identity means that both are present at once; they differ only in the angle from which one looks.
The one exception is the beauty of chaos (0DD). Chaos is the starting point, and before the starting point there is nothing that could chisel chaos out. The beauty of chaos has only completive beauty: the undivided whole needs no process of generation. Its completeness here means lacking nothing, not being whole and not being at rest: looked back upon, it does not stop but changes all the time, and it is not necessarily quiet. Chaos has no "where it came from"; it is simply there.
Chaos itself is a known unknown: we know that it is there and that it is the starting point, but we do not fully understand it. What came before chaos belongs to the unknown unknown: we do not even know whether the question makes sense. Here the SAE framework admits its own boundary. This is not only a statement about the limits of aesthetics; it is a remainder of the SAE system itself. A framework about remainders must admit that it has remainders too; otherwise it contradicts itself.
Only from 1DD (the beauty of philosophy) on does each beauty have both generative and completive beauty. The generative beauty of philosophy is the first generation in the whole chisel-construct chain: the first distinction falls, and a question takes shape for the first time. Before this there is only the completive beauty of chaos; after it, every beauty has a history.
3.2 Theorem Two: The Internality of Context in Beauty
Context is not a condition of beauty; it is a component of beauty.
This is the most novel of the six theorems. It does not say that "beauty is affected by context"; that is common sense. It says that if the context is removed, the beauty is incomplete: not that beauty is "affected" but that a piece of it is "missing." Context is not beauty's clothing; it is one of beauty's organs.
One example makes this clear. The beauty of the starry sky that the ancient Greeks saw and the beauty of the starry sky that we see are not "one beauty experienced differently in different contexts." They are two different beauties. In the context of the sky the Greeks saw, no one knew what the stars were: what they saw was a field of lights turning by their own rule, lights no one could name. In the context of the sky we see, we know that the stars are nuclear fusion: what we see also includes how many years the light has traveled and how a star burns. Mystery, awe and wonder belong to each person; when the context changes, the place that is seen changes. Exchange the contexts and the beauty changes. It is not "one beauty felt differently" but "different beauties."
The internality of context directly resolves one of the most troublesome problems in the history of aesthetics: why do standards of taste change?
There have been two traditional answers. Relativism says that beauty is subjective, there is no objective standard, and standards vary with people and times. Absolutism says that the standard does not change; human understanding changes, and people are gradually approaching the eternal standard of beauty.
The internality of context is a third way. The ground is the structural state of the construct, and it does not vary from person to person; but the context of that structural state changes. It is not the standard that changes but the context. When the context changes, the form of the construct's full unfolding is different. Past beauty is not necessarily present beauty, and present beauty is not necessarily future beauty. This is not relativism: at every moment, the subject who has seen cannot not acknowledge (Proposition One). But every chiseling changes the context, and when the context changes, the beauty changes.
3.3 Theorem Three: The Anti-Correlation of Beauty with Alien Control
The stronger the control imposed from outside, unrelated to the construct's own law, the weaker the beauty.
This theorem must be stated carefully, because it is the easiest to misread. There are two directions of misreading: "all control harms beauty," and "beauty needs disorder." Both are wrong.
The key distinction is between alien control and the construct's own law.
Alien control is a constraint imposed from outside and unrelated to the construct's own law of unfolding. A painter required by a patron to paint in a particular way is under alien control. A mathematical proof required to be done by one particular method is under alien control. A person required by social norms to live in a particular way is under alien control. The more alien control, the fewer the directions in which the construct can unfold, and the weaker the beauty.
A construct's own law is a constraint internal to the construct. The rules of counterpoint in a fugue are not imposed from outside; they are the way this kind of construct, the fugue, unfolds: without counterpoint a fugue is not a fugue. The rules of logic in a mathematical proof are not imposed from outside; they are how mathematics as a construct operates. The rhyme of metrical verse is not imposed from outside; it is the form in which this construct unfolds in language. Constraints of the construct's own law do not weaken beauty; they let the unfolding be fuller, because the constraint is itself part of the construct. Freedom within constraint is often more beautiful than freedom without it.
So the precise statement of the anti-correlation law is this: within each dimension, other things being equal, the stronger the control that is imposed from outside and that the construct cannot reclaim, revise or withdraw from, the narrower the space in which the construct unfolds by its own law, and the weaker the beauty. An outside constraint is sometimes taken over by the construct and becomes its own law; then it is no longer alien control. But this depends on whether the construct itself can reclaim it, revise it and withdraw from it; one cannot, after the fact, rename every beneficial constraint as the construct's own law.
This also explains why people often stop more readily before nature than before made things: in nature there is no alien control, the construct unfolds wholly by its own law, and those who look find it easier to see that fullness. It explains why improvisation is often more moving than a perfect rehearsal: excessive control in rehearsal is alien control (the pursuit of an outside standard of "perfection"), while improvisation lets the construct go by its own law. It explains why over-ornamented works lose their beauty: ornament is alien control over the construct, and every added layer of ornament is one more foreign constraint.
A person's personal aesthetic can also be colonized: a ruler that is not his own takes the place of his own law. Having a history is not the same as being colonized; it may also be cultivation (see 5.1 and the beauty of purpose).
3.4 Theorem Four: Dimensional Irreducibility
Beauty at a higher dimension cannot be reduced to beauty at a lower dimension.
The beauty of the self (13DD) is not "complex cognitive beauty." The beauty of purpose (14DD) is not "advanced beauty of the self." The beauty of mutual non-doubt (16DD) is not "twice the beauty of non-doubt." Each level's beauty is wholly new, because each level's construct is wholly new: it has its own way of fully unfolding, its own remainder, its own place where asking begins.
This theorem directly rebuts reductionist aesthetics. Reductionist aesthetics takes many forms: neuroaesthetics tries to reduce all beauty to the brain's reward circuitry (the level of perception); evolutionary aesthetics tries to reduce all beauty to reproductive advantage (the level of reproduction); social constructionism tries to reduce all beauty to relations of power. Each of these theories has insight at its own dimension, but they share one mistake: trying to explain beauty at every dimension by beauty at one dimension.
Reductionism is not wrong; it answers questions at the wrong dimension. To ask "what is the neural basis of the beauty of the self?" is like asking "what is the chemical composition of a mathematical proof?": the question itself crosses dimensions, and the answer cannot help missing the point.
Dimensional irreducibility also means that the thirteen beauties have no ranking. One cannot say that the beauty of the self is "higher" than the beauty of chaos, or that the beauty of cognition is "deeper" than the beauty of causation. Each beauty is full at its own dimension, and those who have seen it cannot not acknowledge it. This corresponds directly to the second dimension of "ignorance" in the subject conditions, ignorance about beauty: no subject has final authority over aesthetics (4.3).
3.5 Theorem Five: Conservation of Beauty's Locus
Being chiseled is not being negated. Beauty at a lower dimension does not disappear when a higher dimension appears.
The chisel opens a new dimension, but it does not close the old ones. The appearance of the beauty of philosophy (1DD) did not abolish the beauty of chaos (0DD). The appearance of the beauty of physics (3DD) did not abolish the beauty of mathematics (2DD). The appearance of the beauty of the self (13DD) did not abolish the beauty of perception (9DD+10DD). Every level is still there.
But what exactly is conserved? A precise distinction is needed here: what is conserved is the dimensional locus (the type), not the particular instance of beauty (the token).
At each dimension, as long as the construct of that level can still be instantiated, the possibility of its full unfolding is there: this is the conservation of locus. But the concrete form of full unfolding changes with context: this is not conservation; it is thickening (Theorem Six).
The conservation of locus has a ground of its own; it does not follow directly from dimensional irreducibility (Theorem Four). Irreducibility says only that beauty at a higher dimension cannot be reduced to beauty at a lower one; it does not guarantee that lower beauty remains. The conservation of locus rests on the way the dimensions unfold: SAE's hierarchy of dimensions adds layers and does not replace them (2.4), and the appearance of a new dimension does not presuppose the erasure of the conditions under which the older dimensions can be instantiated. So as long as a lower construct can still be instantiated, its locus can still be seen. Theorem Four says that a new level cannot swallow an old one as part of itself; Theorem Five says that the appearance of a new level does not, of itself, cancel an old one. Each level is independent, and none is extinguished by the appearance of a new one.
3.6 Theorem Six: Thickening of Beauty
Conservation is not simply "still being there."
From the internality of context (Theorem Two) it follows that context is a component of beauty, and the appearance of each new level of beauty is a renewal of context. So whenever a new level of beauty appears, the beauty at every older dimension is rewritten and thickened by the renewed context.
After philosophy appeared, the beauty of chaos became "the beauty of chaos in a context where philosophy already exists." After physics appeared, the beauty of mathematics became "the beauty of mathematics in a context where physics already exists." This is not the same beauty grown thicker; it is a new, thicker beauty that takes the place of the old at the same dimensional locus.
The conservation of locus (Theorem Five) says that the dimensional locus does not perish: every level is still there. Thickening (Theorem Six) says that the concrete beauty at the same locus is rewritten: the beauty at every level grows thicker as the context is renewed. The type is conserved; the token is rewritten.
It follows that the space of realizable beauty does not merely accumulate. Each unfolding of a new dimension not only adds a new dimensional locus but also thickens the beauty at every older dimension by rewriting its context. The space of realizable beauty thickens superlinearly.
4. Subject Conditions
The first three sections dealt with the full unfolding of the construct, its movement and structural regularities, and the place that the subject who has seen cannot not acknowledge. The unfolding of the construct waits for no one: chaos, number, the forms of the world and what has already happened were unfolding before any "I" appeared. Aesthetics always waits for subjects; that is the other half of Proposition One.
After the phase transition between 12DD and 13DD, what changes is the object acknowledged. From 13DD on, in the beauty of the self, of purpose, of non-doubt and of mutual non-doubt, the construct acknowledged is itself a subject: the beauty of the self is the full unfolding of the construct "I," and the beauty of purpose is the full unfolding of "my direction."
Two kinds of subject must be distinguished here. The subject of a personal aesthetic is anyone who has subjectivity: someone moved by music, someone who stops under the stars, someone turning over an old bowl used for many years. Feeling beauty has no threshold; whoever has subjectivity has it. Which beauty moves a person and where he stops is his personal aesthetic. This section is not about the subject of a personal aesthetic.
This section is about the subject of aesthetics: one whose chiseling and constructing face the overlap. He does not only see other constructs fully unfold; he unfolds his own, and when he chisels he keeps his eye on the place that whoever looks cannot not see. Only this needs conditions, and it is what "The Artist Is Dead" really diagnosed: the artist did not die as the subject of a personal aesthetic (he can still appreciate beauty); he died as the subject of aesthetics, the subject who creates. Zeami said that an actor must see himself with "detached seeing," looking at himself from the side of the audience; what is seen that way is seeing of one heart with the audience (「離見の見にて見る所は、則ち見所同心の見なり」).[^23] He said this about how an actor is seen on stage, and his audience is the real audience below the stage. This paper takes from him only the single act of seeing oneself from the audience's side: this is the overlap on the creator's side.
What kind of subject, then, can bear the creation of beauty from 13DD on?
4.1 Condition One: Cannot Not See
A subject from 13DD on has an "I," and judgment has an owner. If he looks, not in order to use what he looks at for something else, and has the power of judgment for this dimension, he cannot not see; having seen, he cannot not acknowledge. This holds for whoever looks (5.1); what is added at this level is that the seeing becomes his seeing.
This does not mean that everyone with a self is always looking, or always feeling something: that would be an empirical psychological claim, too sweeping, and acknowledgment is not made by feeling in the first place. The point is structural. With an "I," a living thing that sees wrongly does not say the world was wrong; it says, I saw wrongly. The seeing is his, and the mistake is his. So too when the subject of aesthetics looks at his own construct: where it has fully unfolded and where it is stuck, what he sees is his seeing; if he sees wrongly, it is he who has seen wrongly, and it is he who corrects it.
Condition One is the starting point of the chain of subject conditions. It needs no outside defense: once judgment has an owner, the seeing belongs to him, and he cannot push his mistakes onto the world.
4.2 Condition Two: Cannot Not Pursue (Continuing from Condition One)
Having seen, he cannot not pursue. This step goes in two stages.
The first stage is overlap. Whoever sees where a construct fully unfolds also sees what it cannot contain: the remainder. Having seen the remainder of his own construct, he cannot not acknowledge that his construct is not finished: he may choose not to go there, but he cannot say that the place has been closed (2.2). Having seen the beauty of the self, he has also seen the part of the self's remainder that he knows about (the known unknown); what he does not know that he does not know (the unknown unknown) has to wait until it shows itself in the pursuit (4.3).
The second stage is his own. The remainder gives a direction, but it does not push; going there is his own cannot-not. From the same remainder one person begins to ask and another does not; the one who can stop is not wrong, and that is his personal aesthetic. The subject of aesthetics this section speaks of is the person in whom this second stage takes hold: he has seen that things are not finished, and he cannot stop.
This is the aesthetic meaning of audacity. Audacity is not blind confidence and not a denial of ignorance; it is a structural courage: the subject of aesthetics, having seen the remainder, cannot not push at the boundary. It is not that he chooses to pursue; having seen, he cannot stop.
Pursuit takes two forms. The first is directed chiseling: the subject knows where his known unknowns lie, knows what the remainder is, and pushes at that boundary. This is research, practice, deepening: he knows what he is chiseling. The second is exploratory chiseling: the subject does not know where his unknown unknowns lie but believes he may run into one. This is risk, experiment, a leap across dimensions: he does not know what he will chisel out, but he sets to work.
Audacity includes bearing the cost: knowing that chiseling oneself will hurt (the old construct broken, the remainder exposed) and setting to work anyway. This need not be listed as a fourth condition: audacity itself is "daring to push the boundary, including bearing whatever the push brings."
4.3 Condition Three: Cannot Not Be Questioned (Derived from Condition Two)
Once he pursues, he stands before a question that cannot be closed: what is it, after all, that he is pursuing?
This questioning is not something the subject chooses to start; the pursuit itself brings it on. Pursuit, once it moves, is a chiseling; and within the postulate that the remainder cannot be eliminated, chiseling always leaves a new remainder. As SAE: The First Critique puts it, the act of eliminating the remainder is precisely an act that produces remainder.[^24] So this chiseling cannot secure for his judgment a standing exempt from questioning: the new construct still has a remainder, and it can still be questioned again by new facts, by refutation, by failure, or by later seeing. When the new remainder will show itself, in what shape, and whether he will see it, the postulate does not guarantee. If it shows itself and he sees it, he cannot seal it off with "I have already pursued this"; he finds that his understanding of "what is beauty" was incomplete. He thought he knew what he was pursuing; the unfolding of the pursuit tells him he did not. The position of being open to questioning does not close because of one pursuit; whether he answers is up to him. Whoever refuses to be questioned has stopped, as a subject of aesthetics (4.6).
This is ignorance: not the ignorance admitted before pursuing (that is textbook modesty), but the ignorance that shows itself while the pursuit is under way. If he discovers his ignorance, he discovers it in acting, rather than knowing it before he acts.
Ignorance has two dimensions.
The first is ignorance of oneself. What the pursuit exposes is that the subject's understanding of himself is incomplete. This has two layers: the known unknown, knowing that there is something one does not know, knowing that the remainder is there, but not yet understanding it; and the unknown unknown, not knowing that there is something one does not know, not even aware that the remainder exists. As the pursuit deepens, an unknown unknown sometimes becomes a known unknown, and that in itself is a chiseling.
The second is ignorance about beauty. What the pursuit exposes is that the subject's understanding of beauty is incomplete. The subject admits that he does not stand above any beauty: he cannot say that the beauty of the self is "higher" than the beauty of chaos, or that the beauty of cognition is "deeper" than the beauty of causation. The thirteen beauties have no ranking, only dimensions (Theorem Four).
A key distinction has to be made here: aesthetics (美学) and personal aesthetics (审美). An SAE application paper first separated this pair of Chinese words;[^25] this paper draws the line as follows.
Aesthetics is the part that subjects with judgment cannot not acknowledge together, which this paper calls the overlap. The overlap is large; what does not overlap is larger. No subject has final authority over aesthetics: aesthetics is the overlap, and no one holds the sole right to legislate for it. When someone says "it is beautiful," he is claiming that this time he has landed on the overlap, and that claim can be right or wrong.
A personal aesthetic is each person's own. A subject has authority over his own personal aesthetic and may well say, "I am more moved by the beauty of mathematics": which beauty moves him and where he stops comes from his own cannot-not. That personal aesthetics differ does not mean that anyone is wrong; only saying "it is beautiful" can be wrong.
The two do not conflict, because they lie at different levels. This comes very close to Kant's common sense: he says that the determining ground of a judgment of taste can only be subjective,[^26] and yet it demands the agreement of everyone. The differences lie in the ground and the starting point: he places the common ground in the free play of the faculties, this paper in the construct and its dimension; the place where he begins to ask falls, on this paper's view, in the stretch of perception, while this paper asks from 0DD (see 4.4 and "To Kant").
Readers will think of Rawls's overlapping consensus: various reasonable doctrines, each from its own point of view, endorse the same political conception.[^27] The shapes are alike: in both the reasons differ and what is acknowledged lands in one place. But that is politics. It concerns the legitimacy of coercion, counts only reasonable doctrines, and aims at stability; and it does not take the truth of any one comprehensive doctrine as the shared public ground, leaving the question of truth to each doctrine itself.[^28] What is spoken of here is beauty: no doctrines are filtered, and no stability is sought; to call something beautiful is a claim that can be right or wrong. Nor is the overlap a conception drafted in advance, after which one sees whether each doctrine can endorse it from its own side; it is that those who have seen each come upon the same place.
4.4 Where the Overlap Comes From
The idea of the overlap is not this paper's invention. It has a long history, mostly under other names. Each figure below is reported as he is: what he discerned, why he looked, where he presses on the overlap, and where this paper parts from him. Other traditions appear in their own words.
First, cut off a false friend. The common sense of Aristotle and the common sense (al-ḥiss al-mushtarak) of Ibn Sīnā are, for each, the place in an animal where the senses converge.[^29] The word has "common" in it, but it is not the same matter: it is what is common within one body, not what is common between persons.
Sameness and harmony. Shi Bo said to Duke Huan of Zheng: "Harmony truly gives birth to things; sameness does not carry on. To balance one thing with another is called harmony; so things can grow abundant and be born from it. If sameness is added to sameness, it is used up and discarded." He also said: "A single sound is not worth hearing; a single thing has no pattern; a single flavor makes no meal; a single thing admits no comparison."[^30] When Duke Jing of Qi said that Liangqiu Ju was in harmony with him, Yan Ying said that this was sameness, not harmony: "What my lord calls right, Ju also calls right; what my lord calls wrong, Ju also calls wrong. If you add water to water, who could eat it? If the zither and the lute played a single note, who could listen?"[^31] Confucius said: "The gentleman is in harmony but does not conform; the petty man conforms but is not in harmony."[^32] They spoke about governing a state, about how ruler and minister should speak to each other, about how a gentleman treats others. What they discerned: where there is only one kind of thing, there is no pattern; adding water to water is not harmony. They press on the overlap: might the overlap be sameness, everyone saying the same thing? This paper's answer: no. The overlap counts only each person's own cannot-not; a "beautiful" said by following along is an echo and does not count; that is exactly adding water to water. That what does not overlap is larger is not a defect either; it is the side of harmony. The parting: the harmony of Shi Bo and Yan Ying is mostly about organizing different things into a whole, which is the business of the construct; the overlap is about different people who cannot not acknowledge the same place.
What hearts affirm alike. Mencius said: "The mouth has the same relish for flavors, the ear the same hearing for sounds, the eye the same sense of beauty in colors. Should the heart alone have nothing it affirms alike?" Earlier in the same chapter he said: "As for Zidu, there is no one under heaven who does not know his handsomeness. Whoever does not know Zidu's handsomeness has no eyes."[^33] He spoke about human nature: since people are of one kind and their senses are alike, their hearts too affirm some things alike, and the sage is only the first to grasp what our hearts affirm alike. What he discerned is stronger than what this paper says: all the world looks to Yi Ya for flavor and to Shi Kuang for music, and whoever does not know Zidu's handsomeness has no eyes. This is the kind of universal quantifier this paper will not use. He presses on the overlap: since people are of one kind and so affirm alike, why not simply say "everyone"? This paper's answer: it does not say everyone, only those who have seen; those who have not seen are not eyeless; perhaps they have not looked yet, perhaps they are looking elsewhere. The parting is in two places: the ground is in the construct, not in being of one kind; and those who see first have only seen first; they are not the yardstick.
A rasa that can be shared. Bharata's Nāṭyaśāstra says that rasa arises from the conjunction of the determinants, the consequents and the transitory states (vibhāvānubhāvavyabhicārisaṃyogād rasaniṣpattiḥ).[^34] Later, Bhaṭṭa Nāyaka said that poetry makes the determinants and the rest common, a doctrine later called generalization; his book is lost, and the doctrine survives through Abhinavagupta's report.[^35] Abhinavagupta defined the sahṛdaya, "one of like heart": a person whose mirror of mind has been made clear by repeated immersion in poetry, who is able to become one with what is described, in accord with his own heart.[^36] They spoke about how poetry and drama move people. They discerned three things, and this paper goes with them on two: seeing takes practice, and the mirror of mind becomes clear only through immersion; acknowledgment is one's own, in accord with one's own heart, not heard from others. The third, the ability to become one with what is described, this paper does not take: the one who has seen still stands on his own side, and that is what makes the acknowledgment his. The doctrine of generalization presses on this paper: is what can be shared a feeling? This paper's answer: feeling may come along, or may not (5.1); the overlap is the place that those who have seen cannot not acknowledge, not a shared feeling. A work turns something private into something the viewer can see without sharing the author's private life; this belongs to the side of the construct, and on this point this paper goes with them. They also press on the overlap: those of like heart are a class of people; does the overlap count only this class? This paper's answer: it sets up no such class. Subjects with judgment are not a rank; seeing is seeing an object, anyone may do it, only some constructs take time and training. The parting: no class of people, and no becoming one with what is described.
The sense of community. In his essay "Sensus Communis," Shaftesbury reports the commentators' reading: the sensus communis of Juvenal is a sense of the public weal and of the common interest, a love of the community.[^37] Vico said that common sense is judgment without reflection, shared by an entire class, an entire people, an entire nation or the whole human race.[^38] Gadamer later took up this humanist line again: common sense was first the sense of the community, judgment grown in common life, and only later was it narrowed into aesthetic taste.[^39] They spoke about formation (Bildung), civic virtue and the ground of the human sciences. What they discerned: judgment grows in common life, before reflection. Vico's sentence presses hardest on this paper: might each person's own cannot-not be something the community has grown into him, without reflection? This paper's answer: having a history is not the same as being colonized; it may also be cultivation; where the drive is at work now and how the drive grew are two different questions. To tell them apart, take away the ruler and see: if he still acknowledges, and can change it himself, it is his. The parting: their commonness is something the community has first; the overlap of this paper is what those who have seen each come upon, and requires no community in advance.
The manner of looking. That acknowledgment is neither inferred nor put to use was said early. Hutcheson said that the pleasure of beauty does not come from knowledge of principles, proportions, causes or usefulness; he ascribed this pleasure to an internal sense.[^40] Kant said that in asking whether something is beautiful we do not ask whether the thing's existence matters to us, but only how we judge it in mere contemplation.[^41] Sibley said that aesthetic concepts are not condition-governed: no set of non-aesthetic features guarantees that an aesthetic term applies.[^42] They spoke to explain what kind of capacity taste is. What they discerned is what this paper means by "looking, not in order to use it for something else": seeing is not derived step by step from rules, nor gained incidentally while using the thing for something else. The parting is in the ground: they place it in a sense, in the faculties or in taste; this paper places it in the construct. Hutcheson also called beauty a pleasure, and here he presses on this paper: if beauty is the pleasure of an internal sense, why is acknowledgment not simply that pleasure? This paper's answer: seeing need not be pleasant; beauty is not necessarily pleasant, and what is pleasant is not necessarily beautiful (5.1). This paper goes with him in "not inferred, not used," and parts from him here.
Standards. Hume granted that differences of taste are everywhere, and that the demand for a standard of judgment has never ceased. He first reports a philosophy according to which beauty is no quality in things themselves and exists only in the mind that contemplates them; he then says at once that common sense modifies and restrains this view. He did not hand reliable taste to a majority vote but to capacities: strong sense, delicate sentiment, long practice, wide comparison, freedom from prejudice; the joint verdict of such true judges is the standard of taste. He also granted that, even with all these conditions, age, temper and manner of life still produce blameless differences.[^43] He wrote to find a standard of taste. What he discerned: taste has higher and lower, and also has personal preferences that need not be removed. He is the first modern thinker to leave room for what does not overlap. He presses on this paper: since the standard lies in the joint verdict of true judges, why is the overlap not simply what that group shares? This paper's answer: it sets up no body of judges; those who have seen each come upon the place, and no one is sorted in advance. The parting: the standard is in the construct, not in a group of people. This paper agrees with the second half of what he says more than with the first: what does not overlap is larger.
Ought. The idea of the overlap comes closest to Kant. He first separates the beautiful from the agreeable: in what is agreeable, each has his own taste (the taste of sense), and no one demands the agreement of others.[^44] To call a thing beautiful, however, is to speak with a universal voice and demand the assent of everyone; this universal voice is only an idea.[^45] This demand does not come from concepts; it is an exemplary necessity,[^46] and its ground is a common sense: common sense does not say that everyone will agree with our judgment, but that everyone ought to.[^47] In reflecting, the one who judges takes account in thought of everyone else's way of representing, as if holding his judgment up against collective human reason, and so avoids the illusion of taking private conditions for objective ones.[^48] He wrote to explain by what right a judgment of taste may demand the agreement of others. This runs in the same direction as the overlap: not by statistics, not by concepts, each starting from himself and landing on a common place. He presses on this paper: without "ought," what makes the overlap more than everyone happening to say the same sentence? This paper's answer: the ground is in the construct; that those who have seen come upon the same place is because the construct is there, not by chance (5.1). The difference in ground has been stated above (2.1, 4.3); four more may be named here. He says "ought"; this paper says only that whoever looks cannot not see, and whoever has seen cannot not acknowledge. He says "everyone"; this paper says "those who have seen." He holds judgment up before the whole of human reason; this paper speaks of subjectivity, not of reason. The place where he begins to ask falls, on this paper's view, in the stretch of perception; this paper asks from 0DD. There is one further point that Kant himself left open: whether common sense is a constitutive principle of experience, or a regulative principle that a higher principle of reason requires us to bring about; he says that he does not yet wish, and is not able, to investigate this here.[^49] This paper does not decide it for him either.
Three pressures after Kant. Arendt said that the power of judgment rests on a potential agreement with others; the thinking active in judging, even when I am quite alone in making up my mind, is in an anticipated communication with others.[^50] She wrote about political judgment. What she discerned: judgment is not a matter behind closed doors. Her question: must the overlap bring in the standpoint of others? This paper's answer: the standpoint of others can come in to test a person's judgment; but the overlap is not an agreement reached by talking; it is what those who have seen each come upon. Bourdieu said that taste classifies, and it classifies the classifier.[^51] He wrote to trace the social origins of taste. What he discerned: taste is learned, and the places where it is learned are ranked. His question: is each person's own cannot-not given by society? The more successfully society shapes it, the more it feels like "this is simply how I feel," and introspection cannot tell the difference. This paper's answer: having a history is normal, not colonization; where the drive is at work now and how it grew are two questions. The test of taking away the ruler can go wrong, and Bourdieu points to exactly where it goes wrong; but judgment can be right or wrong anyway, and no further threshold is needed. The debate on aesthetic testimony arose to clarify how aesthetic judgment differs from other judgment in matters of testimony; it asks whether what others tell me counts as my judgment. Wollheim's acquaintance principle says that judgments of aesthetic value must be based on one's own first-hand experience and, except within narrow limits, cannot be passed from one person to another;[^52] C. Thi Nguyen says that we ought to use our own faculties and abilities to arrive at aesthetic judgments.[^53] What they discerned: aesthetic judgment cannot be handed on as received. This paper's answer: only each person's own cannot-not counts; a "beautiful" said by following fame, price or authority does not count, even if the sentence is the same. The parting: Nguyen says one ought to judge for oneself, and Wollheim says that such judgment cannot be transmitted; this paper does not say "ought," only that what is heard from others is not seeing.
This history shows two things. First, the overlap is not this paper's invention. Second, where this paper parts from each figure, it parts in the same few places: it places the ground in the construct, not in being of one kind, in a sense, in the faculties, in the community or in true judges; it does not say "ought," only that those who have seen cannot not acknowledge; it sorts no one in advance, and it does not say "everyone."
4.5 The Chain and Its Unfolding in Time
The three conditions form a chain: cannot not see is the starting point; cannot not pursue is audacity; cannot not be questioned is ignorance. Each link has its own antecedent, and each rests on SAE's postulates (2.4): that the seeing is his rests on judgment having an owner from 13DD on; that whoever sees the remainder cannot not acknowledge that things are not finished is overlap; going there comes from the subject of aesthetics' own cannot-not; that pursuit secures no exemption from questioning for his judgment is a consequence within the postulate that the remainder cannot be eliminated, while whether and when a new question will actually come is not guaranteed by that postulate. That is why the heading of 4.2 says "continuing from Condition One" and the heading of 4.3 says "derived from Condition Two": the first step adds an antecedent, his own cannot-not; what the second step derives is only that the position of being open to questioning cannot be closed, and within the postulate, the pursuit is enough; no further antecedent is required.
In the subject of aesthetics, when he has seen the remainder and his own cannot-not falls on it, pursuit takes place; pursuit secures no exemption from questioning for his judgment, and if a new remainder shows itself and he sees it, the questioning arrives; the questioning exposes ignorance. And the exposure of ignorance leads back to seeing: he sees a new remainder, his own cannot-not falls on it again, a new pursuit begins, and a new questioning arrives if and when he sees the next remainder. This is a closed loop, not a straight line.
In time, the chain unfolds as three stances.
Letting go of the past self. The past construct is complete; if one clings to it, it becomes an obstacle to present chiseling. By the internality of context (Theorem Two), past beauty had a past context, and the present context has already changed. To hold on to past beauty is to use an old context to constrain a new construct. Letting go is not denying the past: past beauty has grown thicker through the renewal of context (Theorem Six), but the subject cannot stay trapped in the old thickness.
Attending to the present self. Chiseling and constructing can only happen in the present (Theorem One, the Chisel-Construct Identity). Not chiseling in memory, not chiseling in a plan, but chiseling going on now. Full unfolding happens only in the present. A subject distracted by past or future does not chisel all the way, the construct does not fully unfold, and those who look have nothing to see.
Opening to the future self. I do not know what my future self will be, but I stay open. This is the temporal expression of the unknown unknown: I trust that future chiseling will bring constructs I cannot now foresee. A subject who closes off the future denies the unknown unknown in advance, and in effect declares in advance, "I have reached the supreme beauty of aesthetics; there is nothing left to ask." And we already know that there is no supreme beauty.
4.6 Correspondence with "The Artist Is Dead"
The chain of subject conditions provides the most precise diagnostic tool for "The Artist Is Dead."
The artist died not because he lacked ability, but because something went wrong at every step of the chain.
At the step of seeing: he saw beauty, but thought that beauty lay only in the few dimensions he worked in. A painter thinks beauty is only in the visual, a musician only in the auditory. This is a narrowing of seeing: the subject of aesthetics is willing to look in every dimension, not only in the few he knows.
At the step of pursuit: he pursued beauty, but thought he had already mastered its direction. He knew what a "good painting" looks like and how "good music" sounds, and pursued in that direction. This is the hardening of pursuit: the audacity in the subject conditions is the courage to push at the boundary, not the inertia of repeating along a known direction.
At the step of being questioned: he refused to be questioned, and above all refused to admit that his understanding of beauty contains unknown unknowns. He thought he already knew what beauty is, and "thinking one already knows" is precisely a symptom that ignorance is absent.
A subject broken somewhere along the chain has, as a subject of aesthetics, come to a stop. The artist's death was not caused by outside forces but by a break within the chain. And the prescription is in the chain too: restore the breadth of seeing, restore the openness of pursuit, restore the capacity to be questioned.
5. Rays: Unfolding in Thirteen Directions
The general outline sets up the framework, but the framework is not beauty itself. Beauty has its own form at each dimension, and each form needs to be unfolded on its own. There are thirteen rays; each is a separate paper dealing with the full form of one beauty.
A ray paper does more than explain what the beauty of its level is; it must also deal with two questions the general outline cannot. First, at that dimension, what full unfolding concretely is, and what seeing concretely sees: the outline gives a general account, but "full" and "seeing" mean something different at each dimension. Second, at that dimension, what is overlap and what is left to each person: aesthetics is the overlap and a personal aesthetic is each person's own, and the concrete shape of both differs from dimension to dimension.
5.1 How to Read the Rays
Each of the thirteen ray papers stands on its own; none needs another to be read first. They share the reading set out below; each paper mentions it in a few sentences at the start, and the full statement is here.
A personal aesthetic is each person's own. Which beauty moves a person, where he stops and for how long, comes from his own cannot-not. Aesthetics is the part where the cannot-nots of subjects overlap: what subjects with judgment, facing the same construct, cannot not acknowledge together. The overlap is large; what does not overlap is larger. Aesthetics is not the sum of personal aesthetics, nor their average; it is the patch where different personal aesthetics meet.
The overlap is not everyone. Those who acknowledge others as ends are not everyone, and those who acknowledge what a given ray paper has to say are not everyone either; but those who do acknowledge it do so because they cannot not, not by choice. So the ray papers do not say "every subject cannot not"; they say only "the subject who has seen it cannot not." Nor is the overlap everyone happening to say the same sentence, or a sentence everyone ought to say. Kant says that common sense does not say that everyone will agree, but that everyone ought to agree;[^54] here it is exactly the other way round: no "ought," only that whoever looks cannot not see, and whoever has seen cannot not acknowledge. What seeing means differs at each dimension, and each ray paper says it for its own.
The aesthetic judgment sits between the two. When someone says "it is beautiful," his personal aesthetic is making a claim on the overlap: he claims that this time he has landed on the shared patch, not only on himself. This claim can be right or wrong, and it can be discussed; that is what the discussion is about. That personal aesthetics differ does not mean that anyone is wrong; only saying "it is beautiful" can be wrong.
The acknowledgment in aesthetics is acknowledgment in seeing, and seeing is not an attitude one can put on. Where to look and where to stop comes from each person's own cannot-not, and most differences of personal aesthetic lie there. But if he looks, not in order to use what he sees for something else, and before him is a construct fully unfolded at this dimension, then a subject with the power of judgment for this dimension cannot not see, and having seen cannot not acknowledge. All these cannot-nots are inside him; the construct does not force him. The first differs from person to person; the latter two are the same for whoever looks and has the power of judgment for this dimension, and that is where the overlap lies. It is like reading: learning one's characters takes effort, but once you know them, a character set before your eyes cannot help being read. So what is seen is said by the construct; whether it can be seen depends on the power of judgment; where one looks depends on the person. The construct does not wait for anyone; aesthetics waits for people; but once someone looks, seeing does not wait for his nod.
Acknowledgment of this kind is not inferred: rules can secure a conclusion step by step while a person sees nothing. It is not heard from others: if others say something is beautiful and you repeat it, that is a matter of reputation. It is not a matter of use: to use a thing for something else, one need not look at it. Nor is it made by feeling: a warmth in the heart, a rush of delight, is a matter of feeling; feeling may come along or may not; it can make a person stop, but it cannot see for him. So beauty is not correctness, not usefulness, not importance, and not understanding. At the level of perception, where the world begins to have sweetness and pain, the word pleasure first enters; from there on one more thing must be said: beauty is not pleasure, and pleasure is not beauty. The two often come together, and coming together does not mean that one can be derived from the other. Seeing can also be mistaken: a person can think he has seen when nothing is there. "Cannot not see" refers to really seeing; to say "it is beautiful" is to claim that this time one has really seen, and that claim can be right or wrong.
The overlap has a ground, so it is not a vote. The ground is the construct: the structure that settles out of an act of drawing a boundary. When a construct has fully unfolded at a dimension, the subject who has seen it cannot not acknowledge that it is beautiful. The unfolding waits for no one; it is there before any subject appears. Aesthetics waits for people, and so does beauty: without subjects, there is no one who cannot not acknowledge anything. The construct is the ground, not aesthetics itself.
That is also why the overlap counts only each person's own cannot-not. A "beautiful" said by following fame, price or authority does not count, even if the sentence is the same. A person's cannot-not has a history: language, tradition and teachers are all in it. Having a history is not the same as being colonized; it may also be cultivation. Cultivation is helping a person grow his own eyes; what helps him can be another person, or it can be a construct: the things he has kept looking at, the institutions that taught him, the academy he belongs to. Colonization is a ruler that is not his own taking the place of his own law; what holds the ruler can be a person, or it can be a construct: a fashion, an institution, a record of past success. The same academy can cultivate one person and colonize another. To tell them apart, take away the ruler and see: if he still acknowledges, and can change it himself, it is his; if he acknowledges only because the ruler is there, it is not. This is looking back after the fact; it can be mistaken, and it is not a criterion.
Conversely, different sentences may be the same overlap. Someone in a tradition may never use the word "beauty" and yet look at the construct itself, and then he cannot not see the same thing; or he may identify the same construct but for the sake of something else, without looking at the construct itself, and then it is not yet the same overlap. Both are reported as they are, without putting other words in anyone's mouth.
The full unfolding of a construct always exposes something its level cannot contain: this is the remainder. The remainder gives a place where one can go on, but it pushes no one. Since SAE: The First Critique, the remainder is no longer the drive.[^55] What the remainder gives is a direction: a direction of development, a direction of cultivation. A person's power of judgment grows along it; where the way is open, and how to tell when one has gone astray, is said by the construct and the remainder. The drive is the subject's own cannot-not: whether to go, and through which opening, depends on his being unable to stop, not on being forced by the remainder. Cook Ding's knife was moved by his own hand, and it followed the grain of the ox; over nineteen years his way of seeing the ox also grew along that grain: at first he saw nothing but the ox, and after three years "he no longer saw the whole ox."[^56] The object can also move first: a falling leaf, the chirp of an insect, a musical phrase that keeps putting off its return to the tonic; before any of these a person may suddenly stop. This too is not a push: the same leaf moves one person and not another; the movement happens inside the person. So the order of the thirteen rays is the order of asking, not the order of the universe, and not a ladder that lifts people up. One ray leaves a question behind; the next begins to ask from there. Whether anyone asks depends on a person's cannot-not, not on the question.
A beauty has two faces. Completive beauty is the construct come into place: full, quiet, there. Generative beauty is the construct being chiseled out: tense, in motion. The beauty of chaos is the one exception, having only the completive face, because before chaos there is nothing that could chisel chaos out; its completeness means lacking nothing, not being whole, and it is not necessarily quiet: looked back upon, it does not stop but changes all the time. The rays of mathematics, physics and causation have a third face. The remainder marks a place where one can go on, and a direction; on these three rays that place sometimes has a shape of its own, drawn by what already stands. Seeing that shape is also a kind of beauty, called the beauty of the remainder. It does not push anyone to fill the gap.
A ray is a direction of judgment, not a classification of objects. The same field of stars can show the beauty of mathematics, of physics, of causation, of perception, of cognition. A ray paper does not ask to which beauty an object belongs; it asks only what the power of judgment sees in that one direction.
5.2 The Thirteen Rays
Ray One: the beauty of chaos (0DD). Looking back from where things have already been divided. Chaos is the undivided whole: not disorder, not nothingness, not randomness, but the state in which nothing has yet been divided off; it lacks nothing, because there is not yet a standard by which to judge what it lacks. A subject who looks back at chaos cannot not see, and having seen cannot not acknowledge, one thing: no distinction that has been made has the right to pass final judgment on the whole. It is three things at once: lacking nothing; no distinction having the right to final judgment; and, looked back upon, never stopping but changing all the time. Its relation to the Daoist wu. The beauty of chaos is the only beauty with completive beauty alone and no generative beauty, because chaos has no "where it came from." What came before chaos is an unknown unknown, a remainder of the SAE system itself.
Ray Two: the beauty of philosophy (1DD). The beauty of the first distinction. A distinction falls, and an argument that was tangled changes shape: no material has been added and no answer has appeared, but something that could not be put clearly can, for the first time, be asked. The subject who has seen cannot not acknowledge that this distinction has really opened something, and that it has not yet closed itself. The structure of Socratic questioning; a pseudo-problem dissolves once its ambiguity is removed. The generative beauty of philosophy is the first generation in the whole chisel-construct chain.
Ray Three: the beauty of mathematics (2DD). The beauty of pure form. When mathematicians say "elegant," it is not a metaphor: the subject who has seen cannot not acknowledge that this form, by its own rules alone, could not be otherwise, and that it sets its why before our eyes. It has three faces: completive beauty is seeing the why; generative beauty is the why being seen; the beauty of the remainder is seeing even what is missing. The relation between the structure of proof and beauty; Gödel, with mathematics' own rigor, marked out what a class of formal systems cannot reach.
Ray Four: the beauty of physics (3DD). The beauty of form when it settles its account with reality. The subject who has seen cannot not acknowledge that the world has answered this form, and answered it exactly where the form could not be otherwise. Symmetry, conservation laws and the brevity of an equation are not in themselves beauty; the beauty is in the world's answering at the point where the form is necessary. E=mc² is beautiful not because it is short, but because the world answered it exactly where that equation could not be otherwise. Duality lets two very different forms receive the same answer. This ray also has the beauty of the remainder: the forms that already stand and the answers the world has already given draw a gap together.
Ray Five: the beauty of causation (4DD). What has happened cannot be undone. The subject who has seen cannot not acknowledge that what has happened cannot become not having happened; it remains in what comes after, and what comes after thereby has a history. The rings of a tree, the patina on an old object, the broken edge of a ruin are the shape that what has happened leaves on things; what the subject who sees them cannot not acknowledge is that shape, and the sadness it stirs belongs to each person. The increase of entropy is one way the world writes before and after; it is not the construct of this level. How the direction of causation relates to the direction of entropy is a question left open. This ray also has the beauty of the remainder: records point only to the past, while the fundamental equations mostly do not distinguish before from after, and what is missing is a special starting point.
Ray Six: the beauty of biology (5DD+6DD). The leap from chemistry to life. The subject who has seen cannot not acknowledge that a living thing, exchanging its material, is still itself; that its offspring are not it and yet carry on its pattern; and that what it keeps and what it hands on cannot be completely accounted for by outside conditions. Why this beauty needs two DD levels: it is two halves of one beauty. The inward half is self-maintenance, keeping itself while its material is exchanged; the outward half is replication, offspring that resemble it and are not it. Both halves have the same source: a living thing has a remainder of its own, which stays with it and is not averaged away by large numbers; this is what distinguishes it from a stone.
Ray Seven: the beauty of reproduction (7DD+8DD). Division of labor and reproduction. The subject who has seen cannot not acknowledge that the parts of a living thing differ, each in its own place, and only together are they the thing; that it dies, but its pattern does not die with it, and the whole of it grows again from a single cell; and that what grows each time is not entirely the same. Difference becomes role, and offspring grow their complex selves again from a single cell. This too is two halves of one beauty: the half within the body is the division of labor, the half across generations is reproduction. Replication belongs to the beauty of biology; inheritance and variation belong here. Of the beauty spoken of in sexual selection, this ray says only what kind it is not; what it is, is left to the beauty of perception.
Ray Eight: the beauty of perception (9DD+10DD). Weight and appearance. The subject who has seen cannot not acknowledge that the world has weight for a living thing and appears to it; what appears is not everything, it is about something, and it has a look of its own: even unused, it is still as it is. This is two halves of one beauty: the half of selection is weight, the half of perception is appearance; in a single act of looking, what the weight reveals is the very cut and the very "about" of what appears. Kant's common sense corresponds to aesthetics itself, with the opposite modality (see 5.1); his disinterestedness (not looking in order to use) and purposiveness without a purpose (even unused, it is still as it is) correspond to looking at the level of perception. Pleasure is not the mark of beauty: beauty is not necessarily pleasant, and what is pleasant is not necessarily beautiful.
Ray Nine: the beauty of cognition (11DD+12DD). Memory and anticipation: the absent is still there, the not-yet-come arrives first, and for the first time the construct goes beyond the present. The subject who has seen cannot not acknowledge that a living thing still remembers what is no longer before it and anticipates what has not yet come; that what it remembers is not the original, and what it anticipates may, when the time comes, fall through; what is remembered reaches forward and becomes what is anticipated, and when that falls through, what moves in return is the remembered. What has just passed and still sounds in the ear, what will come on the next beat, is the breadth of perception and belongs to the beauty of perception; the beauty of cognition begins with what is no longer before one. Reflexivity is not here; it belongs to the beauty of the self. The difference between the beauty of philosophy and the beauty of cognition: the beauty of philosophy is a first distinction giving shape to a question; the beauty of cognition is the construct going beyond the present for the first time.
Ray Ten: the beauty of the self (13DD). The first beauty after the phase transition. The appearance of the "I": the construct becomes itself, and judgment has an owner. The subject who has seen cannot not acknowledge that a living thing, when it sees wrongly, does not say the world was wrong but says, I saw wrongly; that judgment has an owner; and that the owner is finite: it has an origin and edges, and where it is going, the direction is not yet its own. Reflexivity, knowing that one is looking, remembering, waiting, belongs to this ray, not to the beauty of cognition. Heidegger's "being-toward-death" serves only as a contrast, not as the definition of this level; finitude here is written as origin, edges and direction, not as the fear of death. A wholeness that only returns to itself, with no "not" folding back upon it, is counted by Ray Ten as a counterfeit.
Ray Eleven: the beauty of purpose (14DD). One's own cannot-not: a direction has come, not pushed by others, not set on a whim, but one I cannot not follow. The subject who has seen cannot not acknowledge that a person is going somewhere, not pushed by others and not on a whim; other paths also make sense, but he cannot exchange his; the direction has come and he has taken it up; not going is something he cannot do. Purpose here is not a set goal. The colonization of a personal aesthetic is also written on this ray: a ruler that is not his own takes the place of his own law; having a history is not the same as being colonized; it may also be cultivation.
Ray Twelve: the beauty of non-doubt (15DD). Inwardly, self-legislation; outwardly, acknowledging others as ends too: I do not need your confirmation, and I do not confirm on your behalf. Not needing your confirmation means that your agreement is not a precondition of my judgment; it does not mean that you may not ask me on what grounds. Non-doubt is not "I have no doubts"; it is "I do not need others to tell me I am right": I can still be wrong, and can still change. Not doubting that you too are an end, without waiting for you to recognize me first: this is one-directional. The subject who has seen cannot not acknowledge that a person stands on his own law: if you do not nod, he still stands; if you ask on what grounds, he can say, and he does not forbid your questioning; your share, he leaves to you; he recognizes you as an end too, without waiting for you to recognize him first.
Ray Thirteen: the beauty of mutual non-doubt (16DD). The beauty of the bridge. Two subjects recognize each other as ends. The bridge is not fusion, not annexation, not rewriting each other: if anything has changed after the chiseling, it grew in each person himself; it was not written in by the other. Mutual chiseling comes first: having chiseled, one finds that the other has not fallen, and this finding is the entrance to 16DD. It is not that once the chiseling is done one stops chiseling; non-doubt is the cannot-not of chiseling;[^57] when one meets the other, one does not hold back the hammer, but it is not that one has to meet. Having recognized each other, neither asks anything of the other, and they may also leave each other alone. The subject who has seen cannot not acknowledge that two people each stand on their own law, each recognizes the other as an end too; you chisel me, I chisel you; after the chiseling, neither has fallen; neither asks the other for a confirmation. The confirmation meant here is finding, after the chiseling, that the other is still standing; it is not a demand, and not a judgment on the other's behalf. Widened, many people who recognize one another in this way are heading toward the kingdom of ends: between two people a first form of it can already be seen, and among many it is still a direction; whether it deserves the name of a kingdom, this paper does not decide. This is the last of the thirteen rays, not the highest.
6. Non-Trivial Predictions
The strength of a theory lies not only in what it can explain but in what it dares to predict, and in the conditions under which it is willing to admit that it is wrong. If any of the following four predictions is falsified, this framework must be revised.
Prediction One: Dimensional Misalignment Is the Main Structural Source of Disagreement about Aesthetic Claims
When two people argue over whether X is beautiful, and both are making claims on the overlap, they will tend toward agreement if they are speaking of beauty at the same dimension. Persistent, irreconcilable disagreement usually means that they are using the word "beautiful" at different dimensions. What is meant here is disagreement about aesthetic claims, not differences of personal aesthetic: which beauty moves each person and where each stops differs anyway, and that is a legitimate personal difference, not a disagreement to be removed.
One person says, "This poem is not beautiful"; another says, "This poem is very beautiful." If the first is speaking of its structure of sound and meter (the beauty of mathematics, 2DD), and the second of a line planted at the poem's opening, which the reader keeps in mind and expects to return at the end (the beauty of cognition, 11DD+12DD), they are not disputing the same beauty; they are talking past each other at different dimensions. Once the dimensions are aligned ("we are both speaking of this poem's structure of sound and meter"), the disagreement will shrink considerably.
Falsification condition: find two people who make opposite claims about the beauty of the same object at the same dimension, whose disagreement persists and cannot be reconciled, where the disagreement cannot be attributed to differing judgments about "full unfolding," cannot be attributed to a difference of context (Theorem Two), and cannot be attributed to one of them not having seen: both meet the standard of seeing for this dimension (as each ray paper sets it out).
Prediction Two: The Anti-Correlation of Beauty with Alien Control Holds at Every Dimension
At any dimension, other things being equal, an increase in alien control that is unrelated to the construct's own law and that the construct cannot reclaim, revise or withdraw from lowers the fullness of beauty. This should hold at both low and high dimensions. A low-dimensional example: an over-axiomatized mathematical system loses its elegance; axiomatizing for its own sake is alien control, not the own law of the mathematical construct. A high-dimensional example: excessive self-monitoring is a ruler that is not one's own taking the place from which one looks at oneself (see 5.1), and then the beauty of the self weakens.
Falsification condition: find a dimension at which, other things being equal, an increase in alien control that is unrelated to the construct's own law and that the construct cannot reclaim, revise or withdraw from systematically increases the fullness of beauty.
Prediction Three: The Transition between 12DD and 13DD Is the Only Subjectivity Transition in the Present Sequence
In the sequence of thirteen beauties, there is only one place where the construct acknowledged changes from not being a subject to being itself a subject: between 12DD and 13DD. The shift from a pair of DDs carrying one ray to each DD standing as a paper of its own also occurs only there.
Falsification condition: at another position, the object acknowledged also changes from not being a subject to being itself a subject, or a discontinuity in the rule of forming papers arises that is likewise caused by subjectivity itself. Changes elsewhere that are only a thickening of the same kind of unfolding do not count.
Prediction Four: The Place Any Successful Theory of Aesthetics Looks at Falls on One or More of the Thirteen Beauties
This is the boldest prediction and also the easiest to test. "Falls on" is this paper's reading: each school uses its own words and looks at its own concerns; this paper does not put words in their mouths, but says only on which ray the place they look at lies. Some theories look not at a particular beauty but at aesthetics itself: how the overlap comes about and how it is colonized. That is not a miss; Kant's common sense and decolonial aesthetics are both here. What falsification must find is a theory that looks at a particular beauty yet falls on none of the rays.
Kantian aesthetics: common sense corresponds to aesthetics itself, with the opposite modality: he says that everyone ought to agree; this paper says that whoever looks cannot not see, and whoever has seen cannot not acknowledge. His disinterestedness and purposiveness without a purpose correspond to looking at the level of perception.
Hegelian aesthetics: he looks at art, and art is one way in which spirit knows itself. Of "the sensuous appearance of the Idea," the half that is appearance falls on the beauty of perception. The half in which spirit knows itself, this paper does not place in the beauty of the self: the owner in the beauty of the self is finite, the place where a mistake can fold back; a wholeness in which everything has returned to itself and nothing remains uncontained is placed by Ray Ten among the counterfeits. "The end of art" says that art is no longer the highest way in which spirit knows itself; this paper does not follow that step: when higher dimensions appear, appearance at the level of perception is still there (Theorem Five).
Analytic aesthetics: it moves the question to "what is art?" and "when is art?" This is a question of the kind that belongs to the beauty of philosophy (1DD): letting a first distinction fall within "anything could be art."
Evolutionary aesthetics: sexual selection connects mainly with the beauty of perception (selection and perception); the beauty of reproduction takes up only inheritance and variation.
Neuroaesthetics: what it describes is mostly the mechanisms of liking, pleasure and reward, which relate to the level of perception; correlation is not constitution, and it cannot tell whether anything has been seen.
Japanese material, in its own words: Yoshida Kenkō asks whether we are to look at cherry blossoms only in full bloom, and at the moon only when there are no clouds. He says that to long for the moon while facing the rain has more aware, and that branches about to open and a garden strewn with fallen blossoms are more worth seeing.[^58] He looks at more than one place. This paper meets him at the fallen blossoms: the shape that what has happened leaves on things, which falls on the beauty of causation (4DD). His aware is his own.
Environmental aesthetics: crosses dimensions, centered on the beauty of perception (9DD+10DD).
Everyday aesthetics: crosses dimensions, centered on the beauty of perception and the beauty of cognition.
Decolonial aesthetics: does not correspond to any one ray. What it asks about is cultivation and colonization (see 5.1), which holds for all thirteen rays.
Falsification condition: find a theory of aesthetics with explanatory power that looks at a particular beauty and yet cannot fall on any of the thirteen beauties. If a new DD had to be set up to hold it, that too counts as falsification: it means that the postulate of the DD hierarchy has been broken and this table must change; it is not recorded as an exemption for this paper.
7. Conclusion
Recovery
Starting from the SAE dimensional sequence, this paper has answered again what beauty is: when a construct fully unfolds at a given dimension, the subject who sees it cannot not acknowledge that it is beautiful; the part that subjects with judgment cannot not acknowledge together is the overlap, and that is aesthetics; a personal aesthetic is each person's own.
This answer recovers the territory abandoned in the two hundred years after the death of aesthetics. The beauty of chaos, of the primes, of causation is no longer a "metaphor": those who have seen cannot not acknowledge it, and the ground is the full unfolding of the construct at each dimension. At the same time the answer keeps the beauty at the levels of perception and cognition that traditional aesthetics cared about: the work of Kant and Hegel was not wrong; it has been placed at its own dimensions. Finally, the answer extends upward to the beauty of subjectivity: the beauty of the self, of purpose, of non-doubt and of mutual non-doubt, territory that traditional aesthetics has rarely treated systematically.
Contributions
First, it places the ground of aesthetics in the construct: the ground precedes the subject, aesthetics does not. The construct does not wait for anyone; aesthetics waits for subjects.
Second, it states three propositions of aesthetics and their chain (cannot not be beautiful, cannot not develop, there is no supreme beauty, cannot not be questioned), with two hinges of derivation, the Remainder Overflow Principle and the subject's own cannot-not: the remainder is the direction, the cannot-not is the drive.
Third, it gives six core theorems (the Chisel-Construct Identity, the Internality of Context, the Anti-Correlation of Beauty with Alien Control, Dimensional Irreducibility, the Conservation of Locus, and Thickening), which make up the mechanics of SAE aesthetics.
Fourth, it identifies the phase transition between 12DD and 13DD: the construct acknowledged changes from not being a subject to being itself a subject.
Fifth, it gives the chain of conditions for the subject of aesthetics (cannot not see, cannot not pursue, cannot not be questioned), and separates the subject of aesthetics (the creator whose chiseling and constructing face the overlap) from the subject of a personal aesthetic.
Sixth, it separates aesthetics from personal aesthetics: aesthetics is the overlap, a personal aesthetic is each person's own; to say "it is beautiful" is a claim on the overlap that can be right or wrong. It also traces where the overlap comes from.
Seventh, it provides the prescription for "The Artist Is Dead": the artist is not the source of beauty but one who carries out the chiseling at a few dimensions; the artist's death was not caused by outside forces but by a break within the chain of subject conditions.
Open Questions
First, the internal structure of each beauty is unfolded separately in the thirteen ray papers; each of these, too, is only one unfolding in the present context, not a final answer.
Second, whether the criterion of "full unfolding" is uniform across dimensions, or whether each dimension needs its own. This may be the point in the whole framework that most needs further work.
Third, whether the chisel-construct chain has a reverse direction: whether beauty at a higher dimension can "chisel downward" into a lower one. Everyday experience suggests that it can (a person with a deep understanding of himself sees the starry sky differently), but this needs a more precise account in theory.
Fourth, the kingdom of ends. Widened, the beauty of mutual non-doubt, many people recognizing one another in this way, is heading toward the kingdom of ends; between two people a first form of it can already be seen, and among many it is still a direction. Whether it deserves the name of a kingdom, this paper does not decide; whether many people who recognize and question one another can grow into a common legislation is, as SAE: The First Critique says, left to SAE: The Second Critique, and it lies beyond the scope of this paper.
Fifth, the concrete shape, at each dimension, of the boundary between aesthetics and personal aesthetics: where the overlap lies and what is left to each person. The ray papers have dealt with part of this, one by one, but not all of it.
To Kant
Kant's Critique of the Power of Judgment built a bridge between nature and freedom. He used judgment to connect understanding and reason, and beauty to connect the true and the good. The bridge was finely designed and carried two hundred years of thinking about aesthetics.
This paper stands very close to him. The idea of the overlap is his direction: to call a thing beautiful is not to say that I like it but to demand the agreement of everyone, a demand that rests neither on concepts nor on statistics. Where the distance lies is clearest in his own words. First, he says that common sense does not say that everyone will agree but that everyone ought to agree;[^59] here it is exactly the other way round: no "ought," only that whoever looks cannot not see, and whoever has seen cannot not acknowledge. Second, he would hold judgment up, as it were, against the whole of human reason;[^60] here we speak of subjectivity, not reason, and of those who have seen, not of everyone. Third, whether common sense is constitutive or regulative, he says he does not yet wish, and is not able, to investigate here;[^61] nor is it decided for him here. Fourth, he takes common sense to be the effect of the free play of the faculties;[^62] here the ground of the overlap is placed in the construct and its dimension. Fifth, for him, to tell whether something is beautiful is to refer the representation to the subject's feeling of pleasure and displeasure, and the determining ground of a judgment of taste can only be subjective;[^63] here, judgment rests on seeing, and whether pleasure comes along differs from person to person. This point concerns what judgment rests on, not the ground of the overlap. The starting points also differ: the place where he begins to ask falls, on this paper's view, in the stretch of perception; here the asking begins at 0DD.
SAE Judgment and Aesthetics tries to do something different. Not to build a bridge between two domains, but to show that beauty from 0DD to 16DD is different stretches of one river. The beauty of chaos is the river's source; the beauty of mutual non-doubt is, for now, its mouth, but not its end: the river is still flowing on. Each stretch in between, philosophy, mathematics, physics, causation, biology, reproduction, perception, cognition, self, purpose, non-doubt, is terrain the river passes through; each terrain gives the river a different form, but the river is one river.
The bridge is not built between two separated things. The bridge is the river itself.
If Kant could see this river, perhaps he would be glad: the bridge he built at the middle stretch, the stretch of perception, has now been seen for what it is. It was not a bridge joining two banks; it was the form the river itself takes at that stretch.
Acknowledgments
This paper is the general outline of the aesthetics branch of the SAE (Self-as-an-End) philosophical system and is published under the sole name of Han Qin. The author made the final decision on all philosophical arguments and choices, and alone is responsible for the final text.
Both drafting assistance and review for the second edition were carried out with large language models. Drafting and internal precision audit were done by Claude (Anthropic); structural gatekeeping and pre-publication sign-off were done by ChatGPT (OpenAI). The material on the history of ideas used in 4.4, "Where the Overlap Comes From," was first gathered by ChatGPT's deep research and then checked item by item against the primary texts; what could not be checked is marked in the notes. The second edition passed final review by both the internal precision audit and the structural gate, followed by a key-sentence check. I thank these systems and the research and engineering teams behind them. Their comments were decided by the author one by one, and both acceptances and rejections are on record; the record of revisions and withdrawals across rounds is not reproduced here.
Notes
[^1]: Han Qin, SAE Methodological Overview: The Chisel-Construct Cycle (2026), DOI: 10.5281/zenodo.18842449; The Epistemological Map of Chisel-Construct (2026), DOI: 10.5281/zenodo.18918194; How to Find Remainders with AI (2026), DOI: 10.5281/zenodo.18929390.
[^2]: Han Qin, One's Own Law: The SAE Critique of Ethics and Morality (2026), DOI: 10.5281/zenodo.19037566.
[^3]: Plato, Symposium 210a–212a, in Platonis Opera, ed. John Burnet, vol. 2 (Oxford: Clarendon Press, 1910); Philebus 65a.
[^4]: Aristotle, Metaphysics M.3, 1078a36–b1, in Aristotle's Metaphysics, ed. W. D. Ross (Oxford: Clarendon Press, 1924).
[^5]: Alexander Gottlieb Baumgarten, Aesthetica (Frankfurt an der Oder: Kleyb, 1750), §§1, 14.
[^6]: David Hume, "Of the Standard of Taste," in Essays: Moral, Political, and Literary, ed. Eugene F. Miller, rev. ed. (Indianapolis: Liberty Fund, 1987), 241, 244.
[^7]: Immanuel Kant, Kritik der Urtheilskraft, in Kant's gesammelte Schriften, ed. Königlich Preußische Akademie der Wissenschaften, vol. 5 (Berlin: Reimer, 1913), §8, 5:216.
[^8]: Kant, Kritik der Urtheilskraft, §62, 5:366.
[^9]: F. W. J. Schelling, Philosophie der Kunst, lectures of 1802–3, first published in Sämmtliche Werke, pt. 1, vol. 5 (Stuttgart: Cotta, 1859).
[^10]: G. W. F. Hegel, Vorlesungen über die Ästhetik I, in Werke, vol. 13 (Frankfurt am Main: Suhrkamp, 1970), 13–14; English in Aesthetics: Lectures on Fine Art, trans. T. M. Knox, vol. 1 (Oxford: Clarendon Press, 1975), 1–2. Edited by H. G. Hotho from lecture manuscripts and students' notes.
[^11]: Hegel, Vorlesungen über die Ästhetik I, Werke 13:151; Knox, 111.
[^12]: Hegel, Vorlesungen über die Ästhetik I, Werke 13:25; Knox, 11.
[^13]: Martin Heidegger, "Der Ursprung des Kunstwerkes," in Holzwege, Gesamtausgabe, vol. 5 (Frankfurt am Main: Klostermann, 1977), 68; English in Poetry, Language, Thought, trans. Albert Hofstadter (New York: Harper & Row, 1971), 80.
[^14]: Nelson Goodman, "When Is Art?," in Ways of Worldmaking (Indianapolis: Hackett, 1978), 57–70; Arthur Danto, "The Artworld," Journal of Philosophy 61, no. 19 (1964): 571–84; George Dickie, Art and the Aesthetic: An Institutional Analysis (Ithaca, NY: Cornell University Press, 1974).
[^15]: Theodor W. Adorno, Ästhetische Theorie, in Gesammelte Schriften, vol. 7 (Frankfurt am Main: Suhrkamp, 1970), 97; English in Aesthetic Theory, trans. Robert Hullot-Kentor (Minneapolis: University of Minnesota Press, 1997), 61.
[^16]: Pierre Bourdieu, Distinction: A Social Critique of the Judgement of Taste, trans. Richard Nice (Cambridge, MA: Harvard University Press, 1984); Jacques Rancière, The Politics of Aesthetics, trans. Gabriel Rockhill (London: Bloomsbury, 2013), 8.
[^17]: Mary Mothersill, Beauty Restored (Oxford: Clarendon Press, 1984); Elaine Scarry, On Beauty and Being Just (Princeton, NJ: Princeton University Press, 1999); Nick Zangwill, The Metaphysics of Beauty (Ithaca, NY: Cornell University Press, 2001); Alexander Nehamas, Only a Promise of Happiness (Princeton, NJ: Princeton University Press, 2007).
[^18]: Han Qin, The Artist Is Dead: One-Dimensional Civilization Is the Killer (2026), DOI: 10.5281/zenodo.19104160.
[^19]: Kant, Kritik der Urtheilskraft, §20, 5:238; cf. §9, 5:217.
[^20]: Han Qin, SAE: The First Critique (2026), DOI: 10.5281/zenodo.21439120.
[^21]: Han Qin, SAE: The First Critique, chap. 1, §3, "With Kant: Opposite Directions of Travel, One Formal Meeting Point."
[^22]: Han Qin, SAE: The First Critique, chap. 1, §2, "Dismantling Three Things Mistaken for Necessities"; chap. 5, §1, "The Question and the Method: Grading, Not Grounding."
[^23]: Zeami, Kakyō 花鏡, the section 「舞声為根」, in Nose Asaji 能勢朝次, Zeami jūrokubushū hyōshaku 世阿彌十六部集評釋, vol. 1 (Tokyo: Iwanami Shoten, 1940); also in Omote Akira 表章 and Katō Shūichi 加藤周一, eds., Zeami, Zenchiku 世阿弥 禅竹, Nihon shisō taikei 24 (Tokyo: Iwanami Shoten, 1974).
[^24]: Han Qin, SAE: The First Critique, chap. 1, §2, "Dismantling Three Things Mistaken for Necessities."
[^25]: Han Qin, Aesthetics as a Structural Field of Subject-Conditions (2026), DOI: 10.5281/zenodo.18748930.
[^26]: Kant, Kritik der Urtheilskraft, §1, 5:203.
[^27]: John Rawls, Political Liberalism, expanded ed. (New York: Columbia University Press, 2005), lecture 4.
[^28]: Rawls, Political Liberalism, lecture 3, 94 (page as cited in secondary literature).
[^29]: Aristotle, De anima 3.1–2, ed. W. D. Ross (Oxford: Clarendon Press, 1956); Ibn Sīnā, Kitāb al-Nafs (al-Shifāʾ), 4.1, in Avicenna's De Anima, ed. F. Rahman (London: Oxford University Press, 1959), 163–69.
[^30]: Guoyu 國語, "Zheng yu" 鄭語, with the commentary of Wei Zhao 韋昭, juan 16, Sibu congkan edition. The passage reads 以它平它謂之和，故能豐長而物生之. For 它, most current editions read 他; for 物生之, most read 物歸之. This paper follows the Sibu congkan text.
[^31]: Chunqiu Zuozhuan 春秋左傳, Duke Zhao, year 20, with the commentary of Du Yu 杜預, in Chunqiu jingzhuan jijie 春秋經傳集解, juan 24, Sibu congkan edition.
[^32]: Lunyu 論語, "Zilu" 子路, 13.23 (chapter numbering follows the CHANT text).
[^33]: Mengzi 孟子, "Gaozi I" 告子上, chap. 7, with the commentary of Zhao Qi 趙岐, in Mengzi zhushu 孟子注疏, juan 11, Wenyuange Siku quanshu edition.
[^34]: Bharata, Nāṭyaśāstra, chap. 6, prose after verse 31, GRETIL e-text; English in The Nāṭyaśāstra, trans. Manomohan Ghosh, vol. 1 (Calcutta: Royal Asiatic Society of Bengal, 1950), 105.
[^35]: Raniero Gnoli, The Aesthetic Experience According to Abhinavagupta, 2nd ed. (Varanasi: Chowkhamba Sanskrit Series Office, 1968), xxi–xxii.
[^36]: Abhinavagupta, Locana on Dhvanyāloka 1.1, Kashi Sanskrit Series ed. (Benares, 1940), GRETIL e-text.
[^37]: Anthony Ashley Cooper, Third Earl of Shaftesbury, Sensus Communis: An Essay on the Freedom of Wit and Humour (London, 1709), pt. 3, sec. 1.
[^38]: Giambattista Vico, Principj di scienza nuova (Naples, 1744), §142; English in The New Science of Giambattista Vico, trans. Thomas Goddard Bergin and Max Harold Fisch (Ithaca, NY: Cornell University Press, 1984).
[^39]: Hans-Georg Gadamer, Wahrheit und Methode (Tübingen: Mohr, 1960), pt. 1, I.1.b, β, "Sensus communis," and δ, "Geschmack."
[^40]: Francis Hutcheson, An Inquiry into the Original of Our Ideas of Beauty and Virtue, 2nd ed. (1726), treatise 1, sec. 1, in the edition by Wolfgang Leidhold (Indianapolis: Liberty Fund, 2004), 25 (page as cited in secondary literature).
[^41]: Kant, Kritik der Urtheilskraft, §2, 5:204.
[^42]: Frank Sibley, "Aesthetic Concepts," Philosophical Review 68, no. 4 (1959): 421–50, at 428.
[^43]: Hume, "Of the Standard of Taste," 226–49.
[^44]: Kant, Kritik der Urtheilskraft, §7, 5:212.
[^45]: Kant, Kritik der Urtheilskraft, §8, 5:216.
[^46]: Kant, Kritik der Urtheilskraft, §18, 5:237.
[^47]: Kant, Kritik der Urtheilskraft, §22, 5:239.
[^48]: Kant, Kritik der Urtheilskraft, §40, 5:293.
[^49]: Kant, Kritik der Urtheilskraft, §22, 5:239–40.
[^50]: Hannah Arendt, "The Crisis in Culture," in Between Past and Future, enl. ed. (New York: Viking, 1968), 220 (page as cited in secondary literature).
[^51]: Bourdieu, Distinction, 6.
[^52]: Richard Wollheim, Art and Its Objects, 2nd ed. (Cambridge: Cambridge University Press, 1980), 233 (page as cited in secondary literature).
[^53]: C. Thi Nguyen, "Autonomy and Aesthetic Engagement," Mind 129, no. 516 (2020): 1127–56.
[^54]: Kant, Kritik der Urtheilskraft, §22, 5:239.
[^55]: Han Qin, SAE: The First Critique.
[^56]: Guo Qingfan 郭慶藩, Zhuangzi jishi 莊子集釋, "Yangsheng zhu" 養生主 (CHANT text, Kanripo KR5c0126), 119 (page as marked in the TLS text).
[^57]: Han Qin, SAE: The First Critique, chap. 5, §3, "The Road's Later Stretch: from Selection to Mutual Non Dubito," the summit station (16DD).
[^58]: Yoshida Kenkō 吉田兼好, Tsurezuregusa 徒然草, sec. 137, in Tsukamoto Tetsuzō 塚本哲三, ed., Makura no sōshi, Hōjōki, Tsurezuregusa 枕草紙・方丈記・徒然草 (Tokyo: Yūhōdō Shoten, 1911), 395.
[^59]: Kant, Kritik der Urtheilskraft, §22, 5:239.
[^60]: Kant, Kritik der Urtheilskraft, §40, 5:293.
[^61]: Kant, Kritik der Urtheilskraft, §22, 5:239–40.
[^62]: Kant, Kritik der Urtheilskraft, §20, 5:238.
[^63]: Kant, Kritik der Urtheilskraft, §1, 5:203.
References
Works of the SAE system cited here are archived on Zenodo, with the Chinese and English versions in the same record. The DOIs cited are concept DOIs, which always resolve to the latest version, so version numbers and access dates are not given. All are single-authored (Han Qin). Drafting and review assistance is described in the Acknowledgments.
Abhinavagupta. Dhvanyālokalocana. Kashi Sanskrit Series. Benares, 1940. GRETIL e-text.
Adorno, Theodor W. Ästhetische Theorie. In Gesammelte Schriften, vol. 7. Frankfurt am Main: Suhrkamp, 1970.
———. Aesthetic Theory. Translated by Robert Hullot-Kentor. Minneapolis: University of Minnesota Press, 1997.
Arendt, Hannah. Between Past and Future. Enl. ed. New York: Viking, 1968.
Aristotle. Aristotle's Metaphysics. Edited by W. D. Ross. Oxford: Clarendon Press, 1924.
———. De anima. Edited by W. D. Ross. Oxford: Clarendon Press, 1956.
Baumgarten, Alexander Gottlieb. Aesthetica. Frankfurt an der Oder: Kleyb, 1750.
Bharata. Nāṭyaśāstra. GRETIL e-text.
———. The Nāṭyaśāstra. Translated by Manomohan Ghosh. Vol. 1. Calcutta: Royal Asiatic Society of Bengal, 1950.
Bourdieu, Pierre. Distinction: A Social Critique of the Judgement of Taste. Translated by Richard Nice. Cambridge, MA: Harvard University Press, 1984.
Chunqiu jingzhuan jijie 春秋經傳集解. Commentary by Du Yu 杜預. Sibu congkan edition.
Danto, Arthur. "The Artworld." Journal of Philosophy 61, no. 19 (1964): 571–84.
Dickie, George. Art and the Aesthetic: An Institutional Analysis. Ithaca, NY: Cornell University Press, 1974.
Gadamer, Hans-Georg. Wahrheit und Methode. Tübingen: Mohr, 1960.
Gnoli, Raniero. The Aesthetic Experience According to Abhinavagupta. 2nd ed. Varanasi: Chowkhamba Sanskrit Series Office, 1968.
Goodman, Nelson. Ways of Worldmaking. Indianapolis: Hackett, 1978.
Guo Qingfan 郭慶藩. Zhuangzi jishi 莊子集釋. CHANT text (Kanripo KR5c0126).
Guoyu 國語. Commentary by Wei Zhao 韋昭. Sibu congkan edition.
Hegel, G. W. F. Aesthetics: Lectures on Fine Art. Translated by T. M. Knox. 2 vols. Oxford: Clarendon Press, 1975.
———. Vorlesungen über die Ästhetik I. In Werke, vol. 13. Frankfurt am Main: Suhrkamp, 1970.
Heidegger, Martin. Holzwege. Gesamtausgabe, vol. 5. Frankfurt am Main: Klostermann, 1977.
———. Poetry, Language, Thought. Translated by Albert Hofstadter. New York: Harper & Row, 1971.
Hume, David. Essays: Moral, Political, and Literary. Edited by Eugene F. Miller. Rev. ed. Indianapolis: Liberty Fund, 1987.
Hutcheson, Francis. An Inquiry into the Original of Our Ideas of Beauty and Virtue. Edited by Wolfgang Leidhold. Indianapolis: Liberty Fund, 2004. First published 1725; 2nd ed. 1726.
Ibn Sīnā. Avicenna's De Anima. Edited by F. Rahman. London: Oxford University Press, 1959.
Kant, Immanuel. Kritik der Urtheilskraft. In Kant's gesammelte Schriften, edited by Königlich Preußische Akademie der Wissenschaften, vol. 5. Berlin: Reimer, 1913. First published 1790.
Lunyu 論語. CHANT text (Kanripo KR1h0004).
Mengzi zhushu 孟子注疏. Commentary by Zhao Qi 趙岐, subcommentary by Sun Shi 孫奭. Wenyuange Siku quanshu edition.
Mothersill, Mary. Beauty Restored. Oxford: Clarendon Press, 1984.
Nehamas, Alexander. Only a Promise of Happiness. Princeton, NJ: Princeton University Press, 2007.
Nguyen, C. Thi. "Autonomy and Aesthetic Engagement." Mind 129, no. 516 (2020): 1127–56.
Plato. Platonis Opera. Vol. 2. Edited by John Burnet. Oxford: Clarendon Press, 1910.
Qin, Han. Aesthetics as a Structural Field of Subject-Conditions. 2026. DOI: 10.5281/zenodo.18748930.
———. The Artist Is Dead: One-Dimensional Civilization Is the Killer. 2026. DOI: 10.5281/zenodo.19104160.
———. The Epistemological Map of Chisel-Construct. 2026. DOI: 10.5281/zenodo.18918194.
———. How to Find Remainders with AI. 2026. DOI: 10.5281/zenodo.18929390.
———. One's Own Law: The SAE Critique of Ethics and Morality. 2026. DOI: 10.5281/zenodo.19037566.
———. SAE: The First Critique. 2026. DOI: 10.5281/zenodo.21439120.
———. SAE Methodological Overview: The Chisel-Construct Cycle. 2026. DOI: 10.5281/zenodo.18842449.
Rancière, Jacques. The Politics of Aesthetics. Translated by Gabriel Rockhill. London: Bloomsbury, 2013.
Rawls, John. Political Liberalism. Expanded ed. New York: Columbia University Press, 2005.
Scarry, Elaine. On Beauty and Being Just. Princeton, NJ: Princeton University Press, 1999.
Schelling, F. W. J. Philosophie der Kunst. In Sämmtliche Werke, pt. 1, vol. 5. Stuttgart: Cotta, 1859.
Shaftesbury, Anthony Ashley Cooper, Third Earl of. Sensus Communis: An Essay on the Freedom of Wit and Humour. London, 1709.
Sibley, Frank. "Aesthetic Concepts." Philosophical Review 68, no. 4 (1959): 421–50.
Vico, Giambattista. Principj di scienza nuova. Naples, 1744.
———. The New Science of Giambattista Vico. Translated by Thomas Goddard Bergin and Max Harold Fisch. Ithaca, NY: Cornell University Press, 1984.
Wollheim, Richard. Art and Its Objects. 2nd ed. Cambridge: Cambridge University Press, 1980.
Yoshida Kenkō 吉田兼好. Tsurezuregusa 徒然草. In Makura no sōshi, Hōjōki, Tsurezuregusa 枕草紙・方丈記・徒然草, edited by Tsukamoto Tetsuzō 塚本哲三. Tokyo: Yūhōdō Shoten, 1911.
Zangwill, Nick. The Metaphysics of Beauty. Ithaca, NY: Cornell University Press, 2001.
Zeami 世阿弥. Kakyō 花鏡. In Nose Asaji 能勢朝次, Zeami jūrokubushū hyōshaku 世阿彌十六部集評釋, vol. 1. Tokyo: Iwanami Shoten, 1940.
———. Kakyō 花鏡. In Zeami, Zenchiku 世阿弥 禅竹, edited by Omote Akira 表章 and Katō Shūichi 加藤周一. Nihon shisō taikei 24. Tokyo: Iwanami Shoten, 1974.