Toward an Epistemology of Art

Arnold Cusmariu

Abstract: An epistemology of art has seemed problematic mainly because of

arguments claiming that an essential element of a theory of knowledge, truth,
has no place in aesthetic contexts. For, if it is objectively true that something is
beautiful, it seems to follow that the predicate “is beautiful” expresses a
property – a view asserted by Plato but denied by Hume and Kant. But then, if
the belief that something is beautiful is not objectively true, we cannot be said
to know that something is beautiful and the path to an epistemology of art is
effectively blocked. The article places the existence aesthetic properties in the
proper context; presents a logically correct argument for the existence of such
properties; identifies strategies for responding to this argument; explains why
objections by Hume, Kant, and several other philosophers fail; and sketches a
realization account of beauty influenced by Hogarth.
Keywords: epistemology of art, aesthetic properties, the problem of universals,
realization, Plato, David Hume, Immanuel Kant

1. Preliminaries
Philosophers have argued that truth, an essential component of any theory of
knowledge, has no place in aesthetic contexts, thereby raising a seemingly
decisive objection to efforts aimed at formulating an epistemology of art. Thus,
while some philosophers might agree that we can be justified in believing that
something is beautiful, others would categorically deny that such beliefs are
objectively true because this would be to grant that there is such a property as
being beautiful. But, it has been argued, there is no such property as being
beautiful. In fact, there are no aesthetic properties at all; it’s just a façon de parler.
If aesthetic judgments are not objectively true, the path to an epistemology of art
seems effectively blocked.
As a sculptor and a philosopher, I consider the formulation of an
epistemology of art1 essential to building a philosophical foundation for my
artwork.2 Accordingly, I will defend the thesis that there are aesthetic properties.
I will do so by reference to what has traditionally been considered the archetypal
aesthetic property, beauty – for me the key goal of art. The defense I will present
will cover aesthetic properties generally.

1 Cusmariu 2012 and Cusmariu 2016 present and defend an epistemology of science and
mathematics. Whether a semantic epistemology of art is attainable is discussed in the last
section of this article.
2 Cusmariu 2009, Cusmariu 2015a, and Cusmariu 2015b explain why such a foundation is

important.

© Symposion, 3, 1 (2016): 37-64

Arnold Cusmariu
The article proceeds as follows:
Sections 2 and 3 place the issue at hand in the proper context3 by
presenting in technical detail a Platonist solution to a key aspect of the problem
of universals.
Section 4 presents a logically correct argument to show that beauty is a
property, which can be generalized to all aesthetic properties.
Section 5 lists challenges to the soundness of this argument discussed
later.
Section 6 explains the distinction between the analysis of predication and
the analysis of predicates, whose significance is made clear subsequently.
Sections 7-16 state and then answer objections to beauty as a property
raised in the following works: Hume 2008 [1757], Kant 1987 [1781], Ayer 1946,
Scarry 1999, Zangwill 2001, McMahon 2007, and Scruton 2009.
Section 17 sketches a realization account of beauty in general terms and
Section 18 follows up with details based on the views of William Hogarth.
Finally, Section 19 explores the prospects for a semantic epistemology of
art.

2. The Problem of Universals: A Key Aspect

Four clearly distinct meanings of “is” require philosophical analysis:
(i) the “is” of predication, e.g., “7 is a prime number;”
(ii) the “is” of existence, e.g., “there is a number greater than 5;”
(iii) the “is” of identity, e.g., “7 + 5 = 12;” and
(iv) the “is” of composition, e.g., “a chair is a seat, back, legs and arm rests.”

Analysis of predication entails completing the schemas,

(1) x(Fx ≡ _____)
(2) x1 … xn(R(x1 … xn) ≡ _____),
where “Fx” is any meaningful monadic predicative open sentence and “R(x1 …
xn)” is any meaningful relational predicative open sentence.4

3. A Platonist Solution
Platonism completes (1) and (2) by appealing to “one over many” properties and
relations (in intension) understood as abstract, non-contingent universalia ante

3 In Art & Abstract Objects, editor Christy Mag Uidhir (2012, 1) comments: “… aesthetics has
long cultivated a disturbingly insular character …” I entirely agree. This is one of the points of
this article.
4 The term “meaningful” is used here without any commitment to a theory of meaning or

meaningfulness.

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 Toward an Epistemology of Art
rem independent of mind, time, space, and empirical reality in general – what
Frege called “the third realm” (Frege 1956 [1918], 302):
(1*) x(Fx ≡ x exemplifies F-ness)
(2*) x1 … xn(R(x1 … xn) ≡ <x1 … xn> exemplifies R-ness)
Platonism interprets (1*) and (2*) as quantifying over properties and
relations (in intension),5 allowing substitutions for “Fx” in (1*) and “R(x1 … xn)” in
(2*) whatever degree of latitude is necessary for a general analysis of
predication. Thus, truth-values are properties of propositions (Frege 1970
[1892]); mathematics studies properties and relations of and between abstract
objects, including properties and relations themselves (Gödel 1944); and laws of
nature are causal or probabilistic relations between generic events understood
as property exemplifications (Kim 1976; Brown 1992).
Restrictions on (1*) are needed to block counterexamples such as the
equivalence class Bertrand Russell discovered that bears his name (Russell
1967[1902], 124-125). The Russell sentence “~(x exemplifies x)” is a meaningful
monadic predicative open sentence, hence may be substituted for “Fx” in (1*) but
fails to express a property because a contradiction follows from this
substitution.6 Under Platonism, no restrictions are placed on (1*) and (2*)
beyond logical form and those required to secure consistency.
Only unbridled Platonism, which I hold (cf. Bealer 1982; Tooley 1977;
Wolterstorff 1970), can solve the problem of universals for the whole of science
and mathematics (cf. Whitehead 1925; Church 1951; Penrose 2005).7 Unbridled
Platonism entails the existence of properties and relations of any type or
complexity whatever.
Popular ways of begging the question against Platonist unversalia ante rem
is to assert that existence of properties and relations depends on whether:
(a) they are exemplified or exemplifiable;

5 Shapiro 1991 covers technical issues involved in such quantification.

6 I discuss this problem informally in Cusmariu 1978a and more formally in Cusmariu 1979b.
Three other problems for Platonism, negative existentials, the Bradley-Ryle exemplification
regress and the “Third Man” argument are discussed in Cusmariu 1978b, 1980, and 1985,
respectively. A recent attack on abstract entities (Dorr 2008), considers the Bradley argument
definitive (44), evidently unaware that, as shown in Cusmariu 1980, Platonism can easily
escape the regress. Briefly: there is no infinite regress of exemplification relations because,
being a recurring universal, the same exemplification relation holds throughout, so all stages
of the regress collapse into one; even if there were such a regress, an infinity (denumerable or
not) of relations is not vicious under Platonism; finally, to insist on a different exemplification
relation at every stage of the regress is to beg the question against “one over many” Platonism.
7 Predication is implicit in the φ(x) condition of the comprehension schema of Zermelo-

Fraenkel (ZF) set theory, (∃y)(x)(x∈ y ↔ x∈ v & φ(x)). Only unbridled Platonism meets the
requirement that attributes match the logical complexity of predicative open-sentence
substitutions of φ(x) in the language of ZF.

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Arnold Cusmariu
(b) they are related causally, counterfactually, or probabilistically to anything;
(c) exemplification is contingent or necessary, analytic or synthetic;
(d) exemplification supervenes on the exemplification of other properties;
(e) exemplification is “objective,” “subjective,” “contextual,” or “conceivable;”
(f) exemplification is inferable from other properties an object might have;
(g) exemplification is justified only if some other property is exemplified;
(h) an empirical test exists or can be devised for observing exemplification;
(i) any of (a)-(h) are justified, a priori or a posteriori.

4. Proving That Beauty is a Property

What about “x is beautiful”? This is a meaningful monadic open sentence in
which the copula has predicative meaning, hence its account falls under (1*):
(1*a) x(x is beautiful ≡ x exemplifies Beauty)
However, Platonism formally implies the existence of Beauty as the
property exemplified by all and only beautiful objects if and only if substituting
“x is beautiful” for “Fx” in (1*) yields a consistent sentence. (1*a) seems to be a
consistent sentence. The question whether beauty is a property, then, has an
easy answer under unbridled Platonism: it is the same as the answer to every
question whether an open sentence expresses a property. On this view, the
ontology of “x is beautiful” is nothing special. The same is true of every
meaningful open sentence of the form “x is F” where “F” is an aesthetic predicate.
The existence of Beauty can be proved by a simple argument:
(AC1) If “Gx” is a meaningful monadic predicative open sentence and the result
of substituting “Gx” for “Fx” in (1*) is a consistent sentence, then there is a
property expressed by “Gx.”
(AC2) “x is beautiful” is a meaningful monadic predicative open sentence and
the result of substituting “x is beautiful” for “Fx” in (1*) is a consistent
sentence.8

Therefore,
(AC3) There is a property expressed by “x is beautiful,” being beautiful.

5. Challenging the Argument

Those who wish to reject the conclusion of a logically correct argument must
offer grounds for rejecting its premises, in this case (AC1) or (AC2).

8 Syntactically, “x is beautiful” is the simplest member of an equivalence class of open

sentences that includes, e.g., (y)(y = x → y is beautiful),” meaning that the consistency
requirement must apply to the entire equivalence class. This is complex technical issue best
left to a paper with a different scope.

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 Toward an Epistemology of Art
(AC1) is a conditional, so the simplest strategy in the present context is to
grant that the (conjunctive) antecedent of (AC1) is true for “x is beautiful” and
show that the negation of the consequent is true for “x is beautiful.” That is, show
the following:
(AC1.1) There is no property expressed by “x is beautiful.”

(AC2) is a conjunction, so there are two are strategies for challenging it.
The first strategy is to show that the negation of the first conjunct is true:
(AC2.1) “x is beautiful” is not a meaningful monadic predicative open sentence.

The second strategy is to show that the negation of the second conjunct is
true:
(AC2.2) The result of substituting “x is beautiful” for “Fx” in (1*) is not a
consistent sentence.

Strategies for defending (AC1.1) discussed below in connection with the

objections of philosophers named earlier are:
(AC1.11) “x is beautiful” does not express a property because aesthetic
judgments only describe attitudes or states of mind and are intended to evoke
responses.
(AC1.12) “x is beautiful” does not express a Platonist property because
aesthetic properties can be analyzed in terms of “projections of sentiment.”
(AC1.13) “x is beautiful” does not express a Platonist property because beauty
does not exist independently of mind; beautiful objects; or properties common
to all and only beautiful objects.
(AC1.14) Science does not recognize the property of being beautiful.
(AC1.15) “x is beautiful” does not express a property because a property
provides information relevant to object recognition or to an object’s function or
purpose; being beautiful provides no such information.
(AC1.16) “x is beautiful” does not express a property because this property is
not the reason why things are beautiful.
(AC1.17) If “x is beautiful” expresses a property, then we must analyze it in
terms of properties had by all beautiful things; but this is unwarranted.

I am not aware of anyone who has adopted strategies (AC2.1) or (AC2.2). I will
skip the latter but will discuss the former in the case of Hume and Kant because
of the opportunity to apply tools of modern logic to the views of two great and
influential philosophers.
It is beyond the scope of an article such as this to discuss the following
claims:
(i) “x is beautiful” does not express a Platonist property because there are no
abstract objects of any kind.

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Arnold Cusmariu
(ii) Sentences containing an apparent reference to the property of being
beautiful can be paraphrased into logically equivalent sentences without such
reference.
(iii) An adequate theory of the aesthetic dimension is possible without
assuming there is such a property as being beautiful, or any other aesthetic
property.

6. A Basic Distinction Explained

Though the term “aesthetics” is a 17th century invention (Baumgarten 2013
[1739], §533, 205) the subject itself has been in philosophy ever since Plato put
beauty on the philosophical map. He singled it out as a special form and placed it
alongside truth and justice at the foundations of civilization.
When we apply Plato’s Theory of Forms to the problem of universals, we
find that the ontological status of beauty, truth, and justice is the same – indeed,
no different from that of other forms. A conundrum arises: How can the ontology
of these forms be the same when the analyses of the forms themselves are so
very different, belonging to three branches of philosophy: aesthetics,
epistemology, and ethics?
The appearance of inconsistency can be dispelled by drawing a basic
distinction between the analysis of predication and the analysis of predicates.
(AP1) “x is beautiful,” “x is true” and “x is just” univocally express monadic
predication, which Platonism analyzes according to (1*) as exemplification of
Truth, Justice and Beauty. Flowers are beautiful, sentences (propositions, beliefs,
statements) are true, and actions are just in the same sense of “are.” Moreover,
the ontology of the forms involved must be treated the same way under the
Theory of Forms for a simple and technically sound reason: quantifiers must be
given the same interpretation for all objects so that the system can define rules
of inference for quantifiers (the usual four). “There is” must have the same
interpretation in “there is a property all and only beautiful things have in
common,” “there is a property all and only true sentences have in common” and
“there is a property all and only just acts have in common” even though the
properties in question are different and are exemplified by objects of different
categories.
(AP2) Logically separate from the analysis of predication and its ontology
is the analysis of predicative content, e.g., how the predicate “F” in “x is F” is to be
analyzed and even whether such an analysis is possible, necessary or justified. It
would be irrelevant to object to an analysis of predication or its ontology by
raising problems for an analysis of predicative content. Thus, while Plato
proposed an analysis of what it is to be just as well as an analysis of the form
justice, he might well not have done both. It would be irrelevant to object to the
Theory of Forms as an analysis of predication in “x is just” by raising problems
for Plato’s principle of non-interference in his analysis of justice.

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7. Hume 2008 [1757]: Objection Answered
Hume stated the following in a famous and often-quoted passage:
Beauty is no quality of things themselves: it exists merely in the mind which
contemplates them; and each mind perceives a different beauty. To seek the
real beauty is as fruitless as to pretend to ascertain the real sweet or real bitter.
(2008 [1757]: 136-137).9

Objection: There is no property expressed by “x is beautiful” because

beauty exists merely in the contemplating mind. 10
Comment: The argument below is a reconstruction using modern
terminology to make Hume’s objection easier to grasp in the present context.
(H1) Beauty exists merely in the contemplating mind.
(H2) If beauty exists merely in the contemplating mind, then the open sentence
“x is beautiful” is not objectively true of anything.
(H3) If the open sentence “x is beautiful” is not objectively true of anything,
then it is not a proper substitution in the abstraction schema for properties (1*).
(H4) If the open sentence “x is beautiful” is not a proper substitution in the
abstraction schema for properties (1*), then the open sentence “x is beautiful”
does not express a property.
Therefore,
(H5) The open sentence “x is beautiful” does not express a property.

Reply: (H3) is false. An open sentence need not be objectively true of

anything to be a proper substitution in the abstraction schema for properties
(1*). It is sufficient that the open sentence “x is beautiful” is meaningful, monadic,
and its substitution does not lead to contradiction. The Humean condition would
severely hamstring (1*) as part of the solution of the problem of universals.

8. Restating Hume’s Objection

Comment: The objection below was not available to anyone writing philosophy
during the 18th century. I raise it only to answer what I think is an interesting
“what if” question. The same applies to the restatement of Kant’s objection in
Section 10.
Objection: “x is beautiful” does not express a property because this
sentence is not monadic; hence it is not a proper substitution in the abstraction
schema (1*).

9Hutcheson 1973 and Burke 1958 held a similar view.

10Another discussion of Hume’s objection is Mothersill 1984, 177-208. This book also
approaches the question whether beauty is a property without regard to the problem of
universals; nor is there an effort to extract technically detailed arguments from Hume (or
Kant, Mothersill 1984, 209-246.)

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Arnold Cusmariu
A promising approach here is Russellian (Russell 1905): Show that the
apparent logical form of “x is beautiful” is not its real form. That is, appearances
to the contrary notwithstanding, the logical form of “x is beautiful” is not
monadic. The argument would go this way: Propose an analysis showing the
logical form of “x is beautiful” to be very different from what it seems to be – call
it H* – such that H* may no longer be substituted for “Fx” in (1*), thus blocking
the existence of the property being beautiful.
What, then, is the logical form of “x is beautiful” that Hume can be
construed as proposing? His comment that beauty “exists merely in the
contemplating mind” suggests that the logical form of “x is beautiful” can be
rendered not as monadic but rather as relational because the relational terms
“considered” and “contemplates” occur in it:
(H*) “whoever contemplates x considers x to be beautiful.”

Thus, substituting (H*) for “Fx” in (1*) is inappropriate because only

monadic substitutions are allowed, whereas (H*) seems not to have that form.
Reply: Let us make the logical form of (H*) explicit:
(H**) “(y)(y contemplates x → y considers x to be beautiful).”

What determines the degree (power) of an open sentence is the number of

variables occurring free in it, as decided by Frege’s development of
quantification theory. (H**) contains only one free variable, “x.” The fact that this
variable occurs twice, once on each side of the conditional, does not mean that
(H**) is not monadic, nor is it relevant that relational terms occur in it. Therefore,
(H**) may legitimately be substituted for “Fx” in (1*), resulting in the property
being considered to be beautiful by whoever contemplates it. Of course, from the
fact that this property is exemplified it does not follow that anything is beautiful,
just as Hume correctly implied.
However, the issue is whether the existence of the property being beautiful
follows from the existence of the property being considered to be beautiful by
whoever contemplates it. Further analysis is necessary to make this clear. In a
paper of this scope I can only explain informally how syntactical requirements
on substitution in (1*) would handle logically complex open sentences such as
(H**).
The consequent of (H**), where the aesthetic predicate “beautiful” occurs,
is ambiguous between a de re interpretation,
(H**a) “y considers x to be beautiful,”

and a de dicto interpretation

(H**b) “y considers that x is beautiful.”

(H**a) shows a relation between a person, an object and a property as an

instance of de re attitudes, which are triadic. Therefore, on the de re
interpretation of (H**), the complex property being considered to be beautiful by

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whoever contemplates it has the property being beautiful as a constituent; hence
the existence of this property follows.
In (H**b) monadic predication occurs in the propositional clause owing to
the predicative use of the copula. When this use is analyzed as part of a solution
to the problem of universals, the existence of the property being beautiful follows.
Thus, the property being beautiful is a constituent of the complex property being
considered to be beautiful by whoever contemplates it under a de dicto
interpretation as well.
Therefore, the existence (not exemplification) of the property being
beautiful follows from the existence of the property being considered to be
beautiful by whoever contemplates it. Modern logic does not help Hume avoid
having to grant that there is a property expressed by “x is beautiful.”
Counter: Another parsing of “x is beautiful” that would change its logical
form in a way that is consistent with Hume’s view on the nature of aesthetic
judgments is this:
(H***) “Pleasurable sensations are experienced while contemplating x.”
Reply: (H***) won’t do because pleasurable sensations can be experienced
in contexts having nothing whatever to do with beauty or any other aesthetic
property. Changing logical form does not render a parsing immune to
counterexamples. 11
Counter: Perhaps Hume can complicate the parsing of “x is beautiful”
slightly:
(H***a) “Pleasurable sensations are experienced while contemplating x
aesthetically.”

Reply: (H***a) won’t do because predication of “beautiful” is embedded in

the true counterfactual this parsing entails: “Were it not for the fact that x is
beautiful or has aesthetic value or has properties that are beautiful or have
aesthetic value, x would not invite aesthetic contemplation.” Counterfactuals
have properties as constituents by virtue of predication as well. Thus, a
proposition expressed by a sentence of the form “were it not for the fact that-p, it
would not be the case that-q” entails the existence of whatever properties are
entailed by predication implicit in p and q, as we already saw in (H**b). Finally,
there is the very real possibility that pleasurable sensations could be
experienced while contemplating aesthetically something grotesque. It is easy to
find examples in modern art that prove the inequivalence of “x is beautiful” and
(H***a).

11Ramsey’s comment that Russell theory of descriptions as a “paradigm of philosophy”

(Ramsey 1965, 263) is true also in this sense: The theory contained the novel methodological
insight that the analysis of logical form requires nothing less than logically necessary and
sufficient conditions. On methodological aspects of Russell’s theory, see Black 1944, 242-244.

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Arnold Cusmariu
I conclude that a Russellian construal of Hume’s view that “beauty exists
merely in the mind which contemplates them” does not show that “x is beautiful”
is not a proper substitution in (1*). It appears that modern logic cannot rescue
Hume.

9. Kant (1987 [1781]): Objection Answered

Remarks at several junctures of the Critique of Judgment indicate that Kant
agrees with Hume on fundamental issues regarding judgments of taste:
A judgment of taste is not a cognitive judgment and so is not a logical judgment
but an aesthetic one, by which we mean a judgment whose determining basis
cannot be other than subjective. (Kant 1987 [1781], §1, 204)
He will talk about the beautiful as if beauty were a characteristic of the object
and the judgment were logical (namely a cognition of the object through
concepts of it) even though in fact the judgment is only aesthetic and refers the
object’s presentation merely to the subject. (Kant 1987 [1781], §6, 211)
Just as if, when we call something beautiful, we had to regard beauty as a
characteristic of the object, determined in it according to concepts, even though
in fact, apart from a reference to the subject’s feeling, beauty is nothing by itself.
(Kant 1987 [1781], §9, 218)

Objection 1: “x is beautiful” does not express a property because

judgments of beauty only refer to feelings experienced in reaction to an object’s
presentation.
Reply: Kant’s views about the nature of judgments of taste appear prima
facie to be equivalent to Hume’s. Thus, we could generate a Kantian argument for
the conclusion that “x is beautiful” does not express a property with only slight
revisions of the Humean argument presented above:
(K1) Judgments of beauty only refer to feelings experienced in reaction to an
object’s presentation.
(K2) If judgments of beauty only refer to feelings experienced in reaction to an
object’s presentation, then the open sentence “x is beautiful” is not objectively
true of anything.
(K3) If the open sentence “x is beautiful” is not objectively true of anything, then
it is not a proper substitution in the abstraction schema for properties (1*).
(K4) If the open sentence “x is beautiful” is not a proper substitution in the
abstraction schema for properties (1*), then the open sentence “x is beautiful”
does not express a property.
Therefore,
(K5) The open sentence “x is beautiful” does not express a property.

Reply: (K3) is still false and for the same reasons as before.

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10. Restating Kant’s Objection
Objection 2: “x is beautiful” does not express a property because this sentence is
not monadic; hence it is not a proper substitution in the abstraction scheme for
properties (1*).
Kant has available in his aesthetic theory resources that may allow him to
defend this objection for different reasons.12
Judgments of taste are part of Kant’s effort to explain how judgments in
general are possible – the possibility of judgment being a key concern in all three
Critiques. Judgments of taste are possible, says Kant, only after a kind of
conceptual purity has been achieved at the last of four “moments” – a
notoriously difficult concept to interpret that I can only sketch here (cf. Allison,
Guyer, and Wenzel).
In the first moment, one frees the mind of expectations of personal gain.
This poses significant challenges because it runs counter to the mindset required
to accomplish goals needed for survival. With self-interest switched off, one
moves on to the second moment, where creativity occurs in the form of free play
of the imagination. In the third moment, one withholds the application of
concepts related to objects of aesthetic appreciation, including concepts related
to purpose or function. Having reached the fourth moment, one is now “open” to
the aesthetic dimension and judgments of taste are possible, i.e., seeing an object
only as an aesthetic “end-in-itself.”13
If Kant is to block the substitution of “x is beautiful” for “Fx” in (1*) under a
Russellian variant of strategy S3, he must also supply an explanation of why this
open sentence does not have a logical form that implies the existence of being
beautiful.
The four moments together with Kant’s views on judgments of beauty
suggest the following parsing of “x is beautiful:”
(K*) “x is an object of disinterested and purpose-free satisfaction unmediated
by concepts.”

However, (K*) fails to capture the subjectivist aspect of beauty in the Kant
quotes above. Let us also be explicit about the logical structure of (K*):
(K**) “(y)(if y is a person, then x is an object of disinterested and purpose-free
satisfaction unmediated by concepts for y.)”

(K**) is a meaningful open sentence in one free variable, hence may be

substituted for “Fx” in (1*). The result is the complex property being the object of

12 In light of the “antinomy of taste” (Kant 1987: §5), S3 may be an option for Kant as well; how
exactly is beyond the scope of this article. An insightful recent discussion of the antinomy is
Allison 2001, Ch. 11.
13 Kant’s description of the four moments suggests he is an aesthetic attitude theorist in a

sense that leaves him open to well-known objections (Dickie 1964).

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Arnold Cusmariu
disinterested and purposeless satisfaction unmediated by concepts for any person,
which does not seem to entail the property being beautiful.
Reply: The inequivalence of (K**) and “x is beautiful” leaps to the eye. We
can easily choose aesthetic predicates other than “beautiful” and find cases of
“disinterested and purpose-free satisfaction unmediated by concepts for a
person.”
Counter: Kant can try to block the substitution of “x is beautiful” for “Fx” in
(1*) on grounds of logical form without claiming equivalence between (K**) and
“x is beautiful,” regarding which here are three options.
Option 1: A deductive argument with the conclusion,
(C) “x is beautiful” is not a monadic predicative open sentence.
Give his fourth-moment view about the possibility of aesthetic judgments,
the premise Kant has available to support this conclusion is,
(P1) x is an object of disinterested and purpose-free satisfaction unmediated by
concepts for a person.

However, P1 is insufficient for a valid inference to (C). To secure validity, a

second premise would be needed, such as
P2. If x is an object of disinterested and purpose-free satisfaction unmediated
by concepts for a person, then “x is beautiful” is not a monadic predicative open
sentence.

Reply: The problem here is that the logical form of sentences about an
object x does not depend on psychological factors about the sort of attention that
a person can direct upon x. Thus, Kant is open to Frege’s critique of psychologism
(Frege 1974 [1884]), which warns against going from psychology to logic. So
Option 1 is a failure.
Option 2: Assert a non-logical relation R between “x is beautiful” and “x is
an object of disinterested and purpose-free satisfaction unmediated by concepts
for a person,” such that “x is beautiful” features neither monadic nor relational
predication owing to bearing R to “x is an object of disinterested and purpose-
free satisfaction unmediated by concepts for a person.”
Reply: The problem here is that it is not easy to say what R might be. A
possible candidate is supervenience. However, supervenience is usually
understood (Kim 1984, 1990) as a relation between sets of properties, not
properties taken singly. Second, if Kant chose to redefine supervenience to hold
between properties, he would have to agree that “x is beautiful” expressed a
property, which is precisely what he is trying to deny! In any case, even if a
suitable definition of property-property supervenience could be formulated
according to which judgments of taste supervened on satisfying disinterested
and purpose-free satisfaction unmediated by concepts for a person, it would not
follow that the logical form of judgments of taste supervened on the conditions
that must be satisfied in order for someone to be in position to make such

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judgments. Supervenience is also a non-starter. What this relation R might be
remains a mystery. Option 2 also fails.
Option 3: Kant could give up on “x is an object of disinterested and
purpose-free satisfaction unmediated by concepts for a person” as the logical
form of “x is beautiful” and try to block substitution of “x is beautiful” for “Fx” in
(1*) by regarding the logical form of judgments of taste as inferable from the
three moments prior to the fourth – where, by definition, one is not yet in a
position to make judgments of taste, including whether something is beautiful.
Reply: The problem here is that, unlike truth and justification, logical form
is not the sort of property that can be passed from step to step even in a
deductive sequence. So, Kant is not entitled to expect the logical form of “x is
beautiful” to be other than monadic in the fourth moment just because
(assuming for the sake of argument) it is not monadic in the three prior
moments.
I conclude that Kant’s four-moment theory of aesthetic judgments does
not show that “x is beautiful” is not a proper substitution in (1*). It seems that
modern logic cannot help rescue Kant either.

11. A Different Problem for Kant

Kant’s “disinterested purposelessness unmediated by concepts” constraint is
beset by a serious problem that is independent of whether he can block
substitution of “x is beautiful” for “Fx” in (1*): Such a constraint would make it all
but impossible to appreciate, let alone derive satisfaction from, the beauty of
works of art that are conceptually challenging (Wenzel 2005, 70), some created
in Kant’s own day.
Consider Beethoven’s String Quartet in F Op. 59 (1806), whose four
sonata-form movements require grasping complex musical concepts to fully
appreciate their beauty.14 Without the mediation of such concepts, this music
will seem disconnected noise, as it did to contemporaries unfamiliar with the
new idiom.15 It will not do to respond that appreciating such music involves
technical rather than aesthetic judgments, which Kant can admit entail the
mediation of concepts, because the beauty of technical innovation in matters of
musical form is central to Beethoven’s music and musical form qualifies as an
aesthetic property in its own right. Beethoven’s predecessors Mozart and Haydn
went to great lengths to make it such; he strove to realize it in his own music as
well.

14 Cf. Radcliffe (1965, 48-60) and Kerman (1979, 117-154). Bell (1913, 23-24) makes similar
points in his observations on conceptual demands involved in music appreciation.
15 Kerman writes (1979, 119-120) “They [the Razumovsky Quartets, of which Op. 59 is No. 1]

were the first great works by Beethoven to have been lost on their essential audience;” and
later (153-154) about the same music: “In their own day they puzzled and even repelled
listeners.”

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Arnold Cusmariu
An even more dramatic example is the Grosse Fuge in B-flat Op. 133
(1826), which achieves terrifying aesthetic effects by beautiful technical means,
tearing tonality apart in a feat of virtuosity whose lessons took the rest of the
19th century, and beyond, to absorb. The paradox that is the Grosse Fuge drew
the admiration of Stravinsky.16
It might be argued that Kant’s theory has merit because it predicted the
course of modern art, which took an abstract turn in the twentieth century. The
beauty of abstract art can seemingly be appreciated only if viewers are willing to
suspend mediation of concepts.17 What is closer to the truth, however, is that
aesthetic appreciation in a modern art museum or a modern music concert need
only suspend familiar concepts about sight and sound. These must be replaced
not by a fourth-moment conceptual tabula rasa but rather by new and even more
complicated concepts of tonality and form if what is seen and heard is to make
sense, let alone be judged aesthetically.18
Tristan Tzara famously asked (1989 [1922], 248): “What good did the
theories of the philosophers do us? Did they help us to take a single step
forward?” I argued (Cusmariu 2009 and Cusmariu 2015) in the context of
sculpture that conceptual change – and with it progress – in art is as real as it is
in science. Those articles contain paradigm shifts to which mediation of concepts
from ontology and epistemology is essential, to the artist during the creative
process as well as the art lover seeking interpretation. As a working artist, my
most serious reservation about Kant is that the third Critique makes no room
even for the possibility of such developments. Philosophers writing on the arts
need to keep this in mind, if only to avoid Barnett Newman’s famous barb
(Newman 1952) that “aesthetics is for me like ornithology must be for the birds.”

12. Ayer 1946: Objection Answered

In a passage that echoes Hume and Kant, A.J. Ayer wrote:
Such aesthetic words as “beautiful” and “hideous” are employed, not to make
statements of fact, but simply to express certain feelings and evoke a certain
response. [T]here is no sense in attributing objective validity to aesthetic
judgments. (Ayer 1946, 113)

Objection 1: “x is beautiful” does not express a property

because the term “beautiful” is only used to expresses feelings and
evoke a response, not to make a statement of objective fact.

16 Radcliffe notes (1965, 181) that Beethoven’s late quartets at the time “were generally
considered repellently eccentric” and that the Grosse Fuge was “dismissed as an unintelligible
freak” (121).
17 A new theory of abstraction in art is presented in Cusmariu 2015a.
18 Hume observed (2008, 151): “A common audience can never divest themselves so far of

their usual ideas and sentiments, as to relish pictures which nowise resemble them.”

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Comment: To put Ayer’s point in argument form, we need only restate
slightly the Humean and Kantian arguments above:
(A1) People use the term “beautiful” to express feelings and evoke a response.
(A2) If people use the term “beautiful” to express feelings and evoke a response,
then the open sentence “x is beautiful” is not objectively true of anything.
(A3) If the open sentence “x is beautiful” is not objectively true of anything, then
it is not a proper substitution in the abstraction schema for properties (1*).
(A4) If the open sentence “x is beautiful” is not a proper substitution in the
abstraction schema for properties (1*), then the open sentence “x is beautiful”
does not express a property.
Therefore,
(A5) The open sentence “x is beautiful” does not express a property.

Reply: The problem, once again, is that (A3) is false. An open sentence
need not be objectively true of anything to be a proper substitution in the
abstraction schema for properties (1*). It is sufficient that the open sentence “x is
beautiful” is meaningful and monadic.
Objection 2: Here is what Ayer has to say about universals:
The assertion that relations are universals provokes the question, ‘What is a
universal?’; and this question is not, as it has traditionally been regarded, a
question about the character of real objects but a request for a definition of a
certain term. Philosophy, as it is written, is full of questions like this, which
seem to be factual but are not. (Ayer 1946, 58-59)

Reply: The problem of universals arises in part because of the need for “a
definition of a certain term,” i.e., the predicative meaning of the copula, whose
analysis must be necessary and sufficient for science and mathematics as well as
ordinary language. Such an analysis is not a simple matter.

13. McMahon 2007: Objections Answered

Echoing Hume, Kant and Ayer, Jennifer McMahon wrote:
Beauty is not a property of objects. A property is something that either exists
independently of mind, like solidity or mass, or is a subpersonal response to
properties that exist independently of mind, like color or shape. In addition, a
property provides us with information relevant to object recognition, the
object’s function or some determinate purpose. Most succinctly, a property is a
feature recognized by science. Beauty, on the other hand, is a subpersonal
response to the perception of properties whose construal in perception pleases
us. (McMahon 2007, 198-9)

There are three objections to consider here.

Objection 1: “x is beautiful” does not express a property independently of
mind; but only exists as a “subpersonal response to the perception of properties
whose construal in perception pleases us.”

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Arnold Cusmariu
Reply 1: This is essentially a restatement of the views of Hume, Kant and
Ayer presented above. The argument corresponding to McMahon’s objection is
subject to problems already indicated and as such need not be spelled out in
detail.
Reply 2: McMahon’s “subpersonal response to the perception of properties
whose construal in perception pleases us” understates the effects of being in the
presence of beauty. In a famous passage of the Phaedrus (1961, 251a, 497), Plato
put it this way:19
But when one … beholds a godlike face or bodily form that truly expresses
beauty, first there come upon him a shuddering and a measure of that awe
which the vision inspired, and then reverence as at the sight of a god, and but
for fear of being deemed a very madman he would offer sacrifice to his beloved,
as to a holy image of deity.

However, as Plato well understood, such accounts are a separate matter

from the analysis of predication and its ontological implications. Unless reasons
are given why aesthetic predication (not predicates) deserves special treatment,
which McMahon does not provide, a schema such as (1*) applies and the
argument above shows that “x is beautiful” does indeed express a property.
McMahon also begs the question against the Platonist conception of
properties, according to which all properties, including aesthetic ones, are
abstract objects existing independently of mind, as universalia ante rem. Beauty
exemplars might well cause a “subpersonal response” in us but this does not
mean that the existence of the property itself is contingent upon a “subpersonal
response” to instances of it. The objection also begs the question against
Platonism in requiring properties to be properties of something, which rejects
the Platonist distinction between existence and exemplification. Finally, turning
psychological concepts such as “existing independently of mind” and “being a
subpersonal response to properties that exist independently of mind” into
restrictions on substitutions for “Fx” in (1*) severely limits this schema as a
general solution to the problems of universals.
Objection 2: “x is beautiful” does not express a property because science
does not recognize beauty as a property.
Reply: It is stating the obvious that aesthetic sentences are not (yet?)
sentences of science. But so what? The ontological status of aesthetic properties
is determined by an abstraction principle such as (1*), not by empirical science.
In any case, science does recognize beauty as a property. Scarry (1999, 52) says
as much. Physicists Paul Dirac and Hermann Weyl took beauty very seriously
(Farmelo 2002, 158; Chandrasekar 1987, 65). The Dirac equation – where space
and time, energy and momentum, appear on an equal footing – is beautiful in an
abstract, mathematical sense, making it reasonable to suppose that its
exemplification in nature is beautiful in an empirical sense in light of the general

19 For a cinematic portrayal of what Plato had in mind, see Cusmariu 2015b, 98.

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 Toward an Epistemology of Art
metaphysical relation under Platonism (Penrose 2005) between things
mathematical and things empirical, borne out by modern physics. Moreover,
logicians and mathematicians routinely attribute aesthetic properties such as
elegance to proofs.
Objection 3: “x is beautiful” does not express a property because a
property provides information relevant to object recognition or to the object’s
function or purpose; being beautiful provides no such information.
Reply: This requirement is much too strong. It rules out properties closed
under the usual Boolean operations: (a) conditional properties such as being
colored if red; (b) properties everything has such as being red or not red; (c)
properties nothing has such as being a unicorn; (d) properties nothing can have
such as and being odd and even; (e) vague properties such as being taller than
someone and having less money than last year; and (f) properties expressed by
what George Boolos (1998, 57) has called “nonfirstorderizable” sentences such
as “being a man who walked into a room unaccompanied by anyone else,” which
could be true of several people at the same time. Counterexamples could be
easily multiplied. Moreover, if McMahon is understood to use “property”
generically to include relations, a list of counterexamples is easily compiled once
again. Being taller than at least one other person provides no information
“relevant to object recognition or to the object’s function or purpose;” nor does
sitting next to someone at the movies.
Platonist schemas (1*) and (2*) allow any meaningful monadic open
sentences to be substituted in (1*) and any meaningful relational open sentences
to be substituted in (2*) for sound philosophical reasons: to have available an
analysis of predication suitable for any context whatever. Adding an
informativeness requirement hamstrings (1*) and (2*) to the point where they
can no longer offer truly general solutions to the problem of universals, including,
as noted, science and mathematics.

14. Scarry 1999: Objections Answered

Elaine Scarry writes:
At no point will there be any aspiration to speak in these pages of unattached
Beauty, or of the attributes of unattached Beauty. But there are attributes that
are, without exception, present across different objects (faces, flowers,
birdsongs, men, horses, pots, and poems) one of which is this impulse toward
begetting. It is impossible to conceive of a beautiful thing that does not have
this attribute. (Scarry 1999, 9)

Scarry also raises two objections here and a third later in the book.
Objection 1: “x is beautiful” does not express a property of the sort that
exists “unattached” to beautiful objects.
Reply: Aristotle’s seems to have held such a view of properties in general –
known as universalia in rem. Though the context of Scarry’s comment is
aesthetics, the implication seems to be that an Aristotelian account of

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Arnold Cusmariu
predication works just as well as a Platonist one; that “unattached Beauty” as an
ante rem property is dispensable. This is certainly not the case, as Cusmariu
1979a shows. Nor is it the case that predication can be analyzed piecemeal, in
terms of ante rem properties and relations in one context and in rem properties
and relations in other contexts such as aesthetics.
Objection 2: The property “x is beautiful” expresses is such that we cannot
conceive of a beautiful object without an “impulse toward begetting.”
Reply: “Begetting” for Scarry means imitation or copying or replication,
not what Plato found objectionable in the Phaedrus. While it may be true that
people react in unique ways in the presence of a beautiful object and that such
objects have special causal properties, this is neither necessary nor sufficient to
an analysis of “beautiful” – counterexamples are easy to devise. “Begetting” does
nothing to help us understand the ontological issues involved in solving the
problem of universals, even in aesthetics.
Though familiar with Plato’s metaphysics, Scarry erroneously thinks that
the role of beauty in the Theory of Forms is to “verify the weight and attention
we confer” on beautiful exemplars and “justify or account for the weight of their
beauty” (Scarry 1999, 47). As we saw, however, Plato’s analysis of predication in
“x is beautiful” appeals to the property being beautiful as part of a general
solution to the problem of universals.
Scarry writes (1999, 47):
The author of the Greater Hippias, widely believed to have been Plato, points
out that while we know with relative ease what a beautiful horse or a beautiful
man or possibly even what a beautiful pot is … it is much more difficult to say
what ‘Beauty’ unattached to any object is.

Objection 3: “x is beautiful” does not express a property of the sort that

exists “unattached to” beautiful objects because this notion is hard to explain.
Reply: The author of the Parmenides, the Republic and the Theaetetus had
no such difficulty when he proposed the Theory of Forms as a solution to the
problem of universals. It is easy to specify categories of “unattached” properties:
(a) logically impossible properties such as being red and not red; (b) physically
impossible properties such as moving faster than light; (c) fictional properties
such as being a unicorn; (d) extensionless properties such as being the present
King of France; and (e) mereological oddities such as being a sparkplug and an
eyeball.

15. Scruton 2009: Objections Answered

Roger Scruton writes:
The reader will have noticed that I have not said what beauty is. I have
implicitly rejected a neo-Platonist view of beauty, as a feature of Being itself.
God is beautiful but not for this reason. And I have avoided the many attempts
to analyse beauty in terms of some property or properties supposed to be
exhibited by all beautiful things. I have not discussed the tradition of thinking,

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which again goes back to Plotinus and the neo-Platonists, which sees beauty as
a kind of organic wholeness. (Scruton 2009, 195, original emphasis)

There are three objections here. Let us consider them in turn.

Objection 1: “x is beautiful” does not express a Platonist property.
Reply: Scruton’s characterization of Platonism as implying that beauty (or
any other property) is a “feature of Being itself” and possesses “a kind of organic
wholeness” is unnecessarily obscure. (1*) and (2*) are best characterized in
technical terms as implying second-order quantification over properties and
relations as part of a Platonist solution to the problem of universals. It won’t do
to reject this solution out of hand as if the problem of universals is irrelevant in
aesthetics.20 Scruton has no solution to propose and appears unaware that the
issue even needs to be addressed.
Objection 2: “x is beautiful” does not express a property because this
property is not the reason why things are beautiful.
Reply: The Platonist schema (1*) is not about the reason why things are
thus-and-such but rather about the analysis of monadic predication as part of a
solution to the problem of universals. (1*) is about what it is to be F in the
predicative sense, as distinct from the identity, existence, and composition
senses. Moreover, analysis and explanation are logically independent concepts. It
is consistent with (1*) to suggest an explanation of why things are beautiful in
terms of properties exemplified by beautiful things – even in terms of properties
understood non-Platonistically.
Objection 3: If “x is beautiful” expresses a property, then we must analyze
it in terms of properties had by all beautiful things, but this is unwarranted.
Reply: This objection seems to confuse the analysis of predication with the
analysis of predicates. The analysis of predication in “x is beautiful” entails
nothing whatever about the analysis of the predicate “beautiful”; nor whether
such an analysis is possible, desirable, necessary or justified; nor whether
criteria exist by which to judge competing analyses; and so on. It is indeed a task
in aesthetics to analyze aesthetic properties; but whether or not this is done, or
how it is done, has no bearing on the ontological status of such properties.

16. Zangwill 2001: Objections Answered

Nick Zangwill writes:
Beauty does not stand alone. It cannot exist by itself. Things are beautiful
because of the way they are in other respects. Beauty is a property that
depends on other properties. Moreover, when we appreciate the beauty of a
thing, we appreciate its beauty as it is realized in its other properties. For
example, suppose we find a rose beautiful. What we find beautiful is a specific

20Zemach 1997 agrees with my top-down approach though he takes a different tack on the
problem of universals. I find his critique of Platonism and his solution to the problem of
universals unpersuasive but that is story for another time.

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Arnold Cusmariu
arrangement of colored petals, leaves, and stems. Beauty cannot float free of the
way things are in other respects, and we cannot appreciate beauty except
insofar as it is embodied in other respects. Beauty cannot be solitary and we
cannot appreciate it as such. (Zangwill 2001, 1)

There are three objections to consider here.

Objection 1: “x is beautiful” does not express a property understood as
existing independently of properties in virtue of which objects are beautiful.
Reply: This is a good place to distinguish several concepts of dependence.
Ontological-1: Where F and G are distinct properties, F depends on G =df
Necessarily, F exists only if G exists. 21 The obvious example is where G is a logical
constituent of F. Thus, the property being red and round is ontologically-1
dependent on its two constituent properties, being red and being round. There is
such a property as being red and round only if the properties being red and being
round also exist.
Reply: Ontological-1 dependence is trivially true under Platonism. Once
quantification over properties in (1*) has yielded F and G, which are non-
contingent entities like all abstract object, it cannot happen that F exists but G
does not, so that it is necessarily true that F exists only if G exists. The
ontological-1 dependence of beauty on properties in which it is realized is
harmless. It holds for every property derived from the predication schema (1*).
All Platonist properties “float free” in the sense of being ante rem, including those
on which beauty is ontologically-1 dependent, whatever they are.
Ontological-2: Where F and G are distinct properties, F depends on G =df
Necessarily, F exists only if G is exemplified.
Reply: Zangwill does not seem to claim that beauty is ontologically-2
dependent on other properties. In addition to begging the question against
Platonism, ontological-2 dependence would be a strange claim to make in the
general case. For example, what other properties must be exemplified in order
for the property being round to exist?
Ontological-3: Where F and G are distinct properties, F depends on G =df
Necessarily, F is exemplified only if G is exemplified. This is the case for
properties such as being equilateral and being equiangular.
Reply: The exemplification of beauty may well entail the exemplification of
some other property (or properties). This, however, is consistent with the
Platonist conception of universalia ante rem.
Analytical-1: Property F is dependent on a non-empty set of properties G
(of which F is not a member) =df Necessarily, the exemplification of F is nothing
over and above the exemplification of F by relation R between properties in the
set G. To use Zangwill’s example, the beauty of a rose is nothing over and above
the beauty of “a specific arrangement of colored petals, leaves, and stems.”

21 We must add “necessarily” because a material-conditional construal of “only if” is too weak.

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Reply: This sense of dependence is consistent with Platonism because it
does not entail that the existence of beauty is analytical-1 dependent on other
properties. For that we need a stronger sense of analytical dependence.
Analytical-2: Property F is dependent on a non-empty set of properties G
(of which F is not a member) =df Necessarily, the existence of F is nothing over
and above the exemplification of F by relation R between properties in the set G.
To use Zangwill’s example again, the beauty of a rose is nothing over and above
the beauty of “a specific arrangement of colored petals, leaves, and stems.”
Reply: (a) Requiring the existence of a property to be analytically
dependent-2 begs the question against Platonism, which rejects such a
requirement on property existence, for any property. (b) In any case, even if we
grant that “a specific arrangement of colored petals, leaves, and stems” unpacks
the predicate “beautiful,” this has no effect on the ontological status of the
property of being beautiful. Zangwil is confusing the analysis of predication with
an analysis of predicates.
Aesthetic: Property F is dependent on a non-empty set of properties G (of
which F is not a member) =df aesthetic appreciation of F is nothing over and
above appreciating whether “a specific arrangement of” the properties in G is F.
Reply: It may well be, as Zangwill says, that things are appreciated to be
beautiful because of the way they are in other respects. As already noted,
however, the ontological status of beauty is determined by quantification in
schema (1*). Construing aesthetic dependence as an ontological replacement for
(1*) comes dangerously close to ignoring the distinction between the analysis of
predication and the analysis of predicates. Moreover, aesthetic dependence
appears to be an epistemic concept; it is problematic to say the least that a valid
ontological inference can be drawn from such a concept.
Nomological: Where F and G are distinct properties, F depends on G =df
There is a law of nature connecting an event of which F is a constituent to an
event of which G is a constituent.
Reply: Zangwill does not object to the existence of beauty on ground that it
lacks a nomological connection to properties in virtue of which things are
beautiful. I bring up nomological dependence in case a scientifically minded
philosopher is tempted to deny the existence of beauty because (allegedly) there
are no laws of nature connecting this property to other properties. The point to
make is that nomological dependence holds for property exemplification, not
property existence. In other words, laws of nature connect events, which are
property exemplifications (Kim 1976), not properties themselves.
Objection 2: “x is beautiful” expresses a property only as a subjective
response to certain physical features (color, shape, etc.) contingently associated
with beauty.
Reply 1: This is close to the objections of Hume, Kant, Ayer and McMahon
already answered above and as such does not require additional comment.

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Arnold Cusmariu
Reply 2: Platonism grants that judgments about exemplified beauty can be
based on psychological factors that might as a matter of empirical fact vary from
person to person; and even that disagreements about aesthetic preferences are
not easily settled. However, these facts only apply to conditions under which
exemplifications of beauty can be judged or observed, not to whether there is
such a property as being beautiful – unless one (i) begs the question against
Platonism; (ii) ignores the distinction between the analysis of predication and
the analysis of predicates; or (iii) claims (falsely) that the subjectivity of some
judgments justifies an inference regarding the ontological status of what the
judgments are about.
Interestingly, Zangwill is not opposed to metaphysical entities as such. He
considers supervenience (2001, 49) “… a relation between two families of
properties, and therefore a metaphysical relation,” signaling acceptance of a
realist metaphysics of relations. Why the supervenience relation can “stand
alone,” “float free” and “be solitary” but properties – aesthetic or otherwise –
cannot is unclear. This is clear: A predication schema for relations but not
properties solves only half the problem of universals.22
Later, Zangwill writes (2001, 19):
Talk of aesthetic properties does not necessarily involve a commitment to a
realist metaphysics of aesthetic properties. There could be some kind of
Humean analysis of aesthetic properties in terms of projections of sentiment.

Objection 3: “x is beautiful” does not express a property in the sense of

commitment to a Platonist view of properties because aesthetic properties can
be analyzed in terms of “projections of sentiment” as Hume suggested.
Reply: This confuses the analysis of predication with the analysis of
predicates. Hume’s objections have already been answered.

17. A Realization Account of Beauty

Platonists are unsympathetic to a supervenient unpacking of the predicative
content of “x is F,” where “F” is an aesthetic predicate, because we see no reason
why non-aesthetic properties must necessarily “fix” aesthetic properties; nor
why the exemplification of non-aesthetic properties must necessarily “fix” the
exemplification of aesthetic properties. Much more congenial to our “one-over-
many” view of aesthetic properties as a way of avoiding reductionism is the idea
of realization. In this section I sketch a realization approach to Beauty in general
terms and in the next section provide details based on the views of William
Hogarth (2010 [1753]) that complements the general tenets of Platonism,
leaving a full theory for another time.

22 Having found no theory of relations in Aristotle, Cresswell 1975 reconstructs only

Aristotle’s view of properties. Cusmariu 1979a shows that Cresswell’s reconstruction is
seriously flawed. Russell 1912 famously took Berkeley and Hume to task for ignoring relations
in their rejection of abstract ideas.

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Modern physics tells us in Platonist fashion (Penrose 2005, Ch. 1; Dirac
1977, 113; Whitehead 1925) that empirical reality is an approximation of
mathematical reality. One construal of such a view is that abstract relationships
asserted as true simpliciter in mathematical contexts are only approximately true
under empirical interpretations, the stricter relationship being asserted in
empirical contexts for ease of computation because we cannot replace the
equality symbol = with the approximate equality symbol ≈ for computational
purposes. Thus, the equality sign in the Ideal Gas Law, PV = NRT, is not in
laboratory practice identity in the strict Leibnizian sense but denotes
approximate equality because of approximations on measurements of pressure,
volume and temperature due to instrumental limitations and rounding in the
value of the gas constant R, 8.3144621(75); the values in brackets are the
uncertainty (standard deviation) in the last two digits of the value of R.
The realization view of beauty I wish to hold is very similar:23
(R) An object a is beautiful if and only if where is A is a set of properties of
perfect or ideal form and B is a set of properties a, properties in B approximate
properties in A. 24

Comment: A full analysis, beyond the scope of this article, would address
the following issues: (a) which specific properties in set B are to approximate
properties in the realization set A, and (b) what exactly is the meaning of
property approximation.
To be beautiful, then, is to approximate maximal aesthetic greatness. The
properties in the base set A are a sort of limit or upper bound, which the
properties in set B approach but never reach, as Plato told us. Moreover, to say
that a is more beautiful than b is to say that properties of a are a closer
approximation of the properties in the base set A than properties of b.
The realization view of beauty is Baudelairean, who defined beauty
(Baudelaire 1976, 636) as the infinite in the finite – l’infini dans le fini.

18. A Hogarthean Variant

A theory due to William Hogarth leads to a realization analysis of the predicative
content of “x is beautiful” along the above lines, though only as a sufficient
condition of beauty in physical objects. Hogarth suggests that beauty is realized
in S-shaped curvature appearing in an object, from the vantage point of the
sagittal or coronal planes25 (or both) in one or more of the following ways: (a) a
sinuous line is suggested by the object’s posture, (b) a sinuous line traces the

23 Shoemaker 2007 expounds a different view of property realization.

24 This is a way of capturing Bell’s famous “significant form” concept (Bell 1913).
25 The sagittal plane is the imaginary vertical plane dividing the human body (and other

bilateral animals’) into left and right volumes that are approximate mirror images of one
another. Orthogonal to the sagittal plane is the coronal plane, also top-to-bottom, dividing
bilateral objects into front and back volumes.

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Arnold Cusmariu
object’s boundary line, (c) a sinuous line traces the boundary line of its
component parts, or (d) a sinuous line connects major parts. Hogarth associated
S-shaped curvature with beauty on grounds that curvature signifies liveliness
and activity, and thus attracts viewer almost instinctively as contrasted with
straight, parallel, or right-angled intersecting lines which he contended signify
stasis, death, or inanimate objects.
Now, S-curvature has mathematical meaning definable by a sigmoid
function, of which there are several varieties depending on whether both
asymptotes (tangents) are approached by the curve symmetrically, which they
are in the case of the logistic and serpentine curves but not the Gompertz curve.
On the view I am suggesting, beauty properties in some physical objects are
those that describe perfect or ideal form defined mathematically by S-curvature,
forming a realization base in the sense that, as with any mathematically
describable curvature, what is exemplified in a physical object is an
approximation. In a nutshell, beauty in a physical object means approximating S-
curvature in any of (a)-(d) that Hogarth suggested.
On this view, there is an intuitive association of beauty in physical objects
with the female form. The female figure exhibits S-curvature in all of (a)-(d) as
observed from the vantage point of the sagittal and the coronal planes, as the
reader can easily verify without my having to describe specifics. This may
explain why the female figure has been a key subject in art for such a long time.

19. A Semantic Epistemology of Art?

A semantic epistemology of art would supply semantic concepts of belief, truth
and evidence and show that they are applicable to aesthetic sentences. There are
two options:
Option (A): Proceed along the lines of semantic epistemology for science
or mathematics developed in Cusmariu 2012.
Option (B): Proceed along different lines.
Option (A): This option is available only for aesthetic sentences to which
Hogarthean realization applies, as they are the only ones that (right now) could
be translated into a scientific or mathematical language. This set of aesthetic
sentences is comparatively small, so this option is not realistic.
Option (B): For the time being, I can only indicate some of the problems to
be solved under this option.
Semantic Belief: Indexing an aesthetic belief to a language is easy enough:
(B1) Smith believes that the Mona Lisa is beautiful

becomes
(B2) Smith believes-in-English that the Mona Lisa is beautiful.

However, (B1) and (B2) are not equivalent as shown in Cusmariu 1982
and Cusmariu 1983, contrary to Carnap’s analysis (1947, 62):

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(C) There is a sentence Z in a semantical system S’ such that (a) Z in S’ is
intensionally isomorphic to “The Mona Lisa is beautiful” in English, and (b)
persons are disposed to an affirmative response to Z as a sentence of S’.

Now, (B2) could certainly be taken as primitive but that does not eliminate
the need to explain its relationship to such key properties of (B1) as that
speakers of different languages can believe the same thing or hold logically
equivalent beliefs.
Semantic Evidence: Perhaps changing the evidence-bearers of a non-
semantic theory from propositions or beliefs to sentences would be sufficient to
yield a semantic theory of evidence for natural languages that would cover
aesthetic sentences. It remains to be seen, however, which non-semantic theory
of evidence – foundationalism, coherentism, reliabilism, etc. – could be made to
work and how.
Semantic Truth: Tarski had sound technical reasons for restricting
Convention T to formal languages (Tarski 1944; see also Kirkham 1992):
(a) There appears to be no systematic way of deciding whether sentences of a
natural language are well-formed.
(b) Natural languages can describe semantic characteristics of their own
sentences, such as truth, which we know leads to the Liar Paradox.

Thus, merely changing the truth-bearers of a non-semantic conception of

truth, e.g., the correspondence theory, from propositions or beliefs to sentences
would not be sufficient to yield a semantic conception of truth for natural
languages that would cover aesthetic sentences. What would be sufficient is a
very difficult question.26

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