Scientific realism is the philosophical view that the universe
described by science (including both observable and unobservable
aspects) exists independently of our perceptions, and that verified
scientific theories are at least approximately true descriptions of what
is real. Scientific realists typically assert that science, when successful,
uncovers true (or approximately true) knowledge about nature, including
aspects of reality that are not directly observable.
Within philosophy of science,
this view is often an answer to the question "how is the success of
science to be explained?" The discussion on the success of science in
this context centers primarily on the status of unobservable entities apparently talked about by scientific theories.
Generally, those who are scientific realists assert that one can make
valid claims about unobservables (viz., that they have the same ontological status) as observables, as opposed to instrumentalism.
In a 2020 PhilPapers Survey 72% of academic philosophers favored scientific realism vs only 15% favoring antirealism.
Main features
Scientific realism involves two basic positions:
Ideal-theory thesis. It offers a set of criteria for an ideal scientific theory; one that science aims to approximate.
Convergence thesis. It maintains that, in at least some
well-established domains, the theories scientists now accept already
approximate that ideal and will do so ever more closely as inquiry
progresses.
Realists often adopt this thesis selectively; one may be realist
about mature fields such as fundamental physics while remaining agnostic
about less-settled areas.
An ideal scientific theory, on the realist view, satisfies three interconnected commitments:
Semantic: Its central claims are either true or false because they purport to describe the real world.
Metaphysical: The entities it posits (e.g. electrons, genes) exist objectively and independent of the mind.
Epistemic:
We have good reason to believe many of those claims because the
theory's explanatory and predictive success would be improbable if they
were not at least approximately true.
Taken together, the first two commitments imply that an ideal theory
makes definite assertions about genuinely exists entities, while the
third justifies believing a significant subset of those assertions.
Realists therefore argue that science progresses: later theories
generally answer more questions or do so more accurately, thus moving
closer, though never necessarily reaching, the ideal of a literally true
account of nature.
Characteristic claims
The
following claims are typical of those held by scientific realists. Due
to the wide disagreements over the nature of science's success and the
role of realism in its success, a scientific realist would agree with
some but not all of the following positions.
The best scientific theories are at least partially true.
To say that a theory is approximately true is sufficient explanation of the degree of its predictive success.
The approximate truth of a theory is the only explanation of its predictive success.
Even if a theory employs expressions that do not have a reference, a scientific theory may be approximately true.
Scientific theories are in a historical process of progress towards a true account of the physical world.
Scientific theories make genuine, existential claims.
Theoretical claims of scientific theories should be read literally and are definitively either true or false.
The degree of the predictive success of a theory is evidence of the referential success of its central terms.
The goal of science is an account of the physical world that is
literally true. Science has been successful because this is the goal
that it has been making progress towards.
History
Scientific realism is related to much older philosophical positions including rationalism and metaphysical realism.
However, it is a thesis about science developed in the twentieth
century. Portraying scientific realism in terms of its ancient,
medieval, and early modern cousins is at best misleading.
Scientific realism is developed largely as a reaction to logical positivism.
Logical positivism was the first philosophy of science in the twentieth
century and the forerunner of scientific realism, holding that a sharp
distinction can be drawn between theoretical terms and observational terms, the latter capable of semantic analysis in observational and logical terms.
Troubles with the analytic-synthetic distinction—see Quine (1950).
The theory-ladenness of observation—see Hanson (1958) Kuhn (1970) and Quine (1960).
Difficulties moving from the observationality of terms to observationality of sentences—see Putnam (1962).
The vagueness of the observational-theoretical distinction—see G. Maxwell (1962).
These difficulties for logical positivism suggest, but do not entail,
scientific realism, and led to the development of realism as a
philosophy of science.
Realism became the dominant philosophy of science after positivism.Bas van Fraassen in his book The Scientific Image (1980) developed constructive empiricism
as an alternative to realism. He argues against scientific realism that
scientific theories do not aim for truth about unobservable entities. Responses to van Fraassen have sharpened realist positions and led to some revisions of scientific realism.
Arguments for and against scientific realism
No miracles argument
One
of the main arguments for scientific realism centers on the notion that
scientific knowledge is progressive in nature, and that it is able to
predict phenomena successfully. Many scientific realists (e.g., Ernan McMullin, Richard Boyd)
think the operational success of a theory lends credence to the idea
that its more unobservable aspects exist, because they were how the
theory reasoned its predictions. For example, a scientific realist would
argue that science must derive some ontological support for atoms from the outstanding phenomenological success of all the theories using them.
Arguments for scientific realism often appeal to abductive reasoning
or "inference to the best explanation" (Lipton, 2004). For instance,
one argument commonly used—the "miracle argument" or "no miracles
argument"—starts out by observing that scientific theories are highly
successful in predicting and explaining a variety of phenomena, often
with great accuracy. Thus, it is argued that the best explanation—the
only explanation that renders the success of science to not be what Hilary Putnam
calls "a miracle"—is the view that our scientific theories (or at least
the best ones) provide true descriptions of the world, or approximately
so.
Bas van Fraassen
replies with an evolutionary analogy: "I claim that the success of
current scientific theories is no miracle. It is not even surprising to
the scientific (Darwinist) mind. For any scientific theory is born into a
life of fierce competition, a jungle red in tooth and claw. Only the
successful theories survive—the ones which in fact latched on to actual
regularities in nature." (The Scientific Image, 1980)
It has been argued that the no miracles argument commits the base rate fallacy.
Pessimistic induction
Pessimistic induction,
one of the main arguments against realism, argues that the history of
science contains many theories once regarded as empirically successful
but which are now believed to be false. Additionally, the history of
science contains many empirically successful theories whose unobservable
terms are not believed to genuinely refer. For example, the effluvium
theory of static electricity (a theory of the 16th Century physicist William Gilbert) is an empirically successful theory whose central unobservable terms have been replaced by later theories.
Realists reply that replacement of particular realist theories
with better ones is to be expected due to the progressive nature of
scientific knowledge, and when such replacements occur only superfluous
unobservables are dropped. For example, Albert Einstein's theory of special relativity showed that the concept of the luminiferous ether could be dropped because it had contributed nothing to the success of the theories of mechanics and electromagnetism. On the other hand, when theory replacement occurs, a well-supported concept, such as the concept of atoms, is not dropped but is incorporated into the new theory in some form. These replies can lead scientific realists to structural realism.
Constructivist epistemology
Social constructivists might argue that scientific realism is unable to account for the rapid change that occurs in scientific knowledge during periods of scientific revolution. Constructivists may also argue that the success of theories is only a part of the construction.
Another argument against scientific realism, deriving from the underdetermination problem,
is not so historically motivated as these others. It claims that
observational data can in principle be explained by multiple theories
that are mutually incompatible. Realists might counter by saying that
there have been few actual cases of underdetermination in the history of
science. Usually the requirement of explaining the data is so exacting
that scientists are lucky to find even one theory that fulfills it.
Furthermore, if we take the underdetermination argument seriously, it
implies that we can know about only what we have directly observed. For example, we could not theorize that dinosaurs once lived based on the fossil evidence because other theories (e.g., that the fossils are clever hoaxes) can account for the same data.
Incompatible models argument
According
to the incompatible models argument, in certain cases the existence of
diverse models for a single phenomenon can be taken as evidence of
anti-realism. One example is due to Margaret Morrison, who worked to show that the shell model and the liquid-drop model give contradictory descriptions of the atomic nucleus, even though both models are predictive.
In metaphysics, nominalism is the view that universals and abstract objects do not actually exist other than being merely names or labels.There are two main versions of nominalism. One denies the existence of
universals—that which can be instantiated or exemplified by many
particular things (e.g., strength, humanity). The other version
specifically denies the existence of abstract objects as such—objects that do not exist in space and time.
Most nominalists have held that only physical particulars in space and time are real, and that universals exist only post res, that is, subsequent to particular things. However, some versions of nominalism hold that some particulars are abstract entities (e.g., numbers),
whilst others are concrete entities – entities that do exist in space
and time (e.g., pillars, snakes, and bananas). Nominalism is primarily a
position on the problem of universals. It is opposed to realist philosophies, such as Platonic realism, which assert that universals do exist over and above particulars, and to the hylomorphic substance theory of Aristotle, which asserts that universals are immanently real within them; however, the name "nominalism" emerged from debates in medieval philosophy with Roscellinus.
The term nominalism stems from the Latinnomen, "name". John Stuart Mill summarised nominalism in his aphorism "there is nothing general except names". In philosophy of law, nominalism finds its application in what is called constitutional nominalism.
... We customarily hypothesize a single form in
connection with each of the many things to which we apply the same
name. ... For example, there are many beds and tables. ... But there are
only two forms of such furniture, one of the bed and one of the table.
(Republic 596a–b, trans. Grube)
What about someone who believes in beautiful things, but
doesn't believe in the beautiful itself ...? Don't you think he is
living in a dream rather than a wakened state? (Republic 476c)
The Platonic universals corresponding to the names "bed" and "beautiful" were the Form of the Bed and the Form of the Beautiful, or the Bed Itself and the Beautiful Itself. Platonic Forms were the first universals posited as such in philosophy.
Our term "universal" is due to the English translation of Aristotle's technical term katholou which he coined specially for the purpose of discussing the problem of universals. Katholou is a contraction of the phrase kata holou, meaning "on the whole".
Aristotle famously rejected certain aspects of Plato's Theory of Forms, but he clearly rejected nominalism as well:
... 'Man', and indeed every general predicate, signifies
not an individual, but some quality, or quantity or relation, or
something of that sort. (Sophistical Refutations xxii, 178b37, trans. Pickard-Cambridge)
The first philosophers to explicitly describe nominalist arguments were the Stoics, especially Chrysippus.
Medieval philosophy
In medieval philosophy, the French philosopher and theologianRoscellinus (c. 1050 – c. 1125) was an early, prominent proponent of nominalism. Nominalist ideas can be found in the work of Peter Abelard and reached their flowering in William of Ockham, who was the most influential and thorough nominalist. Abelard's and Ockham's version of nominalism is sometimes called conceptualism, which presents itself as a middle way between nominalism and realism, asserting that there is
something in common among like individuals, but that it is a concept in
the mind, rather than a real entity existing independently of the mind.
Ockham argued that only individuals existed and that universals were
only mental ways of referring to sets of individuals. "I maintain", he
wrote, "that a universal is not something real that exists in a
subject ... but that it has a being only as a thought-object in the mind
[objectivum in anima]". As a general rule, Ockham argued against
assuming any entities that were not necessary for explanations.
Accordingly, he wrote, there is no reason to believe that there is an
entity called "humanity" that resides inside, say, Socrates, and nothing
further is explained by making this claim. This is in accord with the
analytical method that has since come to be called Ockham's razor,
the principle that the explanation of any phenomenon should make as few
assumptions as possible. Critics argue that conceptualist approaches
answer only the psychological question of universals. If the same
concept is correctly and non-arbitrarily applied to two
individuals, there must be some resemblance or shared property between
the two individuals that justifies their falling under the same concept
and that is just the metaphysical problem that universals were brought
in to address, the starting-point of the whole problem (MacLeod &
Rubenstein, 2006, §3d). If resemblances between individuals are
asserted, conceptualism becomes moderate realism; if they are denied, it
collapses into nominalism.
Lately, some scholars have been questioning what kind of influences nominalism might have had in the conception of modernity and contemporaneity. According to Michael Allen Gillespie,
nominalism profoundly influences these two periods. Even though
modernity and contemporaneity are secular eras, their roots are firmly
established in the sacred. Furthermore, "Nominalism turned this world on its head," he argues.
"For the nominalists, all real being was individual or particular and
universals were thus mere fictions."
Another scholar, Victor Bruno, follows the same line. According
to Bruno, nominalism is one of the first signs of rupture in the
medieval system. "The dismembering of the particulars, the dangerous
attribution to individuals to a status of totalization of possibilities
in themselves, all this will unfold in an existential fissure that is
both objective and material. The result of this fissure will be the
essays to establish the nation state."
Indian philosophy encompasses various realist and nominalist traditions. Certain orthodox Hindu schools defend the realist position, notably Purva Mimamsa, Nyaya and Vaisheshika,
maintaining that the referent of the word is both the individual object
perceived by the subject of knowledge and the universal class to which
the thing belongs. According to Indian realism, both the individual and
the universal exist objectively, with the second underlying the former.
Buddhists take the nominalist position, especially those of the Sautrāntika and Yogācāra schools;they were of the opinion that words have as referent not true objects,
but only concepts produced in the intellect. These concepts are not real
since they do not have efficient existence, that is, causal powers.
Words, as linguistic conventions, are useful to thought and discourse,
but even so, it should not be accepted that words apprehend reality as
it is.
Dignāga formulated a nominalist theory of meaning called apohavada, or theory of exclusions.
The theory seeks to explain how it is possible for words to refer to
classes of objects even if no such class has an objective existence.
Dignāga's thesis is that classes do not refer to positive qualities that
their members share in common. On the contrary, universal classes are
exclusions (apoha).
As such, the "cow" class, for example, is composed of all exclusions
common to individual cows: they are all non-horse, non-elephant, etc.
The problem of universals
Nominalism arose in reaction to the problem of universals,
specifically accounting for the fact that some things are of the same
type. For example, Fluffy and Kitzler are both cats, or, the fact that
certain properties are repeatable, such as: the grass, the shirt, and
Kermit the Frog are green. One wants to know by virtue of what are Fluffy and Kitzler both cats, and what makes the grass, the shirt, and Kermit green.
The Platonist answer is that all the green things are green in virtue of the existence of a universal: a single abstract thing that, in this case, is a part
of all the green things. With respect to the color of the grass, the
shirt and Kermit, one of their parts is identical. In this respect, the
three parts are literally one. Greenness is repeatable because there is
one thing that manifests itself wherever there are green things.
Nominalism denies the existence of universals. The motivation for
this flows from several concerns, the first one being where they might
exist. Plato famously held, on one interpretation, that there is a realm of abstract forms or universals apart from the physical world (see theory of the forms).
Particular physical objects merely exemplify or instantiate the
universal. But this raises the question: Where is this universal realm?
One possibility is that it is outside space and time. A view
sympathetic with this possibility holds that, precisely because some
form is immanent in several physical objects, it must also transcend
each of those physical objects; in this way, the forms are
"transcendent" only insofar as they are "immanent" in many physical
objects. In other words, immanence implies transcendence; they are not
opposed to one another. (Nor, in this view, would there be a separate
"world" or "realm" of forms that is distinct from the physical world,
thus shirking much of the worry about where to locate a "universal
realm".) However, naturalists assert that nothing is outside of space and time. Some Neoplatonists, such as the pagan philosopher Plotinus and the Christian philosopher Augustine, imply (anticipating conceptualism) that universals are contained within the mind of God. To complicate things, what is the nature of the instantiation or exemplificationrelation?
Conceptualists hold a position intermediate between nominalism and realism, saying that universals exist only within the mind and have no external or substantial reality.
Moderate realists
hold that there is no realm in which universals exist, but rather there
universals are located in space and time however they are manifest.
Suppose that a universal, for example greenness, is supposed to be a
single thing. Nominalists consider it unusual that there could be a
single thing that exists in multiple places simultaneously. The realist
maintains that all the instances of greenness are held together by the
exemplification relation, but that this relation cannot be explained.
Additionally, in lexicology there is an argument against color realism,
namely the subject of the blue-green distinction. In some languages the equivalent words for blue and green may be colexified
(and furthermore there may not be a straightforward translation either –
in Japanese "青", which is usually translated as "blue", is sometimes
used for words which in English may be considered as "green" (such as
green apples).)
Finally, many philosophers prefer simpler ontologies populated with only the bare minimum of types of entities, or as W. V. O. Quine
said "They have a taste for 'desert landscapes.'" They try to express
everything that they want to explain without using universals such as
"catness" or "greenness."
Varieties
There are various forms of nominalism ranging from extreme to almost-realist. One extreme is predicate nominalism,
which states that Fluffy and Kitzler, for example, are both cats simply
because the predicate 'is a cat' applies to both of them. And this is
the case for all similarity of attribute among objects. The main
criticism of this view is that it does not provide a sufficient solution
to the problem of universals. It fails to provide an account of what
makes it the case that a group of things warrant having the same
predicate applied to them.
Proponents of resemblance nominalism believe that 'cat' applies to both cats because Fluffy and Kitzler resemble an exemplar cat closely enough to be classed together with it as members of its kind,
or that they differ from each other (and other cats) quite less than
they differ from other things, and this warrants classing them together. Some resemblance nominalists will concede that the resemblance relation
is itself a universal, but is the only universal necessary. Others
argue that each resemblance relation is a particular, and is a
resemblance relation simply in virtue of its resemblance to other
resemblance relations. This generates an infinite regress, but many
argue that it is not vicious.
Class nominalism argues that class membership forms the
metaphysical backing for property relationships: two particular red
balls share a property in that they are both members of classes
corresponding to their properties – that of being red and of being
balls. A version of class nominalism that sees some classes as "natural
classes" is held by Anthony Quinton.
Conceptualism
is a philosophical theory that explains universality of particulars as
conceptualized frameworks situated within the thinking mind. The conceptualist view approaches the metaphysical concept of
universals from a perspective that denies their presence in particulars
outside of the mind's perception of them.
Another form of nominalism is trope nominalism.
A trope is a particular instance of a property, like the specific
greenness of a shirt. One might argue that there is a primitive, objective
resemblance relation that holds among like tropes. Another route is to
argue that all apparent tropes are constructed out of more primitive
tropes and that the most primitive tropes are the entities of complete physics. Primitive trope resemblance may thus be accounted for in terms of causal indiscernibility.
Two tropes are exactly resembling if substituting one for the other
would make no difference to the events in which they are taking part.
Varying degrees of resemblance at the macro level can be explained by
varying degrees of resemblance at the micro level, and micro-level
resemblance is explained in terms of something no less robustly physical
than causal power. David Armstrong,
perhaps the most prominent contemporary realist, argues that such a
trope-based variant of nominalism has promise, but holds that it is
unable to account for the laws of nature in the way his theory of
universals can.
Ian Hacking has also argued that much of what is called social constructionism
of science in contemporary times is actually motivated by an unstated
nominalist metaphysical view. For this reason, he claims, scientists
and constructionists tend to "shout past each other".
Mark Hunyadi characterizes the contemporary Western world as a
figure of a "libidinal nominalism." He argues that the insistence on the
individual will that has emerged in medieval nominalism evolves into a
"libidinal nominalism" in which desire and will are conflated.
Mathematical nominalism
A notion that philosophy, especially ontology and the philosophy of mathematics, should abstain from set theory owes much to the writings of Nelson Goodman (see especially Goodman 1940 and 1977), who argued that concrete and abstract entities having no parts, called individuals,
exist. Collections of individuals likewise exist, but two collections
having the same individuals are the same collection. Goodman was himself
drawing heavily on the work of Stanisław Leśniewski, especially his mereology, which was itself a reaction to the paradoxes associated with Cantorian set theory. Leśniewski denied the existence of the empty set and held that any singleton
was identical to the individual inside it. Classes corresponding to
what are held to be species or genera are concrete sums of their
concrete constituting individuals. For example, the class of
philosophers is nothing but the sum of all concrete, individual
philosophers.
The principle of extensionality
in set theory assures us that any matching pair of curly braces
enclosing one or more instances of the same individuals denote the same
set. Hence {a, b}, {b, a}, {a, b, a, b} are all the same set. For Goodman and other proponents of mathematical nominalism, {a, b} is also identical to {a, {b}}, {b, {a, b}}, and any combination of matching curly braces and one or more instances of a and b, as long as a and b are names of individuals and not of collections of individuals. Goodman, Richard Milton Martin, and Willard Quine all advocated reasoning about collectivities by means of a theory of virtual sets (see especially Quine 1969), one making possible all elementary operations on sets except that the universe of a quantified variable cannot contain any virtual sets.
In the foundations of mathematics, nominalism has come to mean doing mathematics without assuming that sets in the mathematical sense exist. In practice, this means that quantified variables may range over universes of numbers, points, primitive ordered pairs,
and other abstract ontological primitives, but not over sets whose
members are such individuals. Only a small fraction of the corpus of
modern mathematics can be rederived in a nominalistic fashion.
Criticisms
Historical origins of the term
As
a category of late medieval thought, the concept of 'nominalism' has
been increasingly queried. Traditionally, the fourteenth century has
been regarded as the heyday of nominalism, with figures such as John Buridan and William of Ockham
viewed as founding figures. However, the concept of 'nominalism' as a
movement (generally contrasted with 'realism'), first emerged only in
the late fourteenth century, and only gradually became widespread during the fifteenth century. The notion of two distinct ways, a via antiqua, associated with realism, and a via moderna,
associated with nominalism, became widespread only in the later
fifteenth century – a dispute which eventually dried up in the sixteenth
century.
Aware that explicit thinking in terms of a divide between
'nominalism' and 'realism’ emerged only in the fifteenth century,
scholars have increasingly questioned whether a fourteenth-century
school of nominalism can really be said to have existed. While one might
speak of family resemblances between Ockham, Buridan, Marsilius and
others, there are also striking differences. More fundamentally, Robert
Pasnau has questioned whether any kind of coherent body of thought that
could be called 'nominalism' can be discerned in fourteenth century
writing. This makes it difficult, it has been argued, to follow the twentieth
century narrative which portrayed late scholastic philosophy as a
dispute which emerged in the fourteenth century between the via moderna, nominalism, and the via antiqua, realism, with the nominalist ideas of William of Ockham foreshadowing the eventual rejection of scholasticism in the seventeenth century.
Nominalist reconstructions in mathematics
A critique of nominalist reconstructions in mathematics was undertaken by Burgess (1983) and Burgess and Rosen
(1997). Burgess distinguished two types of nominalist reconstructions.
Thus, hermeneutic nominalism is the hypothesis that science,
properly interpreted, already dispenses with mathematical objects
(entities) such as numbers and sets. Meanwhile, revolutionary nominalism
is the project of replacing current scientific theories by alternatives
dispensing with mathematical objects (see Burgess, 1983, p. 96). A
recent study extends the Burgessian critique to three nominalistic
reconstructions: the reconstruction of analysis by Georg Cantor, Richard Dedekind, and Karl Weierstrass that dispensed with infinitesimals; the constructivist re-reconstruction of Weierstrassian analysis by Errett Bishop that dispensed with the law of excluded middle; and the hermeneutic reconstruction, by Carl Boyer, Judith Grabiner, and others, of Cauchy's foundational contribution to analysis that dispensed with Cauchy's infinitesimals.
Mathematical beauty is a type of aesthetic value that is experienced in doing or contemplating mathematics.
The testimonies of mathematicians indicate that various aspects of
mathematics—including results, formulae, proofs and theories—can trigger
subjective responses similar to the beauty of art, music, or nature.
The pleasure in this experience can serve as a motivation for doing
mathematics, and some mathematicians, such as G.H. Hardy, have characterized mathematics as an art form that seeks beauty. The logician and philosopher Bertrand Russell made a now-famous statement of this position:
Mathematics, rightly viewed, possesses not only truth, but supreme
beauty—a beauty cold and austere, like that of sculpture, without appeal
to any part of our weaker nature, without the gorgeous trappings of
painting or music, yet sublimely pure, and capable of a stern perfection
such as only the greatest art can show.
Beauty in mathematics has been subject to examination by
mathematicians themselves and by philosophers, psychologists, and
neuroscientists. Understanding beauty
in general can be difficult because it is a subjective response to
sense-experience but is perceived as a property of an external object,
and because it may be shaped by cultural influence or personal
experience. Mathematical beauty presents additional problems, since the
aesthetic response is evoked by abstract ideas which can be
communicated symbolically, and which may only be available to a minority
of people with mathematical ability and training. The appreciation of
mathematics may also be less passive than (for example) listening to
music. Furthermore, beauty in mathematics may be connected to other aesthetic
or non-aesthetic values. Some authors seem identify mathematical
elegance with mathematical beauty; others distinguish elegance as a
separate aesthetic value, or as being, for instance, limited to the form
mathematical exposition.
Beauty itself is often linked to, or thought to be dependent on, the
abstractness, purity, simplicity, depth or order of mathematics.
Examples of beautiful mathematics
Results
Starting at e0 = 1, travelling at the velocity i relative to one's position for the length of time π, and adding 1, one arrives at 0. (The diagram is an Argand diagram.)
Euler's identity is often given as an example of a beautiful result:
This expression ties together arguably the five most important mathematical constants (e, i, π, 1, and 0) with the two most common mathematical symbols (+, =). Euler's identity is a special case of Euler's formula, which the physicist Richard Feynman called "our jewel" and "the most remarkable formula in mathematics".
In a survey in which mathematicians were asked to evaluate 24 theorems for their beauty, the top-rated three theorems were: Euler's equation; Euler's polyhedron formula, which asserts that for a polyhedron with V vertices, E edges, and F faces, ; and
Euclid's theorem that there are infinitely many prime numbers, which was also given by Hardy as an example of a beautiful theorem.
Proofs
An example of "beauty in method"—a simple and elegant visual descriptor of the Pythagorean theorem.
The mathematician Paul Erdős spoke of The Book,
an imaginary infinite book in which God has written down all the most
beautiful mathematical proofs. When Erdős wanted to express particular
appreciation of a proof, he would proclaim it "straight from The Book!". His rhetorical device inspired the creation of Proofs from THE BOOK, a collection of such proofs, including many suggested by Erdős himself.
Objects
In Plato's Timaeus, the five regular convex polyhedra, called the Platonic solids for their role in this dialogue, are called the "most beautiful" ("κάλλιστα") bodies. In the Timaeus, they are described as having been used by the demiurge, or creator-craftsman who builds the cosmos, for the four classical elements plus the heavens, because of their beauty.
Kepler's Platonic solid model of the solar system
In his 1596 book Mysterium Cosmographicum, Johannes Kepler argued that the orbits of the then-known planets in the Solar System have been arranged by God to correspond to a concentric arrangement of the five Platonic solids, each orbit lying on the circumsphere of one polyhedron and the insphere
of another. For Kepler, God had wanted to shape the universe according
to the five regular solids because of their beauty, and this explained why there were six planets (according to the knowledge of the time).
Petrie projection of
A more modern example is the exceptional simple Lie group, which has been called "perhaps the most beautiful structure in all of mathematics".
Scientific theories
The
mathematical statements of scientific theories, especially in physics,
are sometimes considered to be mathematically beautiful. For example, Roger Penrose thought there was a "special beauty" in Maxwell's equations of electromagnetism:
Einstein's theory of general relativity has been characterized as a work of art, and, among other aesthetic praise, was described by Paul Dirac as having "great mathematical beauty" and by Penrose as having "supreme mathematical beauty".
(There can be more to the beauty of a scientific theory than just
its mathematical statement. For example, whether a theory is
visualizable or deterministic might have an influence on whether it is
seen as beautiful.)
Properties of beautiful mathematics
Many
mathematicians and philosophers who have written about mathematical
beauty have tried to identify properties or criteria that are conducive
to the perception of beauty in a piece of mathematics. It is debated
whether beauty can be clarified or explained by such properties: Paul Erdős
thought that it was no more possible to convince someone of the beauty
of a piece of mathematics than to convince them of the beauty of Beethoven's Ninth Symphony, if they couldn't see it for themselves.
Results
In his 1940 essay A Mathematician's Apology, G. H. Hardy
said that a beautiful result, including its proof, possesses three
"purely aesthetic qualities", namely "inevitability", "unexpectedness",
and "economy". He particularly excluded enumeration of cases as "one of
the duller forms
of mathematical argument".
In 1997, Gian-Carlo Rota, disagreed with unexpectedness as a necessary condition for beauty and proposed a counterexample:
A great many theorems of
mathematics, when first published, appear to be surprising; thus for
example some twenty years ago [from 1977] the proof of the existence of non-equivalent differentiable structures
on spheres of high dimension was thought to be surprising, but it did
not occur to anyone to call such a fact beautiful, then or now.
In contrast, Monastyrsky wrote in 2001:
It is very difficult to find an analogous invention in the past to Milnor's
beautiful construction of the different differential structures on the
seven-dimensional sphere... The original proof of Milnor was not very
constructive, but later E. Briscorn showed that these differential
structures can be described in an extremely explicit and beautiful form.
This disagreement illustrates both the subjective nature of
mathematical beauty and its connection with mathematical results: in
this case, not only the existence of exotic spheres, but also a
particular realization of them.
Proofs
Besides
Hardy's properties of "unexpectedness", "inevitability", "economy",
which he applied to proofs as well as results, mathematicians have
customarily thought beautiful proofs that are short and simple.
In the search for an elegant proof, mathematicians often look for
different independent ways to prove a result—as the first proof that is
found can often be improved. The theorem for which the greatest number
of different proofs have been discovered is possibly the Pythagorean theorem, with hundreds of proofs having being published. Another theorem that has been proved in many different ways is the theorem of quadratic reciprocity. In fact, Carl Friedrich Gauss alone had eight different proofs of this theorem, six of which he published.
In contrast, results that are logically correct but involve
laborious calculations or consideration of many cases, are not usually
considered beautiful, and may be even referred to as ugly or clumsy. For example, Kenneth Appel and Wolfgang Haken's proof of the four color theorem made use of computer checking of over a thousand cases. Philip J. Davis and Reuben Hersh
said that when they first heard that about the proof, they hoped it
contained a new insight "whose beauty would transform my day", and were
disheartened when informed the proof was by case enumeration and
computer verification.Paul Erdős said it was "not beautiful" because it gave no insight into why the theorem was true.
Philosophical analysis
Aristotle thought that beauty was found especially in mathematics, writing in the Metaphysics that
those who assert that the mathematical sciences say nothing of the
beautiful or the good are in error. For these sciences say and prove a
very great deal about them; for if they do not expressly mention them,
but prove attributes which are their results or their formulae, it is
not true to say that they tell us nothing about them. The chief forms of
beauty are order and symmetry and definiteness, which the mathematical
sciences demonstrate in a special degree.
In the twentieth century, some philosophers questioned whether there
was genuinely beauty in mathematics. The philosopher of science Rom Harré argued that there were no true aesthetic appraisals of mathematics, but only quasi-aesthetic
appraisals. Any mathematical success described by an aesthetic term was
a second-order success besides understanding and correctness. In
contrast, aesthetic appraisal of a work of art was first-order. Harré
considered this to be the difference between a quasi-aesthetic and a
genuinely aesthetic appraisal.
Nick Zangwill thought that there were no true aesthetic experiences of mathematics and that a proofs or theories could only be metaphorically
beautiful. His argument had two bases. First, he thought that aesthetic
properties depended on sensory properties, and so abstract entities
could not have aesthetic properties. Second, he thought that proofs,
theorems, theories, and so on had purposes such as demonstrating
correctness or granting understanding, and that any praise of them
reflected only how well they achieved their purpose.
Scientific analysis
Information-theory model
In the 1970s, Abraham Moles and Frieder Nake analyzed links between beauty, information processing, and information theory. In the 1990s, Jürgen Schmidhuber formulated a mathematical theory of observer-dependent subjective beauty based on algorithmic information theory: the most beautiful objects among subjectively comparable objects have short algorithmic descriptions (i.e., Kolmogorov complexity) relative to what the observer already knows. Schmidhuber explicitly distinguishes between beautiful and interesting. The latter corresponds to the first derivative of subjectively perceived beauty:
the observer continually tries to improve the predictability and compressibility of the observations by discovering regularities such as repetitions and symmetries and fractalself-similarity. Whenever the observer's learning process (possibly a predictive artificial neural network) leads to improved data compression such that the observation sequence can be described by fewer bits
than before, the temporary interesting-ness of the data corresponds to
the compression progress, and is proportional to the observer's internal
curiosity reward.
Neural correlates
Brain imaging experiments conducted by Semir Zeki, Michael Atiyah
and collaborators show that the experience of mathematical beauty has,
as a neural correlate, activity in field A1 of the medial orbito-frontal cortex
(mOFC) of the brain and that this activity is parametrically related to
the declared intensity of beauty. The location of the activity is
similar to the location of the activity that correlates with the
experience of beauty from other sources, such as visual art or music. Moreover, mathematicians seem resistant to revising their judgment of
the beauty of a mathematical formula in light of contradictory opinion
given by their peers.
Sacred geometry
is a field of its own, giving rise to countless art forms including
some of the best known mystic symbols and religious motifs, and has a
particularly rich history in Islamic architecture. It also provides a means of meditation and comtemplation, for example the study of the KaballahSefirot (Tree Of Life) and Metatron's Cube; and also the act of drawing itself.
Some painters and sculptors create work distorted with the mathematical principles of anamorphosis, including South African sculptor Jonty Hurwitz.
Origami, the art of paper folding, has aesthetic qualities and many mathematical connections. One can study the mathematics of paper folding by observing the crease pattern on unfolded origami pieces.
British constructionist artist John Ernest created reliefs and paintings inspired by group theory. A number of other British artists of the constructionist and systems
schools of thought also draw on mathematics models and structures as a
source of inspiration, including Anthony Hill and Peter Lowe. Computer-generated art is based on mathematical algorithms.
Aesthetics[a] is the branch of philosophy that studies beauty, taste, and related phenomena. In a broad sense, it includes the philosophy of art, which examines the nature of art, artistic creativity, the meanings of artworks, and audience appreciation.
Aesthetic properties
are features that influence the aesthetic appeal of objects. They
include aesthetic values, which express positive or negative qualities,
like the contrast between beauty and ugliness. Philosophers debate whether aesthetic properties have objective existence or depend on the subjective experiences of observers. According to a common view, aesthetic experiences are associated with disinterested pleasure
detached from practical concerns. Taste is a subjective sensitivity to
aesthetic qualities, and differences in taste can lead to disagreements
about aesthetic judgments.
Diverse fields investigate aesthetic phenomena, examining their roles in ethics, religion, and everyday life as well as the psychological
processes involved in aesthetic experiences. Comparative aesthetics
analyzes the similarities and differences between traditions such as Western, Indian, Chinese, Islamic, and African
aesthetics. Aesthetic thought has its roots in antiquity but only
emerged as a distinct field of inquiry in the 18th century when
philosophers systematically engaged with its foundational concepts.
Definition
The nature of aesthetic experiences, like the admiration of artworks, is a central topic of aesthetics.
Aesthetics, sometimes spelled esthetics, is the systematic study of beauty, art, and taste.
As a branch of philosophy, it examines which types of aesthetic
phenomena there are, how people experience them, and how objects evoke
them. This field also investigates the nature of aesthetic judgments,
the meaning of artworks, and the problem of art criticism. Key questions in aesthetics include "What is art?", "Can aesthetic judgments be objective?", and "How is aesthetic value related to other values?". One characterization distinguishes between three main approaches to
aesthetics: the study of aesthetic concepts and judgments, the study of
aesthetic experiences and other mental responses, and the study of the nature and features of aesthetic objects. In a slightly different sense, the term aesthetics can also refer to particular theories of beauty or to beautiful appearances.
Aesthetics is closely related to the philosophy of art and the
two terms are often used interchangeably since both involve the
philosophical study of aesthetic phenomena. One difference is that the
philosophy of art focuses on art, whereas the scope of aesthetics also
includes other domains, such as beauty in nature and everyday life. This
leads some theorists to argue that the philosophy of art is a subfield
of aesthetics. However, the precise relation between the two fields is disputed and
another characterization holds that the philosophy of art is the broader
discipline. This view argues that aesthetics mainly addresses aesthetic
properties, while the philosophy of art also investigates non-aesthetic
features of artworks, belonging to fields such as metaphysics, epistemology, philosophy of language, and ethics.
Even though the philosophical study of aesthetic problems originated in antiquity,
it was not until the 18th century that aesthetics emerged as a distinct
branch of philosophy when philosophers engaged in systematic inquiry
into its principles. The term "aesthetics" was coined by the German philosopher Alexander Baumgarten in 1735, initially defined as the study of sensibility or sensations of beautiful objects. The term comes from the ancient Greek words aisthetikos, meaning 'perceptible things', aisthesthai, meaning 'perceive, see', and aisthesis, meaning 'sensation, perception'. The earliest known use in the English language happened in a translation by W. Hooper in the 1770s.
Basic concepts
The domain of the aesthetic encompasses a variety of properties, objects, experiences, and judgments
associated with beauty and artistic expression. However, the exact
boundaries of this domain are disputed—it is controversial whether there
is a group of essential features shared by all aesthetic phenomena or whether they are more loosely related through family resemblances.
Another central topic concerns the relation between different aesthetic
concepts, for example, whether the concept "aesthetic object" is
defined through the concept of "aesthetic experience".
Aesthetic properties and objects
Aesthetic
properties of an object are features that shape its aesthetic appeal or
factors that influence aesthetic evaluations. For instance, when an art
critic describes an artwork as great, vivid, or amusing, they express aesthetic properties of this artwork. Some aesthetic properties focus on aesthetic value in general, like beautiful and ugly, while others center on more specific forms of value, such as graceful and elegant. Aesthetic properties can also refer to perceptual qualities of objects like balanced and vivid, to representational aspects like realistic and distorted, or to emotional responses such as joyful and angry.
The precise distinction between aesthetic and non-aesthetic
properties is disputed. According to one proposal, aesthetic properties
require a specific aesthetic sensitivity in addition to the sensory
perception of non-aesthetic properties, going beyond simple colors,
shapes, and sounds. Aesthetic properties are associated with
evaluations, but not all are intrinsically good or bad. For example, being a realistic representation may be aesthetically good in some artistic contexts and bad in others.
Diagram of the relation between aesthetic concepts. Philosophers debate whether aesthetic objects are material or intentional objects.
The school of realism argues that aesthetic properties are objective, mind-independent features of reality. A related proposal asserts that they are emergent properties
dependent on non-aesthetic properties. According to this view, the
beauty of a painting may emerge from the right combination of colors and
shapes. A different position holds that aesthetic properties are
response-dependent, for example, that features of objects only qualify
as aesthetic properties if they evoke aesthetic experiences in
observers. The terms "aesthetic property" and "aesthetic quality" are often used
interchangeably to refer to aspects such as beauty, sublimity, and
grandeur. However, some philosophers distinguish the two, associating
aesthetic properties with objective features and aesthetic qualities
with subjective experiences and emotional responses.
An aesthetic object is an object with aesthetic properties. One interpretation suggests that aesthetic objects are material entities that evoke aesthetic experiences. According to this view, if a person admires an oil painting then the physical canvas and paint make up the aesthetic object. Another interpretation, associated with the school of phenomenology, argues that aesthetic objects are not material but intentional objects. Intentional objects are part of the content of experiences and their existence
depends on the perceiver. An intentional object may accurately reflect a
material object, as in the case of veridical perceptions, but can also
fail to do so, which happens during perceptual illusions.
The phenomenological perspective focuses on the intentional object
given in experience rather than the material object considered
independently of the perceiver.
Aesthetic values and beauty
Aesthetic
values are a special type of aesthetic properties. They express the
sensory appeal of an object as a qualitative measure of its aesthetic
merit. Aesthetic values contrast with values in other domains, such as moral, epistemic, religious, and economic values. Beauty is usually considered the main aesthetic value, but not the only one. For example, the sublime is another value of things that inspire a feeling of awe and fear. Further suggested values include charm, elegance, harmony,
and grace. Historically, pre-modern philosophers typically rejected the
idea of multiple distinct aesthetic values. They tended to argue that
beauty alone encompasses all that is aesthetically commendable and
serves as a unifying concept of the whole domain of aesthetics.
Aesthetic values are either positive, like beautiful and sublime, or negative, such as clumsy and boring. Various attempts have been made to explain why some objects have
positive aesthetic values, proposing features like unity, intensity, and
the right level of complexity.
The aesthetic value of beauty is often singled out as a central topic of aesthetics. It is a key aspect of human experience, influencing both personal decisions and cultural developments. Often-cited examples of beautiful objects include landscapes, sunsets,
humans, and artworks. As a positive value, beauty contrasts with ugliness
as its negative counterpart. Beauty is typically understood as a
quality of objects that involves balance or harmony and evokes
admiration or pleasure when perceived, but its precise definition is
debated.
Various theoretical disputes surround the nature of beauty and
its role in aesthetics. Some theories understand beauty as an objective
feature of external objects. Others emphasize its subjective nature,
linking it to personal experience and perception. They argue that
"beauty is in the eye of the beholder" rather than in the perceived
object. Another central debate concerns the features that all beautiful objects have in common. The so-called classical conception of beauty is rooted in classical antiquity and the Italian Renaissance. Focusing on objective features, it asserts that beauty is an harmonious arrangement of parts into a coherent whole. Aesthetic hedonism,
by contrast, is a subjective theory holding that a thing is beautiful
if it acts as a source of aesthetic pleasure. Other conceptions define
beautiful objects in terms of intrinsic value, the manifestation of
ideal forms, or as what evokes love and passion.
Aesthetic experiences, attitude, and pleasure
An
aesthetic experience is an appreciation of beauty or an awareness of
other aesthetic features. In its most typical form, it is a sensory
perception of a natural object or an artwork. However, it can also take
other forms, such as aesthetic imagination of fictional objects described in literature. Internalist theories, like Monroe Beardsley's
view, explain aesthetic experience from a first-person perspective,
focusing on aspects internal to the experience, such as focus and
intensity. By contrast, externalist theories, such as George Dickie's
position, argue that the key element of aesthetic experiences comes
from the experienced external objects and their aesthetic properties.
Diverse features are associated with aesthetic experiences, but
it is controversial whether any of them are essential. Aesthetic
experiences usually appreciate an object for its own sake because of its
sensory properties, resulting in aesthetic pleasure from a positive
evaluation of the object. This pleasure is typically said to be detached
from practical concerns and can involve selfless absorption, allowing
imaginative freedom or free play of mental faculties
in addition to sensory perception. Some theorists associate this free
play with an absence of conceptual activity. Aesthetic experiences may
also be normative,
meaning that certain responses are appropriate, like the positive
appreciation of beauty, but others are not, such as the positive
appreciation of ugliness.
A central aspect of aesthetic experience is the aesthetic
attitude—a special way of observing or engaging with art and nature.
This attitude involves a form of pure appreciation of perceptual
qualities detached from personal desires and practical concerns. It is disinterested
in this sense by engaging with an object for its own sake without
ulterior motives or practical consequences. For example, the experience
of a violent storm through the aesthetic attitude may focus on its
intricate patterns of lightning and thunder rather than preparing for
its immediate dangers. One characterization understands the aesthetic
attitude as a natural form of apprehension that occurs on its own in
certain situations. Another outlook holds that the aesthetic attitude is
a voluntary stance people can choose to adopt towards any object. There is debate about the extent and type of emotional engagement a
disinterested stance requires, for instance, whether fear during a horror movie can be disinterested.
The aesthetic attitude is sometimes contrasted with other
attitudes, such as the practical attitude, which is interested in
usefulness and seeks to utilize or manipulate objects to achieve
specific goals. Similarly, it differs from the scientific attitude,
which aims to explain phenomena and acquire factual knowledge about the world. Some philosophers, such as Arthur Schopenhauer and Martin Heidegger, suggest that the aesthetic attitude can reveal aspects of reality obscured in other attitudes.
Aesthetic experience is further associated with aesthetic
pleasure—a form of enjoyment in response to natural and artistic beauty.
It is typically characterized as disinterested pleasure. It contrasts
with interested pleasure that arises from the satisfaction of desires,
such as the joy of achieving a personal goal or indulging in a particular type of food one craved.
Another difference is that aesthetic pleasure does not depend on the
existence of the enjoyed object, like enjoying the beauty of a sunset in
a dream.
The joy in achieving a personal goal, by contrast, would be frustrated
if one discovered that the achievement was merely a dream. Philosophers like Immanuel Kant
argue that aesthetic pleasure is pre-conceptual, meaning that it arises
from a free interplay between imagination and understanding rather than
from cognitive judgments or conceptual analysis. Some theorists distinguish refined from unrefined aesthetic pleasures
based on whether the pleasure is evoked by a cultivated taste or an
immediate, instinctual response.
Aesthetic pleasure is central to the characterization of various
aesthetic phenomena, which are said to involve or evoke such pleasure.
However, the view that aesthetic pleasure is the defining characteristic
of the entire aesthetic domain is controversial. It faces challenges in
explaining phenomena such as the sublime, drama, tragedy, and various forms of modern art, which may evoke diverse emotions not primarily linked to pleasure.
Aesthetic judgments and taste
According to Immanuel Kant,
aesthetic judgments are subjective, universal, disinterested, and
involve an interplay of sense, imagination, and understanding.
Aesthetic judgments are assessments of the aesthetic features and
values of objects, expressed in statements like "this music is
beautiful". They can apply both to natural objects and artworks.
Aesthetic judgments also include assessments about how or why an object
has aesthetic value without explicitly determine its overall aesthetic
worth, as in the statement "this music is balanced". Many debates in
aesthetics concern the nature of aesthetic judgments, in particular,
whether they can be as objective and universal as empirical judgments made by natural scientists.
Subjectivists argue that aesthetic judgments express personal feelings
and dislikes without universal validity. This view is contested by
objectivists, who hold that aesthetic judgments describe objective
features that are independent of the particular preferences
of the judging individual. Intermediate views suggest that the
standards of aesthetic judgment are grounded in stable shared
dispositions rather than variable individual preferences, resulting in a
form of subjective universality. This position is reflected in Kant's view, which identifies four core
features of aesthetic judgments: they are subjective, universal,
disinterested, and involve an interplay of sense, imagination, and
understanding.
Philosophers such as Francis Hutcheson and David Hume
argue that there are general aesthetic principles or universal criteria
that are applied when making aesthetic judgments. Particularists, by
contrast, assert that the unique nature of each aesthetic object
requires a case-by-case evaluation that cannot be fully subsumed under
general principles. A related debate between rationalism and the immediacy thesis concerns
whether aesthetic judgments are mediated through concept application and
reasoning or emerge directly from sensory intuition.
Aesthetic judgments rely on taste, which is a sensitivity to aesthetic qualities, a capacity to feel
aesthetic pleasure, or an ability to discern beauty and other aesthetic
qualities. Taste is a type of preference expressed in immediate
reactions and is sometimes understood as an inner sense or cognitive
faculty. Differences in taste are often used to explain why people
disagree about aesthetic judgments and why the judgments of some people,
such as art critics with extensive experience and a refined sense,
carry more weight than those of casual observers. Taste varies both
between cultures and between individuals within a culture.[e]
However, there are also some cross-cultural agreements. Various
philosophers argue that taste can be learned to some extent and that the
judgments of experienced observers follow similar standards, suggesting
the existence of social norms of right and wrong aesthetic assessments.
The term "aesthetic universal" refers to aspects of taste and
other aesthetic phenomena that are shared across different cultures and
societies, indicating common features of human nature underlying
aesthetics. Suggested general tendencies include the dispositions to
engage in artistic expressions or to derive aesthetic pleasure from
appreciating these expressions. The existence of more specific shared
tendencies is debated. An example is the idea that humans generally find
savanna-like landscapes with open grassy plains and scattered trees pleasing.
Art is a central topic of aesthetics and the main subject of the
philosophy of art. It encompasses diverse forms, including painting,
sculpture, music, dance, literature, and theater. This field covers both
artworks and the skills or activities involved in their creation.
Artworks are artifacts or performances
typically created by humans. They differ in this respect from naturally
occurring aesthetic objects, like landscapes and sunsets.
Definitions
A central debate in the philosophy of art concerns the definition of art or how to distinguish it from non-art. There are diverse theories, each offering a unique perspective about the nature of art.
Conventionalist definitions of art assert that art is a socially constructed category. They explain that readymade objects like Marcel Duchamp's Fountain are considered art by reference to established conventions.
Essentialist approaches argue that there is an essence or a set of inherent features shared by all artworks and only by them. They often define artworks in terms of other aesthetic concepts, such as representation, beauty, or aesthetic experience. An early object-centered approach, first proposed by Plato, characterizes artworks as representations that seek to reflect or imitate certain aspects of reality. Another definition suggests that artworks are objects designed to evoke
aesthetic experiences or pleasure. A related approach proposes that all
artworks have certain aesthetic properties in common, such as beauty. Aesthetic formalism argues that specific formal features, such as a "significant form", are the hallmark of art. Artist-centered approaches see artistic activity as the essential
aspect of artworks. One conception understands artworks as special
vehicles through which artists express emotions and other mental states.
Conventionalist definitions view art as a socially constructed
category. This means that it does not primarily depend on the inherent
properties of objects, for example, what they represent or what forms
they have. Instead, art is defined by social and cultural agreements,
which are subject to change. A key motivation for this approach has been
the emergence of modern art, which has challenged many earlier
conceptions. Conventionalist definitions can explain, for instance, that
even mundane ready-made objects like a urinal
are considered art if conventions say so. Institutional theories argue
that the conventions are set by social institutions of the art world. Because of this social dependence, an object considered art in one society
may not be art in another society. Historical theories, another form of
conventionalism, assert that the category of art depends on established
traditions and historical contexts. They claim that an object becomes
part of this category if it stands in the right relation to these
traditions, for example, by being created in an artistic context and
resembling other recognized artworks.
There are also hybrid theories that combine elements from other
theories. For instance, one approach holds that an object is an artwork
if it either meets certain aesthetic standards or is conventionally
regarded as art. The diversity of proposed definitions and the difficulties in reconciling them have led some philosophers to
argue against the existence of precise criteria. Some conclude that a
definition is strictly impossible. Others provide vague
characterizations, suggesting that the domain of art is characterized by
overlapping similarities, known as family resemblance.
Ontology and categories
The ontology of art seeks to discern the fundamental categories of being to which all artworks belong. Universalists argue that artworks are universals—general
or repeatable entities that can have several instances at the same
time. For example, a novel can have many copies, a film can have many
screenings, and a photo can have many prints. One version of this view
distinguishes artworks as types
from their instances, which are considered tokens of this type.
Particularists reject the idea that artworks are universals, arguing
instead that they are particulars
or unique concrete entities. For them, if there are several instances
then the artwork is the collection or sum of all instances. According to
this view, Alfred Stieglitz's photograph The Steerage is not a type underlying its prints but rather the collection or sum of all prints together.
A similar discussion addresses whether artworks are material objects, which exist independent of observers, or intentional objects, which exist in the experience of observers. Pluralists argue that different types of artworks belong to distinct
ontological categories. Contextualists accept this view and further
propose that the ontological category depends on the context of
discussion. Deflationism is skeptical about the fundamental existence of artworks in any form. It acknowledges that the term art may be practically useful in everyday language but rejects that it refers to any fundamental entities of reality.
Some categorizations of art forms focus on the medium used to express artistic ideas, such as the use of oil paint.
Artworks are categorized in various ways. Some distinctions focus on the medium used to express artistic ideas. For example, paintings typically use paint, such as oil or acryl paint,
which is distributed on a surface, whereas dance involves bodily
movements. Similarly, music is performed using instruments and voice to
produce sounds, and literature relies on language. Hybrid forms like opera and film combine several of these elements. Another distinction is between performance works and object works.
Performance works, like a song performed on stage, are dynamically
enacted in time, whereas object works, like a painting, have a more
static nature. Artworks can also be classified by style, such as impressionism and surrealism, and by their intended purpose, like political and religious art.
Meaning
The
meaning of an artwork is what is involved in understanding it or
comprehending what it communicates, encompassing factors such as
representation and expression. Certain aspects of meaning may be
directly accessible while others require in-depth interpretation, for
example, to grasp symbolic or metaphorical
elements. Understanding influences aesthetic experience and for certain
artworks, a comprehensive understanding may be required to fully
appreciate them. One approach to the analysis of meaning is the distinction between form and content.
Content refers to what is presented, such as the depicted topic,
expressed ideas, and conceptual messages. Form refers to how the content
is presented, such as medium, technique, composition, and style. Form encompasses diverse modes of presentation in different art forms, like color and spatial arrangement in painting, harmony and rhythm in music, and narrative voice and plot structure in literature.
Representation is a depiction of real or imagined entities. For example, a portrait painting represents a person, while a fantasy novel
represents an imaginary chain of events. Similarity is a crucial
element in many forms of artistic representation, meaning that the
artwork resembles the depicted entity. However, representation can also
happen through other means, such as conventional symbols and established codes. It is particularly prevalent in some art forms and styles, such as classical art and realism. Since antiquity, representation has been a key concept in theories of art,
such as Plato's idea of defining art as imitation. However, it is
controversial whether representation plays a central role in all art
forms, including music and abstract modern art.
Expression is the conveyance of psychological states, such as emotions, moods, and attitudes. For example, a painter may depict a barren landscape in muted colors to express sadness,
while a musician might use a fast tempo and upbeat melody to convey
excitement. The expressed mental states often align with the artist's
personal experience. However, this is not necessarily the case and
artists may explore psychological states they observed in others or
entirely fictional experiences. An artwork can express a mental state
like sadness by evoking it in the experience of the audience.
Alternatively, the expression can also happen if observers recognize the
presence of sadness in the artwork even if they do not personally feel
it. Expression theories consider expression a core feature of artworks.
They characterize artworks as expressions of the artist's mind, focusing
on creativity and originality in the manifestation of aesthetic experiences.
Interpretation and criticism
The process of interpretation is the attempt to uncover the meaning of an artwork to understand its significance and value. In
the widest sense, interpretation encompasses any way of assigning meaning, including obvious descriptions of depicted entities and explanations of literal word meanings.
In philosophy of art, the term is typically used in a more narrow sense
for assignments of meaning that involve deeper analysis and creative
thought. Interpretations aim to discover underlying aspects that are
relevant to the understanding and appreciation of the artwork. The terms interpretation and criticism
are sometimes used interchangeably. However, criticism is typically
associated with more components, like a general description of the
criticized artwork and a classification of style and genre. Criticism also explains the art-historical background and evaluates positive and negative qualities.
Critics sometimes propose conflicting interpretations of the same
artwork. According to critical monism, there is only one comprehensive
correct interpretation, implying that conflicting interpretations cannot
both be correct. Critical pluralism, by contrast, asserts that there
can be different but equally valid interpretations and that it is not
always possible to determine which of two conflicting interpretations is
superior. A similar issue involves whether interpretations can be true
or false in an objective sense.
Various frameworks of interpretation have been proposed. According to intentionalism, the meaning of an artwork is determined by the author's intent—their reasons and motives that led to the creation of the artwork. This typically involves analyzing the ideas the artist aimed to express but can also include a biographical analysis to learn about psychological and social circumstances in the artist's life.
Intentionalism is a controversial theory, termed intentional fallacy
by its critics. Some objections point to cases where the author's
intention cannot be known, where the author themselves cannot be
identified, or where no traditional author exists, as artworks created
by artificial intelligence. In these cases, meaning would be inaccessible or non-existent. Other objections assert that an artist may fail to accurately express
their intention or may manifest unintended aesthetic features,
suggesting that an artwork can contain both less and more than the
artist intended.
An alternative to intentionalism argues that meaning is determined by artistic, stylistic, linguistic, and other cultural conventions.
For example, linguistic conventions determine the literal meanings of
words and thereby influence the overall meaning of a poem. Another
framework holds that meaning is shaped by how the audience, rather than
the author, interprets or would interprets the intention underlying the
work. Artistic formalism proposes a different approach by focusing
interpretation exclusively on formal or perceptual features of artworks.
Aestheticism and instrumentalism are theories about the value of
art. Aestheticism asserts that the primary value of art lies in its
intrinsic aesthetic merits, independent of any external purposes. This
idea of the autonomy of art is expressed in the slogan "art for art's sake".
Strong forms of aestheticism not only disregard external purposes but
see them as detrimental influences that undermine artistic integrity.
Instrumentalism, by contrast, explains the value of art by the effects
it has on other domains. It understands art as a means to things such as
moral education, spiritual growth, therapeutic benefits, and social cohesion.
The individual arts are diverse practices or disciplines in the
domain of art. They encompass a wide range of fields, including
traditionally established forms such as painting, music, and literature,
as well as newer types like video games. One classification divides them into visual arts, literary arts, and performance arts. However, the boundaries between these categories are not always clear, and alternative classifications have been proposed.
Dance is a performance art involving a series of bodily movements.
Painting
is a visual art in which a painter applies colors to a surface. It
allows for a diverse range of motives and styles, and is often
considered a paradigm form of art. The representation of real entities plays a central role in many forms
of painting, ranging from landscapes and people to historic events. This
process involves artistic choices that go beyond simple replication,
such as guiding the viewer's attention to specific aspects or
highlighting important but easily overlooked features. The issue of representation is also crucial in photography, a visual art shaped by technological developments in camera design and editing
processes. A key topic in the philosophy of photography concerns its
mechanical manner of authentically representing real objects, frequently
drawing parallels and distinctions with painting. The status of
photographs as true artworks is disputed, with critics arguing that the
mechanical nature of capturing images lacks the necessary artistic
creativity.
Music is a performance art in which sounds are combined to create aesthetic patterns, relying on aspects such as melody and rhythm.
Unlike painting and photography, music is typically less associated
with objective representation, having a closer link to the expression of
emotions. A key discussion in the philosophy of music revolves around the definition of music
or the criteria under which a combination of sounds is music. Proposals
range from objective criteria, such as the organization of sounds, to
subjective criteria, like the way sounds are interpreted or experienced. Dance is another performance art in which dancers perform a series of bodily movements, often following a choreography. It is typically accompanied by music and shares with music an emphasis on expressive features.
Architecture is an art that typically combines aesthetic with functional goals, such as Antoni Gaudí's Sagrada Família.
Architecture is the art or craft of designing and building, encompassing a wide range of structures from monuments and cathedrals to skyscrapers
and residential homes. It typically combines aesthetic with functional
goals, seeking to create buildings that are both visually appealing and
practically useful. This dual nature is a central topic of the philosophy of architecture,
with one theory suggesting that mere buildings can be distinguished
from artistic architecture by the presence of decorative elements. Sculpture
is another art form that, like architecture, involves the creation of
three-dimensional works. Sculptures are usually static objects made of
robust materials like stone, metal, and wood. However, the field of
sculpture is broader and covers diverse three-dimensional objects,
including kinetic sculptures.
Key discussions in the philosophy of sculpture address the definition,
representational aspects, and aesthetic features of sculptures as well
as the influence of the chosen material.
Literature has language as its primary medium. In its widest
sense, literature encompasses any written document. However, the term is
typically used in a more narrow sense in aesthetics for forms of
writing that belong to the high arts, such as poems, novels, and drama.
Literature as an art is often characterized by its deliberate,
elaborate, and organized use of language, but there is no universally
accepted demarcation between artistic literature and other forms of
writing. Poetry is a distinct form of literature often written in verses composed of several lines that may follow specific patterns, such as meter and rhyme.
Many poems are characterized by a deliberate economical use of language
that seeks to evoke specific experiences while being difficult to paraphrase.
Theater
is a performance art that combines elements from other art forms. It
typically includes a carefully prepared set or stage where actors
perform, usually incorporating storytelling and sound design to create
immersive experiences. Theater is performed before a live audience,
which can create a sense of immediacy that is less prevalent in related
art forms, such as film. Film
also integrates aspects from various artistic disciplines but relies
more heavily on technological means of recording and editing. Films can
involve actors but may also include animated characters or document
real-life events. They are normally the result of collaborative efforts
of many people, which complicates the identification of a singular
author in the traditional sense.
Video games
are a more recent form of art. Like theater and film, they usually
blend visual, auditory, and narrative elements. They typically stand out
through their emphasis on player interaction, allowing active
exploration of and engagement with the game world. The status of films and video games as serious forms of art is
disputed. Proponents tend to emphasize their aesthetic qualities, while
critics often point to their association with mass production and popular culture as counterarguments. For video games, a related debate centers on the elements of
competition and winning, questioning whether these elements run counter
to the spirit of art.
In various fields
Aesthetic
phenomena are investigated in diverse fields. They cover the relation
between aesthetics and other branches of philosophy, scientific inquiry
using empirical methods, comparisons of different artistic traditions, and the study of aesthetic elements in specific areas of life.
Ethics
Ethics is the branch of philosophy that studies moral phenomena in general and right behavior
in particular. Artworks can have various ethical consequences by
influencing how people feel, perceive, and evaluate their circumstances.
For example, artworks can glorify violence and reinforce biases, just
as they can inspire empathy and challenge societal norms. As a result,
art is also relevant to the field of politics since it can steer
political sentiment to legitimize authority or mobilize resistance,
thereby influencing voter attitudes. However, artworks can also explore
morally relevant topics without expressing a clear positive or negative
evaluation.
Since both ethics and aesthetics deal with values, philosophers seek to clarify the relation between moral and aesthetic values, proposing diverse theories of their interaction. Ethicism asserts that the moral value of an artwork can increase its aesthetic value, while ethical defects may undermine its artistic merit.
This view is reversed by immoralism, which suggests that in some cases,
moral flaws enhance aesthetic experience. Autonomism rejects both
positions, arguing that these domains of evaluation are independent.
Psychology and related fields
Scientific approaches rooted in psychology and related fields employ empirical methods to conduct inquiries and justify hypotheses. The psychology of aesthetics examines the mental processes involved in the perception and appreciation of beauty and art, using methods such as experimentation, observation, and surveys.
Experimental aesthetics is an early and influential approach pioneered by Gustav Fechner. It follows a bottom-up methodology that starts with human sensation, investigating preferences to simple physical stimuli, such as basic colors and shapes. Gestalt psychology
relies on a more holistic outlook, examining how composition and object
placement influence aesthetic experience, like the relation between
balanced organization and a sense of calm. Some works, such as Daniel Berlyne's
approach, shift the focus from perception to emotion, suggesting that
features like novelty and complexity cause arousal and that the right
amount of arousal is pleasurable.
Psychological analysis also examines the temporal structure of
aesthetic experiences of art. One outlook identifies two phases: an
initial first impression in which the observer forms a rough general
idea of the artwork's topic, structure, and meaning, followed by a focal
analysis of more specific features. Research further explores how circumstances influence aesthetic
experience, like the contrast between encountering a painting in a
museum or a shopping mall. In addition to physical circumstances, social
and personal factors also influence aesthetic experience, such as group dynamics, prior knowledge, and the motivation for seeking the experience.
Evolutionary
psychology examines the evolutionary function of aesthetic
sensitivities, like preferences for environments conducive to survival,
such as landscapes resembling the African savannah.
Evolutionary psychology analyzes mental phenomena as products of natural selection. It asserts that genetic variations responsible for new capacities are passed on to future generations if they enhance survival and reproduction. Adopting this approach, evolutionary aesthetics interprets beauty and other aesthetic experiences as adaptive traits that serve diverse functions. Examples are aesthetic preferences for environments conducive to survival, such as landscapes resembling the African savannah, and sexual selection by identifying genetically fit mates. By focusing on the relatively permanent biological nature of humans,
evolutionary psychology sees aesthetic values as universal or
transcultural patterns of taste and appreciation, contrasting with
theories in the philosophy of art that understand aesthetic values as
cultural constructs.
Neuroaesthetics applies neuroscientific
insights and methods to study the relation between brain activity and
aesthetic experience. Aesthetic experiences arise from diverse brain
processes responsible for organizing sensory stimuli, forming cognitive
interpretations, and generating emotional responses. Neuroaesthetics
examines these processes using various methods, including neuroimaging techniques like fMRI.
In one type of experiment, participants view diverse artworks, some
considered beautiful and others ugly. By comparing brain responses
measured through neuroimaging, researchers can discern, for example,
that the brain area known as the orbitofrontal cortex is more active when viewing beautiful paintings.
Cognitive science employs an interdisciplinary approach to study mental phenomena by examining how they access and transform information. An influential theory, suggested by Ernst Gombrich,
analyzes aesthetic experience through the interplay of low-level and
high-level information processes: human sensation provides low-level
information, which is organized and interpreted using high-level
conceptual background knowledge. Specific frameworks in cognitive science have also been used to analyze aesthetic phenomena. For instance, the modularity of mind—the
hypothesis that the mind is composed of mental modules that function
independently—has been employed to explain that paintings can represent
real objects by triggering the same mental modules responsible for the recognition of real objects.
Comparative aesthetics
Comparative
aesthetics examines diverse aesthetic traditions, analyzing the
similarities and differences in their standards of beauty and
theoretical approaches. For example, the focus in Western
aesthetics on high art and its separation from everyday affairs is not
common in most other traditions, for which art is typically closely
integrated with practical functions in everyday life, including religion
and moral education. Artistic differences between different traditions also encompass dominant media, common styles, and chosen motifs.
The comparison of cultural products from different traditions
presents various conceptual challenges associated with
tradition-specific aesthetic concepts and standards of evaluation. The
uncritical application of standards from one tradition to evaluate the
works of another can result in cultural imperialism. However, these differences also provide opportunities to artists and
philosophers to incorporate new elements and explore novel perspectives.
Indian aesthetics draws a close connection between artistic activity and religious practice. It argues that artistic expression is a spiritual endeavor that should be informed by knowledge of the self and reality, express devotion to the divine, and avoid attachments to the fruits of the activity. Indian aesthetics analyzes art in terms of basic life emotions, called rasas, such as delight, humor, sadness, and anger. It sees art as a play
that imitates reality by conveying experiences of the rasas. Its focus
is on the universal expressions of human emotional life rather than
person-specific feelings. This school of thought identifies artistic
creativity as the ability to harness the full potential of the medium,
like colors, sounds, and words, to convey experiential universals. For
the audience, it recommends an aesthetic attitude characterized by a
psychic distance from private concerns to transcend the personal self
and become receptive to universal elements.
Chinese aesthetics
emphasizes the spontaneous nature of artistic creativity and its
connection to the moral and spiritual domains. It argues that art should
foster harmony within society and align with the natural order of the universe. In this role, art is both self-expression and self-cultivation aimed to promote social well-being. The main focus of Chinese aesthetics is on poetry, painting, and calligraphy, known as the three perfections. This tradition influenced Japanese aesthetics,
which is characterized by its interest in nature. Different art styles
in this tradition are shaped by religious outlooks, particularly Shinto and Buddhism. Japanese theories of art stress the interrelation between the experience of the artist and the response of the audience.
Islamic philosophers
see art as a means of communicating philosophical and religious truths,
making them accessible to the general public without requiring abstract
theoretical thought. Thinkers such as Al-Farabi and Avicenna
argued that imagination rather than reasoning underlies artistic
creation and appreciation. According to this view, art imitates reality
and evokes emotions to convey underlying truths and positively influence
behavior. Religious teachings play a central role in Islamic aesthetics. For example, the belief that Allah is transcendent and boundless has resulted in the avoidance of figurative depictions and the emphasis on abstract art forms.
African aesthetics emphasizes the intuitive and emotional nature
of art, highlighting its communal function in social life. Early
scholarship on this tradition was typically conducted from an ethnocentric
perspective using Western aesthetic standards to interpret and evaluate
African art. This usually resulted in the portrayal of African artworks
as exotic curiosities that lack the sophistication of high art. The
emergence of indigenous scholarship
in the 20th century sought to correct this interpretation, arguing that
the emphasis on moral, emotional, and intuitive aspects reflects
different artistic standards rather than a deficiency. This school of
thought, often associated with the concept of Négritude, focuses on the importance of feelings in contrast to abstraction and intellectual analysis.
Environment, everyday life, and religion
Environmental aesthetics deals with the appreciation of nature, including elements such as forests, mountain ranges, rivers, and flowers. It encompasses both transient appearances, such as the fleeting beauty
of a landscape during sunset, and enduring aspects, such as the majesty
of a centuries-old tree. This field focuses on sensory and formal qualities associated with
beauty and related aesthetic qualities. It contrasts in this respect
with the philosophy of art, which typically emphasizes the
interpretation of underlying meanings associated with expression and
representation. However, some approaches to environmental aesthetics also consider the
impact of background knowledge on the aesthetic experience of nature.
For instance, ecological awareness of the intricate relationships within an ecosystem can shape the appreciation of a woodland environment by understanding it as a habitat of diverse species.
Religious art serves specific religious functions, such as conveying moral teachings or aiding devotional practices.
In its broadest sense, environmental aesthetics encompasses the
appreciation of any environment, including those created by humans. This inquiry is closely associated with everyday aesthetics,
which examines aesthetic phenomena encountered in daily life. Everyday
aesthetics covers both public and private environments, ranging from
modern cities and industrial sites to private homes and backyards, as
well as personal adornments and consumer products, such as clothing,
hairstyles, industrial design, and web design. The aesthetics of popular art,
a related discipline, investigates aesthetic qualities in popular
culture and compares the evaluative standards of popular art with high
or fine art. For example, it studies the contrast between commercial mass art and experimental avant-garde and explores specific types of popular art, such as kitsch.
Art plays a central role in the field of religion
and manifests in many forms, including paintings, sculptures,
architecture, music, dance, and literature. Its key characteristic comes
from its religious function, such as conveying theological and moral
teachings, representing symbolic truths, inspiring religious
experiences, and aiding devotional practices. Religious art is part of
all major religions and was the dominant art form during ancient and medieval times. However, its influence began to wane in the modern period due to secularization.
This shift is also reflected in developments in the philosophy of art
that introduced a focus on disinterestedness and the autonomy of
aesthetic experience from external purposes, including religious goals.
Others
Various theories of aesthetics are associated with specific philosophical schools of thought. Marxist aesthetics examines the relation between art, class structure, and social ideology, exploring how art can enforce or challenge established power hierarchies. Feminist aesthetics
criticizes male biases in aesthetic theory and artistic practice while
exploring alternatives. It investigates unfair social institutions and
aesthetic standards that disadvantage women and exclude them from the
art world. An example is the male gaze—a cultural phenomenon that treats women as objects of male spectatorship rather than as artistic creators. Postmodern
aesthetics is a diverse movement that challenges established concepts
and theories in the field of aesthetics. It typically rejects the focus
on disinterested pleasure, the autonomy of art from other domains, and
the distinction between high and popular art. It tends to promote a pluralism that embraces diversity, playfulness, and irony.
The term mathematical beauty refers to aesthetic qualities of abstract mathematical concepts and theories. For instance, a mathematical proof
may be considered beautiful if it demonstrates a profound insight in an
effective manner or reveals an underlying unity of seemingly disparate
mathematical ideas.
Computer art involves the use of computers in the creation of artworks. It can take many forms, ranging from minor digital enhancements of
existing artworks to entirely new creations generated using complex algorithms.
Its abstract nature based on symbolic representation and manipulation
of electronic signals distinguishes computer art from traditional forms
of art, which rely on more tangible media. This medium offers new
artistic possibilities, such as virtual reality and interactivity. Rapid developments in artificial intelligence in the 21st century have significantly impacted computer art. They include the emergence of generative models—systems that are trained on existing media to create new texts, images, music, or videos in response to verbal descriptions of the intended result. Examples include ChatGPT, Stable Diffusion, MuseNet, and RunwayML.
Meta-aesthetics examines the fundamental assumptions and concepts
underlying aesthetics. It asks about the existence of aesthetic facts,
the meaning of aesthetic statements, and the ways of acquiring aesthetic
knowledge. A central meta-aesthetic debate between realism and anti-realism addresses whether there are mind-independent aesthetic facts. A related discussion between cognitivism and non-cognitivism considers whether aesthetic statements can be objectively true or primarily express personal emotions.
Aesthetics has its roots in ancient thought, which typically interpreted beauty as a metaphysical phenomenon associated with the order of the cosmos. In ancient Greek philosophy, early explorations of the nature of beauty are found in Pythagorean philosophy
in the 5th and 4th centuries BCE. This tradition proposed that beauty
arises from the proportion and harmony between different elements, an
idea later also examined by the Stoics. Plato (427–347 BCE) analyzed pure beauty as an immutable form
that exists independent of matter. He argued that material entities are
beautiful if they participate in the form of beauty. Plato understood
art as a craft that seeks to imitate and represent material entities. He acknowledged that art has some didactic
value but was overall critical of it, asserting that its derivative
nature, based on imitation of sensible features, cannot lead to true
knowledge.
Aristotle
(384–322 BCE) examined aesthetics through the lens of poetry. He agreed
with Plato's idea that art is a form of imitation but adopted a more
positive outlook, proposing that it can reveal universal truths.
Aristotle suggested that successful artistic imitation is pleasurable
and can have therapeutic or cathartic effects. By linking this pleasure to beauty, he tried to explain why the imitation of unpleasurable phenomena, like tragic stories, can be enjoyable. Also influenced by Plato, Plotinus
(204–270 CE) argued that beauty is not based on sensory symmetries or
simple proportions but embodies an underlying order, harmony, and unity
associated with the ultimate source of creation.
In ancient India, the Natya Shastra, traditionally attributed to Bharata (c. 200 BCE–200 CE), formulated the rasa theory of art. This theory posits that the goal of art is to convey fundamental life emotions as experiential universals of human existence. In ancient China, the philosophy of art was shaped by Confucianism. It emphasized self-cultivation and the relation between nature and human culture.
Medieval
During the medieval period, the rise of Christianity led Western aesthetic thinkers to blend ancient Greek thought with religious teachings, often in the form of philosophical theology. Influenced by Plato and Plotinus, Augustine of Hippo
(354–430 CE) explored the distinction between artistic creation, which
transforms matter, and divine creation, which brings forth existence out of nothing. He thought that all beauty originates from God and analyzed it in terms of unity, equality, number, proportion, and order. Thomas Aquinas
defined beauty as what brings pleasure upon perception. For him, the
mind plays a central role in this process since beauty lies in the
immaterial form of the perceived object that the mind recognizes in the
sensory data. Aquinas saw beauty as a basic category of being and identified it with proportion, radiance, and integrity.
Al-Farabi saw beauty as a divine attribute of Allah.
An integration of Greek philosophy and religious thought also happened in the Islamic world. Al-Farabi (c. 878–950 CE) associated beauty with pleasure and saw it as a degree of perfection and a divine attribute of Allah. Avicenna
(980–1037 CE) distinguished sensible from intelligible beauty and
explored psychological processes underlying aesthetic judgments, such as
the role of imagination.
Meanwhile in India, the rasa theory of art expanded to also encompass devotional practices, including efforts to portray or evoke profound religious experiences of the union with the divine. For example, Abhinavagupta (c. 950–1025 CE) elaborated the spiritual dimension of the rasa theory, drawing a sharp distinction between ordinary worldly emotions and rasas as transcendent aesthetic emotions.
In Chinese thought, Xie He (c. 5th to 6th centuries CE) combined Daoist and Confucian ideas, suggesting that artists align with the natural order of the universe and spontaneously express the movement of life in their artworks. He also proposed a set of basic principles of painting. Guo Xi
(c. 1020–1090 CE) argued that artworks reflect the moral character and
spiritual outlook of the artist, which he saw as a central factor of the
artwork's aesthetic value. During this period, the growing influence of Buddhism
on Chinese aesthetic thought led to an artistic shift from objective
reality to subjective experiences as a result of Buddhist teachings on
the illusory nature of reality.
The medieval period in the West came to an end with the emergence of the Renaissance starting in the 15th century. This change led to the revival of classical aesthetic ideals while secularization paved the way for rationalist inquiries into general laws of beauty and empiricist analyses of sensory and emotional experiences in the subsequent Age of Enlightenment.
Modern and contemporary
David Hume understood beauty as a pleasurable sentiment and explored taste as the inner sense responsible for this sentiment.
Modern aesthetics emerged in the 18th century as philosophers
systematically engaged with its foundational concepts while carefully
formulating and critiquing major positions. A key step in this process happened through the philosophy of Alexander Baumgarten
(1714–1762), who first conceived aesthetics as a distinct field of
inquiry: the science of sensory cognitions or the study of what is
sensed and imagined. In British philosophy, Francis Hutcheson (1694–1746) followed ideas of the third Earl of Shaftesbury (1671–1713) and provided an early theory of taste, conceptualizing it as an inner sense responsible for aesthetic apprehension. This outlook inspired David Hume
(1711–1776) to develop a subjective theory of beauty, understanding it
as a pleasurable sentiment caused by perceptions. He integrated this
perspective with the existence of intersubjective standards of beauty as
principles of taste governing which objects are experienced as
beautiful.
Immanuel Kant
(1724–1804) expanded Hume's idea that aesthetic judgments are both
subjective and universally valid, arguing that the underlying pleasure
must be disinterested to follow universal standards. According to Kant,
this type of pleasure comes from a free play in which the mental
faculties of imagination and understanding harmoniously interact. In response to earlier theories by Edmund Burke (1729–1797), Kant also examined the sublime as a distinct aesthetic quality.
Kant's thought inspired diverse developments in German philosophy. Friedrich Schiller (1759–1805) saw art as a unifying phenomenon that synthesizes different basic human drives in a type of play. F. W. J. von Schelling
(1775–1854) shared a similar perspective, arguing that art reconciles
opposites and reveals the underlying unity of the self and nature. G. W. F. Hegel (1770–1831) explored aesthetics through his philosophical system of absolute idealism,
seeing artistic beauty as the sensory manifestation of ideas. He
analyzed art history from antiquity to his present day as a series of
progressive stages of this manifestation.
Combining Kantian and Indian philosophy, Arthur Schopenhauer
(1788–1860) saw disinterested aesthetic experience as a suspension of
the will, resulting in a temporary peace of mind by interrupting the
cycle of striving and suffering. He inspired the Chinese philosopher Wang Guowei
(1877–1927), who integrated Schopenhauer's ideas with Buddhist thought.
Wang viewed the goal of art as the creation of worlds within the world,
which are open to disinterested reflection. Friedrich Nietzsche
(1844–1900) rejected the disinterestedness of aesthetic experience and
the autonomy of art from other domains. Instead, he considered art an
expression of the struggle between opposing life forces and saw art as a vehicle of transformation and life affirmation.
Following the thought of Karl Marx (1818–1883), Marxist aesthetic philosophers like Leon Trotsky (1879–1940) and Georg Lukács (1885–1971) examined how art reflects and shapes social ideologies and power hierarchies. Drawing from Marxist ideas, Theodor Adorno (1903–1969) critiqued the commodification of art and explored its ability to express alienation and challenge societal norms. Also adopting a Marxist perspective, Walter Benjamin (1892–1940) studied how advances in technological reproducibility transform art.
Romanticist thought, expressed in the works of J. W. von Goethe (1749–1832), William Wordsworth (1770–1850), and Samuel Taylor Coleridge
(1772–1834), emphasized artistic originality, creativity, and the
expression of profound feelings. It saw artworks as products of human genius that defy rule-based understanding. This school of thought inspired the theory of expressionism, which
asserts that the primary function of art is to communicate emotions and
other mental states. It was explored by thinkers such as Leo Tolstoy (1828–1910), Benedetto Croce (1866–1952), and R. G. Collingwood (1889–1943). Intentionalism, a closely related position, focuses on the author's intent as the source of meaning of artworks. Monroe Beardsley (1915–1985) opposed this view, arguing that meaning is not fixed by the author's intent. Sigmund Freud (1856–1939) and Carl Jung (1875–1961) interpreted art through a psychoanalytic perspective as expressions of the unconscious, an approach also later explored by Richard Wollheim (1923–2005).
In the late 19th and early 20th centuries, aestheticism became a prominent view in English-speaking philosophy. For example, Walter Pater (1839–1894) and Oscar Wilde (1854–1900) proposed that art is an end in itself without an ulterior purpose. Pragmatists rejected this outlook and the idea that aesthetic experience is disinterested. For instance, John Dewey
(1859–1952) proposed that the value of art lies in the unique
experiences it provides, which can lead to individual and societal
improvements. Formalism
became another influential theory of art in the early 20th century. It
dismisses the focus on expressive and representational aspects and
argues instead that artworks are defined by formal features, like the
arrangement of perceptual qualities. Clive Bell (1881–1964), a major proponent of this view, termed this arrangement "significant form".
Martin Heidegger proposed that artworks can reveal truths about human existence and provide new perspectives of understanding.
The emergence of Dadaism and conceptual art challenged traditional definitions of art based on intrinsic features of artworks. As a result, anti-essentialism, which understands art as a social construct without an inherent essence, gained prominence in the second half of the 20th century, exemplified in the theories of Frank Sibley (1923–1996) and Nelson Goodman (1906–1998). These developments inspired Arthur C. Danto (1924–2013) and George Dickie (1926–2020) to propose institutional definitions, arguing that social conventions set by the art world determine which objects are artworks. Mary Mothersill
(1923–2008) challenged these developments. She aimed to restore earlier
conceptions of beauty associated with Aquinas, Hume, and Kant, focusing
on the apprehension of aesthetic qualities.
In continental philosophy, the school of phenomenology
explored diverse aspects of the immediate experience of art. For
example, it examined how artworks can depict unreal objects, how
imagination is involved in the process, and how art can reveal features
of reality. This tradition is closely related to existentialist aesthetics, which views artworks as expressions of human freedom that can authentically portray central aspects of the human condition. The philosophy of Martin Heidegger
(1889–1976) influenced both traditions. He criticized the focus on
disinterested pleasure found in modern philosophy of art, arguing that
artworks can reveal truths about human existence and provide new
perspectives of understanding. Heidegger's student Hans-Georg Gadamer
(1900–2002) further explored the relation between art and truth,
examining aesthetic experience and traditional theories through
phenomenological analysis and hermeneutic interpretation.
Postmodern thinkers, like Roland Barthes (1915–1980) and Jacques Derrida
(1930–2004), challenged the separation of art from everyday life and
the idea that artworks have a stable meaning or universal value. They
suggested instead that artistic merit depends on historical and cultural
contexts. Starting in the 1970s, feminist perspectives in aesthetics challenged male-centric theories and practices within aesthetic philosophy and the art world. For example, Simone de Beauvoir (1908–1986) and Luce Irigaray (1930–present) explored how feminine perspectives are marginalized by masculine standards.
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