I'm with Plato (et al.): I agree that beauty is real aspect of the world. Actually, even though Plato is considered the primary champion, the metaphysics of beauty was a standard topic among Western philosophers at least until about the 18th century. In several respects, my views are closer to those of later proponents than to Plato's--I always thought Diotima gave Socrates bum advice about the progression toward ultimate beauty beginning with erotic desire for the human body. Humans are not the most beautiful animal, far from it. Try zebras, peacocks, mandarinfish, red tree frogs, for starters.
Philosophers have defined beauty in various ways (getting better at it over the millennia), but one constant has been reference to elements or expressions of mathematics. While he gives a somewhat anemic description of beauty, Aristotle makes the important point: “The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.” (Metaphysics.) The relationship between mathematics and beauty continues to be elucidated by serious thinkers. Note the many quotes and explications in the article Why Mathematics Is Beautiful and Why It Matters, by mathematics professors David H. Bailey and Jonathan M. Borwein, and in the Wikipedia article on Mathematical Beauty.
As made clear in his 1939 James Scott Prize lecture, Paul Dirac considered beauty an essential attribute of the mathematics of physics. Mathematicians Sir Roger Penrose and Michael Atiyah are among other contemporary scholars who espouse beauty in mathematics; in his 2012 Stanislaw Ulam lecture., physicist Robert May offers broad new insights. Professor David Percy explains the beauty of Euler's Identity.
Three brief TEDx Talks by:
Jonathan Matte
Margot Gerritson
William Tavernetti (The best one. Must see.)
Professor Vicky Neale demonstrates two examples of beauty in mathematical problem-solving.
I would say that Bailey and Borwein have stated the case well when they describe the source of mathematical beauty as “simplicity in complexity, pattern in chaos, structure in stasis. In the arts, 'beauty' can be accounted for, at least in part, by well-understood harmonies, distributions of colors or other factors.” When it comes to the application of beautiful mathematics to empirical reality, my thoughts migrate toward the dazzling and graceful workings-out of nonlinear dynamics, chaos theory and fractal geometry. The axioms and basic theorems of set theory--especially as the foundational theory of mathematics, and especially as applicable to countable and uncountable infinite sets--seem to me to border on perfection. To border on perfection definitely counts as beautiful.
But I do not wish to restrict the concept or discussion of beauty here to mathematics--even though ultimately there may not be a real distinction: as Pythagoras revealed, the beautiful musical relationships of the octave, fifth and fourth are beautiful mathematical relationships. The elegant ratios of the Fibonacci sequence are found in the branching of trees, the spiral arrangement of flower petals and seeds of plants, and elsewhere, illustrating the mathematical essence of empirical reality. Nevertheless, my own experiences of beauty are mostly uninformed by mathematical considerations, involving natural settings unsullied by humans; animals; art forms such as music, painting, sculpture, literature and architecture; and the selfless and loving acts of humans and other animals. Perhaps other people's experiences of beauty are not so different.
The dominant topic of the SEP article on Beauty seems to be the issue of realism vs. anti-realism. Its first section begins:
I agree that it isn't tenable to claim that beauty is either a wholly objective or wholly subjective phenomenon. Aristotle's analogy with the sensation of taste is partly flawed but still informative: it's difficult to argue that the sweetness of a strawberry exists without an experiencer. The glucose, fructose and volatile compounds that are preconditions for the taste of sweetness among humans can exist without an experiencer, but in a universe without taste buds there is no reason to call these chemical compounds “sweet”. All sensations similarly involve objective and subjective components. Beauty is more than mere sensation, but the experience of beauty does not wipe out either the objective or subjective components of sensations.
The stance that beauty is merely a subjective phenomenon is apparently more common today, so I wish to pick it apart more thoroughly. As the SEP article notes, the attempt to give a purely subjective explanation for beauty empties the word of meaning (if everything that anyone can claim to be beautiful is therefore beautiful, then “beautiful” means nothing). Imagine two people sitting on a ledge overlooking the Grand Canyon at sunset, and one says to the other, “It's just . . . indescribably beautiful.” The subjectivist illogically claims that the person is saying something about her own internal state, not about the various visual features of the Grand Canyon at sunset. It's absurd. People can and do know what they are referring to when they make such statements; people can and do distinguish between the external world and their own internal states. She could have made a statement about her own happiness or pleasure. But what her comment refers to as beautiful is the Grand Canyon as the sun goes down.
It is true that it's difficult to pin down and name the confluence of elements in all the different contexts where we experience beauty--it's likewise difficult to pin down all of the elements and procedures of the scientific method, or to pin down a definition of “mathematics”. As a species of beauty, philosophers and mathematicians have done best at identifying the traits of mathematical beauty, which is a more circumscribed subject. Yet one cannot logically deny that such elements exist--symmetry (Plato lacked a word for “symmetry” but Timaeus describes the identical relation of the center to every point as the characteristic that makes the sphere the most perfect 3-dimensional object), proportion, unity and harmonious working together of parts, “simplicity in complexity, pattern in chaos, structure in stasis . . . distribution of colors.” To acknowledge these elements yet deny that beauty exists is like saying that houses don't exist, only structures that have walls, a floor and a roof.
Then there are those more complicated or ethereal examples of beauty that have nothing to do with sensory perception, such as selfless acts of good-doing. To my mind these noblest expressions of love are examples of and proof of the existence of beauty. It's difficult to avoid the association between beauty and sensory perception, but they shouldn't be equated. Beauty may often involve sensory data, but it is invariably more than that--as illustrated by the beauty of an idea expressed in a passage of poetry.
--from ”The Guardian Angel Of The Private Life” by Jorie Graham
The electric colors of Birds of Paradise certainly thrill our eyes, but the entirety of their strange, elaborate mating rituals, which their peculiar arrangements of feathers are usually involved in, is equally beautiful. Their beauty is almost unbearable. (Note how many times David Attenborough, Miriam Supuma and Paul Igag say “beautiful,” “beauty” and synonyms.) Similarly the bower of the Bowerbird is, by itself, not necessarily the most elegant thing that one will see today; the beauty arises from the totality of the facts concerning the bower--its purpose, ingenuity, the birds' serious comical behavior in relation to it, etc.
In any case, to summarize this digression, I find the arguments against the mere subjectivity of beauty conclusive, and I am not aware of any good arguments by which to conclude that beauty is entirely subjective. It seems to me that efforts to try to account for beauty as a confused psychological event are highly misguided.
Philosophers have defined beauty in various ways (getting better at it over the millennia), but one constant has been reference to elements or expressions of mathematics. While he gives a somewhat anemic description of beauty, Aristotle makes the important point: “The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.” (Metaphysics.) The relationship between mathematics and beauty continues to be elucidated by serious thinkers. Note the many quotes and explications in the article Why Mathematics Is Beautiful and Why It Matters, by mathematics professors David H. Bailey and Jonathan M. Borwein, and in the Wikipedia article on Mathematical Beauty.
As made clear in his 1939 James Scott Prize lecture, Paul Dirac considered beauty an essential attribute of the mathematics of physics. Mathematicians Sir Roger Penrose and Michael Atiyah are among other contemporary scholars who espouse beauty in mathematics; in his 2012 Stanislaw Ulam lecture., physicist Robert May offers broad new insights. Professor David Percy explains the beauty of Euler's Identity.
Three brief TEDx Talks by:
Jonathan Matte
Margot Gerritson
William Tavernetti (The best one. Must see.)
Professor Vicky Neale demonstrates two examples of beauty in mathematical problem-solving.
I would say that Bailey and Borwein have stated the case well when they describe the source of mathematical beauty as “simplicity in complexity, pattern in chaos, structure in stasis. In the arts, 'beauty' can be accounted for, at least in part, by well-understood harmonies, distributions of colors or other factors.” When it comes to the application of beautiful mathematics to empirical reality, my thoughts migrate toward the dazzling and graceful workings-out of nonlinear dynamics, chaos theory and fractal geometry. The axioms and basic theorems of set theory--especially as the foundational theory of mathematics, and especially as applicable to countable and uncountable infinite sets--seem to me to border on perfection. To border on perfection definitely counts as beautiful.
But I do not wish to restrict the concept or discussion of beauty here to mathematics--even though ultimately there may not be a real distinction: as Pythagoras revealed, the beautiful musical relationships of the octave, fifth and fourth are beautiful mathematical relationships. The elegant ratios of the Fibonacci sequence are found in the branching of trees, the spiral arrangement of flower petals and seeds of plants, and elsewhere, illustrating the mathematical essence of empirical reality. Nevertheless, my own experiences of beauty are mostly uninformed by mathematical considerations, involving natural settings unsullied by humans; animals; art forms such as music, painting, sculpture, literature and architecture; and the selfless and loving acts of humans and other animals. Perhaps other people's experiences of beauty are not so different.
The dominant topic of the SEP article on Beauty seems to be the issue of realism vs. anti-realism. Its first section begins:
1. Objectivity and Subjectivity
Perhaps the most familiar basic issue in the theory of beauty is whether beauty is subjective -- located ‘in the eye of the beholder’ -- or whether it is an objective feature of beautiful things. A pure version of either of these positions seems implausible, for reasons we will examine, and many attempts have been made to split the difference or incorporate insights of both subjectivist and objectivist accounts.
Perhaps the most familiar basic issue in the theory of beauty is whether beauty is subjective -- located ‘in the eye of the beholder’ -- or whether it is an objective feature of beautiful things. A pure version of either of these positions seems implausible, for reasons we will examine, and many attempts have been made to split the difference or incorporate insights of both subjectivist and objectivist accounts.
I agree that it isn't tenable to claim that beauty is either a wholly objective or wholly subjective phenomenon. Aristotle's analogy with the sensation of taste is partly flawed but still informative: it's difficult to argue that the sweetness of a strawberry exists without an experiencer. The glucose, fructose and volatile compounds that are preconditions for the taste of sweetness among humans can exist without an experiencer, but in a universe without taste buds there is no reason to call these chemical compounds “sweet”. All sensations similarly involve objective and subjective components. Beauty is more than mere sensation, but the experience of beauty does not wipe out either the objective or subjective components of sensations.
The stance that beauty is merely a subjective phenomenon is apparently more common today, so I wish to pick it apart more thoroughly. As the SEP article notes, the attempt to give a purely subjective explanation for beauty empties the word of meaning (if everything that anyone can claim to be beautiful is therefore beautiful, then “beautiful” means nothing). Imagine two people sitting on a ledge overlooking the Grand Canyon at sunset, and one says to the other, “It's just . . . indescribably beautiful.” The subjectivist illogically claims that the person is saying something about her own internal state, not about the various visual features of the Grand Canyon at sunset. It's absurd. People can and do know what they are referring to when they make such statements; people can and do distinguish between the external world and their own internal states. She could have made a statement about her own happiness or pleasure. But what her comment refers to as beautiful is the Grand Canyon as the sun goes down.
It is true that it's difficult to pin down and name the confluence of elements in all the different contexts where we experience beauty--it's likewise difficult to pin down all of the elements and procedures of the scientific method, or to pin down a definition of “mathematics”. As a species of beauty, philosophers and mathematicians have done best at identifying the traits of mathematical beauty, which is a more circumscribed subject. Yet one cannot logically deny that such elements exist--symmetry (Plato lacked a word for “symmetry” but Timaeus describes the identical relation of the center to every point as the characteristic that makes the sphere the most perfect 3-dimensional object), proportion, unity and harmonious working together of parts, “simplicity in complexity, pattern in chaos, structure in stasis . . . distribution of colors.” To acknowledge these elements yet deny that beauty exists is like saying that houses don't exist, only structures that have walls, a floor and a roof.
Then there are those more complicated or ethereal examples of beauty that have nothing to do with sensory perception, such as selfless acts of good-doing. To my mind these noblest expressions of love are examples of and proof of the existence of beauty. It's difficult to avoid the association between beauty and sensory perception, but they shouldn't be equated. Beauty may often involve sensory data, but it is invariably more than that--as illustrated by the beauty of an idea expressed in a passage of poetry.
All this was written on the next day's list.
On which the busyness unfurled its cursive roots,
pale but effective,
and the long stem of the necessary, the sum of events,
built-up its tiniest cathedral...
(Or is it the sum of what takes place? )
If I lean down, to whisper, to them,
down into their gravitational field, there where they head busily on
into the woods, laying the gifts out one by one, onto the path,
hoping to be on the air,
hoping to please the children --
(and some gifts overwrapped and some not wrapped at all) -- if
I stir the wintered ground-leaves
up from the paths, nimbly, into a sheet of sun,
into an escape-route-width of sun, mildly gelatinous where wet, though mostly
crisp,
fluffing them up a bit, and up, as if to choke the singularity of sun
with this jubilation of manyness, all through and round these passers-by --
just leaves, nothing that can vaporize into a thought,
no, a burning bush's worth of spidery, up-ratcheting, tender-cling leaves,
oh if -- the list gripped hard by the left hand of one,
the busyness buried so deep into the puffed-up greenish mind of one,
the hurried mind hovering over its rankings,
the heart -- there at the core of the drafting leaves -- wet and warm at the
zero of
the bright mock-stairwaying-up of the posthumous leaves -- the heart,
formulating its alleyways of discovery,
fussing about the integrity of the whole,
the heart trying to make time and place seem small,
sliding its slim tears into the deep wallet of each new event
on the list
then checking it off -- oh the satisfaction -- each check a small kiss . . .
On which the busyness unfurled its cursive roots,
pale but effective,
and the long stem of the necessary, the sum of events,
built-up its tiniest cathedral...
(Or is it the sum of what takes place? )
If I lean down, to whisper, to them,
down into their gravitational field, there where they head busily on
into the woods, laying the gifts out one by one, onto the path,
hoping to be on the air,
hoping to please the children --
(and some gifts overwrapped and some not wrapped at all) -- if
I stir the wintered ground-leaves
up from the paths, nimbly, into a sheet of sun,
into an escape-route-width of sun, mildly gelatinous where wet, though mostly
crisp,
fluffing them up a bit, and up, as if to choke the singularity of sun
with this jubilation of manyness, all through and round these passers-by --
just leaves, nothing that can vaporize into a thought,
no, a burning bush's worth of spidery, up-ratcheting, tender-cling leaves,
oh if -- the list gripped hard by the left hand of one,
the busyness buried so deep into the puffed-up greenish mind of one,
the hurried mind hovering over its rankings,
the heart -- there at the core of the drafting leaves -- wet and warm at the
zero of
the bright mock-stairwaying-up of the posthumous leaves -- the heart,
formulating its alleyways of discovery,
fussing about the integrity of the whole,
the heart trying to make time and place seem small,
sliding its slim tears into the deep wallet of each new event
on the list
then checking it off -- oh the satisfaction -- each check a small kiss . . .
--from ”The Guardian Angel Of The Private Life” by Jorie Graham
The electric colors of Birds of Paradise certainly thrill our eyes, but the entirety of their strange, elaborate mating rituals, which their peculiar arrangements of feathers are usually involved in, is equally beautiful. Their beauty is almost unbearable. (Note how many times David Attenborough, Miriam Supuma and Paul Igag say “beautiful,” “beauty” and synonyms.) Similarly the bower of the Bowerbird is, by itself, not necessarily the most elegant thing that one will see today; the beauty arises from the totality of the facts concerning the bower--its purpose, ingenuity, the birds' serious comical behavior in relation to it, etc.
In any case, to summarize this digression, I find the arguments against the mere subjectivity of beauty conclusive, and I am not aware of any good arguments by which to conclude that beauty is entirely subjective. It seems to me that efforts to try to account for beauty as a confused psychological event are highly misguided.
