460.02 plato on mimesis, ideals, inspiration
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MIMESIS AND THE IDEALPlato on Representation and Beauty
Escher, Relativity
Really?
For every one, as I think, must see that astronomy compels the soul to look upwards and leads us from this world to another.
Plato, Republic
The spangled heavens should be used as a pattern and with a view to that higher knowledge; their beauty is like the beauty of figures or pictures excellently wrought by the hand of Daedalus, or some
other great artist, which we may chance to behold; any geometrician who saw them would appreciate the exquisiteness of their workmanship, but he would never dream of thinking that in
them he could find the true equal or the true double, or the truth of any other proportion.
How do you know? What is real?
You k
now
best
that
whic
h c
hanges
least
That w
hich
changes le
ast is m
ost re
al
How do you know?
What is real?
illusions, shadows
imaginings
You k
now
best
that
whic
h c
hanges
least
That w
hich
changes le
ast is m
ost re
al
How do you know?
What is real?
ordinary things
beliefs sensation
simagining
s
You k
now
best
that
whic
h c
hanges
least
That w
hich
changes le
ast is m
ost re
al
How do you know?
What is real?
illusions, shadows
The The SunSunThe EyeThe Eye
ordinary things
beliefs sensation
simaginin
gs
You k
now
best
that
whic
h c
hanges
least
That w
hich
changes le
ast is m
ost re
al
How do you know?
What is real?
illusions, shadows
understanding
reasoningproofs
formsgeometric
formsfunctionsformulae
The The SunSunThe EyeThe Eye
ordinary things
beliefs sensations
imaginings
You k
now
best
that
whic
h c
hanges
least
That w
hich
changes le
ast is m
ost re
al
How do you know?
What is real?
illusions, shadows
The TrueThe Beautiful
Recognition of:The GoodThe True
The Beautiful
understanding
reasoningproofs
formsgeometric
formsfunctionsformulae
The The SunSunThe EyeThe Eye
ordinary things
beliefs sensation
simaginin
gs
You k
now
best
that
whic
h c
hanges
least
That w
hich
changes le
ast is m
ost re
al
How do you know?
What is real?
illusions, shadows
The GoodThe GoodThe MindThe Mind
The TrueThe Beautiful
Recognition of:The GoodThe True
The Beautiful
understanding
reasoningproofs
formsgeometric
formsfunctionsformulae
The The SunSunThe EyeThe Eye
ordinary things
beliefs sensations
imaginings
You k
now
best
that
whic
h c
hanges
least
That w
hich
changes le
ast is m
ost re
al
How do you know?
What is real?
illusions, shadows
visible world
The GoodThe GoodThe MindThe Mind
The TrueThe Beautiful
Recognition of:The GoodThe True
The Beautiful
understanding
reasoningproofs
formsgeometric
formsfunctionsformulae
The The SunSunThe EyeThe Eye
ordinary things
beliefs sensation
simaginin
gs
You k
now
best
that
whic
h c
hanges
least T
hat w
hich
changes le
ast is m
ost re
al
How do you know?
What is real?
illusions, shadows
Intelligible World
visible world
The GoodThe GoodThe MindThe Mind
The TrueThe Beautiful
Recognition of:The GoodThe True
The Beautiful
understanding
reasoningproofs
formsgeometric
formsfunctionsformulae
The The SunSunThe EyeThe Eye
ordinary things
beliefs sensation
simaginin
gsYou k
now
best
that
whic
h c
hanges
least T
hat w
hich
changes le
ast is m
ost re
al
How do you know?
What is real?
illusions, shadows
Intelligible World
visible world
The GoodThe GoodThe MindThe Mind
The TrueThe Beautiful
Recognition of:The GoodThe True
The Beautiful
understanding
reasoningproofs
formsgeometric
formsfunctionsformulae
The The SunSunThe EyeThe Eye
ordinary things
beliefs sensations
imaginingsYou k
now
best
that
whic
h c
hanges
least T
hat w
hich
changes le
ast is m
ost re
al
How do you know?
What is real?
<3 sided figure>
illusions, shadows
<Pythagorean Theorem>
Intelligible World
visible world
The GoodThe GoodThe MindThe Mind
The TrueThe Beautiful
Recognition of:The GoodThe True
The Beautiful
understanding
reasoningproofs
formsgeometric
formsfunctionsformulae
The The SunSunThe EyeThe Eye
ordinary things
beliefs sensation
simaginin
gs
You k
now
best
that
whic
h c
hanges
least T
hat w
hich
changes le
ast is m
ost re
al
How do you know?
What is real?
<3 sided figure>
illusions, shadows
<Pythagorean Theorem>instantiation
ideals
things
Ideals
Where does art go?
art
According to Plato art copies things which
copies ideals
Mimesis is, according to Plato, a copy of a copy of an ideal, thrice removed from the truth.
Polykleitos: Doryphorus Lysippos: Apoxyomenos
Art from ideals
Polykleitos: Doryphorus: 7:1
Lysippos: Apoxyomenos: 8:1
Leg to Body Ratio
Cultural ideals
Contemporary ideals
Could art manipulate things like shapes to
express ideals?
ideals
art?
Ideals
Where could art go?
Early evidence?
Ideals, with a capital ‘I’, often called Forms are, according to Plato, are what is most real,—they are abstract, intelligible,
eternal and unchanging. There are three Ideals: Goodness, Truth, and Beauty. For Plato, Beauty is abstract it is not apprehended through the
senses.lesser ideals, also abstract and intelligible, participate in
in the Ideals. Examples of lesser ideals, with a small ‘i’,
might be ratios, formulae and geometric forms.
Participation and Instances
Shapes such as those found in architecture, architectonics, perspective, compositional forms
(such as the Platonic Solids—the cube, octahedron, tetrahedron, dodecahedron, and
icosahedron which have identical regular polygons as faces that meet at the same angles) and ratios (such as the Golden Mean and the Unison) in turn
participate in lesser ideals.
PERMUTATIONS OF MIMESIS AND IDEALS
DRAWING FROM SHAPES
Drawing from ideals
Leonardo, Tetrahedron
Leonardo, Dodecahedron
Paolo Ucello, Chalice
Drawing from ideals
EMPIRICAL ASTRONOMY VERSUS TRUE ASTRONOMY
The starry heaven which we behold is wrought upon a visible ground, and therefore, although the fairest and most perfect of visible things, must necessarily be deemed inferior far to the true motions of absolute swiftness and absolute slowness, which are relative to each other, and carry with them that which is contained in them, in the true number and in every true figure. Now, these are to be apprehended by reason and intelligence, but not by sight.
—Plato, The Republic
PERMUTATIONS OF IDEALSArt in the service of knowledge
Knowledge through Art
Knowledge through Art
Knowledge through Art
Knowledge through Art
Knowledge through Art
Knowledge through Art
Knowledge through Art
Knowledge through Art
PERMUTATIONS OF IDEALSA contemporary notion of truth in the fashion of Plato
The statue is on the pedestal.The statue is on the pedestal.
Truth: when a claim matches what isTruth: when a claim matches what isThe
ClaimWhat is: reality
((designates) expresses)((designates) expresses)
((subject) Predicate)((subject) Predicate)
The statue is on the pedestal.The statue is on the pedestal.
The Claim
What is: reality
<<thing> property><<thing> property>
<<statue> being on the <<statue> being on the pedestal>pedestal>
<<statue> being on the <<statue> being on the pedestal>pedestal>
Truth: when a claim matches what isTruth: when a claim matches what is
((designates) ((designates) expresses(designates))expresses(designates))
((subject) Verb(object))((subject) Verb(object))
The statue is on the pedestal.The statue is on the pedestal.
The Claim
What is: reality
<<thing> relation<thing>><<thing> relation<thing>>
<<statue> being on <the <<statue> being on <the pedestal>>pedestal>>
<<statue> being on <the <<statue> being on <the pedestal>>pedestal>>
Truth: when a claim matches what isTruth: when a claim matches what is
The Golden Mean is a ratio represented by a The Golden Mean is a ratio represented by a point on a line segment (C) that divides it point on a line segment (C) that divides it
such that the smaller segment (A) stands in such that the smaller segment (A) stands in relation to the larger segment (B) in the relation to the larger segment (B) in the same relation that the larger segment same relation that the larger segment
stands to the whole (A:B = B:C).stands to the whole (A:B = B:C).
<<The Golden Mean> a ratio represented <<The Golden Mean> a ratio represented by a point on a line segment (C) that divides by a point on a line segment (C) that divides it such that the smaller segment (A) stands it such that the smaller segment (A) stands in relation to the larger segment (B) in the in relation to the larger segment (B) in the
same relation that the larger segment same relation that the larger segment stands to the whole (A:B = B:C).>stands to the whole (A:B = B:C).>
=
Truth: when a claim matches what isTruth: when a claim matches what isDoes the thing designated by the subject have the property expressed by
the predicate?Does the thing designated by the subject have the property expressed by
the predicate?
The Claim
What is: reality
AB
C
The Golden Mean is a ratio represented by a The Golden Mean is a ratio represented by a point on a line segment (C) that divides it point on a line segment (C) that divides it
such that the smaller segment (A) stands in such that the smaller segment (A) stands in relation to the larger segment (B) in the relation to the larger segment (B) in the same relation that the larger segment same relation that the larger segment
stands to the whole (A:B = B:C).stands to the whole (A:B = B:C).
<<The Golden Mean> a ratio represented <<The Golden Mean> a ratio represented by a point on a line segment (C) that divides by a point on a line segment (C) that divides it such that the smaller segment (A) stands it such that the smaller segment (A) stands in relation to the larger segment (B) in the in relation to the larger segment (B) in the
same relation that the larger segment same relation that the larger segment stands to the whole (A:B = B:C).>stands to the whole (A:B = B:C).>
=
Truth: when a claim matches what isTruth: when a claim matches what isDoes the thing designated by the subject have the property expressed by
the predicate?Does the thing designated by the subject have the property expressed by
the predicate?
The Claim
What is: reality
A
B
C
((The Parthenon) is exhibits the Golden ((The Parthenon) is exhibits the Golden Mean.)Mean.)
((Subject) predicate)((Subject) predicate)
<<Thing> property><<Thing> property><<Parthenon> exhibiting the Golden Mean><<Parthenon> exhibiting the Golden Mean>≠
Not true False
Falsehood: when a claim fails to match what isFalsehood: when a claim fails to match what isThe
ClaimWhat is: reality
A
B C
Matters of Taste or OpinionMatters of Taste or Opinion
Matters of ConventionMatters of Convention
Matters of FactMatters of Fact
Matters of NecessityMatters of Necessity
What is the difference
between the truth, an honest mistake, and a
lie?
Truthsome preliminaries
Matters of Taste or OpinionMatters of Taste or OpinionMatters of Taste or OpinionMatters of Taste or Opinion
Matters of ConventionMatters of Convention
Matters of FactMatters of Fact
Matters of NecessityMatters of NecessityThe ocean is prettier than the desert
& the desert is prettier than the woods.Does this exhaust all
truths?
Truthfour types of truth
Can be indexed to
a individuals, places, and
times.
Truthsome claims are true when indexed to the the proper speaker or audience.
some claims are true when indexed to the proper place.
some claims are true when indexed to the proper time.
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Here is Patagonia THere is Patagonia T
Barack Obama is our President TBarack Obama is our President T
Enrique Peña Nieto is our President ⊥Enrique Peña Nieto is our President ⊥
Here is Patagonia ⊥Here is Patagonia ⊥
George W. Bush is President TGeorge W. Bush is President T
George W. Bush is President ⊥George W. Bush is President ⊥
Can be indexed to a register—a convention in culture or
society:According to the music
business, Tupac is gangsta is while My Chemical Romance is
emo.
Does this exhaust all truths?
Truthfour types of truth
Matters of Taste or OpinionMatters of Taste or OpinionMatters of Taste or OpinionMatters of Taste or Opinion
Matters of ConventionMatters of ConventionMatters of ConventionMatters of Convention
Matters of FactMatters of Fact
Matters of NecessityMatters of Necessity
Consider a world without
people or conventions, would there
still be light at the
wavelength we call cyan,
ceteris paribus?
Truth
Matters of Taste or OpinionMatters of Taste or OpinionMatters of Taste or OpinionMatters of Taste or Opinion
Matters of ConventionMatters of ConventionMatters of ConventionMatters of Convention
Matters of FactMatters of FactMatters of FactMatters of Fact
Matters of NecessityMatters of Necessity
four types of truth
Such truths, often
considered contingent, are
often expressed
ceteris paribus:‘Cyan’ is
identified by R 0, G 255, B
255 all other things being
equal.
Truth
Matters of Taste or OpinionMatters of Taste or OpinionMatters of Taste or OpinionMatters of Taste or Opinion
Matters of ConventionMatters of ConventionMatters of ConventionMatters of Convention
Matters of FactMatters of FactMatters of FactMatters of Fact
Matters of NecessityMatters of Necessity
four types of truth
Does this exhaust all truths?
ππ == 3.141592...3.141592...
Truthfour types of truth
Matters of Taste or OpinionMatters of Taste or OpinionMatters of Taste or OpinionMatters of Taste or Opinion
Matters of ConventionMatters of ConventionMatters of ConventionMatters of Convention
Matters of FactMatters of FactMatters of FactMatters of Fact
Matters of NecessityMatters of NecessityMatters of NecessityMatters of Necessity
π needs to have this value for circles to be
round.
ππ == 3.141592...3.141592...
Truthfour types of truth
Matters of Taste or OpinionMatters of Taste or OpinionMatters of Taste or OpinionMatters of Taste or Opinion
Matters of ConventionMatters of ConventionMatters of ConventionMatters of Convention
Matters of FactMatters of FactMatters of FactMatters of Fact
Matters of NecessityMatters of NecessityMatters of NecessityMatters of Necessityartart == ??
In pursuit of truths about art
When preparing to evaluate the truth of a claim, stabilize its truth value by indexing it to speaker and audience, place
and time, state the ceteris paribus, and define key terms by giving one clear meaning.
A rule of thumb for philosophy of art
TOM SHANNON
“I do not mean by beauty of form such beauty as that of animals or pictures, which the many would suppose to be
my meaning; but understand me to mean straight lines and circles, and the plane and solid figures which are formed out
of them by turning lathes and rulers and measures of angles; for these I affirm to be not only relatively beautiful, like other works of art, but they are eternally and abstractly
beautiful.”
–Plato Philebus 51c
IDEALSImplementations through the centuries
Ictinus & Callicrates, Parthenon
Ictinus & Callicrates, Parthenon
Ictinus & Callicrates, Parthenon
A
B
C
A
B CIctinus & Callicrates, Parthenon
Myron, Discobolus
Myron, Discobolus
Myron, Discobolus
Myron, Discobolus
–Vasari
“…sculpture and painting are in truth sisters, born from one father, that is, design, at one and the same birth, and have
no precedence one over the other…” “…design, which is their foundation, nay rather, the very
soul that conceives and nourishes within itself all the parts of man's intellect, was already most perfect before the
creation of all other things, when the Almighty God, having made the great body of the world and having adorned the
heavens with their exceeding bright lights, descended lower with His intellect into the clearness of the air and the solidity
of the earth…”
Paolo Ucello, St George & the Dragon
Paolo Ucello, Battle of San Romano
Leonardo, Vitruvious Man
Leonardo, Tetrahedron
Leonardo, Dodecahedron
Paolo Ucello, Chalice
Raphael,Engagement
Raphael,Engagement
Raphael, School of Athens
Raphael, School of Athens
Massaccio, Trinity
“Perspective is to painting what the bridle is to the horse, the rudder to a ship.”—Leonardo
Massaccio, Trinity—Perspectives
“There are three aspects to perspective. The first has to do with how the size of objects seems to diminish according to distance: the second, the manner in which colors change the farther away they are from the eye; the third defines how objects ought to be finished less carefully the farther away they are.”—Leonardo
Leonardo, Last Supper
Leonardo, Last Supper
Since geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art. —Dürer
Dürer, Melancholia
The new art must be based upon science — in particular, upon mathematics, as the most exact, logical, and graphically constructive of the sciences.—Dürer
There is no man on earth who can give a final judgment on what the most beautiful shape may be. Only God knows.—Dürer
If my rough hammer shapes the obdurate stone
to a human figure, this or that one, say,it’s the wielder’s fist, vision, and mind at
playthat gives it momentum—another’s, not its
own.
But the heavenly hammer working by God’s throne
by itself makes others and self as well. We know
it takes a hammer to make a hammer. Sothe rest derive from that primal tool alone.
–Michelangelo, If My Rough Hammer
Since any stroke is mightier the higherit’s launched from over the forge, one kind
and wisehas lately flown from mine to a loftier
sphere.
My hammer is botched, unfinished in the fire
until God’s workshop help him supervisethe tool of my craft, that alone he trued,
down here.
Cezanne, Still Life
“treat nature by the cylinder, the sphere, the cone…”—Cezanne
Cezanne, Bibemus Quarry
“treat nature by the cylinder, the sphere, the cone…”—Cezanne
Cezanne, Mt St Victiore
“treat nature by the cylinder, the sphere, the cone…”—Cezanne
Cezanne, Mt St Victoire
“treat nature by the cylinder, the sphere, the cone…”—Cezanne
Cezanne, Mt St Victoire
“The fact that for a long time Cubism has not been understood and that even today there are people who cannot see anything in it means nothing. I do not read English, an English book is a blank book to me. This does not mean that the English language does not exist. Why should I blame anyone but myself if I cannot understand what I know nothing about?”—Picasso Picasso, House with Garden
Picasso, Landscape with Bridge
“It is a pity that no one in Paris bothered to quote Coleridge, who wrote, long before cubism, that the true poet is able to reduce 'succession to an instant.' Simultaneity in this sense is the property of all great poetry.—LeRoy C. Breunig
Juan Gris, Still Life with Fruit and Mandolin
DuChamp, Nude Descending a Staircase #2 Braque, Little Harbor in Normandy
Klee, Ancient Sounds
Kandinsky, Composition X Klee, Highways and Byways
The more abstract is form, the more clear and direct its appeal.—Kandinsky
Klee, Ad Parnassum
O ’Keeffe, Blue and Green Music O ’Keeffe, Cross
I found I could say things with color and shapes that I couldn't say any other way - things I had no words for.
—O ’Keeffe
O ’Keeffe, Cross
Wayne Thibaud, Hill
Richard Diebenkorn, Cityscape
Richard Diebenkorn, Seawall
Local form
MAYA LIN
INSPIRATIONPlato on the affects of poetry, music, and performance
For the poet is a light and winged and holy thing…
“For the poet is a light and winged and holy thing, and there is no invention in him until he has been inspired and is out of
his senses, and the mind is no longer in him: when he has not attained to this state, he is powerless and is unable to
utter his oracles.”
–Plato, Ion
“The gift which you possess of speaking excellently about Homer is not an art, but, as I was just saying, an inspiration;
there is a divinity moving you, like that contained in the stone which Euripides calls a magnet, but which is
commonly known as the stone of Heraclea. This stone not only attracts iron rings, but also imparts to them a similar
power of attracting other rings; and sometimes you may see a number of pieces of iron and rings suspended from one another so as to form quite a long chain: and all of them
derive their power of suspension from the original stone. In like manner the Muse first of all inspires men herself; and
from these inspired persons a chain of other persons is suspended, who take the inspiration.”–Plato, Ion
TRIPARTITE SOUL
Plato’s Psychology
Reason
Emotions
Appetites
Rulers
Soldiers
Crafts workers
Wisdom
Courage
Self-controlJustic
e
Plato’s Ideal Polis
Do you know that the spectator is the last of the rings which, as I am saying, receive the power of the original magnet from one another? The rhapsode like yourself and the actor are intermediate links, and the poet himself is the first of them.
Reason
Emotions
Appetites
Reason
Emotions
Appetites
Reason
Emotions
AppetitesReaso
n
Emotions
Appetites
MuseMuse
Artist
Audience
“For all good poets, epic as well as lyric, compose their beautiful poems not by art, but because they are inspired
and possessed. And as the Corybantian revellers when they dance are not in their right mind, so the lyric poets are not in their right mind when they are composing their beautiful
strains: but when falling under the power of music and metre they are inspired and possessed; like Bacchic
maidens who draw milk and honey from the rivers when they are under the influence of Dionysus but not when they are in their right mind. And the soul of the lyric poet does
the same, as they themselves say; for they tell us that they bring songs from honeyed fountains, culling them out of the gardens and dells of the Muses; they, like the bees, winging
their way from flower to flower.”–Plato, Ion
Dürer, Melancholia
GORECKI
II. Lento E Largo - Tranquillissimo
Socrates. Why, does not Homer speak in many passages about arts? For example, about driving; if I can only remember the lines I will repeat them. Ion. I remember, and will repeat them. Socrates. Tell me then, what Nestor says to Antilochus, his son, where he bids him be careful of the turn at the horse-race in honour of Patroclus.
Ion. He says: Bend gently in the polished chariot to the left of them, and urge the horse on the right hand with whip and voice; and slacken the rein. And when you are at the goal, let the left horse draw near, yet so that the nave of the well-wrought wheel may not even seem to touch the extremity; and avoid catching the stone.
Socrates. Enough. Now, Ion, will the charioteer or the physician be the better judge of the propriety of these lines? Ion. The charioteer, clearly. Socrates. And will the reason be that this is his art, or will there be any other reason? Ion. No, that will be the reason.Socrates. Then he who has no knowledge of a particular art will have no right judgment of the sayings and doings of that art? Ion. Very true. Socrates. Then which will be a better judge of the lines which you were reciting from Homer, you or the charioteer? Ion. The charioteer. Socrates. Why, yes, because you are a rhapsode and not a charioteer. Ion. Yes. Socrates. And the art of the rhapsode is different from that of the charioteer? Ion. Yes. Socrates. And if a different knowledge, then a knowledge of different matters? Ion. True.
BEN HUR
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