460.02 Plato on Mimesis, Ideals, Inspiration

MIMESIS AND THE IDEAL
Plato on Representation and Beauty

For every one, as I think, must see that astronomy compels the soul to look
upwards and leads us from this world to another.
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.

Plato, Republic

How do you know?

What is real?

That which changes least is most real

You know best that which changes least

How do you know?
What is real?

How do you know?

What is real?



imaginings

illusions,
shadows

What is real?



How do you know?

beliefs
sensations

ordinary things

imaginings

illusions,
shadows

The Eye

What is real?



How do you know?

beliefs
sensations

ordinary things

imaginings

illusions,
shadows

The Sun

What is real?

understanding
reasoning
proofs
The Eye

forms
geometric forms
functions
formulae

beliefs
sensations

ordinary things

imaginings

illusions,
shadows



How do you know?

The Sun


What is real?

Recognition of:
The Good
The True
The Beautiful

The True
The Beautiful

understanding
reasoning
proofs
The Eye

forms
geometric forms
functions
formulae

beliefs
sensations

ordinary things

imaginings

illusions,
shadows

The Sun


How do you know?

How do you know?

What is real?

The Good

Recognition of:
The Good
The True
The Beautiful

The True
The Beautiful

understanding
reasoning
proofs
The Eye

forms
geometric forms
functions
formulae

beliefs
sensations

ordinary things

imaginings

illusions,
shadows

The Sun



The Mind

How do you know?

What is real?

The Good

Recognition of:
The Good
The True
The Beautiful

The True
The Beautiful

understanding
reasoning
proofs
The Eye
visible world

forms
geometric forms
functions
formulae

beliefs
sensations

ordinary things

imaginings

illusions,
shadows

The Sun



The Mind

How do you know?

What is real?

Intelligible World

The Good

Recognition of:
The Good
The True
The Beautiful

The True
The Beautiful

understanding
reasoning
proofs
The Eye
visible world

forms
geometric forms
functions
formulae

beliefs
sensations

ordinary things

imaginings

illusions,
shadows

The Sun



The Mind

How do you know?

What is real?

Intelligible World

The Good

Recognition of:
The Good
The True
The Beautiful

The True
The Beautiful
<Pythagorean
Theorem>

understanding
reasoning
proofs
The Eye
visible world

forms
geometric forms
functions
formulae

beliefs
sensations

ordinary things

imaginings

illusions,
shadows

<3 sided figure>

The Sun



The Mind

How do you know?

What is real?

Intelligible World

The Good

Recognition of:
The Good
The True
The Beautiful

The True
The Beautiful
<Pythagorean
Theorem>

instantiation

understanding
reasoning
proofs
The Eye
visible world

forms
geometric forms
functions
formulae

beliefs
sensations

ordinary things

imaginings

illusions,
shadows

<3 sided figure>

The Sun



The Mind

Where does art go?

Ideals

According to Plato art copies
things which copies ideals

ideals
things
art

Mimesis is, according to Plato, a copy of a copy of an ideal, thrice removed
from the truth.

Art from ideals

Polykleitos: Doryphorus

Lysippos: Apoxyomenos

Cultural ideals

Polykleitos: Doryphorus: 7:1

Lysippos: Apoxyomenos: 8:1

Leg to Body Ratio

Where could art go?

Ideals

Could art manipulate things like
shapes to express ideals?

ideals
art?

Participation and
Instances

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.
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 ideals

DRAWING FROM
SHAPES

Drawing from ideals

Leonardo, Dodecahedron

Paolo Ucello, Chalice

Leonardo, Tetrahedron

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 IDEALS
Art in the service of knowledge

PERMUTATIONS OF IDEALS
A contemporary notion of truth in the fashion of Plato

Truth: when a claim matches what
is
What is:
The Claim

The statue is on the pedestal.

reality

is
What is:
The Claim

reality

((subject) Predicate)
((designates) expresses)
<<thing> property>
<<statue> being on the pedestal>

<<statue> being on the pedestal>

is
What is:
The Claim

reality

((subject) Verb(object))
((designates) expresses(designates))
<<thing> relation<thing>>
<<statue> being on <the pedestal>>

<<statue> being on <the pedestal>>

is subject have the property
Does the thing designated by the
expressed by the predicate?

The Claim

The Golden Mean is a ratio represented by a point on a
line segment (C) that divides it such that the smaller
segment (A) stands in relation to the larger segment (B)
in the same relation that the larger segment stands to
the whole (A:B = B:C).

=

<<The Golden Mean> a ratio represented by a point
on a line segment (C) that divides it such that the
smaller segment (A) stands in relation to the larger
segment (B) in the same relation that the larger
segment stands to the whole (A:B = B:C).>

What is:
reality

A

B
C

is subject have the property
Does the thing designated by the
expressed by the predicate?

The Claim

The Golden Mean is a ratio represented by a point on a
line segment (C) that divides it such that the smaller
segment (A) stands in relation to the larger segment (B)
in the same relation that the larger segment stands to
the whole (A:B = B:C).

=

<<The Golden Mean> a ratio represented by a point
on a line segment (C) that divides it such that the
smaller segment (A) stands in relation to the larger
segment (B) in the same relation that the larger
segment stands to the whole (A:B = B:C).>

What is:
reality

A
B
C

Falsehood: when a claim fails to match
what is
The Claim

((The Parthenon) is exhibits the Golden Mean.)
((Subject) predicate)

What is: reality

≠

<<Thing> property>
<<Parthenon> exhibiting the Golden Mean>

A
B
Not true

C
False

Truth
some preliminaries

Matters of Taste or Opinion
Matters of Convention
Matters of Fact
Matters of Necessity

What is the
difference between
the truth, an honest
mistake, and a lie?

Truth
four types of truth


Can be
indexed to a
individuals,
places, and
times.

Matters of Fact

Does this exhaust all truths?

The ocean is prettier than the desert & the
desert is prettier than the woods.

Truth
some claims are true when indexed to the the
proper speaker or audience.

Barack Obama is our President T

Here is Patagonia T

some claims are true when indexed to the
proper place.

some claims are true when indexed to the
proper time.

George W. Bush is President ⊥

George W. Bush is President T

Enrique Peña Nieto is our President ⊥

Here is Patagonia ⊥

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Truth
four types of truth

Matters of Fact


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.

Truth
four types of truth

Matters of Fact
Matters of Fact

Consider a world
without people or
conventions,
would there still
be light at the
wavelength we
call cyan, ceteris
paribus?

Truth
four types of truth

Matters of Fact
Matters of Fact

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
four types of truth

π needs to have
this value for
circles to be
round.


π
Matters of Fact
Matters of Fact

=

3.141592...

Truth
four types of truth


π

Matters of Fact
Matters of Fact

In pursuit of truths about art

a rt

=

=

3.141592...

?

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

“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

IDEALS
Implementations through the centuries

Ictinus & Callicrates, Parthenon

C

A

B

A
B

C

“…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…”
–Vasari

Paolo Ucello, St George & the Dragon

Paolo Ucello, Battle of San Romano

Leonardo, Tetrahedron

Leonardo, Vitruvious Man

Leonardo, Dodecahedron

“Perspective is to painting what the
bridle is to the horse, the rudder to a
ship.”
—Leonardo

Massaccio, Trinity

“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

Massaccio, Trinity—Perspectives

Dürer, Melancholia

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
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 play
that 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. So
the rest derive from that primal tool alone.

Since any stroke is mightier the higher
it’s launched from over the forge, one kind and wise
has lately flown from mine to a loftier sphere.

My hammer is botched, unfinished in the fire
until God’s workshop help him supervise
the tool of my craft, that alone he trued, down here.

“treat nature by the
cylinder, the sphere, the
cone…”
—Cezanne

Cezanne, Still Life

cone…”
—Cezanne

Cezanne, Bibemus Quarry

cone…”
—Cezanne

Cezanne, Mt St Victiore

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

“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

Picasso, Landscape with Bridge

Juan Gris, Still Life with Fruit and Mandolin

DuChamp, Nude Descending a Staircase #2

Braque, Little Harbor in Normandy

The more abstract is form, the more clear and direct its appeal.—
Kandinsky

Klee, Ancient Sounds

Kandinsky, Composition X

Klee, Highways and Byways

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, Blue and Green Music

O’Keeffe, Cross

Local form

Richard Diebenkorn, Cityscape

Wayne Thibaud, Hill

Richard Diebenkorn, Seawall

For the poet is a light and winged and holy thing…

INSPIRATION
Plato on the affects of poetry, music, and performance

“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

Plato’s Psychology

Reason

TRIPARTITE SOUL
Wisdom
Rulers

Courage
Emotions

Self-control
Soldiers

Justice

Crafts workers
Plato’s Ideal Polis

Appetites

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.

Audience

Reason

Emotions

Appetites

Muse

Reason

Reason

Emotions

Emotions

Appetites

Reason

Emotions

Artist

Appetites
Appetites

“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

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.

460.02 Plato on Mimesis, Ideals, Inspiration

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460.02 Plato on Mimesis, Ideals, Inspiration