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Partitions of Reality

Barry Smith

http://ontology. buffalo.edu

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Leon Battista Alberti (1404-1472)

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Alberti (Medal)

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Leon Battista Alberti (1404-1472)

architect and town planner

moral philosopher

cryptographer

painter

mathematician

Papal adviser and Doctor of Canon Law

land surveyor

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Della pittura 1435–36

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The goal of the artist:

to produce a picture that will represent the visible world

as if the observer of the picture were looking through a window

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Panofsky:

one can properly speak of a perspectival intuition of space only wherea whole picture is as it were transformed into a “window” through which we should then believe ourselves to be looking into the space

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Alberti’

s Grid

c.1450

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Machines for seeingfor measuring the visible surfaces of external reality

‘reticolato’

‘grill’ (graticola)

‘veil’ (velo)

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Dürer’s treatise on

measurement

Underweysung der Messung (1527)

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Dürer

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15Artist’s Grid

transparent grid

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Practical problem of

perspective

solved by Brunelleschi in 1425

with painting of Baptistery of St. John in Florence

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Peepshow

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Theoretical problem of

perspectivesolved by Alberti in Book 1of Della pittura

The solution is captured in the diagram of the reticolato

… belongs to projective geometry

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‘true’ or correct

perspective

= what is captured on a plane intersecting the visual pyramid

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Alberti influence on

Dürer

Piero della Francesca

Leonardo da Vinci

transformed painting in realist direction, freed European art from bad geometry

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Giotto

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Giotto

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Ideal City

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The Flagellation

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School of Athens

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School of Athens

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How, 1700 years after Euclid’s

geometry, did Alberti solve the

theoretical problem of linear

perspective ?

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Rediscovery of Ptolemy’s

Geographia (c. 140 A.D.)

Greek text arrived in Florence from Constantinople in 1400

Ptolemy used regular mathematical grid system to map the entire known world

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Florence by 1424 a center

of cartographic and

geographic study

commentaries on Florentine versions of the Geographia influenced Christopher Columbus

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Hecataeus 6th Century B.C:

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Ptolemaic World Map, J.

Scotus 1505

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Ptolemy’s grid system

transformed relationship between astronomy vs. sublunar physicsfor the first time made the world below susceptible to uniform mathematical treatment

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Ptolemaic World Map

12th-13th Century

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Ptolemaic World Map,

13th Century

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Ptolemaic World Map, J.

Scotus 1505

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Ptolemy‘s Regional World

Divisions

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Ptolemy’s grid system

not just mathematical regularity

also transparency

... the grid helps us to see the world aright

... it partitions reality

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Periodic Table

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Kansas

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Alberti extended Ptolemy’s

method to pictures

Ptolemy applied his perspective construction only in the construction of maps and in stage design

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Uccello: Gridded Challice c. 1450

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Alberti’s Ontology of

Painting

Two kinds or levels of matter

linked together by projective geometry

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Alberti’s Ontology of

Painting

1. the three-dimensional matter of the observable world (macrocosm)

composed of surfaces in three-dimensional reality

2. the two-dimensional matter of the painting (microcosm, simulacrum)

composed of marks on a flat plane

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Two kinds of matterthe two-dimensional matter of the painting exists in the form of an istoria

constructed out of points, lines and planes (marks)

grouped together to form limbs, bodies and groups of bodies

in a way that is analogous to the logical structure of words, phrases, sentences and paragraphs in a story

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The artist’s job

is to project the objective array of planes into the microcosm of the painting in such a way as to achieve a maximally beneficial (moral) effect

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Rules for manipulating

the elements of an istoriadignità

varietà

modestia

verisimilitudo

together with geometry, these four principles constitute the basis of a rational art

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Leonardo:

Non mi legga chi non e matematico.

(‘Let no one read me who is not a mathematician.’)

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Rays of marvelous

subtletyqualities of color, shape and size of planes in the objective array are ‘measured with sight.’

rays that serve sight carry the form of the thing seen to the sense

‘by a certain marvelous subtlety’

they penetrate the air and ‘all thin and clear objects’

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Rays of marvelous

subtlety... until they strike against something

dense and opaque, where they strike with a point and adhere to the mark they make.

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„Among the ancients there was no little dispute whether these rays come from the eye or the plane. This dispute is very difficult and is quite useless for us. It will not be considered.

„We can imagine those rays to be like the finest hairs of the head, or like a bundle, tightly bound within the eye where the sense of sight has its seat.“

Rays of marvelous

subtlety

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Intromission vs. extromission

„The rays, gathered together within the eye, are like a stalk; the eye is like a bud which extends its shoots rapidly and in a straight line on the plane opposite.”

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Extromissionism

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Intromissionism

rays of light

come into the eye

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The laws of optics are the same

whether intromissionism or extromissionism is true

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we perceive through the intromission of bodies (Democritus)

we perceive through the intromission of spirits/forms/species (Aristotle)

Intromissionism

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Extromissionism

We perceive through the extromission of rays (Empedocles, Pythagorians, Euclid, Stoics, Ptolemy, Galen)

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Extromissionism

Euclid’s geometry and optics relates not to rays of light in the physical sense but to extromissionist ‘visual rays’

Galen: the eye’s crystalline lens is a transmitter of visual force

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Euclid:

rays are sent out of the observer’s eyes to apprehend the object observed

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Atomist argument for

extromissionismThe effluxes of, say, a camel or a mountain could not very well pass through the tiny pupil of the eye

How could every point on so large a visual surface be transmitted simultaneously to the eye, with its finite compass, via atoms of light?

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The intromissionist

answerAlhazen:

refraction and the curvature of the lens of the eye work to filter out excess information in the light,

every point on the surface of an object can convey its form to the seat of vision within the eye – in an exact one-for-one, place-for-place proportionate way.

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Lux gratiae

Robert Grosseteste, Roger Bacon and John Pecham:

the new optical theories of the transmission of light provide a model of how God spreads the light of grace to his subjects in the world.

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Physics and physiology are

nowadays thoroughly

intromissionist

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Yet extromissionism lives

on,

through the arrow of intentionality

in phenomenology

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Intentionality

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corrected

content, meaningrepresentations

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Frege

referent

expression

sense

intentionality Fregeanized

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concepts, contents, meanings belong here

they are not isolated

but form complex grids

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concepts, contents, meanings belong here

and they are transparent

they form partitions of reality

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Intentional directedness

… is effected via partitions/grids

we reach out to objects because partitions are transparent

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Foreground/Background

with the help of grids we determine what is foreground, what is background

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Transparent partitions

are involved in simple acts of naming, classifying, seeing, recognizing, mapping

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Intentionality can be Many-

Rayed‘people’

‘my three sons’

‘Benelux’

‘die Deutschen’

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1 2 3 4

Counting

with the help of grids weare able to count

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Intentionality is

foregroundedsingle-rayed or many-rayedmediated via partitions of reality

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J. J. Gibson’s Dual

Extromissionist-

Intromissionist ViewThere is information in the light, which comes in from the outside

We are pre-tuned to grasp this information with the help of the grids which we project outwards onto reality

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Partitions of reality can

be good and bad

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The Empty Mask

(Magritte)mama

mouse

milk

Mount Washington

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The DER-DIE-DAS partition

DER

(masculine)

moon

lake

atom

DIE

(feminine)

sea

sun

earth

DAS

(neuter)

girl

firedangerous

thing

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the Spinoza partition

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Universe

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Intentional directedness

… is effected via partitions

we reach out to the objects themselves because partitions are transparent

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A transparent partition is

like an open window

a window on reality

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Panofsky

perspective is not a true theory of the way light is projected by three-dimensional surfaces onto a two-dimensional plane

rather: it is a system of conventions bound to a certain time and culture.

Perspective as Symbolic Form 1927

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Against the veridicality of

intentionality

partitions, concepts, contents are not transparent

Midas-touch epistemology

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Windowless monads

post Duchamp: visual arts are freed from connection to everyday life (and to beauty and harmony)

recontextualized in the museum

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The Domain of Arnheim

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The Fair Captive

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After Duchamp

No place for talk of ‘correct’ perspectival representation, with its implication to the effect that there is some single detached master point of view

no method of painting can be ‘true’ or ‘correct’ for there is no single notion of reality against which its results could be matched

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Pipe

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The realist response to

Panofskyeven granting the simplifying assumptions of geometrical optics, perspective paintings correspond to the way we see the world around us with a very high degree of approximation.

best explanation for this: the mathematical forms captured in the geometry of perspective are out there in the world

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The realist response

the strange fascination which perspective had for the Renaissance mind ‘was the fascination of truth.’ (Pirenne 1952)

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The geometry of

perspective is purely

objectivethe geometrical relationship between an object and its image on the picture plane obtains independently of whether there is an eye at the vanishing point

(cf. laser-guided missiles)

the laws of perspective hold independently of the existence of subjects, observers, artists or cultures

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How to Tell the Truth with

MapsA good map casts a transparent net over the surface of the earth

Alberti’s reticolato casts its transparent net over the array of planes out there in objective reality in such a way as to cast into relief a visual scene.

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Optical Projection

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Cartographic Projection

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EVERY MAP MUST HAVE SOME SCALE

EVERY MAP MUST USE SOME METHOD OF PROJECTION

EVERY MAP MUST INVOLVE SOME SELECTION FROM THE WHOLE OF REALITY

THEREFORE: EVERY MAP IS FALSE

A bad argument

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Therefore: No ‘God’s eye

perspective’ No ‘view from

nowhere’Therefore: every single one of the myriad perspectives we enjoy embodies a false view of reality

This inference from partiality to falsehood would be valid only in a world without windows.

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Grids of Reality (Mercator

1569)

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The railway tracks on the Circle

Line are not in fact yellow:

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Every projection system is

correctthe point is merely to use it properlyintelligence of the projective technique vs. stupidity of the interpreter(maps do not lie)

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Almost all of our

partitionsare transparentintentional directedness

succeeds

fit happens

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THE END

THE END