1. 1 Intentionalität als Projektion Barry Smith http://buffalo.ontology.edu

2. 2 Leon Battista Alberti (1404-1472)

3. 3 Alberti (Medal)

4. 4 Leon Battista Alberti (1404-1472) architect and town planner moral philosopher cryptographer painter mathematician Papal adviser and Doctor of Canon Law land surveyor

5. 5 Della pittura 1435–36

6. 6 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

7. 7 Panofsky: one can properly speak of a perspectival intuition of space only where a whole picture is as it were transformed into a “window” through which we should then believe ourselves to be looking into the space

8. 8 Alberti’s Grid c.1450

9. 9 Machines for seeing for measuring the visible surfaces of external reality ‘reticolato’ ‘grill’ (graticola) ‘veil’ (velo)

10. 10 Dürer’s treatise on measurement Underweysung der Messung (1527)

11. 11 Dürer

12. 12 Dürer

13. 13 Artist’s Grid transparent grid

14. 14 Practical problem of perspective solved by Brunelleschi in 1425 with painting of Baptistery of St. John in Florence

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16. 16 Peepshow

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18. 18 Theoretical problem of perspective solved by Alberti in Book 1 of Della pittura The solution is captured in the diagram of the reticolato … belongs to projective geometry

19. 19 ‘true’ or correct perspective = what is captured on a plane intersecting the visual pyramid

20. 20 Alberti influence on Dürer Piero della Francesca Leonardo da Vinci transformed painting in realist direction, freed European art from bad geometry

21. 21 Ideal City

22. 22 The Flagellation

23. 23 School of Athens

24. 24 Giotto

25. 25 Giotto

26. 26 School of Athens

27. 27 How, 1700 years after Euclid’s geometry, did Alberti solve the theoretical problem of linear perspective ?

28. 28 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

29. 29 Florence by 1424 a center of cartographic and geographic study commentaries on Florentine versions of the Geographia influenced Columbus

30. 30 Ptolemaic World Map 12th-13th Century

31. 31 Ptolemaic World Map, 13th Century

32. 32 Ptolemaic World Map, J. Scotus 1505

33. 33 Ptolemy‘s Regional World Divisions

34. 34 Hecataeus 6th Century B.C:

35. 35 Ptolemy’s grid system transformed relationship between astronomy vs. sublunar physics for the first time made the world below susceptible to uniform mathematical treatment

36. 36 Grids of Reality (Mercator 1569)

37. 37 Every projection system is correct the point is merely to use it properly intelligence of the projective technique vs. stupidity of the interpreter (maps do not lie)

38. 38 The railway tracks on the Circle Line are not in fact yellow:

39. 39 Ptolemy’s grid system not just mathematical regularity also transparency... the grid helps us to see the world aright

40. 40 Ptolemy’s ‘third cartographic method’: how to make a picture based on a projection from a single point representing the eye of an individual human beholder.

41. 41 Alberti extended Ptolemy’s method to pictures Ptolemy applied his perspective construction only in the construction of maps and in stage design Alberti: the veil affords the greatest assistance in executing your pictures, since you can see any object that is round and in relief, represented on the flat surface of the veil.

42. 42 Uccello: Gridded Challice c. 1450

43. 43 Alberti’s Ontology of Painting Two kinds or levels of matter linked together by projective geometry

44. 44 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

45. 45 Two kinds of matter Compare Gibson’s 1980 “essay on the perception of surfaces versus the perception of markings on a surface.”

46. 46 Two kinds of matter the 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

47. 47 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

48. 48 Rules for manipulating the elements of an istoria dignità varietà modestia verisimilitudo together with geometry, these four principles constitute the basis of a rational art

49. 49 Leonardo: Non mi legga chi non e matematico. (‘Let no one read me who is not a mathematician.’)

50. 50 global selection the visible scene made of finite planes or surfaces the totality of planes in the macrocosm exists objectively it changes from moment to moment with changes in the ambient light

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65. 65 Fiat lux Light effects global selection

66. 66 The subject effects local selection

67. 67 but even the result of local selection is still perfectly objective compare what happens on the stage in the theater selection does not imply distortion

68. 68 Rays of marvelous subtlety qualities 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’

69. 69 Optical Projection

70. 70 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.

71. 71 Intromission vs. extromission 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.

72. 72 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 intromissionist vs. extromissionist views of visual perception

73. 73 Extromissionists: Pythagorians, Euclid, Stoics, Ptolemy, Galen Euclid’s geometry 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

74. 74 Euclid: rays are sent out of the observer’s eyes to apprehend the object observed

75. 75 Atomist argument for extromissionism The 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?

76. 76 The intromissionist answer Alhazen: 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.

77. 77 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. Grosseteste: light stands in the same relation to the natural world as abstract space stands to geometry.

78. 78 Physics and physiology are nowadays thoroughly intromissionist

79. 79 Yet extromissionism lives on, through the arrow of intentionality in phenomenology

80. 80 Intentionality

81. 81 corrected content, meaning representations

82. 82 concepts, contents, meanings belong here

83. 83 Frege referent expression sense intentionality Fregeanized

84. 84 Idealism propositions, senses, meanings noemata, contents... the incorrect view pretends that meanings can be in the target position

85. 85 Idealism propositions, senses, meanings noemata,... the road to philosophical pseudo-problems

86. 86 Examples of Pseudo-Problems What is the ontological status of ‘meanings’? What are the identity criteria for ‘meanings’? How can we ever transcend the realm of meanings / contents / ideas / sensations / noemata and reach out to the realm of objects in themselves ?

87. 87 Intentional directedness … is effected via partitions we reach out to objects because partitions are transparent

88. 88 Idealism propositions, senses, meanings noemata, contents... the incorrect view pretends that meanings can be in the target position

89. 89 Idealism propositions, senses, meanings noemata,... the road to philosophical pseudo-problems

90. 90 Examples of Pseudo-Problems What is the ontological status of ‘meanings’? What are the identity criteria for ‘meanings’? How can we ever transcend the realm of meanings / contents / ideas / sensations / noemata and reach out to the realm of objects in themselves ?

91. 91 Pseudo-Problems also in the sphere of the philosophy of mathematics

92. 92 The correct view mathematical structures belong here „das Mathematische ist primär ein B e z u g s p h ä n o m e n “

93. 93 Foreground/Background foreground/background

94. 94 Intentionality can be Many-Rayed ‘people’ ‘my three sons’ ‘Benelux’ ‘die Deutschen’

95. 95 Counting many-rayed intentionality

96. 96 Intentionality is foregrounded single-rayed or many-rayed mediated via transparent partitions

97. 97 The Empty Mask (Magritte) mama mouse milk Mount Washington

98. 98 The DER-DIE-DAS partition DER (masculine) moon lake atom DIE (feminine) sea sun earth DAS (neuter) girl fire dangerous thing

99. 99 Die Spinoza Aufteilung

100. 100 Universe

101. 101 Globe

102. 102 Globe

103. 103 Transparent partitions are involved in simple acts of naming, classifying, seeing, recognizing, mapping

104. 104 Intentional directedness … is effected via partitions we reach out to the objects themselves because partitions are transparent

105. 105 The partition is like an open window

106. 106 Against the veridicality of intentionality partitions, concepts, contents are not transparent Midas-touch epistemology

107. 107 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

108. 108 Windowless monads post Duchamp: visual arts are freed from connection to everyday life (and to beauty and harmony) recontextualized in the museum

109. 109 The Domain of Arnheim

110. 110 The Fair Captive

111. 111 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

112. 112 Pipe

113. 113 The realist response to Panofsky even 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

114. 114 The realist response the strange fascination which perspective had for the Renaissance mind ‘was the fascination of truth.’ (Pirenne 1952)

115. 115 Reasons for Realism the objective, 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

116. 116 Reasons for Realism the fact that there are pictures embodying various types of distortions and symbolic elements does not imply that all pictures are lacking in transparency the fact that there are rays which deviate from their proper path does not imply that there is no central ray which truly hits its target

117. 117 Reasons for Realism the fact that there are maps which deviate from the reality which they are purporting to depict does not imply that there are no correct maps which truly hit their targets

118. 118 How to Tell the Truth with Maps A 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.

119. 119 The analogy between maps and pictures has nothing to do with perspective but rather with the highly general concept of a transparent grid and with an associated highly general notion of projection

120. 120 Alberti’s Grid c.1450

121. 121 Optical Projection

122. 122 Cartographic Projection

123. 123 Semantic Projection, or: The Picture Theory of Pictures

124. 124 Semantic Projection Blanche is shaking hands with Mary

125. 125 True grids can have different resolutions true maps of the very same reality can be of different scales AND EVERY MAP MUST HAVE SOME SCALE

126. 126 Therefore: No ‘God’s eye perspective’ No ‘view from nowhere’  (some argue) every single one of the myriad perspectives we enjoy embodies a false view of reality This inference from partiality to falsehood is valid only in a world without windows.

127. 127 Almost all of our partitions are transparent intentional directedness succeeds

128. 128 THE END