1 Truth and Categorization Barry Smith

2 A categorization is a sorting, a dividing, a partitioning of reality, or of a certain portion of reality

3 All categorizations are partial (we are finite beings) But nearly all categorizations are true, correct, veridical

4 Borges’ Chinese Encyclopedia animals which belong to the emperor embalmed animals sirens fabulous animals wild dogs which are painted with a fine camelhair brush which have broken the water-pitcher which look like flies from a distiance

5 A Simple Partition

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8 A partition can be more or less refined

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11 Partition A partition is the drawing of a (typically complex) fiat boundary over a certain domain

12 GrGr

13 Partitions are artefacts of our cognition = of our categorizing, sorting, classifying, naming, listing, referring, perceiving, mapping activity

14 A partition is transparent It leaves the world exactly as it is

15 Artist’s Grid

16 Label/Address System A partition typically comes with labels and/or an address system

17 Dewey Decimal Classification

18 Dewey Decimal Classification

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20 All transparent partitions are equal... but some are more equal than others

21 There are many, competing criteria for quality of partitions: completeness naturalness principledness … (Borges’ Chinese Encyclopedia violates them all)

22 Some partitions support reliable predictions

23 Mouse Chromosome Five

24 Some do not …

25 DER (masculine) moon lake atom DIE (feminine) sea sun earth DAS (neuter) girl fire dangerous thing The der-die-das Partition

26 The Empty Mask (Magritte) mama mouse milk Mount Washington

27 Mothers exist

28 The common sense partitions of folk physics, folk psychology, folk biology, are all transparent to reality Aristotelianism for today:

29... rookbishoppawnknight... JohnPaulGeorgeRingo... updowncharmstrange...

30 Even the partitions of reductionists are transparent The objects admitted by the nominalist, the process-metaphysician, the physicalist, truly do exist.

31 Reductionists err only when they add ‘and nothing else exists’ (as if one were to insist that only maps of exactly one preferred scale can be true of reality)

32 are our scientific partitions truly transparent to an independent reality ?

33... what about quantum mechanics ?

34 Refinement a partition can be refined or coarsened by adding or subtracting from its constituent cell-divisions

35 Manipulation of partitions refinement coarsening gluing restricting

36 Enlargement of a partition

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40 The realist’s ideal A total partition of the universe, a super- partition (a God’s eye view) satisfying: “Every element of the physical reality has a counterpart in the physical theory.” (Einstein-Podolsky-Rosen 1935)

41 A universal partition why not just take the product of all partitions covering each successive domain and glue them all together ?

42 Ontological Problem In the quantum domain not all transparent partitions are consistent

43 But still: In relation to the mesoscopic and macroscopic realms sense realism holds with unrestricted validity Indeed we can derive the truths of folk physics rigorously from quantum mechanical laws we do this by moving from finer-grained to coarser-grained histories

44 A partition can comprehend the whole of reality

45 Universe

46 It can do this in different ways

47 The Spinoza Partition

48 Periodic Table

49 Perspectivalism Different partitions may represent cuts through the same reality which are skew to each other

50 (You can cut the cheese in different ways)

51 Universe/Periodic Table

52 Partitions have different granularity just as maps have different scales

53 Partitions can have empty cells

… Partition of people in this room according to: number of years spent in jail

55 Partition of people in this room according to: number of days spent in jail

56 Therefore a good theory of partitions needs more than one empty set. (We can err in many ways.)

57 Partitions can sometimes create objects fiat objects = objects created by partitions

58 Tibble’s Tail fiat boundary

59 Canada Quebec Canada

60 Kansas

61 = objects which exist independently of our partitions (objects with bona fide boundaries) bona fide objects

62 globe

63 Some partitions involve both types of boundaries

64 Cerebral Cortex

65 California Land Cover Reciprocal partitions

66 a partition is transparent (veridical) 1. its fiat boundaries correspond at least to fiat boundaries on the side of the objects in its domain 2. if we are lucky they correspond to bona fide boundaries (JOINTS OF REALITY)

67 In case 1. our partition/categorization is a discretization of a continuum In case 2. our partition/categorization captures discrete divisions on the sides of the objects In both cases our partitions are transparent

68 What is a partition? a way of successfully projecting a system of cells upon reality

69 These are different ways in which cells can be projected successfully onto reality

70 An object can be located in a cell within a partition in any number of ways: – object x exemplifies kind K – object x possesses property P – object x falls under concept C – object x is in spatial location L – object x is in measurement-band B contrast the meager resources of set theory 

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

72 and they always have a certain granularity when I see an apple my partition does not recognize the molecules in the apple

73 This is a mistake propositions, sets, noemata, meanings, models, concepts, senses,... content does not belong in the target position

74 Intentionality this is the correct view

75 corrected content, meaning representations are transparent – they are like spectacles

76 Intentionality

77 AGAINST “PROPOSITIONAL ATTITUDES” Examples of pseudo-problems in philosophy: what are ‘meanings’? what are the identity criteria for meanings? where is the ‘realm of meanings’?

78 The worst example of a pseudo- problem in the history of philosophy: How can we ever transcend the realm of meanings / contents / ideas / sensations / noemata and reach out to the realm of objects in themselves ?

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

Counting requires partitions

81 Frege: “Numbers belong to the realm of concepts” Smith: Numbers belong to the realm of partitions

82 Measurement belongs to the realm of partitions   0 0   massively increased... normal increased chronic...

83 Sets belong to the realm of partitions Sets are not objects in reality, but mathematical tools for talking about reality

84 Another mistake:

85 The correct view set-like structures belong here

86 Defining  Sets are (at best) special cases of partitions Cells are to partitions as singletons are to sets

87 Objects and cells objects are located in cells as guests are located in hotel rooms: L A (x, z) the analogue of the relation between an element and its singleton

88 Set as List Partition A set is a list partition (a set is, roughly, a partition minus labels and address system) The elements exist within the set without order or location —they can be permuted at will and the set remains identical

89 David Lewis on Sets Set theory rests on one central relation: the relation between element and singleton. Sets are mereological fusions of their singletons (Lewis, Parts of Classes, 1991)

90 Cantor’s Hell... the relation between an element and its singleton is “enveloped in mystery” (Lewis, Parts of Classes)

91 Cantor’s Hell... the relation between an element and its singleton is “enveloped in mystery” (Lewis, Parts of Classes)

92 Partitions better than sets Partitions are as we can see better than sets

93 Mystery Lewis:... since all classes are fusions of singletons, and nothing over and above the singletons they’re made of, our utter ignorance about the nature of the singletons amounts to utter ignorance about the nature of classes generally.

94 The ‚mystery‘ of set theory arises from supposing that sets are objects This is the root, also, of Frege’s problem in the Grundgesetze This is the root of the catastrophic high- rise projects of post-Cantorian set theory

95 Demolition

96 Cantor’s Hell arises because set theory confuses the fiat boundaries generated by our partitions (e.g. by our setting certain phenomena into relief in terms of the ‘real numbers’) with bona fide boundaries possessed by special objects (the sets)

97 How do partitions, classifications, categories relate to reality via intentionality (via the projections of conscious subjects) partitions, classifications, categories are cognitive artefacts but they are transparent to what exists on the side of objects in reality

98 An (Irregular) Partition

99 A Portion of Reality

100 Cartographic Hooks

101 A Map

102 A Sentence Blanche is shaking hands with Mary

103 A Portion of Reality

104 Semantic Hooks Blanche is shaking hands with Mary

105 A Sentence Blanche is shaking hands with Mary

106 Wittgenstein‘s Tractatus on Projection the proposition is the propositional sign in its projective relation to the world 3.13 to the proposition belongs everything which belongs to the projection; not however that which is projected

107 Satz und Sachverhalt arb language world names simple objects

108 Satz und Sachverhalt arb language world cells (in coarse-grained partitions) simple and complex objects

109 Satz und Sachverhalt arb language world projection

110 Satz und Sachverhalt arb Semantic Projection „ John is kissing Mary “ John this kiss Mary

111 Truth is a free lunch Truth is easy easy to come by, even for small children; easy to explain (if you avoid Kant and other bad philosophy)

112 Falsehood: A Realist Theory Falsehood is not: successful conformity with some non-existing state of affairs... it is the failure of an attempted conformity, resting on either 1. failure of projection, or 2. failure of coordination

113 Satz und Sachverhalt arb Projection Failure „John is kissing Mary“ John Mary nothing here

114 Nothing really nothing

115 Satz und Sachverhalt arb Projection Failure „John is kissing Mary“ John Mary

116 Coordination Failure arb „John is kissing Mary“ Mary this kiss John Coordination Failure

117 Realist Semantics We begin with a theory of propositions as articulated pictures of reality The theory of truth comes along as a free lunch We then show how to deal with the two kinds of failure which constitute falsehood

118 THE END