1 vt. 2 barry smith department of philosophy (buffalo) institute for formal ontology and medical...

1

VT

2

Barry Smith

Department of Philosophy (Buffalo)

Institute for Formal Ontology and Medical Information Science (Leipzig)

ontology.buffalo.edu

ifomis.de

The Theory of Granular Partitions

3

A Simple Partition

4

5

6

A partition can be more or less refined

A partition can be more or less refined

7

8

9

Partition

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

10

GrGr

11

A partition is transparentIt leaves the world exactly as it is

12

Artist’s Grid

13

Label/Address System

A partition typically comes with labels and/or an address system

14

Montana

Montana

15

Cerebral Cortex

16

Mouse Chromosome Five

17

A partition can comprehend the whole of reality

18

Universe

19

It can do this in different ways

20

Periodic Table

21

Perspectivalism

PerspectivalismDifferent partitions may represent cuts through the same reality which are skew to each other

22

Universe/Periodic Table

23

Partitions can sometimes create objects

fiat objects = objects determined by partitions

24

Kansas

25

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

bona fide objects

26

27

California Land Cover

28

Artist’s Grid

29

a partition is transparent (veridical)

= its fiat boundaries correspond at least to fiat boundaries on the side of the objects in its domain

if we are lucky they correspond to bona fide boundaries (JOINTS OF REALITY)

30

Tibble’s Tail

fiat boundary

31

Partitions are artefacts of our cognition

= of our referring, perceiving, classifying, mapping activity

32

and they always have a certain granularity

when I see an apple my partition does not recognize the molecules in the apple

33

Alberti’s Grid

34

Sets belong not to the realm of objects but to the realm of partitions

Sets are not objects in reality, but mathematical tools for talking about reality

35

Idealism

the road to idealism

propositions,sets,

noemata, ...

36

Goodman: Many worlds

Me: Many partitions

37

we have all been looking in the wrong direction

38

Dürer Reverse

39

Intentionality

40

Intentionality

41

corrected

content, meaningrepresentations

42

The mistaken view

43

The correct view

set-like structures belong here

44

Alberti’s Grid

45

Not propositional attitudes

but object attitudes the attitudes mediated by partitions(thus relatively coarse-grained)

46

Defining

Sets are (at best) special cases of partitions

Cells are to partitions as singletons are to sets

47

Objects and cells

objects are located in cells as guests are located in hotel rooms:

LA(x, z)

the analogue of the relation between an element and its singleton

48

an object x is recognized by a partition A:

x A := z (LA(x, z))

there is some cell in A in which x is located

49

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 withoutorder or location—they can be permuted at will and the set remains identical

50

Partitions better than sets

Partitions are

better than sets

51

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

52

Cantor’s Hell

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

53

Cantor’s Hell

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

54

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.

55

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 location L

56

The theory of partitions

is a theory of foregrounding,

of setting into relief

57

You use the name ‘Mont Blanc’ to refer to a certain mountain

You see Mont Blanc from a distance

In either case your attentions serve to foreground a certain portion of reality

Setting into Relief

58

You use the name ‘Mont Blanc’ to refer to a certain mountain

You see Mont Blanc from a distance

In either case your attentions serve to foreground a certain portion of reality

Setting into Relief

59

You use the name ‘Mont Blanc’ to refer to a certain mountain

You see Mont Blanc from a distance

In either case your attentions serve to foreground a certain portion of reality

Setting into Relief

60

You use the name ‘Mont Blanc’ to refer to a certain mountain

You see Mont Blanc from a distance

In either case your attentions serve to foreground a certain portion of reality

Setting into Relief

61

Foreground/Background

62

The Problem of the ManyThere is no single answer to the question as to what it is to which the term ‘Mont Blanc’ refers. Many parcels of reality are equally deserving of the name ‘Mont Blanc’

– Think of its foothills and glaciers, and the fragments of moistened rock gradually peeling away from its exterior; think of all the rabbits crawling over its surface

63

Mont Blanc from Lake Annecy

64

The world itself is not vague

Rather, many of the terms we use to refer to objects in reality are such that, when we use these terms, we stand to the corresponding parcels of reality in a relation that is one-to-many rather than one-to-one. Something similar applies also when we perceive objects in reality.

65

Many but almost oneDavid Lewis:

There are always outlying particles, questionable parts of things, not definitely included and not definitely not included.

66

Granularity

• Cognitive acts of Setting into Relief: the Source of Partitions

• Partititions: the Source of Granularity

• Granularity: the Source of Vagueness

67

Objects and cells

x A := z (LA(x, z)

there is some cell in A and x is located in that cell

Recall:object x is recognized by partition A

68

John

69

Tracing OverGranularity: if x is recognized by a partition A, and y is part of x, it does not follow that y is recognized by A.When you think of John on the baseball field, then the cells in John’s arm and the fly next to his ear belong to the portion of the world that does not fall under the beam of your referential searchlight. They are traced over.

70

(Recall Husserl’s theory of Abschattungen)

(Ship of Theseus: different partitions of the same unterliegende sachliche

Tatbestandsmaterial)

71

John

72

Granularity the source of vagueness

... your partition does not recognize parts beneath a certain size.

This is why your partition is compatible with a range of possible views as to the ultimate constituents of the objects included in its foreground domain

73

Granularity the source of vaguenessIt is the coarse-grainedness of our partitions which allows us to ignore questions as to the lower-level constituents of the objects foregrounded by our uses of singular terms.

This in its turn is what allows such objects to be specified vaguely

Our attentions are focused on those matters which lie above whatever is the pertinent granularity threshold.

74

Mont Blanc from Chatel

75

Mont Blanc (Tricot)

76

Bill Clinton is one person

– these are both supertrue

Mont Blanc is one mountain

77

they are trueh

no matter which of the many aggregates of matter you assign as precisified referent

78

Bill Clinton is one person

– both are true on the appropriate level of granularity(our normal, common-sense ontology is in perfect order as it stands)

Mont Blanc is one mountain

79

Standard SupervaluationismA sentence is supertrue if and only if it is true under all precisifications. A sentence is superfalse if and only if it is false under all precisifications.

A sentence which is true under some ways of precisifying and false under others is said to fall down a supervaluational truth-value gap. Its truth-value is indeterminate.

80

Are those rabbits part of Mont Blanc?

81

Example of Gaps

On Standard Supervaluationism

Rabbits are part of Mont Blanc

falls down a supertruth-value gap

82

Different Contexts

• In a perceptual context it is supertrue that these rabbits are part of Mont Blanc

• In a normal context of explicit assertion it is superfalse that these rabbits are part of Mont Blanc

• In a real estate context in a hunting community it is supertrue that these rabbits are part of that mountain

83

So, even with

Rabbits are part of Mont Blanc,

there are no gaps.

Are there any naturally occurring contextswith gaps?

84

Supervaluationism Contextualized

We pay attention in different ways and to different things in different contexts

So: the range of available precisified referents and the degree and the type of vagueness by which referring terms are affected will be dependent on context.

85

Supervaluationism Contextualized

The range of admissible precisifications depends on context

The evaluations of supervaluationism should be applied not to sentences taken in the abstract but to judgments taken in their concrete real-world contexts

86

No gapsThe everyday judgments made in everyday contexts do not fall down supervaluational truth-value gapsbecause the sentences which might serve as vehicles for such judgments are in normal contexts not judgeable

87

Gaps and GlutsConsider:

Rabbits are part of Mont Blancis in a normal context unjudgeable

Compare:Sakhalin Island is both Japanese and

not Japanese

88

Problem cases

An artist is commissioned to paint a picture of Jesus Christ and uses himself as a model. Consider the judgment:

‘This is an image of Jesus Christ’

89

No gaps

Just as sentences with truth-value gaps are unjudgeable, so also are sentences with truth-value gluts. (Solution, here, to the liar paradox.

Pragmatic approach to problematic cases (e.g. liar paradox) ontologically clarified by contextualized supervaluationism

90

Normal contexts

including normal institutional contexts have immune systems which protect them against problematic utterances

such utterances are not taken seriously as expressing judgments

91

Judgments

exist only as occurring episodes within natural contexts ... thus they are partly determined by the immune systems which natural contexts standardly possess

92

Judgments and EvolutionMost naturally occurring contexts possess immune systems because those which did not would have been eliminated in the struggle for survival. But the semantics hereby implied has nothing to do with pragmatic eliminations of objective truth normally favored by proponents of evoluationary epistemology

93

Contextualized Supervaluationism

A judgment p is supertrue if and only if:• (T1) it successfully imposes in its context

C a partition of reality assigning to its constituent singular terms corresponding families of precisified aggregates, and

• (T2) the corresponding families of aggregates are such that p is true however we select individuals from the many candidate precisifications.

94

Supertruth and superfalsehood are not symmetrical:

A judgment p is superfalse if and only ifeither:

• (F0) it fails to impose in its context C a partition of reality in which families of aggregates corresponding to its constituent singular referring terms are recognized,

95

Falsehoodor both:

• (F1) the judgment successfully imposes in its context C a partition of reality assigning to its constituent singular terms corresponding families of precisified aggregates, and

• (F2) the corresponding families of aggregates are such that p is false however we select individuals from the many candidate precisifications.

96

Pragmatic presupposition failure:

In case (F0), p fails to reach the starting gate for purposes of supervaluation

Consider: „Karol Wojtyła is more intelligent than the present Pope“

97

Lake Constance

No international treaty establishes where the borders of Switzerland, Germany, and Austria in or around Lake Constance lie.

• Switzerland takes the view that the border runs through the middle of the Lake.

• Austria and Germany take the view that all three countries have shared sovereignty over the whole Lake.

98

Lake Constance

If you buy a ticket to cross the lake by ferry in a Swiss railway station your ticket will take you only as far as the Swiss border (= only as far as the middle of the lake)

99

but for all normal contextsconcerning

fishing rights,taxation,shipping, death at sea, etc., there are

treaties regulating how decisions are to be made (with built in immune-systems guarding against problematic utterances)

100

Lake Constance

an ontological black hole in the middle of Europe

101

Lake Constance (D, CH, A)

Switzerland Austria

Germany

102

That Water is in Switzerland

You point to a certain kilometer-wide volume of water in the center of the Lake, and you assert:

[Q] That water is in Switzerland.

Does [Q] assert a truth on some precisifications and a falsehood on others?

103

NoBy criterion (F0) above, [Q] is simply (super)false.

Whoever uses [Q] to make a judgment in the context of currently operative international law is making the same sort of radical mistake as is someone who judges that Karol Wojtyła is more intelligent than the present Pope.

104

Reaching the Starting Gate

In both cases reality is not such as to sustain a partition of the needed sort. The relevant judgment does not even reach the starting gate as concerns our ability to evaluate its truth and falsehood via assignments of specific portions of reality to its constituent singular terms.

105

Partitions do not care

Our ordinary judgments, including our ordinary scientific judgments, have determinate truth-values

because the partitions they impose upon reality do not care about the small (molecule-sized) differences between different precisified referents.

106

Again:

Enduring types of (social, legal, administrative, planning) contexts have immune systems to prevent the appearance of the sort of problematic vagueness that is marked by gaps and gluts

107

No Gaps

‘Bald’, ‘cat’, ‘dead’, ‘mountain’ are all vague

But corresponding (normal) judgments nonetheless have determinate truth-values.

There are (on one way of precisifying ‘normal’ in the above) no truth-value gaps

108

philosophical contexts are not normal

109

DOWN

WITH

PHILOSOPHY !

110

An ontology

• is a canonical representation of the types of entities in a given domain and of the types of relations between these entities:

• holy grail of a single benchmark ontology, which would make all databases intertranslatable

• an ontological Esperanto

111

Ontological Zooming

112

Universe/Periodic Table

animal

bird

canaryostrich

fishfolk biology

partition of DNA space

113

Universe/Periodic Table

animal

bird

canaryostrich

fish

both are transparent partitions of one and the same reality

114

115

Ontology

• like cartography• must work with maps at different scales and

with maps picking out different dimensions of invariants

116

If ontological realism is right• then there are very many map-like • partitions, at different scales,• which are all transparent

to the reality beyond

• the mistake arises when one supposes• that only one of these partitions is veridical

117

There are not only map-like partitions of reality into material (spatial) chunks

• but also distinct partitions of reality into universals (genera, categories, kinds, types)

• mutually compatible ways of providing inventories of universals

• (among proteins, among cells, among organisms …)

• and distinct ways of partitioning the temporal dimension of processes

118

Varieties of granular partitions• Partonomies: inventories of the parts of

individual entities• Maps: partonomies of space• Taxonomies: inventories of the universals

covering a given domain of reality

119

One example of ‘folk’ partition

• WordNet[1] • developed at the University of Princeton • defines concepts as clusters of terms called synsets. • Wordnet consists of some 100,000 synsets organized

hierarchically via:• A concept represented by the synset {x, x, …} is

said to be a hyponym of the concept represented by the synset {y, y,…} if native speakers of English accept sentences constructed from such frames as « An x is a kind of y ».

120

A Formal Theory of Granular Partitions

Thomas Bittner and Barry Smith

http://ontology.buffalo.edu/smith/articles/partitions.pdf

121

The Parable of the Two Tables

from Arthur Eddington, The Nature of the Physical World (1928)

Table No. 1 = the ordinary solid table made of woodTable No. 2 = the scientific table

122

The Parable of the Two Tables

‘My scientific table is mostly emptiness. Sparsely scattered in that emptiness are numerous electric charges rushing about with great speed; but their combined bulk amounts to less than a billionth of the bulk of the table itself.’

123

Eddington:

Only the scientific table exists.

124

The Parable of the Two Tables

Both of the tables exist – in the same place: in fact they are the same table but pictured in maps of different scales

the job of the theory of granular partitions is to do justice to this identity in (granular) difference

125

Towards a Theory of Intentionality / Reference / Cognitive Directedness

GRANULAR PARTITIONS: THE SECOND DIMENSION

126

Intentional directedness

… is effected via partitions

we reach out to objects because partitions are transparent

127

Applications

• Theory of selectivity of cognition (including natural language cognition)

• Theory of granularity (medical data, genetic data)

• Theory of transformations between partitions of the same reality (SNOMED, UMLS …)

128

THE END

THE END