1 The Theory of Granular Partitions: A New Paradigm for Ontology Barry Smith Department of Philosophy University at Buffalo

2 The Theory of Granular Partitions: A New Paradigm for Ontology Barry Smith Institute for Formal Ontology and Medical Information Science University of Leipzig

3 Gesellschaft für Klassifikation Classification Classifying Studying = Producing ClassificationsClassifications

4 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

5 A Simple Partition

6

7

8 A partition can be more or less refined

9 Coarse-grained Partition

10 Fine-Grained Partition

11 Ontologies Partitions are, roughly, what AI and database people call ontologies but in which granularity is taken seriously

12 An organism is a totality of molecules An organism is a totality of cells An organism is a single unitary substance... all of these express distinct granular partitions An organism is a totality of atoms

13 Ontological Zooming

14 Universe/Periodic Table animal bird canary ostrich fish folk biology partition of DNA space

15 Universe/Periodic Table animal bird canary ostrich fish both are transparent partitions of one and the same reality

16

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

18 all express partitions which are transparent, at different levels of granularity, to the same reality beyond

19 Ontology like cartography must work with maps at different scales and with maps picking out different dimensions of invariants

20 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

21 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

22 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

23 One example of ‘folk’ partition WordNet[1][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 ».

24 A Formal Theory of Granular Partitions Thomas Bittner and Barry Smith

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

26 GrGr

27 Partitions are artefacts of our cognition = of our referring, perceiving, classifying, mapping activity

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

29 Mouse Chromosome Five

30 Periodic Table

31 Partitions have different granularity Maps have different scales

32 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 wood Table No. 2 = the scientific table

33 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.’

34 Eddington: Only the scientific table exists.

35 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

36 Some partitions are completely arbitrary but transparent nonetheless

37 Kansas

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

39 = objects which exist independently of our partitions (objects with bona fide boundaries) planets, tennis balls bona fide objects

40 globe

41 There are also Mixed Partitions

42 Cerebral Cortex

43 and also Reciprocal Partitions

44 California Land Cover Reciprocal partitions

45 A Formal Theory of Granular Partitions Thomas Bittner and Barry Smith

46 Towards a Theory of Intentionality / Reference / Cognitive Directedness GRANULAR PARTITIONS: THE SECOND DIMENSION

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

48 Intentionality

49 Intentional directedness always has a certain granularity when I see an apple my partition does not recognize the molecules in the apple

50 corrected content, meaning representations

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

52 A Theory of Maps

53 An (Irregular) Partition

54 A Portion of Reality

55 Cartographic Hooks

56 A Map

57 A Theory of Websites Barry Smith Department of Philosophy University at Buffalo

58 A theory of language of assertive utterances (der Satz)

59 Die Projektion der Satz ist das Satzzeichen in seiner projektiven Beziehung zur Welt Zum Satz gehört alles, was zur Projektion gehört; aber nicht das Projizierte.

60 The theory of partitions is a theory of foregrounding, of setting into relief

61 You use the name ‘Mont Blanc’ to refer to a certain mountain your utterance serves to foreground a certain portion of reality Setting into Relief

62 Foreground/Background but there is a problem

63 The Problem of the Many Many parcels of reality are equally deserving of the name ‘Mont Blanc’ – Think of its foothills and glaciers think of all the rabbits crawling over its surface

64 Many but almost one There are always outlying particles, questionable parts of things, not definitely included and not definitely not included. Implies when referring to tokens and also when referring to types (outliers, Bordeaux 1997)

65 Granularity Cognitive acts of Setting into Relief: the Source of Partitions

66 Granularity Cognitive acts of Setting into Relief: the Source of Partitions Partititions: the Source of Granularity

67 Granularity Cognitive acts of Setting into Relief: the Source of Partitions Partititions: the Source of Granularity Granularity: the Source of Vagueness

68 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

69 Granularity the source of vagueness Our attentions are focused on those matters which lie above whatever is the pertinent granularity threshold.

70 Partitions do not care Our ordinary judgments in spite of being vague have determinate truth-values because the partitions they impose upon reality do not care about small (molecule-sized) differences

71 Theory of vagueness How can -based classifications be transparent, if the world is shaped like this: ?

72 Species Genera as Tree canary animal bird fish ostrich

73 Species-Genera as Map/Partition animal bird canary ostrich fish canary

74 Tree and Map/Partition

75 Ontological Zooming

76 Universe/Periodic Table animal bird canary ostrich fish folk biology partition of DNA space

77 Granular Partitions, Vagueness and Approximation Thomas Bittner and Barry Smith

78 THE END