The Theory of Granular Partitions: A New Paradigm for Ontology

1. Barry Smith Department of Philosophy University at Buffalo http://ontology.buffalo.edu The Theory of Granular Partitions:A New Paradigm for Ontology

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

3. Classification Classifying Studying = Producing Classifications Classifications Gesellschaft für Klassifikation

4. 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 An ontology

5. A Simple Partition

8. A partition can be more or less refined

9. Coarse-grained Partition

10. Fine-Grained Partition

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

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

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

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

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

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

20. then there are very many map-like partitions, at different scales, which are all transparentto the reality beyond the mistake arises when one supposes that only one of these partitions is veridical If ontological realism is right

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

22. Partonomies: inventories of the parts of individual entities Maps: partonomies of space Taxonomies: inventories of the universals covering a given domain of reality Varieties of granular partitions

23. 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 ». One example of ‘folk’ partition

24. Thomas Bittner and Barry Smith http://ontology.buffalo.edu/smith/articles/partitions.pdf A Formal Theory of Granular Partitions

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

26. GrGr

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

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

29. Mouse Chromosome Five

30. Periodic Table

31. Maps have different scales Partitions have different granularity

32. 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 The Parable of the Two Tables

33. ‘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.’ The Parable of the Two Tables

34. Only the scientific table exists. Eddington:

35. 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 The Parable of the Two Tables

36. but transparent nonetheless Some partitions are completely arbitrary

37. Kansas

38. The DER-DIE-DAS partition

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. Thomas Bittner and Barry Smith http://ontology.buffalo.edu/smith/articles/partitions.pdf A Formal Theory of Granular Partitions

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

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

48. Intentionality

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

50. corrected content, meaning representations