The Ontology of Measurement

1. The Ontology of Measurement Barry Smith ONTOLOGIST.cOm

2. The world knows colour

3. The world knows no redness, greenness, blueness, …These types do not reflect joints in reality

4. The world knows no mild hypertension, moderate hypertension, severe hypertension, … These do not reflect joints in reality

5. The world knows no Poland, Belgium, Utah, Bavaria, …These do not reflect joints in reality

6. The world knows no nation-state, parish, census tract, township, legal jurisdiction …These types do not reflect joints in reality

7. what we think we know what the world knows what we know

8. The world is largely a system of continua, both on the level of instances and on the level of types But what we know (at least as expressed in language) is always in a sense digital rather than analogue

9. All of the mentioned entities arises because of our parcellings, griddings, apportionments, segmentations, ...= partitions

10. Partitions A partition is the result of drawing a (typically complex) fiat boundary over a certain domain Partition

11. GrGr A simple partition on the level of individuals

12. GrGr

13. GrGr

14. partitions can be extended

17. partitions can be split and merged

18. partitions can be split and merged

19. partitions can be split and merged

20. A partition can be more or less refined

23. one partition can be skew to another

24. Perspectival realism Perspectivalism Different partitions which are skew to each other may be equally veridical representations of the same reality

25. We can apply partitions to other partitions Cerebral Cortex

26. Advanced Database Methodology for the Collation of Connectivity Data on the Macaque Brain Klaas E. Stephan, et al., Phil. Trans. Royal Society London B, 2001 Mereotopology of Neuronal Partitions

27. link: Granular partitions http://ontologist.com

28. An ontology is a partition, or a complex partitions, on the level of types

29. Partitions can be created both at the level of instances (Poland vs. Germany) and at the level of types (nation-state vs. colony) Types and instances

30. focusing primarily on types (dog, nation, leaf, cell, lung, lake …) whose instances have their own complete bona fide boundaries An ontology is a partition at the level of types

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

32. bona fide partition of individuals bona fide partition of types

33. a bona fide type classification

34. But there are also fiat partitions

35. = of our referring, perceiving, classifying, counting, measuring, mapping activity GRIDDING ACTIVITY Fiat partitions are artefacts of our cognition

36. Artist’s Grid

37. e.g. they are artefacts for counting 1 2 3 4

38. Better: Numbers belong to the realm of partitions Frege: “Numbers belong to the realm of concepts”

39. how many numbers? Without partitions

40. fiat objects = objects created by partitions Partitions can sometimes create objects

41. fiat partition at the level of types

42. this tail this torso fiat partition at the level of individuals

43. Kansas

44. Ontology of Maps

45. types represented in an ontology

46. domestic cow breed: Brahman domestic cow breed: HOLSTEIN species: Bos TAURus

47. (all scientific language is built around mappings of this sort between instances and types) A label in the zoo is a mapping between an animal instance and an animal type

48. California Land Cover

49. a map is a mapping between points in reality and the types represented in a legend California Land Cover x

50. A Map