1. 1 The Ontology of Measurement Barry Smith ONTOLOGIST.cOm

2. 2 The world knows colour

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

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

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

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

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

8. 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. 9 All of the mentioned entities arises because of our parcellings, griddings, apportionments, segmentations,... = partitions

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

11. 11 GrGr A simple partition on the level of individuals

12. 12 GrGr

13. 13 GrGr

14. 14 partitions can be extended

15. 15

16. 16

17. 17 partitions can be split and merged

18. 18 partitions can be split and merged

19. 19 partitions can be split and merged

20. 20 A partition can be more or less refined

21. 21

22. 22

23. 23 one partition can be skew to another

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

25. 25 Cerebral Cortex We can apply partitions to other partitions

26. 26 Mereotopology of Neuronal Partitions 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

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

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

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

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

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

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

33. 33 a bona fide type classification

34. 34 But there are also fiat partitions

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

36. 36 Artist’s Grid

37. 37 12 34 e.g. they are artefacts for counting

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

39. 39 Without partitions how many numbers?

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

41. 41 mild hypertension moderate hypertension severe hypertension fiat partition at the level of types

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

43. 43 Kansas

44. 44 Ontology of Maps

45. 45 types represented in an ontology

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

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

48. 48 California Land Cover

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

50. 50 A Map

51. 51 A Portion of Reality

52. 52 A Mapping

53. 53 A Map is a Mapping

54. 54 The Ontology of Measurement

55. 55

56. 56 The world knows no Poland, Belgium, Utah, Bavaria, … These do not reflect joints in reality

57. 57 The world knows no inches, feet, centimeters, seconds, grams, pascals, joules, ohms, teslas, volts, kg/m 3 … These, too, do not reflect joints in reality

58. 58 Measurement belongs to the realm of partitions... -20  -10 -10  0 0  10 10  20... massively increased... normal increased chronic...

59. 59

60. 60 Partitions can be skew to each other

61. 61 Partitions can be more and less refined and thereby yield measurements which are more or less vague

62. 62 Units of measurement are fiat types Each inch long thing has a length which is an instance of the fiat type inch (the fiat type inch is like the fiat type blue) Each case of mild hypertension has a disorder which is an instance of the fiat type mild hypertension

63. 63 Length is a bona fide universal But the different ways of slicing up length (creating a set of quasi-discrete portions out of a continuum) create fiat universals Is there a way of slicing up the universal length into minima? (infinitesimal portions?) Is Planck length a bona fide unit type?

64. 64 in the everyday world all the measurements (lengths, temperatures...) with which we have to deal are socially created artefacts subject to phenomena of vagueness, technology-dependence, and using fiat units of measure

65. 65 Phenomenon of vagueness every measurement is vague, to a degree determined by the measuring rod/standard used vagueness is the other side of the coin from granularity every measuring rod (scale) does not recognize differences beneath a certain size

66. 66 Measurement: we lay a grid upon a specific portion of physical reality with a gridding determined by a given unit type, map endpoints to endpoints and count the number of cells between the endpoints

67. 67 An Act of Measurement portion of reality: dependent magnitude (here: distance) + independent bearer

68. 68 The Act of Measurement tape measure (grid) projected onto reality with endpoints mapped to endpoints l l l l l l l l l l l l l l l l l l l l l l l

69. 69 1 234 then you count the cells in the grid

70. 70 Ontological assay of the act of measuring length act of counting cells in a grid determined by the fiat type which is the pertinent unit of measurement and by a certain portion of reality consisting of some independent continuant bearer together with a dependent feature, here: a certain distance between two endpoints

71. 71 THE END