1 The Ontology of Measurement Barry Smith ONTOLOGIST.cOm

2 For individuation or delimitation of individuals, I think we can do better than the fig tree with the adventicious roots hanging down. How about a "sea of mountains"? That is what I usually use. Second, as I hope you realize, the animals in cages are a veal farm, not a zoo. The labels, if they are labels at all, would label individual inmates, not kinds. Incorrect details undermine your credibility and distract people like me from your main points. If you want to talk about kinds of animals in a zoo, with labels, why not use a picture of kinds of animals in a zoo, with labels! Lastly, some animal rights people are offended by veal pens, you might be doing that deliberately too I suppose. Minor point, the "road sign" is obviously (to me) not a "road" sign for driving, it is almost certainly a trail sign for hiking.

3 The world knows colour

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

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

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

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

8 what the world knows what we know what we think we know

9 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

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

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

12 GrGr A simple partition on the level of individuals

13 GrGr

14 GrGr

15 partitions can be extended

16

17

18 partitions can be split and merged

19 partitions can be split and merged

20 partitions can be split and merged

21 A partition can be more or less refined

22

23

24 one partition can be skew to another

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

26 Cerebral Cortex We can apply partitions to other partitions

27 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

28 link: Granular partitions

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

30 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)

31 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

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

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

34 a bona fide type classification

35 But there are also fiat partitions

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

37 Artist’s Grid

e.g. they are artefacts for counting

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

40 Without partitions how many numbers?

41 Partitions can sometimes create objects fiat objects = objects created by partitions

42 mild hypertension moderate hypertension severe hypertension fiat partition at the level of types

43 fiat partition at the level of individuals this tail this torso

44 Kansas

45 Ontology of Maps

46 types represented in an ontology

47 domestic cow breed: Brahman domestic cow breed: HOLSTEIN species: Bos TAURus

48 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)

49 California Land Cover

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

51 A Map

52 A Portion of Reality

53 A Mapping

54 A Map is a Mapping

55 The Ontology of Measurement

56

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

58 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

59 Measurement belongs to the realm of partitions   0 0   massively increased... normal increased chronic...

60

61 Partitions can be skew to each other

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

63 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

64 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?

65 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

66 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

67 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

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

69 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

then you count the cells in the grid

71 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

72 THE END