The Ontology of CLASSIFICATION Barry Smith ONTOLOGIST c

The Ontology of CLASSIFICATION Barry Smith ONTOLOGIST. c. Om 1

The world knows colour 2

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

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

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

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

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

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 8

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

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

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

Gr. Gr 12

Gr. Gr 13

partitions can be extended 14

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partitions can be split and merged 17

partitions can be split and merged 18

partitions can be split and merged 19

A partition can be more or less refined 20

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one partition can be skew to another 23

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

We can apply partitions to other partitions 25

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 26

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

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

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) 29

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

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

bona fide partition of individuals John Paul George Ringo bona fide partition of types. . . up down charm strange . . . 32

a bona fide type classification 33

But there also fiat partitions 34

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

Artist’s Grid 36

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

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

Without partitions 39 how many numbers?

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

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

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

Kansas 43

Ontology of Maps 44

types represented in an ontology 45

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

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) 47

California Land Cover 48

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

A Map 50

A Portion of Reality 51

A Mapping 52

A Map is a Mapping 53

The Ontology of Measurement 54

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

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 57

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

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Partitions can be skew to each other 60

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

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 62

Length is a bona fide type 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? 63

The world knows length continua (as instances) • The world also knows length as a type • which these instances instantiate 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

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

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

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

The Act of Measurement l l ll l l ll l tape measure (grid) projected onto reality with endpoints mapped to endpoints 69

then you count the cells in the grid 1 2 3 4 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

The Periodic Table 72

Ontologies are here 73

or here 74

ontologies represent general structures in reality (leg) 75

Ontologies do not represent concepts in people’s heads 76

They represent universals in reality 77

“leg” is not the name of a concept • • • concepts do not stand in the part_of connectedness causes treats. . . relations used by biomedical ontologies 78

instances A B C 515287 521683 521682 DC 3300 Dust Collector Fan Gilmer Belt Motor Drive Belt universals 79

Inventory vs. Catalog: Two kinds of representational artifact • Databases represent instances • Ontologies represent universals 80

How do we know which general terms designate universals? • • Roughly: terms used by scientists to designate entities about which we have a plurality of different kinds of testable proposition (cell, electron. . . ) 81

Language has the power to create general terms • which go beyond the domain of universals studied by science 82

Problem: fiat demarcations • male over 30 years of age with family history of diabetes • abnormal curvature of spine • participant in trial #2030 83

Problem: roles • fist • patient • FDA-approved drug • accident 84

Administrative ontologies often need to go beyond universals • Fall on stairs or ladders in water transport injuring occupant of small boat, unpowered Railway accident involving collision with rolling stock and injuring pedal cyclist Nontraffic accident involving motor-driven snow vehicle injuring pedestrian 85

Class =def • • a maximal collection of particulars determined by a general term (‘cell’. ‘electron’ but also: ‘ ‘restaurant in Palo Alto’, ‘Italian’) the class A = the collection of all particulars x for which ‘x is A’ is true 86

universals vs. their extensions universals {a, b, c, . . . } collections of particulars 87

Extension =def • The extension of a universal A is the class: instance of the universal A • (it is the class of A’s instances) • (the class of all entities to which the term ‘A’ applies) 88

Problem • The same general term can be used to refer both to universals and to collections of particulars. Consider: • • HIV is an infectious retrovirus HIV is spreading very rapidly through Asia 89

universals vs. classes universals {c, d, e, . . . } classes 90

universals vs. classes universals defined classes 91

universals vs. classes universals populations, . . . 92

Defined class =def • a class defined by a general term which does not designate a universal • the class of all diabetic patients in Leipzig on 4 June 1952 93

OWL is a good representation of defined classes • sibling of Finnish spy • member of Abba aged > 50 years 94

Terminology =def. • a representational artifact whose representational units are natural language terms (with IDs, synonyms, comments, etc. ) which are intended to designate universals together with defined classes. 95

universals, classes, concepts universals defined classes ‘concepts’ ? 96

universals < defined classes < ‘concepts’ • ‘concepts’ which do not correspond to defined classes: • ‘Surgical or other procedure not carried out because of patient's decision’ • ‘Congenital absent nipple’ • because they do not correspond to anything 97

(Scientific) Ontology =def. • • • a representational artifact whose representational units (which may be drawn from a natural or from some formalized language) are intended to represent 1. universals in reality 2. those relations between these universals which obtain universally (= for all instances) lung is_a anatomical structure lobe of lung part_of lung 98

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