1 Part 3 Tools of Ontology: Universals, Partitions

2 Porphyrian Hierarchy

3 Linnaean Hierarchy

4 Medical Diagnostic Hierarchy a hierarchy in the realm of processes

5 Species-genus hierarchies capture the way the world is (Aristotelian realism) – they depict the invariant structures/patterns/regularities in reality

6 or: species-genus hierarchies may capture the way the world should be – by depicting the structures/patterns/regularities in the realm of standards, ideal cases, recipes (cf. a hierarchy of medical therapies)

7 Anglocentric (Aristotelian) Realism The general terms of TEE (or many of them), including terms like ‘Coca Cola’, correspond to universals (species and genera, invariant patterns) in reality

8 Two distinct realms of being universalsparticulars generalindividual typestokens speciesinstances essencefact

9 siamese mammal cat organism substance species, genera animal instances frog

10 Common nouns pekinese mammal cat organism substance animal common nouns proper names

11 siamese mammal cat organism substance types animal tokens frog

12 Accidents: Species and instances substance animal mammal human Irishman types tokens this individual token man

13 There are universals both among substances (man, mammal) and among moments (run, movement)

14 Substance universals pertain to what a thing is at all times at which it exists: cow man rock planet VW Golf

15 Note use of ‘substance’ in the sense of ‘thing’, ‘object’ count sense of substance vs. mass sense of substance (‘milk’, ‘gold’)

16 Moment universals pertain to how a thing is at some time at which it exists: red hot suntanned spinning Clintophobic Eurosceptic

17 Moments, too, instantiate genera and species Thus moment universals form trees

18 quality color red scarlet R232, G54, B24

19 moments too are distinguished as between tokens and types which is to say: between genera and species on the one hand,... and instances on the other

20 Accidents: Species and instances quality color red scarlet R232, G54, B24 this individual accident of redness (this token redness – here, now)

21 One plus Nine Categories (AQL) quid? substance quale? quality quantum? quantity ad quid? relation ubi? place quando? time in quo situ? status/context in quo habitu? habitus quid agit? action quid patitur? passion

22 Not in a Subject Substantial In a Subject Accidental Said of a Subject Universal, General, Type Second Substances man, horse, mammal Non-substantial Universals whiteness, knowledge Not said of a Subject Particular, Individual, Token First Substances this individual man, this horse this mind, this body Individual Accidents this individual whiteness, knowledge of grammar

23 Aristotle’s Ontological Square SubstantialAccidental Second substance man cat ox Second accident headache sun-tan dread First substance this man this cat this ox First accident this headache this sun-tan this dread Universal Particular

24 Aristotle’s Ontological Square SubstantialAccidental Second substance man cat ox Second accident headache sun-tan dread First substance this man this cat this ox First accident this headache this sun-tan this dread Universal Particular

25 Aristotle’s Ontological Square SubstantialAccidental Second substance man cat ox Second accident headache sun-tan dread First substance this man this cat this ox First accident this headache this sun-tan this dread Universal Particular

26 Aristotle’s Ontological Square SubstantialAccidental Second substance man cat ox Second accident headache sun-tan dread First substance this man this cat this ox First accident this headache this sun-tan this dread Universal Particular

27 Aristotle’s Ontological Square SubstantialAccidental Second substance man cat ox Second accident headache sun-tan dread First substance this man this cat this ox First accident this headache this sun-tan this dread Universal Particular

28 Refining the Ontological Square SubstantialAccidental Second substance man cat ox Second accident headache sun-tan dread First substance this man this cat this ox First accident this headache this sun-tan this dread Universal Particular

29 Refining the Ontological Square Substantial Dependent Entities Exercise of power Exercise of function Movement Action Substances Collectives Undetached parts Substantial boundaries Powers Functions Qualities Shapes Occurrents Continuants

30 Refining the Ontological Square Substantial Moments (Dependent) Exercise of power Exercise of function Movement Action Substances Collectives Undetached parts Substantial boundaries Powers Functions Qualities Shapes Occurrents Continuants

31 Refining the Ontological Square Substantial Dependent Entities Exercise of power Exercise of function Movement Action Processes? Substances Collectives Undetached parts Substantial boundaries Powers Functions Qualities Shapes Moments? Occurrents Continuants

32 Refining the Ontological Square Substantial Dependent Entities John‘s reddening John‘s blushing John‘s bruising 4-D Substances Collectives Undetached parts Substantial boundaries John‘s redness John‘s blush John‘s bruise 3-D Occurrents Continuants

33 Refining the Ontological Square Substantial Dependent Entities John‘s reddening John‘s blushing John‘s bruising 4-D (perduring) Stuff (Blood, Snow, Tissue) Mixtures Holes John‘s redness John‘s blush John‘s bruise 3-D (enduring) Occurrents Continuants

34 A Refined Ontological Square Substantial Dependent Entities John‘s reddening John‘s blushing John‘s bruising 4-D (perduring) Stuff (Blood, Snow, Tissue) Mixtures Holes John‘s redness John‘s blush John‘s bruise 3-D (enduring) Occurrents Continuants

35 Aristotle’s Ontological Square SubstantialAccidental Second substance man cat ox Second accident headache sun-tan dread First substance this man this cat this ox First accident this headache this sun-tan this dread Universal Particular

36 Some philosophers accept only part of the Aristotelian multi-categorial ontology

37 Standard Predicate Logic – F(a), R(a,b)... SubstantialAccidental Attributes F, G, R Individuals a, b, c this, that Universal Particular

38 Bicategorial Nominalism SubstantialAccidental First substance this man this cat this ox First accident this headache this sun-tan this dread Universal Particular

39 Process Metaphysics SubstantialAccidental Events Processes “Everything is flux” Universal Particular

40 Problems arise for such partial ontologies arise only if they come along with the claim to be complete (reductionists are nearly always correct in what they hold to exist -- but incorrect when they hold that nothing else exists)

41 Reductionism is like holding that only maps of some one specific scale (say 1:10,000) are true representations of reality

42 Basic Formal Ontology BFO is neutral with regard to mental/intentional entities BFO is neutral with regard to sets/classes … ontology is like every other science a work in progress

43

44 genus Species-genus trees can be represented also as map- like partitions

45 From Species to Genera canary animal bird

46 From Species to Genera animal bird canary

47 Species Genera as Tree canary animal bird fish ostrich

48 Species-Genera as Map/Partition animal bird canary ostrich fish canary

49 Tree and Map-Partitions Together

50 ‘Granularity’ in two senses: depth of a tree hierarchy resolution of a map-like partition

51 There are many different species-genus hierarchies  many different ways to cut through the complex thicket of invariant patterns in reality

52 Recall the distinct temporal partitions of reality as a whole

53 Coarse-grained Partition

54 Fine-Grained Partition

55 Basic Formal Ontology ? ? ?

56 Ontological Zooming

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

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

59 France Regions Departments

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

61 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 veridical partitions An organism is a totality of atoms

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

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

64 Basic Formal Ontology inspired in part by spatial ontologies developed in Geographic Information Science Cf. Th. Bittner map layers

65

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

67 There are not only map-like partitions of reality into spatial chunks but also distinct partitions of reality into universals -- mutually compatible ways of providing inventories of universals (among proteins, among cells, among organisms …)

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

69 come with a labelling and an address system Partitions

70 Lake Tahoe Land Cover two mutually dependent partitions

71 Cerebral Cortex

72 Mouse Chromosome 5

73 Periodic Table Periodic Table of Chemical Elements

74 Set theory is one possible partition of reality is it a transparent partition? or a useful tool of mathematics?

75 Partonomies and taxonomies can be combined

76 Partonomies and taxonomies can be combined

77 Partonomies and taxonomies can be combined

78 Partonomies and taxonomies can be combined

79

80 but should not be confused is-a overloading ulcer parts of ulcer types of ulcer phases of ulcer

81 Artefactual universals have crisp borderlines

82 birds ostrich Natural universals have non-crisp borderlines sparrow marked by borderline cases

83 Natural universals have a kernel/penumbra structure kernel of focal instances penumbra of borderline cases

84 Prototypicality among sub-categories some sub-species of a given genus are more typical, standard, than others canary is more typical than ostrich

85 instances There is prototypicality among instances too albino frog

86 Types of boundaries in the realm of universal partitions Fiat vs. bona fide Crisp vs. non-crisp Natural vs. artefactual Continuous vs. non-continuous …

87 The Ontology of Holes

88 Places are holes

89 Temple at Corinth

90 Pipe

91 The Ontology of Places

92 Varieties of Controlled Airspace

93 Places For Aristotle there are no empty places The place of a substance is the interior boundary of the surrounding body (for example the interior boundary of the surrounding water where it meets a fish’s skin)

94 Places For Aristotle a place is a hole filled by a substance The place occupied by you is the boundary of the surrounding air where it meets your body

95 A more adequate ontology: Places are holes

96 Places are holes

97 A hole in the ground Solid physical boundaries at the floor and walls but with a fiat lid: hole

98 Holes, too, involve two kinds of boundaries bona fide boundaries which exist independently of our demarcating acts fiat boundaries which exist only because we put them there

99 niches, environments are holes

100

101 Ontology of Environments Gibson: affordances geometry of surface layout