1 Rules for Good Ontology Rules of thumb: represent ideals to be approximated to in practice

2 Naturalness A good ontology should include in its basic category scheme only those categories which are instantiated by entities in reality (it should reflect nature at its joints)

3 A good first test: the categories in question should be reflected in the morphologically simple* terms of TEE (for: Technically Extended English = English as extended by the various technical vocabularies of medical and scientific disciplines) Cf. Berlin and Kay, Basic Color Terms (1969)

4 No theoretical artifacts Thus a good ontology should include in its basic category scheme no artifacts of logical, mathematical or philosophical theories (such as: transfinite cardinals, instantaneous rabbit-slices, non-existent golden mountains, and the like).

5 A good category scheme mish-mash should not be a mish-mash of natural and philosophical taxa

6 Tools are just tools If specific logical or mathematical or conceptual tools are needed, for example for semantic purposes, then these should be clearly recognized as tools and thus not be seen as having consequences for basic ontology. Q: At which point does set theory become a mere tool?

7 Cheese-paring principle While a good ontology should use categories which reflect only TEE, it should also have the resources to do justice to the fact that the world can be sliced in many ways, including ways not reflected by TEE

8 Even reductionists are right as far as they go (even their peculiar maps of reality, as consisting of processes, or of spacetime worms, are transparent to reality) The problem with such maps is that they are not complete

9 Fallibilism Traditional ontologists are seeking principles that are true of reality, but this does not mean that they have special powers for discovering the truth. Ontology is, like physics or chemistry, part of a piecemeal, on-going process of exploration, hypothesis-formation, testing and revision.

10 Fallibilism Ontological claims advanced as true today may well be rejected tomorrow in light of further discoveries or new and better arguments

11 Adequatism A good ontology should be adequatist: its taxonomy should comprehend the entities in reality at all levels of aggregation, from the microphysical to the cosmological, and including also the middle world (the mesocosmos) of human-scale entities in between. Adequatists: Aristotle, Ingarden, Chisholm

12 Rules Governing Taxonomies Every (coherent, tested) ontology for a given domain at a given level of granularity should be representable as a tree in the mathematical sense

13 First ontology ( from Porphyry’s Commentary on Aristotle’s Categories)

14 Aristotle Ignored granularity He thought the whole of reality can be represented by means of a single tree (or a small number of trees for: substance the various accidental categories)

15 Tree structure Higher nodes within the tree represent more general universals, lower nodes represent less general universals.

16 Branches connecting nodes represent the relations of inclusion of a lower category in a higher: man is included in mammal mammal is included in animal and so on.

17 An Ontology (Taxonomy) should be Principled Suppose that in counting off the cars passing beneath you on the highway, your checklist includes one box labeled red cars and another box labeled Chevrolets. The resultant inventory will be unprincipled; you will almost certainly be guilty of counting some cars twice. Unprincipled = the two modes of classification belong to two distinct classifications made for two distinct purposes

18 Opposite of principled aD hoC

19 A good ontology should satisfy certain well-formedness rules Tree structure implies:

20 Natural scientific classifications are principled

21 Principled classifications satisfy the no-diamonds rule: A E F G B C D H Good Bad

22 Counterexample in the realm of artifacts ? urban structures buildings car parks multi-story car-parks

23 Eliminating counter-examples urban structures buildingsparking areas multi-story car-parks “Ontoclean”

24 Well-formedness rule Each tree is unified in the sense that it has a single top-most or maximal node, representing the maximum category comprehending all the categories represented by the nodes lower down the tree

25 Why trees? A taxonomy (ontology) with two maximal nodes would be in need of completion by some extra, higher-level node representing the union of these two maxima. Otherwise it would not be one taxonomy at all, but rather two separate taxonomies

26 ‘Entity’ = label for the highest-level category of ontology. Everything which exists is an entity Alternative top-level terms favored by different ontologists: ‘thing,’ ‘object,’ ‘item,’ ‘element,’ ‘existent.’

27 Basis in minimal nodes (leaves) Leaves of the tree represent the lowest categories (infima species) = categories in which no sub-categories are included. ‘Has a basis in minimal nodes’ = the categories at the lowest level of the tree exhaust the maximum category

28 Exhaustiveness The chemical classification of the noble gases is exhausted by: Helium, Neon, Argon, Krypton, Xenon and Radon. …very hard to achieve for epistemological reasons

29 For a taxonomy with a basis in minimal nodes every intermediate node in the tree is identifiable as a combination of minimal nodes.

30 More well-formedness principles There should be a finite number of steps between the maximal category and each minimal category. There should be the same number of steps between the topmost node of the tree and all its lowest-level nodes.

31 Science

32 Well-Formedness The taxonomy as a whole is thereby divided into homogeneous levels, each level represents a jointly exhaustive and pairwise disjoint partition of the corresponding domain of categories on the side of objects in the world.

33 Which rules satisfied by BFO? Concrete Entity [Exists in Space and Time] Entity in 3-D Ontology [Endure. No Temporal Parts] Spatial Region of Dimension 0,1,2,3 Dependent Entity Quality (Your Redness, My Tallness) [Form Quality Regions/Scales] Quasi-Quality Prices, Values, Obligations Role, Function, Power Have realizations (called: Processes) Quasi-Role/Function/Power The Functions of the President Independent Entity Substance [maximally connected causal unity] Aggregate of Substances * (includes masses of stuff? liquids?) Fiat Part of Substance * Nose, Ear, Mountain Boundary of Substance * Fiat or Bona Fide or Mixed Quasi-Substance Church, College, Corporation Entity in 4-D Ontology [Perdure. Unfold in Time] Processual Entity Process [Has Unity] Clinical trial; exercise of role Aggregate of Processes* Fiat Part of Process* Instantaneous Temporal Boundary of Process (= Ingarden’s 'Event’)* Quasi-Process John’s Youth. John’s Life Spatio-Temporal Region Dim = T, T+0, T+1, T+2, T+3

34 Three major categories Substances Qualities belong to snapshot ontology Processes belong to videoscopic ontology

35 Rule for Crossing Granularities If x is part of y, then x is of the same category as y (if x is substantial, then y is substantial) (if x is a quality, then y is a quality) (if x is a process, then y is process)

36 Types of Formal Relation Intracategorial –Mereological (part) –Topological (connected, temporally precedes) –Dependency Intercategorial –Inherence (quality of) –Location –Participation (agent)

37 Relations can also hold across granularities Microbial processes in the human body sustain the human body in existence Neurophysiological processes in the brain cause and provide the substratum for cognitive processes

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

39 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 (a hierarchy of medical therapies)

40 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

41 Two distinct realms of being universalsparticulars generalindividual typestokens speciesinstances essencefact

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

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

44 siamese mammal cat organism substance types animal tokens frog

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

46 There are universals both among substances (man, mammal) and among qualities (hot, red) and among processes (run, movement)

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

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

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

50 Process universals reflect invariants in the spatiotemporal world as a whole

51 Processes and qualities, too, instantiate genera and species Thus process and quality universals form trees

52 quality color red scarlet R232, G54, B24

53 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

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

55 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

56 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

57 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

58 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

59 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

60 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

61 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

62 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

63 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

64 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

65 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

66 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

67 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

68 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

69 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

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

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

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

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

74 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)

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

76

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

78 From Species to Genera canary animal bird

79 From Species to Genera animal bird canary

80 Species Genera as Tree canary animal bird fish ostrich

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

82 Tree and Map-Partitions Together

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

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

85 Distinct temporal partitions of reality as a whole

86 Coarse-grained Partition

87 Fine-Grained Partition

88 Basic Formal Ontology ? ? ?

89 Ontological Zooming

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

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

92 France Regions Departments

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

94 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

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

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

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

98

99 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

100 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 …)

101 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

102 come with a labelling and an address system Partitions

103 Lake Tahoe Land Cover two mutually dependent partitions

104 Cerebral Cortex

105 Periodic Table Periodic Table of Chemical Elements

106 Partonomies and taxonomies can be combined

107 Partonomies and taxonomies can be combined

108 Partonomies and taxonomies can be combined

109 Partonomies and taxonomies can be combined

110

111 Artefactual universals have crisp borderlines

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

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

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

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