1 part 3 tools of ontology: universals, partitions

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

universals particulars

general individual

types tokens

species instances

essence fact

9

siamese

mammal

cat

organism

substancespecies, genera

animal

instances

frog

10

Common nouns

pekinese

mammal

cat

organism

substance

animal

common nouns

proper names

11

siamese

mammal

cat

organism

substancetypes

animal

tokens

frog

12

Accidents: Species and instances

substance

animal

mammal

human

Irishman

types

tokensthis 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 planetVW 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 spinningClintophobic 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 SubjectSubstantial

In a SubjectAccidental

Said of a SubjectUniversal, 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 SquareSubstantial Accidental

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

Uni

vers

alP

artic

ular

24


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

Uni

vers

alP

artic

ular

25


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

Uni

vers

alP

artic

ular

26


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

Uni

vers

alP

artic

ular

27


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

Uni

vers

alP

artic

ular

28

Refining the Ontological Square

Substantial Accidental

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

Uni

vers

alP

artic

ular

29


Substantial Dependent Entities

Exercise of power Exercise of function

Movement

Action

Substances

Collectives

Undetached parts

Substantial boundaries

Powers

Functions

Qualities

Shapes

Occ

urre

nts

Con

tinua

nts

30


Substantial Moments (Dependent)


Movement

Action

Substances

Collectives

Undetached parts


Powers

Functions

Qualities

Shapes

Occ

urre

nts

Con

tinua

nts

31




Movement

Action Processes?

Substances

Collectives

Undetached parts


Powers

Functions

Qualities

Shapes

Moments?

Occ

urre

nts

Con

tinua

nts

32



John‘s reddening

John‘s blushing

John‘s bruising

4-DSubstances

Collectives

Undetached parts


John‘s redness

John‘s blush

John‘s bruise

3-D

Occ

urre

nts

Con

tinua

nts

33



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)

Occ

urre

nts

Con

tinua

nts

34

A Refined Ontological SquareSubstantial 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)

Occ

urre

nts

Con

tinua

nts

35


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

Uni

vers

alP

artic

ular

36

Some philosophers

accept only part of the Aristotelian multi-categorial ontology

37

Standard Predicate Logic – F(a), R(a,b) ...


Attributes

F, G, R

Individuals

a, b, c

this, that

Uni

vers

alP

artic

ular

38

Bicategorial Nominalism


First substance

this man

this cat

this ox

First accident

this headache

this sun-tan

this dread

Uni

vers

alP

artic

ular

39

Process MetaphysicsSubstantial Accidental

Events

Processes

“Everything is flux”

Uni

vers

alP

artic

ular

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

44

Species-genusgenus trees can be represented also as map-like partitions

45

From Species to Genera

canary

animal

bird

46

From Species to Genera

animal

bird

canarycanary

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


??

?

56

Ontological Zooming

57

Universe/Periodic Table

animal

bird

canary

ostrich

fishfolk 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

RegionsDepartments

60

Perspectivalism

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


inspired in part by spatial ontologies developed in Geographic Information Science

Cf. Th. Bittner

map layers

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 TablePeriodic 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


77


78


80

but should not be confused

is-a overloading

ulcer

parts of ulcer types of ulcer phases of ulcer

81

Artefactual universalshave 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 amongsub-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 frogalbino 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 groundSolid 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

101

Ontology of Environments

Gibson: affordancesgeometry of surface layout

1 part 3 tools of ontology: universals, partitions

Documents

b24 slide

reality slide

gold slide

partitions slide

movement slide

passion slide

linnaean hierarchy slide

porphyrian hierarchy