1 Introduction to Ontology Barry Smith. 2 Aristotle author of The Categories Aristotle

1

Introduction to Ontology

Barry Smith

2

Aristotle

author of The Categories

Aristotle

3

From Species to Genera

canary

animal

bird

4

Species Genera as Tree

canary

animal

bird fish

ostrich

5

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

6


canary

animal

bird

7


animal

bird

canarycanary

8

Species Genera as Tree

canary

animal

bird fish

ostrich

9

Species-Genera as Map/Partition

animal

bird

canary

ostrich

fish

canary

10

If Aristotelian realism is right,

then such partitions are transparent to the reality beyond

11

Tree and Map/Partition

12

Alberti’s Grid

c.1450

13

Coarse-grained Partition

14

Fine-Grained Partition

15

Scientific theories

comprehend in their underlying category systems veridical partitions of reality

often there are many veridical partitions of reality,

cross-cutting each other,

differing only in nuances)

16

Question:

what other sorts of partitions have this feature of transparency?

the partitions of common sense (folk biology, folk physics, folk psychology ...)

Answer:

17

Aristotle

the ontologist of common-sense reality

Aristotle

18

The world we grasp in natural language

= the world as apprehended via that conceptualization we call common sense

= the normal environment (the niche) shared by children and adults in everyday perceiving and acting

19

The world of mothers, milk, and mice ...

20

The Empty Mask (Magritte)

mama

mouse

milk

Mount Washington

21

our common-sense partition of the world of common sense is transparent

(common sense, like science, is [mostly*] true)

mothers exist ...

* “mostly” because of the problem of vagueness

22

What is common-sense reality?

the mesoscopic space of everyday human action and perception

– a space centered on objects organized into hierarchies of species and genera

... and subject to prototypicality

23

but more:

24

in addition to objects (substances),

which pertain to what a thing is at all times at which it exists:

cow man rock planet

25

the common-sense world contains also accidents

which pertain to how a thing is at some time at which it exists:

red hot suntanned spinning

26

An accident

= what holds of a substance per accidens

27

= relations of inherence(one-sided existential dependence)

John

hunger

Substances are the bearers of accidents

28

Both substances and accidents

instantiate universals at higher and lower levels of generality

29

siamese

mammal

cat

organism

substancespecies, genera

animal

instances

frog

30

Common nouns

pekinese

mammal

cat

organism

substance

animal

common nouns

proper names

31

siamese

mammal

cat

organism

substancetypes

animal

tokens

frog

32

Our clarification

accidents to be divided into

two large and essential distinct families of

QUALITIES

and

PROCESSES

33

There are universals

both among substances (man, mammal)

and among qualities (hot, red)

and among processes (run, movement)

There are universals also among spatial regions (triangle, room, cockpit)

and among spatio-temporal regions (orbit)

34

Substance universals

pertain to what a thing is at all times at which it exists:

cow human rock planetVW Golf

35

Quality universals

pertain to how a thing is at some time at which it exists:

red hot suntanned spinningClintophobic Eurosceptic

36

Process universals

reflect invariants in the spatiotemporal world taken as an atemporal whole

football match

course of disease

exercise of function

(course of) therapy

37

Processes and qualities, too, instantiate genera and species

Thus process and quality universals form trees

38

Accidents: Species and instances

quality

color

red

scarlet

R232, G54, B24

this individual accident of redness (this token redness – here, now)

39

Substances have slots

which are filled by qualities

(by specific values)

(determinables vs. determinates)

40

substance


accidentsBearers

41

substance


accidents

John = relations of inherence(one-sided existential dependence)

Bearers

hunger

42

s

substance

43

Substance + Accident = State of Affairs

setting into relief

States of Affair

s

44

instances

Prototypicality among instances too

albino frogalbino frog

45

Aristotle 1.0

an ontology recognizing:substance tokensaccident tokenssubstance typesaccident types

46

Aristotle 1.0

in fact however we need more than this

What is missing from Aristotle 1.0 asan ontology of common-sense reality?

47

Is everything in common-sense reality either a substance or an accident?

48

well, what about artefacts ?

49

Standard Aristotelian theory of artefacts:

artefacts are mereological sums of substances

50

Positive and negative parts

positivepart

negativepartor hole

(made of matter)

(not made of matter)

51

quid? substance quantum? quantity quale? qualityad quid? relationubi? placequando? timein quo situ? status/contextin quo habitu? habitusquid agit? actionquid patitur? passion

Nine Accidental Categories

52

Places

For Aristotle 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)

53

What is missing from Aristotle?

Gibson: affordancesniches

Barker: behavior settings

54

The metaphysics of holes

55

Aristotle 1.5

an ontology ofsubstances + accidents+ holes (and other entities not made of matter)+ fiat and bona fide boundaries+ artefacts and environments

is true

56

folk biology

Aristotelian folk biology, folk physics, folk psychology, etc., are true of the common-sense world as it currently exists

(they have nothing to offer regarding its pre-history, its long term evolution, its position in the cosmos)

57

They have not much to offer, either, by way of good explanatory theories of the entities in their respective domains,

but they are transparent to those domainsnonetheless

58

Both scientific partitions and common-sense partitions

are based on reference-systems which have survived rigorous empirical tests

59

The $64000 Question

How do those parts and dimensions of reality which we call the common-sense world

... relate to those parts and dimensions of reality which are studied by science?

60

Granularity

61

Universe/Periodic Table

animal

bird

canary

ostrich

fishfolk biology

partition of DNA space

62


animal

bird

canary

ostrich

fish

both are transparent partitions of one and the same reality

63

many transparent partitions

at different levels of granularity

will operate with species-genus hierarchies

and with an ontology of substances (objects) and accidents (attributes, processes)

along the lines described by Aristotle

64

relative hylomorphism

substances and accidents reappear in the microscopic and macroscopic worlds of e.g. molecular biology and astronomy

(Aristotelian ontological zooming)

65

we do not assert

that every level of granularity is structured in substance-accident form -- perhaps there are pure process levels, perhaps there are levels structured as fields

66

Perspectivalism

PerspectivalismDifferent partitions may represent cuts through the same reality which are skew to each other

67

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

68

all express partitions which are transparent,

at different levels of granularity,

to the same reality beyond

69


what happens when a fringe instance arises ?

70


what happens when a fringe instance arises ?

Aristotle 1.0: you shrug your shoulders

71

Aristotle 2000:you go out to find a finer grained partition which will recognize the phenomenon in question as prototypical

72

Gene Ontology

Molecular Function Ontology: tasks performed by individual gene products; examples: transcription factor, DNA helicase

Biological Process Ontology: broad biological goals accomplished by ordered assemblies of molecular functions; examples: mitosis, purine metabolism

Cellular Component Ontology: subcellular structures, locations, and macromolecular complexes;examples: nucleus, telomere

73

Example from Molecular Function Ontology

hormone ; GO:0005179

%digestive hormone ; GO:0046659 %peptide hormone ; GO:0005180 %adrenocorticotropin ; GO:0017043 %glycopeptide hormone ; GO:0005181 %follicle-stimulating hormone ; GO:0016913

% = IS A

74

as tree (joined by is a links):

hormone

digestive hormone peptide hormone

adrenocorticotropin glycopeptide hormone

follicle-stimulating hormone

75

Problem: There exist multiple databases

genomic cellular

structural phenotypic

… and even for each specific type of information, e.g. DNA sequence data, there exist several databases of different scope and organisation

76

What is a gene?

GDB: a gene is a DNA fragment that can be transcribed and translated into a protein

Genbank: a gene is a DNA region of biological interest with a name and that carries a genetic trait or phenotype

(from Schulze-Kremer)

77

Application ontology

cannot solve the problems of database integration

There can be no mechanical solution to the problems of data fusion in a domain

like medicine

78

Applications ontology:

… grew out of work in AI and in knowledge representation

Ontologies are applications running in real time

79

Applications ontology:

ontologies are inside the computer

thus subject to severe constraints on expressive power

(effectively the expressive power of description logic)

80

Applications ontology cannot solve the data-fusion problem

because of its roots in knowledge mining

81

different conceptual systems

82

need not interconnect at all

83

because of the limits of knowledge mining

84

we cannot make incompatible concept-systems interconnect

just by looking at concepts, or knowledge – we need some tertium quid

85

What is needed

in some sort of wider common framework which is sufficiently rich and nuanced to allow concept systems deriving from different sources to be hand-callibrated

86

What is needed

is not an applications ontology

but

a reference ontology

(something like old-fashioned metaphysics)

87

Reference Ontology

… grew out of logic and analytic metaphysics

An ontology is a theory of the relevant domain of entities

Ontology is outside the computer

seeks maximal expressiveness and adequacy to reality

willing to sacrifice computational tractability for the sake of representational adequacy

88

Reference Ontology

a theory of the tertium quid

– called

reality –needed to hand-callibrate

database/terminology systems

89

Methodology

Get ontology right first

(realism; descriptive adequacy; rather powerful logic);

solve tractability problems later

90

The Reference Ontology Community

IFOMIS (Leipzig) Laboratory for Applied Ontology (Trento/Rome,

Turin)Foundational Ontology Project (Leeds)Ontology Works (Baltimore)Ontek Corporation (Buffalo/Leeds)LandC (Belgium/Philadelphia)(CYC?)

91

Domains of Current Work in Reference Ontology

IFOMIS Leipzig: MedicineLaboratory for Applied Ontology

Trento/Rome: Ontology of Cognition/Language Turin: Law

Foundational Ontology Project (Leeds): Space, PhysicsOntology Works (Baltimore): Genetics, Molecular BiologyOntek Corporation (Buffalo/Leeds): Biological SystematicsLandC (Belgium/Philadelphia): Medical NLP(? CYC : Everything ?)

92

GDB: a gene is a DNA fragment that can be transcribed and translated into a protein

Genbank: a gene is a DNA region of biological interest with a name and that carries a genetic trait or phenotype

(from Schulze-Kremer)

93

Ontology

Note that terms like ‘fragment’, ‘region’, ‘name’, ‘carry’, ‘trait’, ‘type’

… along with terms like ‘part’, ‘whole’, ‘function’, ‘substance’, ‘inhere’ …

are ontological terms in the sense of traditional (philosophical) ontology

94

Three types of reference ontology

1) formal ontology = framework for rigorous definition of the highly general concepts – such as object, event, whole, part – employed in every domain

2) domain ontology, a top-level system with a few highly general concepts, applies formal ontology to a particular domain, such as genetics or medicine

3) terminology-based ontology, a very large system embracing many concepts and inter-concept relations

95

So what is the ontology of blood?

96

We cannot solve this problem just by looking at concepts (by engaging in further

acts of knowledge mining)

97

concept systems may be simply incommensurable

98

the problem can only be solved

by taking the world itself into account

99

By looking not at concepts, representations,

and their semantic models

but rather at organisms acting in the world

and standing at different levels in a range of different sorts of relations to the world

100

We then recognize

that the same object can be apprehended at different levels of granularity:

at the perceptual level blood is a liquid (?)

at the cellular level blood is a tissue

101

This implies a view of ontology

not as a theory of concepts

but as a theory of reality

But how is this possible?

How can we get beyond our concepts?

answer: ontology must be maximally opportunistic

it must relate not to beliefs, concepts, syntactic strings but to the world itself

102

“Maximally opportunistic”

means:

look at concepts and beliefs critically

and always in the context of a wider view which includes independent ways to access the objects themselves

at different levels of granularity

and taking account of tacit knowledge of those features of reality of which the domain experts are not consciously aware

103

“Maximally opportunistic”

means:

look not at what the expert says

but at what the expert does

Experts have expertise = knowing how

Ontologists can have windows on reality, by focusing on categories, and can extract some form of knowing that

Gibsonianism: experts don’t know what the ontologist knows

104

Ontology must be maximally opportunistic

This means:

don’t just look at beliefs

look at the objects themselves

from every possible direction,

formal and informal

scientific and non-scientific …

105

Maximally opportunistic

means:look at the same objects at different levels of granularity:

106

Second step: select out the good conceptualizations

these have a reasonable chance of being integrated together into a single ontological system

• based on tested principles• robust• conform to natural science

107

Ontology

like cartography

must work with maps at different scales

108

Medical ontologies

at different levels of granularity:

cell ontology

drug ontology

protein ontology

gene ontology

anatomical ontology

epidemiological ontology

Rigidly hierachical, modular organization – with many things which can go wrong

109

There are many compatible map-like partitions

many maps at different scales,

all transparent to the reality beyond

110

Partitions should be cuts through reality

a good medical ontology should NOT be compatible with the conceptualization of disease as:

caused by evil spirits and demons and cured by golems

111

Three main sorts of partitions

1. substances and their parts

2. qualities/functions/roles

3. processes

in addition:

spatial regions/niches

spatio-temporal regions

112

1. Substances and their parts

Patterned parts (carved out by fiat)

chess board

football pitch

Broca’s Region

nervous system

113

2. Functions

function of a screwdriver

tied to processes

= generalized four-dimensional shapes (carved out by fiat)

contextual dependence

function of the heart

function of the circulatory system

114

Once we understand functions

we can also understand malfunctions:

broken screwdriver

defective heart

115

Application to Bodily Systems

Immune system, digestive system …

are complex substances paradigm: skeleton

carved out by fiat from the whole organism in terms of their functions

engaging in specific types of processes

116

Mereotopologies: Fiat and Bona Fide Boundaries

117

A substance has a complete physical boundary

The latter is a special sort of part of a substance

… a boundary part

something like a maximally thin extremal slice

118

interiorsubstance

boundary

119

A substance takes up space.

A substance occupies a place or topoid (which enjoys an analogous completeness or rounded-offness)

A substance enjoys a place at a time

120

A substance has spatial parts

… perhaps also holes

121

Each substance is such as to have divisible bulk:

it can in principle be divided into separate spatially extended substances

122

By virtue of their divisible bulk

substances compete for space:

(unlike shadows and holes)

no two substances can occupy the same spatial region at the same time.

123

Substances vs. Collectives

Collectives = unified aggregates: families, jazz bands, empires

Collectives are real constituents of reality (contra sets)

but still they are not additional constituents, over and above the substances which are their parts.

124

Collectives inherit some, but not all, of the ontological marks of substances

They can admit contrary moments at different times.

125

Collectives,

like substances,

may gain and lose parts or members

may undergo other sorts of changes through time.

126

Qualities and processes, too, may form collectives

a musical chord is a collective of individual tones

football matches, wars, plagues are collectives of actions involving human beings

127

Collectives/heaps

are the duals of undetached parts

Both involve fiat boundaries

128

Substances, Undetached Parts and Heaps

Substances are unities.

They enjoy a natural completeness

in contrast to their undetached parts (arms, legs)

and to heaps or aggregates

… these are topological distinctions

129

substance

undetached part

collective of substances

130

special sorts of undetached parts

ulcers

tumors

lesions

…

131

Fiat boundaries

physical (bona fide) boundary

fiat boundary

132

Holes, too, involve fiat boundaries

133

A hole in the ground

Solid physical boundaries at the floor and walls

but with a lid that is not made of matter:

hole

134

Holes 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

135

Examples

of bona fide boundaries:

an animal’s skin, the surface of the planet

of fiat boundaries:

the boundaries of postal districts and census tracts

136

Mountain

bona fide upper boundaries with a fiat base:

137

where does the mountain start ?

... a mountain is not a substance

138

nose

...and it’s not an accident, either

139

Examples

of bona fide boundaries:

an animal’s skin, the surface of the planet

of fiat boundaries:

the boundaries of postal districts and census tracts

140

Mountain

bona fide upper boundaries with a fiat base:

141

Architects Plan for a House

fiat upper boundaries with a bona fide base:

142

where does the mountain start ?

... a mountain is not a substance

143

nose

...and it’s not a process, either

144

One-place qualities and processes

depend on one substance

(as a headache depends upon a head)

145

Relational qualities and processes

John Mary

kiss

stand in relations of one-sided dependence to a plurality of substances simultaneously

146

Examples of relational qualities and processes

kisses, thumps, conversations,

dances, legal systems

Such real relational entities

join their carriers together into collectives of greater or lesser duration

147

Basic Formal Ontology

mereotopologydependencegranularity/partition theory SNAP/SPANaction/participationplans/functions/executionssystems/modularitycausality/powers/dispositionsenvironments/nichesnormativity

148

Medical Beingmereotopology: anatomy with holes, layers

dependence

granularity/partition theory: molecules, genes, cells …

SNAP/SPAN: anatomy, physiology …

action/participation: doctor, patient, drug …

plans/functions/executions: therapy, application of therapy …

causality/powers/dispositions: prevention

environment: environmental influences on disease

normativity: health, disease, ‘normal’ liver

149

Bodily Systems

e.g.nervous systemrespiratory systemimmune system

How do these systems relate together?(a medico-ontological analogue of the

mind-body problem)WHAT IS A SYSTEM? Fiat object?

150

The ontologist’s job

is not to mimic or replace or usurp sciencenot to discover statistical or functional laws

it is to establish the categories involved in given domains of reality and the relations between themvia: taxonomiesand: partonomiesand by addressing NORMATIVE ISSUES such as: what holds in the standard case

151

Rules for Good Ontology

These are rules of thumb:

They represent ideals to be approximated to in practice

(and often come with trade-offs)

152

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)

153

A good first test:

the categories in question should be reflected in Technically Extended English

= English as extended by the various technical vocabularies of medical and scientific disciplines

154

Basic categoriesare reflected by morphologically simple terms:

dogpainfootbloodhungerhotreddiabetes

155

Ontology

like cartography

must work with maps at different scales and with maps picking out different dimensions of invariants

156

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

157

Rule: Respect Granularity

spatial region qualitysubstance

parts of spatial regions are always spatial regions

158

Respect Granularity

spatial region qualitysubstance

parts of substances are always substances

159

Relations crossing the SNAP/SPAN border are not part-relations

John’s lifesubstance John

physiological processes

sustaining in existence

160

Rule: Representations

A representation is never identical with the object which it is a representation of

161

Rule: Fallibilism

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.

162

Fallibilism

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

Ontology is like a small window on reality which, in fits and starts, gets bigger and more refined as we proceed

163

Rule: Adequatism

A good ontology should be adequatist:

its taxonomies and partonomies 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; Johansson, Smith

164

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

Problem cases: shapes, colors ?

165

Natural scientific classifications are principled

166

Principled classifications satisfy the no-diamonds rule:

A E

F G

B C D

HGood Bad

167

Counterexample in the realm of artifacts ?

urban structures

buildings car parks

multi-story car-parks

168

Eliminating counter-examples

urban structures

buildings parking areas

multi-story car-parks

“Ontoclean”

169

Tree structure

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

170

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.

171

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

172

An Ontology (Taxonomy) should be Principled

Principled = Constructed for a single purpose

Principled = Generative (recursive?)

Principled = Double-counting clearly marked

Principled = SNAP-SPAN opposition reflected (so mereological determinateness is guaranteed)

Principled = Clear rules when a new category must be admitted

What else?

CYC is not principled

173

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

174

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 (e.g. SNAP and SPAN)

175

‘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.’

Use of ‘entity’ is dangerous (see Frege)

176

Rule: Aim for Exhaustiveness

The chemical classification of the noble gases is exhausted by:

Helium, Neon, Argon, Krypton, Xenon and Radon.

…normally very hard to achieve

177

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

178

Substances

Mesoscopic reality is

divided at its natural joints

into substances:

animals, bones, rocks, potatoes

179

The Ontology of Substances

Substances form natural kinds

(universals, species + genera)

180

Processes

Processes merge into one another

Process kinds merge into one another

… few clean joints either between instances or between types

181

Processes

t i m e

182

Nouns and verbs

Substances and processes

Continuants and occurrents

Endurants and perdurants

In preparing an inventory of reality

we keep track of these two different categories of entities in two different ways

183

Natural language

glues them together indiscriminately

substance

t i m

e

process

184

Substances and processes

t i m

e

process

demand different sorts of inventories

185

Substances demand 3-D partonomies

space

186

Moments demand 4D-partonomies

t i m e

187

Processes

a whistling, a blushing, a speech

a run, the warming of this stone

188

Processes may have temporal parts

The first 5 minutes of my headache is a temporal part of my headache

The first game of the match is a temporal part of the whole match

189

Substances do not have temporal parts

The first 5-minute phase of my existence is not a temporal part of me

It is a temporal part of that complex moment which is my life

190

How do we glue these two different sorts of entities together mereologically?

How do we include them both in a single inventory of reality?

191

Substances and processes form two distinct orders of being

Substances exist as a whole at every point in time at which they exist at all

Processes unfold through time, and are never present in full at any given instant during which they exist.

When do both exist to be inventoried together?

192

Main problem

English swings back and forth between two distinct depictions of reality

… imposing both 3-D partitions (yielding substances) and 4-D partitions (yielding processes) at the same time

193

Main problem

There is a polymorphous ontological promiscuity of the English sentence,

which is inherited also by the form ‘F(a)’

194

The Four-Dimensionalist Ontology

t i m e

195

boundaries are mostly fiat

t i m e

everything is flux

196

mereology works without restriction everywhere here

t i m e

clinical trial

197

The Time-Stamped Ontology

t1

t3t2

here time exists outside the ontology, as an index or time-stamp

198

mereology works without restriction in every 3-D SNAPti ontology

199

Ontological Dependence

Substances are that which can exist on their own

Processes require a support from substances in order to exist

This holds for qualities, too

200


Substances are such that, while remaining numerically one and the same, they can admit contrary qualities at different times

… I am sometimes hungry, sometimes not

201

Substances

can also gain and lose parts

… as an organism may gain and lose molecules

202

SNAP and SPAN

Substances+qualities and processesContinuants and occurrents

In preparing an inventory of realitywe keep track of these two different categories of entities in two different ways

203

Need for different perspectives

Not one ontology, but a multiplicity of complementary ontologies

Cf. Quantum mechanics: particle vs. wave ontologies

204

Two Orthogonal, Complementary Perspectives

SNAP and SPAN

205

SNAP and SPAN

the tumor and its growth

the surgeon and the operation

the virus and its spread

the temperature and its rise

the disease and its course

the therapy and its application

206

SNAP and SPANSNAP entities

- have continuous existence in time

- preserve their identity through change

- exist in toto if they exist at all

SPAN entities

- have temporal parts

- unfold themselves phase by phase

- exist only in their phases/stages

207

SNAP vs. SPAN

1. SNAP: a SNAPshot ontology of endurants existing at a time

2. SPAN: a four-dimensionalist ontology of processes

208

You are a substance

Your life is a process

You are 3-dimensional

Your life is 4-dimensional

209

Change

Adding SNAP to the fourdimensionalist perspective makes it possible to recognize the existence of change

(SNAP entities are that which endure, thus providing identity through change)

SNAP ontologies provide perspective points – landmarks in the flux – from which SPAN processes can be apprehended as changes

210

Substances do not have temporal parts

The first 5-minute phase of my existence is not a temporal part of me

It is a temporal part of that complex process which is my life

211

How do you know whether an entity is SNAP or SPAN?

http://images.google.com/imgres?imgurl=www.eyespymag.com/shgraph/bnewspic/BILL%2520CLINTON%25201.jpg&imgrefurl=http://www.eyespymag.com/bnews8.html&h=827&w=699&prev=/images%3Fq%3DBill%2BClinton%26svnum%3D10%26hl%3Den%26lr%3D%26ie%3DUTF-8%26oe%3DUTF-8

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http://www.cnn.com/WORLD/europe/9808/29/russia.G7/link.bill.clinton.jpg

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Three kinds of SNAP entities

1. Substances

2. SPQR… entities

3. Spatial regions, contexts, niches, environments

213

SPQR… entities

States, powers, qualities, roles …

Substances are independent

SPQR entities are dependent on substances, they have a parasitic

existence:

a smile smiles only in a human face

214

Other SPQR… entities:

functions, dispositions, plans, shapes

SPQR… entities are all dependent on substances

one-place SPQR entities: temperature, color, height

215

Substances and SPQR… entities

Substances are the bearers or carriers of,

SPQR… entities ‘inhere’ in their substances

216

one-place SPQR… entities

tropes, individual properties

(‘abstract particulars’)

a blush

my knowledge of French

the whiteness of this cheese

the warmth of this stone

217

relational SPQR… entities

John Mary

love

stand in relations of one-sided dependence to a plurality of substances simultaneously

218


Substances are that which can exist on their own

SPQR… entities require a support from substances in order to exist

219


Substances are such that, while remaining numerically one and the same, they can admit contrary qualities at different times

… I am sometimes hungry, sometimes not

220

SNAP ontology

many sharp boundaries

SPAN ontologymany smeered boundaries

many fiat boundaries

(more scope for gerrymandering – why?)

221

Processes, too, are dependent on substances

One-place vs. relational processes

One-place processes:

getting warmer

getting hungrier

222

Examples of relational processes

kissings, thumps, conversations,

dances,

Such relational processes

join their carriers together into collectives of greater or lesser duration

223

Processes, like substances, are concrete denizens of reality

My headache, like this lump of cheese, exists here and now,

and both will cease to exist at some time in the future.

But they exist in time in different ways

224

Each is a window on that dimension of reality which is visible through the given ontology

SNAP and SPAN ontologies are partial only

(Realist perspectivalism)

225

SNAP: Entities existing in toto at a time

226

Three kinds of SNAP entities

1. Substances

2. SPQR… entities

3. Spatial regions, Contexts, Niches

227

228

229

SNAP

230

SPAN: Entities extended in time

SPANEntity extended in time

Portion of Spacetime

Fiat part of process *First phase of a clinical trial

Spacetime worm of 3 + Tdimensions

occupied by life of organism

Temporal interval *projection of organism’s life

onto temporal dimension

Aggregate of processes *Clinical trial

Process[±Relational]

Circulation of blood,secretion of hormones,course of disease, life

Processual Entity[Exists in space and time, unfolds

in time phase by phase]

Temporal boundary ofprocess *

onset of disease, death

231


232


233

Relations between SNAP and SPAN

SNAP-entities participate in processes

they have lives, histories

234

SPQR… entities and their SPAN realizations

the expression of a function

the exercise of a role

the execution of a plan

the realization of a disposition

235


function

role

plan

disposition

therapy

disease

SNAP

236


expression

exercise

execution

realization

application

course

SPAN

237

SNAP and SPAN

space

space-time

substances

SPQR entities (including functions)

processes

238

Gene Ontology

Cellular Component Ontology: subcellular structures, locations, and macromolecular complexes;examples: nucleus, telomere SNAP-INDEPENDENT

Molecular Function Ontology: tasks performed by individual gene products; examples: transcription factor, DNA helicase SNAP-DEPENDENT (SPQR)

Biological Process Ontology: broad biological goals accomplished by ordered assemblies of molecular functions; examples: mitosis, purine metabolism SPAN

239

Substance->Process

PARTICIPATION(a species of dependence)

240

Participation (SNAP-SPAN)

A substance (SNAP) participates in a process (SPAN)

A runner participates in a race

A voter participates in an election

241

Axes of variation

activity/passivity (agentive)

direct/mediated

benefactor/malefactor (conducive to existence) [MEDICINE]

242

SNAP-SPAN

Participation

Perpetration (+agentive)

Initiation

Perpetuation

Termination

Influence

Facilitation

Hindrance

Mediation

Patiency(-agentive)

243

Perpetration

A substance perpetrates an action (direct and agentive participation in a process):

The referee fires the starting-pistol

The captain gives the order

244

Initiation

A substance initiates a process:

The referee starts the race

The attorney initiates the process of appeal

245

Perpetuation

A substance sustains a process:

The singer sings the song

The charged filament perpetuates the emission of light

246

Termination

A substance terminates a process:

The operator terminates the projection of the film

The judge terminates the imprisonment of the pardoned convict

247

Influence

A substance (or its quality) has an effect on a process

The steepness of the slope affects the movement of the troopsThe politicians influence the course of the war

248

Facilitation

A substance plays a secondary role in a process (for example by participating in a part or layer of the process)

The catalyst provides the chemical conditions for the reaction

The traffic-police facilitate our rapid progress to the airport

249

Hindrance, prevention

A substance has a negative effect on the unfolding of a process (by participating in other processes)

The drug hinders the progression of the disease

The strikers prevent the airplane from departing

250

Mediation

A substance plays an indirect role in the unfolding of a process relating other participants:

The Norwegians mediate the discussions between the warring parties

251

Patiency

Dual of agentive participation

John kisses [Mary] (John agent)

Mary is kissed [by John] (Mary patient)

252

Signatures of meta-relations

SNAP Component SPAN Component

Substances

SPQR…

Space Regions

Processuals

Processes

Events

Space-Time Regions

253

2nd Family

REALIZATION

254

Signatures of meta-relations

SNAP Component SPAN Component

Substances

SPQR…

Spatial Regions

Processuals

Processes

Events

Space-Time Regions

participation

realization

255

Realization (SNAP-SPAN)

the execution of a plan, algorithm

the expression of a function

the exercise of a role

the realization of a disposition

256


plan

function

role

disposition

algorithm

SNAP

257


execution

expression

exercise

realization

application

course

SPAN

258

SNAP->SPAN

Participation

Substance -> Process

Realization

SPQR -> Process

259

Ecological Ontology: Niches, Environments, Contexts

260

Formal Ontology

atomism vs. holism

set theory

mereology

261

Environments a Neglected Major Category in the History of Ontology

Substances

States, Qualities, Powers, Roles …

Processes

-- environments missing from Aristotle, from DOLCE, from entity-relationship models

262

environmentplaceniche

habitatsetting

holespatial region

interior

263

Applications of these concepts

in biology, ecologyin anthropologyin lawin politicsin medicinein embryology

264

A Theory of Contexts, Settings, Environments for Social Acts

Searle:

X counts as Y in context C

What kinds of entities are social contexts?

265

The Idea: Contexts can be Nested One Inside Another

Many settings occur in assemblies:

A unit in the middle range of a nesting structure is simultaneously both circumjacent and interjacent,

both whole and part, both entity and environment. (Roger Barker)

266

Human body

Compare the hierarchical organization of the human body into organs, cells, …

modular organization – with many things which can go wrong

267

Large-scale social organizations

are organized as rigidly hierarchical, modular nesting structures, with many things which can go wrong

268

Ecological Niche Concepts

niche as particular place or subdivision of an environment that an organism or population occupies (TOKEN)

vs.

niche as function of an organism or population within an ecological community (TYPE)

269

Eltonthe ‘niche’ of an animal means its place in the biotic environment, its relations to food and enemies. [...] When an ecologist says ‘there goes a badger’ he should include in his thoughts some definite idea of the animal’s place in the community to which it belongs, just as if he had said ‘there goes the vicar’ (Elton 1927, pp. 63f.)

270

The Niche as Hypervolume

temperature

hum

idity

foli

age

den

sity

271


temperature

hum

idity

foli

age

den

sity

272


temperature

hum

idity

foli

age

den

sity

273


temperature

hum

idity

foli

age

den

sity

274

Hypervolume niche is a location in an attribute space

defined by a specific constellation of environmental variables such as degree of slope, exposure to sunlight, soil fertility, foliage density...… John found his niche as a mid-level accounts manager in a small-town bank …

275

But every hypervolume niche must be realized in some specific spatial

location

Niche type must be tokenized in space

or better: it must be tokenized in space-time

276

Niche Construction

Lewontin: niches normally arise in symbiosis with the activities of organisms or groups of organisms;

they are not already there, like vacant rooms in a gigantic evolutionary hotel, awaiting organisms who would evolve into them.

“ecosystem engineering”

maintenance of niches (screwdrivers, paintings)

277

Armchair Ontology

278

Positive and negative parts

positivepart

negativepartor hole

(made of matter)

(not made of matter)

279

Artifacts and Holes

280

niches, environments are holes

281

Places are holes

282

Armchair Ontology

artefacts and niches

the niche-tenant relation

vacant niches

283

Double Hole Structure

Medium (filling the environing hole)

Tenant (occupying the central hole)

Retainer (a boundary of some surrounding structure)

284

The Structure of Niches

media and retainers

the medium of the bear’s niche is a

circumscribed body of air

285

Two Types of Boundary

Fiat boundary Physical boundary

286

Four Basic Niche Types

1 2 3 4

1: a womb;2: a snail’s shell; 3: the niche of a pasturing cow; 4: the niche around a buzzard

287

Types of Niches

a pond, a nest, a cave, a hut, an air-conditioned apartment building

the history of evolution as a history of the development of niches

288

all vacant niches must have a retainerdependence of niche on tenant(s) the armchair nichetransforming niches of type 2 into niches of type 1

289

Four Basic Niche Types

1 2 3 4

1: a house;2: a snail’s shell; 3: the niche of a pasturing cow; 4: the earth’s atmosphere

290

stationary niches

1: your office when the door is closed; 2: a rabbit hole; 3: a seat at Yankee stadium; 4: the Klingon Empire

291

The Ontology of Niches

Niches are in some ways like the interiors of substances

Two concepts of spaceship:John is in the spaceshipThe embryo is in the uterusThe yoghurt is in the refrigerator

Niches and quasi-nichesSubstances and quasi-substances

292

Two concepts of spaceship

John is in LondonJohn saw London from the air London London

IBM IBM

John admired her carJohn was sitting in her car

A is part of B vs. A is in the interior of B as a tenant is in its niche

293

Two concepts of uterus

Issue of parts of the human body

Cavities

Need for Layered Mereotopology

294

The Ontology of Niches

Niches are endurants

(SNAP entities)

295

mobile niches

296

Four Basic Mobile Niche Types

1 2 3 4

1: a womb;2: a snail’s shell; 3: the niche of a pasturing cow; 4: the niche around a buzzard

297

Recall

Lewontin’s ecological engineering

298

niches on different (granularity) levels of the food chain

a. at the bottom of the hiearchy is the saprophytic chain, in which micro-organisms live on dead organic matter;

b. above this is the primary relation between animals and the plants they consume;

c. above this is the predator chain, in which animals of one sort eat smaller animals of another sort;

d. crosscutting all of these is the parasite chain, in which a smaller organism consumes part of a larger host organism.

299

Token Science

selection theory is concerned with phenomena at the level of populations; it is ‘concerned with what properties are selected for and against in a population. We do not describe single organisms and their physical constituents one by one.’ genotypes vs. genotokens

niche theory and set theory

300

Fiat Boundaries

fish and bird niches as volumes of space

demarcatory vs. behavioral fiat boundaries

trade-off between security/comfort and freedom of movement

301

Apertures, Mouths, and Sphincters

security vs. freedom of movement plantsbarnacles and snails fish and birdsskin or hide

302

Security vs. Freedom

the mouth of the bear, the threshold of your office

freedom of movement and fiat boundaries (of niches and of organisms)

the alimentary canal: hole or part ?

303

Double Hole Structure

Medium (filling the environing hole)

Tenant (occupying the central hole)

Retainer (a boundary of some surrounding structure)

304

The Medium for Life

a medium is a medium only relative to a given type of niche

a medium requires either a retainer (in the case of a vacant niche) or a tenant (in the case of an occupied niche)

when a tenant leaves its niche the gap left by the tenant is filled immediately by the surrounding mediumMichelangelo’s Davidexamples of media: air, smoke, water

305

Mixed Media

mixed media (including radioactive impurities, as well as as vitamins, amino acids, salts, and sugars)

Scrooge, crowds, plastic balls

every medium is maximal

what does the job of filling out the niche whose medium is made of air or water? Answer: bodies of vacuum

306

Lexical Semantics

the fruit is in the bowlthe bird is in the nestthe lion is in the cagethe pencil is in the cupthe fish is in the riverthe river is in the valleythe water is in the lakethe car is in the garagethe fetus is in the cavity in the uterine liningthe colony of whooping crane is in its breeding grounds

307

Lexical Semantics

‘She swam across the bay in which the submarine was buried and which supplied oysters for the local population.’

308

The niche around the sleeping bear

There are relations of spatial overlap which do not imply corresponding relations of mereological overlap.

Niches are bounded not just spatially, and not just via physical material (the walls of the cave), but also via thresholds in quality-continua (for instance, temperature).

309

Hence:

distinct niches, may occupy the same spatial region.

Hence need for Layered Mereotopology

(The niche of the fly overlaps with the niche of the horse,

but the two are on different layers)

310

Vagueness

A niche for an entity y may have proper parts that are not niches for y

What of the outer boundaries of niches?

Indoor vs. outdoor niches (fog)

311

Ecological subjects

A niche for a sum y+z is not ipso facto a niche for each of the summed parts.

y+z = John’s head the head plus the rest of John’s body

Not every entity has its own niche. Those which do are natural units

(Compare Aristotle’s theory of places)

312

Defining Substance

A substance (body, thing) is a maximally connected tenant, a tenant which is such that no larger connected tenant includes it as a proper part.

You are a substance, but your heart is only a connected tenant within your interior.

A group is a tenant including substances as proper parts.

313

Extending Mereology

mereology, formalized in terms of the single primitive relation: part of

mereotopology, obtained by adding extra primitive relation boundary for

theory of location, obtained by adding extra primitive relation located at

formal ecology, obtained by adding extra primitive relation niche for

314

AimTo define structural properties such

as: open, closed, connected, compact, spatial coincidence, integrity, aggregate, boundary

315

Primitives

mereological predicate:

P(x, y) (read: “x is part of y”)

topological predicate:

B(x, y) (“x is a boundary for y”),

locational predicate:

L(x, y) (“x is located at y”)

316

Defined TermsD1 O(x, y)=df z (P(z, x) P(z, y))overlap

D2 xx =df xy (O(y, x) z (z O(z, y))) sum

D3 x+y =df z (P(z, x) P(z, y)) sum of x and y

D4 x–y =df z (P(z, x) O(z, y)) difference

D5 l(x) =df x(L(y, x)) location of x

317

Defined Terms

D6 b(x) =df z B(z, x) boundary of x

D7 i(x) =df x–b(x) interior of x

D8 c(x) =df x+b(x) closure of x

D9 Cl(x) =df x=c(x) closedness

D10 Rg(x) =df c(x) = c(i(x)) i(x) = i(c(x))

regularity

318

Defined Terms

D11 C(x, y) =df O(x, y) O(c(x), y) O(x, c(y))

connection

D12 EC(x, y) =df C(x, y) O(x, y)

external connection

D13 IP(x, y) =df P(x, y) z(B(z, y) O(x, z))

interior parthood

D14 Cn(x) =df yz (x=y+z C(y, z))

self-connectedness

319

Some theorems:

T1 B(x, y) B(x, –y).

T2 B(x, y) B(y, z) B(x, z).

T3 P(x, y) B(y, z) B(x, z).

320

niche predicates

N(x, y), read: “x is a niche for y”.

N(x), read: “x is a niche”. This could be defined in terms of the binary predicate, but only if every niche has a tenant

‘N(x, y)’ and ‘N(x)’, where ‘’ ranges over organism-types.

321

medium and retainer

M(x, y)

“x is a medium for y”

R(x, y)

“x is a retainer for y”

322

free niche

D15 N*(x, y) =df N(x, y) zR(z, x) free niche for y

D16 N*(x) =df N(x) zR(z, x)

Every niche is either a free niche, in this sense, or else it has a retainer—

which will imply that it has a solid physical boundary for at least a portion of its exterior surface.

323

further definitions

D17 t(x) =df y N(x, y) tenant of x

D18 r(x) =df z R(z, x) retainer of x

D19 m(x) =df z M(z, x) medium of x

324

The Axioms for N

A1 N(x, y) O(l(x), l(y)) disjointness

A2 N(x, y) IP(l(y), l(x+y)) spatial containment

A3 N(x, y) C(x, y) connection of niche

A4 N(x, y) Cl(y) closure of tenant

A5 N(x, y) Cn(x) connectedness of niche

A6 N(x, y) Rg(y) regularity of tenant

A7 N(x, y) Rg(x) regularity of niche

A8 N(x, y) N(x, z) y = z functionality

325

Every occupied niche is a niche.

A9 yN(x, y) N(x)

326

There are no vacant fiat niches

A10 N*(x) yN(x, y)

Every fiat niche is a niche for something.

327

Media and retainers

A11 M(x, y) N(y)

A12 R(x, y) N(y)

Media are media of niches

Retainers are retainers of niches.

328

Parts

A13 M(x, y) P(z, x) M(z, y)A14 R(x, y) P(z, x) R(z, y)

The parts of a medium for a given niche are themselves media for that niche and the parts of a retainer are themselves retainers.

A15 N(x) x = z(M(z, x) R(z, x))

Niches have no parts other than media and retainers.

329

Retainers and boundaries

A16 R(z, x) B(z, x)

Retainers are boundaries of niches (though not all boundaries of niches are retainers).

A17 N(x) zM(z, x)

Every niche has a medium (though a niche may lack a retainer).

A18 m(x) = m(y) x = y

No two niches have the same medium (though we leave it open whether two niches can have the same retainer).

330

Retainers and tenants

A19 N(x, y) R(z, x) C(z, y)

Retainers and tenants are not connected to each other, i.e., they do not share any physical parts or boundaries (for they are in every case separated by a medium.)

A20 M(z, x) R(w, x) EC(l(z), l(w))

The location of a retainer is externally connected (i.e., connected without overlap) to the location of the medium.

331

Axioms

A2' N(x, y) IP(l(y), l(m(x) + y))It is the medium of an occupied niche that

surrounds the tenant.

A3' N(x, y) C(m(x), y)It is the medium of an occupied niche that is

connected to the tenant. This actually follows from A3 in view of A19.

332

Axioms

A5' N(x) Cn(m(x))The medium of a niche is self-connected (though it

need not be compact, i.e., fill the entire environing hole: consider the bat flying in the bear’s cave).

A7' N(x) Rg(m(x))The medium of a niche is regular.

333

Theorems

T1 N(x) y(N(x, y) R(y, x))Every niche has either a tenant or a retainer. This is

a consequence of A10.

T2 M(x, y) z(N(y, z) R(z, y))Every medium requires either a tenant or a retainer.

This follows from T1 via A12.

334

Theorems

T3 M(z, x) P(z, x)

T4 R(z, x) P(z, x) Media and retainers are parts of niches. More

generally:

T5 M(x, y) P(z, x) P(z, y)

T6 R(x, y) P(z, x) P(z, y) All parts of a medium and all parts of a retainer are

parts of the relevant niche.

335

Theorems

T7 N(x, y) M(y, x)

T8 N(x, y) R(y, x)The tenant of a niche is neither a medium nor a

retainer thereof.

T9 M(z, x) R(w, x) EC(z, w)

The retainer of a niche is externally connected to the medium.

T10 R(z, x) B(z, m(x))

Retainers are boundaries of media.

336

Against multiplication of niches

T11 R(x, y) N(y – x)

A niche minus (part of) its retainer is not a niche.

This excludes the possibility that the difference between two niches might lie entirely in their retainers, which would result in an undue multiplication of niches with what are putatively the same boundaries.

337

Open Problems

X1 N(x, y) N(x', y') N(x + x', y + y') Mereological summing of niches is never additive.

cats whose niches come together to form a new, fused niche: the new niche is not just the mereological sum of the two separate niches;

for even assuming that the fiat boundaries of the two niches survive the fusion and continue to exist within the interior of the new niche, they are still not a part of it but are rather extrinsic to it.

338

Open Problems

X2 M(x, y) B(z, x) R(z, y) B(z, t(x))The boundaries of a medium are either retainers of the niche or boundaries of the tenant.

This would only be true if ‘B’ were understood as standing for physical boundaries, and only if one assumed that a medium has no holes except for the central holes occupied by the tenants.

(But consider again the bat in the bear’s cave, or a cage floating in the sea through which fish can swim.)

339

Open Problems

X3 M(x, y) B(z, x) EC(z, x)A medium never contains its own physical boundaries.

X4 B(b(m(x)), x)

Any boundary of the medium of a niche is a boundary of the niche itself.

This is false if we consider that the medium need not fill the environing hole completely. (The bat flying in the cave would not be part of the medium of the bear’s niche, yet the surface of the bat would not be part of the retainer either.)

340

The Ecological Psychology of J. J. Gibson and Roger Barker

341

Affordances

“The affordances of the environment are what it offers the animal, what it provides or furnishes, either for good or evil.”

James J. Gibson, The Ecological Approach to Visual Perception

342

Organisms are tuning forks

They have evolved to resonate automatically and directly to those quality regions in their niche which are relevant for survival

-- perception is a form of automatic resonation-- cognitive beings resonate to speech acts and

to linguistic records-- cognitive beings resonate deontically

343

affordances: positive and negative features of the environment:

permissions and prohibitions

344

Gibson’s theory of surface layout

Niches = systems of barriers, openings, pathways to which organisms are specifically attuned,

Include: temperature gradients, patterns of movement of air or water molecules, electro-chemical signals guiding the movements of micro-organisms

But also: traffic signs, instructions posted on notice boards or displayed on the computer screen

345

Niches

are in many ways analogous to substances

346

Marks of (bodily) substance

i. Rounded-offness

ii. Occupies space

iii. Complete boundary

iv. May have substantial parts (nesting)

v. May be included in larger substances

vi. Has a life (manifests contrary accidents at different times)

347

Corresponding Marks of Niches

(i) A niche enjoys a certain natural completeness or rounded-offness,

being neither too small nor too large

—in contrast to the arbitrary undetached parts of environmental settings and to arbitrary heaps or aggregates of environmental settings.

348

(ii) A niche takes up space,

it occupies a physical-temporal locale,

and is such as to have spatial parts.

Within this physical-temporal locale is a privileged locus—a hole—

into which the tenant or occupant of the setting fits exactly.

349

(iii) A niche

has an outer boundary:

there are objects which fall clearly within it,

and other objects which fall clearly outside it.

(The boundary itself need not be crisp.)

350

(iv) A niche

may have actual parts which are also environmental settings(hierarchical nesting)

351

(v) A niche

may be a proper part of larger, circumcluding niche.

352

(vi) A niche has a life

is now warm, now cold

now at peace, now at war ….

now expanding, now contracting

353

Marks of (bodily) substance

i. Rounded-offness

ii. Occupies space

iii. Complete boundary

iv. May have substantial parts (nesting)

v. May be included in larger substances

vi. Has a life; is now warm, now cold

354

Where are Niches?Concrete Entity

[Exists in Space and Time]Concrete Entity

[Exists in Space and Time]

Entity in 3-D Ontology[Endure. No Temporal Parts]


Entity in 4-D Ontology[Perdure. Unfold in Time]Entity in 4-D Ontology

[Perdure. Unfold in Time]

Processual EntityProcessual EntitySpatio-Temporal Region

Dim = T, T+0, T+1, T+2, T+3Spatio-Temporal Region

Dim = T, T+0, T+1, T+2, T+3

Spatial Regionof Dimension 0,1,2,3

Spatial Regionof Dimension 0,1,2,3 Dependent EntityDependent Entity

Independent EntityIndependent Entity

Quality (Your Redness, My Tallness)[Form Quality Regions/Scales]

Quality (Your Redness, My Tallness)[Form Quality Regions/Scales]

Role, Function, PowerHave realizations (called: Processes)

Role, Function, PowerHave realizations (called: Processes)

Substance[maximally connected causal unity]

Substance[maximally connected causal unity]

Boundary of Substance *Fiat or Bona Fide or MixedBoundary of Substance *

Fiat or Bona Fide or Mixed

Aggregate of Substances * (includes masses of stuff? liquids?)

Aggregate of Substances * (includes masses of stuff? liquids?)

Fiat Part of Substance * Nose, Ear, Mountain

Fiat Part of Substance * Nose, Ear, Mountain

Process [Has Unity]Clinical trial; exercise of role

Process [Has Unity]Clinical trial; exercise of role

Fiat Part of Process*Fiat Part of Process*

Aggregate of Processes*Aggregate of Processes*

Instantaneous Temporal Boundary of Process (= Ingarden’s 'Event’)*

Instantaneous Temporal Boundary of Process (= Ingarden’s 'Event’)*

Quasi-ProcessJohn’s Youth. John’s Life

Quasi-ProcessJohn’s Youth. John’s Life

Quasi-Quality Prices, Values, Obligations

Quasi-Quality Prices, Values, Obligations

Quasi-SubstanceChurch, College, Corporation

Quasi-SubstanceChurch, College, Corporation

Quasi-Role/Function/PowerThe Functions of the PresidentQuasi-Role/Function/Power

The Functions of the President

355

Where are Places?Concrete Entity









Dim = T, T+0, T+1, T+2, T+3

Spatial Regionof Dimension

0,1,2,3

Spatial Regionof Dimension

0,1,2,3

Dependent EntityDependent Entity


356

Types of PlacesConcrete Entity









Dim = T, T+0, T+1, T+2, T+3

Generalized Spatial Regionof Dimension

0,1,2,3

Generalized Spatial Regionof Dimension

0,1,2,3

Dependent EntityDependent Entity


StationaryStationaryMobileMobile

357

Ecological Psychology

Gibson: Perception

:: Roger Barker: Society

Barker’s

Ecological Ontology of Social Reality

358

Barker on Unity of Social Reality

“The conceptual incommensurability of phenomena which is such an obstacle to the unification of the sciences does not appear to trouble nature’s units.

Within the larger units, things and events from conceptually more and more alien sciences are incorporated and regulated.”

359

Barker on Unity of Social Reality

“As far as our behaviour is concerned, … even the most radical diversity of kinds and categories need not prevent integration”

360

Roger Barker: Niche as Behavioral Setting

Niches are recurrent settings which serve as the environments for our everyday activities:

my swimming pool,

your table in the cafeteria,

the 5pm train to Long Island.

361

Behavior Settings

Each behavior setting is associated with certain standing patterns of behavior.

These standing patterns of behavior present everywhere in the domain of medical treatment

(and correspondingly also in the domain of unstructured patient records)

362

Settings, for Barker,

are natural units in no way imposed by an investigator.

To laymen they are as objective as rivers and forests

— they are parts of the objective environment that are experienced as directly as rain and sandy beaches are experienced. (Barker 1968, p. 11)

363

SettingsEach setting has a boundary which separates an organized internal (foreground) pattern from a differing external (background) pattern.

364

Nesting

Many settings occur in assemblies:

A unit in the middle range of a nesting structure is simultaneously both circumjacent and interjacent,

both whole and part,

both entity and environment.

365

Unity of Behaviour and Ecological Setting

A physical-behavioural unit is a unit: its parts are unified together, but not through any similarity or community of substance.

366

The Systematic Mutual Fittingness of Behaviour and Ecological Setting

The behaviour and the physical objects … are intertwined in such a way as to form a pattern that is by no means random: there is a relation of harmonious fit between the standard patterns of behaviour occurring within the unit and the pattern of its physical components.

Compare the way in which the processes in the body are constrained by the hierarchical organization of body, organs, cells …

367

The Systematic Mutual Fittingness of Behaviour and Ecological Setting

(The seats in the lecture hall face the speaker.

The speaker addresses his remarks out towards the audience.

The boundary of the football field is, leaving aside certain predetermined exceptions, the boundary of the game.)

368

Non-transposability

This mutual fittingness of behaviour and physical environment extends to the fine, interior structure of behaviour in a way which will imply a radical nontransposability of standing patterns of behaviour from one environment to another.

The physical or historical or ceremonial conditions obtaining in particular settings are in addition as essential for some kinds of behaviour as are persons with the requisite authority, motives and skills.

369

Power and Authority

There are various forces which help to bring about and to sustain this mutual fittingness and thus to constitute the unity of the physical-behavioural unit through time. Forces which flow in the direction from setting to behaviour include physical constraints exercised by hedges, walls or corridors or by persons with sticks; they include social forces manifested in the authority of the teacher, in threats, promises, warnings;

370

The Unifying Effects of the Physical Environment

they include the physiological effects of climate, the need for food and water; and they include the effects of perceived physiognomic features of the environment

(open spaces seduce children, a businesslike atmosphere encourages businesslike behaviour).

371

Mutual Fittingness

can be reinforced by learning, and also by a process of selection of the persons involved, whether this be one of self-selection (of children who remain in Sunday school class in light of their ability to conform to the corresponding standing patterns of behaviour), or of externally imposed mental or physical entrance tests.

372

Behaviour shapes Setting

Influences which flow from behaviour to setting, include all those ways in which a succession of separate and uncoordinated actions can have unintended consequences in the form of new types of actions and new, modified types of settings in the future (as the passage of many feet causes pathways to form in the hillside).

373

Settings shape Persons

Each person has many strengths, many intelligences, many social maturities, many speeds, many degrees of liberality and conservativeness, and many moralities, depending in large part on the particular contexts of the person’s behavior.

For example, the same person who displays marked obtusiveness when confronted with a mechanical problem may show impressive skill and adroitness in dealing with social situations.

374

Aurel Kolnai

a human society

… comprehends the same individual over and over again in line with his various social affiliations …

375

Daily life

= passage through a succession of physical-behavioural units which are as much a part of the furniture of reality as are garden-variety continuants and occurrents (such as you and me). Physical-behavioural units have parts.And they have consequences:contracts signed, orders issued, judgments passed, medals awarded.

376

Where are behavior settings?















spatio-temporal volumes

377

4-dimensional environments

Lobsters have evolved into environments marked by cyclical patterns of temperature change

Tudor EnglandThe Afghan winterThe window of opportunity for an

invasion of IraqThe surgical ward during early

morning

378

1















spatio-temporal volumes

standardizedpatterns of

behavior

379

The Theory of Granular Partitions

380

A Simple Partition

381

382

383

A partition can be more or less refined

A partition can be more or less refined

384

385

386

Partition

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

387GrGr

388

A partition is transparent

It leaves the world exactly as it is

389Artist’s Grid

390

Label/Address System

A partition typically comes with labels and/or an address system

391

Montana

Montana

392

Cerebral Cortex

393

Mouse Chromosome Five

394

A partition can comprehend the whole of reality

395

Universe

396

It can do this in different ways

397

Periodic Table

398

Perspectivalism

PerspectivalismDifferent partitions may represent cuts through the same reality which are skew to each other

399


400

Partitions can sometimes create objects

fiat objects = objects determined by partitions

401

Kansas

402

= objects which exist independently of our partitions

(objects with bona fide boundaries)

bona fide objects

403

404

California Land Cover

405Artist’s Grid

406

a partition is transparent (veridical)

= its fiat boundaries correspond at least to fiat boundaries on the side of the objects in its domain

if we are lucky they correspond to bona fide boundaries (JOINTS OF REALITY)

407

Tibble’s Tail

fiat boundary

408

Partitions are artefacts of our cognition

= of our referring, perceiving, classifying, mapping activity

409

and they always have a certain granularity

when I see an apple my partition does not recognize the molecules in the apple

410

Alberti’s Grid

411

Sets belong not to the realm of objects but to the realm of partitions

Sets are not objects in reality, but mathematical tools for talking about reality

412

Idealism

the road to idealism

propositions,sets,

noemata, ...

413

Goodman: Many worlds

Me: Many partitions

414

we have all been looking in the wrong direction

415

Dürer Reverse

416

Intentionality

417

Intentionality

418

corrected

content, meaningrepresentations

419

The mistaken view

420

The correct view

set-like structures belong here

421

Alberti’s Grid

422

Not propositional attitudes

but object attitudes

the attitudes mediated by partitions

(thus relatively coarse-grained)

423

Defining

Sets are (at best) special cases of partitions

Cells are to partitions as singletons are to sets

424

Objects and cells

objects are located in cells as guests are located in hotel rooms:

LA(x, z)

the analogue of the relation between an element and its singleton

425

an object x is recognized by a partition A:

x A := z (LA(x, z))

there is some cell in A in which x is located

426

Set as List Partition

A set is a list partition (a set is, roughly, a partition minus labels and address system)

The elements exist within the set withoutorder or location—they can be permuted at will and the set remains identical

427

Partitions better than sets

Partitions are

better than sets

428

David Lewis on Sets

Set theory rests on one central relation: the relation between element and singleton.

Sets are mereological fusions of their singletons (Lewis, Parts of Classes, 1991)

429

Cantor’s Hell

... the relation between an element and its singleton is “enveloped in mystery” (Lewis, Parts of Classes)

430

Cantor’s Hell



431

MysteryLewis:

... since all classes are fusions of singletons, and nothing over and above the singletons they’re made of, our utter ignorance about the nature of the singletons amounts to utter ignorance about the nature of classes generally.

432

An object can be located in a cell within a partition in any number of ways:

– object x exemplifies kind K

– object x possesses property P

– object x falls under concept C

– object x is in location L

433

The theory of partitionsis a theory of foregrounding,

of setting into relief

434

You use the name ‘Mont Blanc’ to refer to a certain mountain

You see Mont Blanc from a distance

In either case your attentions serve to foreground a certain portion of reality

Setting into Relief

435




Setting into Relief

436




Setting into Relief

437




Setting into Relief

438

Foreground/Background

439

The Problem of the Many

There is no single answer to the question as to what it is to which the term ‘Mont Blanc’ refers. Many parcels of reality are equally deserving of the name ‘Mont Blanc’

– Think of its foothills and glaciers, and the fragments of moistened rock gradually peeling away from its exterior; think of all the rabbits crawling over its surface

440Mont Blanc from Lake Annecy

441

The world itself is not vague

Rather, many of the terms we use to refer to objects in reality are such that, when we use these terms, we stand to the corresponding parcels of reality in a relation that is one-to-many rather than one-to-one.

Something similar applies also when we perceive objects in reality.

442

Many but almost one

David Lewis:

There are always outlying particles, questionable parts of things, not definitely included and not definitely not included.

443

GranularityCognitive acts of Setting into Relief: the Source of Partitions

Partititions: the Source of Granularity

Granularity: the Source of Vagueness

444

Objects and cells

x A := z (LA(x, z)

there is some cell in A and x is located in that cell

Recall:object x is recognized by partition A

445

John

446

Tracing Over

Granularity: if x is recognized by a partition A, and y is part of x, it does not follow that y is recognized by A.

When you think of John on the baseball field, then the cells in John’s arm and the fly next to his ear belong to the portion of the world that does not fall under the beam of your referential searchlight.

They are traced over.

447

(Recall Husserl’s theory of Abschattungen)

(Ship of Theseus: different partitions of the same unterliegende sachliche

Tatbestandsmaterial)

448

John

449

Granularity the source of vagueness

... your partition does not recognize parts beneath a certain size.

This is why your partition is compatible with a range of possible views as to the ultimate constituents of the objects included in its foreground domain

450

Granularity the source of vagueness

It is the coarse-grainedness of our partitions which allows us to ignore questions as to the lower-level constituents of the objects foregrounded by our uses of singular terms.

This in its turn is what allows such objects to be specified vaguely

Our attentions are focused on those matters which lie above whatever is the pertinent granularity threshold.

451

Mont Blanc from Chatel

452

Mont Blanc (Tricot)

453

Bill Clinton is one person

– these are both supertrue

Mont Blanc is one mountain

454

they are trueh

no matter which of the many aggregates of matter you assign as precisified referent

455

Bill Clinton is one person

– both are true on the appropriate level of granularity(our normal, common-sense ontology is in perfect order as it stands)

Mont Blanc is one mountain

456

Standard Supervaluationism

A sentence is supertrue if and only if it is true under all precisifications. A sentence is superfalse if and only if it is false under all precisifications.

A sentence which is true under some ways of precisifying and false under others is said to fall down a supervaluational truth-value gap. Its truth-value is indeterminate.

457

Are those rabbits part of Mont Blanc?

458

Example of Gaps

On Standard Supervaluationism

Rabbits are part of Mont Blanc

falls down a supertruth-value gap

459

Different Contexts

In a perceptual context it is supertrue that these rabbits are part of Mont Blanc

In a normal context of explicit assertion it is superfalse that these rabbits are part of Mont Blanc

In a real estate context in a hunting community it is supertrue that these rabbits are part of that mountain

460

So, even with

Rabbits are part of Mont Blanc,

there are no gaps.

Are there any naturally occurring contextswith gaps?

461

Supervaluationism Contextualized

We pay attention in different ways and to different things in different contexts

So: the range of available precisified referents and the degree and the type of vagueness by which referring terms are affected will be dependent on context.

462

Supervaluationism Contextualized

The range of admissible precisifications depends on context

The evaluations of supervaluationism should be applied not to sentences taken in the abstract but to judgments taken in their concrete real-world contexts

463

No gapsThe everyday judgments made in everyday contexts do not fall down supervaluational truth-value gaps

because the sentences which might serve as vehicles for such judgments are in normal contexts not judgeable

464

Gaps and GlutsConsider:

Rabbits are part of Mont Blancis in a normal context unjudgeable

Compare:Sakhalin Island is both Japanese and

not Japanese

465

Problem cases

An artist is commissioned to paint a picture of Jesus Christ and uses himself as a model. Consider the judgment:

‘This is an image of Jesus Christ’

466

No gaps

Just as sentences with truth-value gaps are unjudgeable, so also are sentences with truth-value gluts. (Solution, here, to the liar paradox.

Pragmatic approach to problematic cases (e.g. liar paradox) ontologically clarified by contextualized supervaluationism

467

Normal contexts

including normal institutional contexts have immune systems which protect them against problematic utterances

such utterances are not taken seriously as expressing judgments

468

Judgments

exist only as occurring episodes within natural contexts

... thus they are partly determined by the immune systems which natural contexts standardly possess

469

Judgments and Evolution

Most naturally occurring contexts possess immune systems because those which did not would have been eliminated in the struggle for survival.

But the semantics hereby implied has nothing to do with pragmatic eliminations of objective truth normally favored by proponents of evoluationary epistemology

470

Contextualized Supervaluationism

A judgment p is supertrue if and only if:

(T1) it successfully imposes in its context C a partition of reality assigning to its constituent singular terms corresponding families of precisified aggregates, and

(T2) the corresponding families of aggregates are such that p is true however we select individuals from the many candidate precisifications.

471

Supertruth and superfalsehood are not symmetrical:

A judgment p is superfalse if and only if

either:

(F0) it fails to impose in its context C a partition of reality in which families of aggregates corresponding to its constituent singular referring terms are recognized,

472

Falsehood

or both:

(F1) the judgment successfully imposes in its context C a partition of reality assigning to its constituent singular terms corresponding families of precisified aggregates, and

(F2) the corresponding families of aggregates are such that p is false however we select individuals from the many candidate precisifications.

473

Pragmatic presupposition failure:

In case (F0), p fails to reach the starting gate for purposes of supervaluation

Consider: „Karol Wojtyła is more intelligent than the present Pope“

474

Lake Constance

No international treaty establishes where the borders of Switzerland, Germany, and Austria in or around Lake Constance lie.

Switzerland takes the view that the border runs through the middle of the Lake.

Austria and Germany take the view that all three countries have shared sovereignty over the whole Lake.

475

Lake Constance

If you buy a ticket to cross the lake by ferry in a Swiss railway station your ticket will take you only as far as the Swiss border (= only as far as the middle of the lake)

476

but for all normal contextsconcerning

fishing rights,

taxation,

shipping,

death at sea, etc., there are treaties regulating how decisions are to be made (with built in immune-systems guarding against problematic utterances)

477

Lake Constance

an ontological black hole in the middle of Europe

478

Lake Constance (D, CH, A)

SwitzerlandAustria

Germany

479

That Water is in SwitzerlandYou point to a certain kilometer-wide volume of water in the center of the Lake, and you assert:

[Q] That water is in Switzerland.

Does [Q] assert a truth on some precisifications and a falsehood on others?

480

No

By criterion (F0) above, [Q] is simply (super)false.

Whoever uses [Q] to make a judgment in the context of currently operative international law is making the same sort of radical mistake as is someone who judges that Karol Wojtyła is more intelligent than the present Pope.

481

Reaching the Starting GateIn both cases reality is not such as to sustain a partition of the needed sort.

The relevant judgment does not even reach the starting gate as concerns our ability to evaluate its truth and falsehood via assignments of specific portions of reality to its constituent singular terms.

482

Partitions do not care

Our ordinary judgments, including our ordinary scientific judgments, have determinate truth-values

because the partitions they impose upon reality do not care about the small (molecule-sized) differences between different precisified referents.

483

Again:

Enduring types of (social, legal, administrative, planning) contexts have immune systems to prevent the appearance of the sort of problematic vagueness that is marked by gaps and gluts

484

No Gaps‘Bald’, ‘cat’, ‘dead’, ‘mountain’ are all vague

But corresponding (normal) judgments nonetheless have determinate truth-values.

There are (on one way of precisifying ‘normal’ in the above) no truth-value gaps

485

philosophical contexts are not normal

486

DOWN

WITH

PHILOSOPHY !

487

An ontology

is a canonical representation of the types of entities in a given domain and of the types of relations between these entities:

holy grail of a single benchmark ontology, which would make all databases intertranslatable

an ontological Esperanto

488

Ontological Zooming

489


animal

bird

canary

ostrich

fishfolk biology

partition of DNA space

490


animal

bird

canary

ostrich

fish

both are transparent partitions of one and the same reality

491

492

Ontology

like cartography

must work with maps at different scales and with maps picking out different dimensions of invariants

493

If ontological realism is rightthen 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

494

There are not only map-like partitions of reality into material (spatial) chunks

but also distinct partitions of reality into universals (genera, categories, kinds, types)

mutually compatible ways of providing inventories of universals

(among proteins, among cells, among organisms …)

and distinct ways of partitioning the temporal dimension of processes

495

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

496

One example of ‘folk’ partition

WordNet[1] developed at the University of Princeton defines concepts as clusters of terms called synsets. Wordnet consists of some 100,000 synsets

organized hierarchically via:A concept represented by the synset {x, x, …} is

said to be a hyponym of the concept represented by the synset {y, y,…} if native speakers of English accept sentences constructed from such frames as « An x is a kind of y ».

497

A Formal Theory of Granular Partitions

Thomas Bittner and Barry Smith

http://ontology.buffalo.edu/smith/articles/partitions.pdf

498

The Parable of the Two Tables

from Arthur Eddington, The Nature of the Physical World (1928)

Table No. 1 = the ordinary solid table made of wood

Table No. 2 = the scientific table

499


‘My scientific table is mostly emptiness. Sparsely scattered in that emptiness are numerous electric charges rushing about with great speed; but their combined bulk amounts to less than a billionth of the bulk of the table itself.’

500

Eddington:

Only the scientific table exists.

501


Both of the tables exist – in the same place: in fact they are the same table but pictured in maps of different scales

the job of the theory of granular partitions is to do justice to this identity in (granular) difference

502

Towards a Theory of Intentionality / Reference / Cognitive Directedness

GRANULAR PARTITIONS: THE SECOND DIMENSION

503

Intentional directedness

… is effected via partitions

we reach out to objects because partitions are transparent

504

Applications

Theory of selectivity of cognition (including natural language cognition)

Theory of granularity (medical data, genetic data)

Theory of transformations between partitions of the same reality (SNOMED, UMLS …)

505

THE END

THE END

Documents

1 Introduction to Ontology Barry Smith. 2 Aristotle author of The Categories Aristotle