1 vt the language of set theory is a folwut language

1

VT

The language of set theory is a FOLWUT language

2

Against Fantology:The Case of Properties

Barry Smithhttp://ifomis.de

3

Armstrong’s

spreadsheet ontology

4

F G H I J K L M N O P Q R S T U V

a

b

c

d

e

f

g

h

i

j

k

5


a x x x x x

b

c

d

e

f

g

h

i

j

k

6


a x x x x x

b x x x x x

c

d

e

f

g

h

i

j

k

7


a x x x x x

b x x x x x

c x x x x x

d

e

f

g

h

i

j

k

8


a x x x x x

b x x x x x

c x x x x x

d x x

e

f

g

h

i

j

k

and so on …

9

Fantology

The doctrine, usually tacit, according to which ‘Fa’ (or ‘Rab’) is the key to ontological structure

The syntax of first-order predicate logic is a mirror of reality

(Fantology a special case of linguistic Kantianism: the structure of language is they key to the structure of [knowable] reality)

10

Formal Ontology vs. Formal Logic

Formal ontology deals with the interconnections of things

with objects and properties, parts and wholes, relations and collectives

Formal logic deals with the interconnections of truths

with consistency and validity, or and not

11

Formal Ontology vs. Formal Logic

Formal ontology deals with formal ontological structures

Formal logic deals with formal logical structures

‘formal’ = obtain in all material spheres of reality

12

Formal Ontology and Symbolic Logic

Great advances of Frege, Russell, Wittgenstein, Peano

(in logic, and in philosophy of mathematics)

Leibnizian idea of a universal characteristic

…symbols are a good thing

13

But Russell, Wittgenstein, Armstrong …

Entails is a logical relation

Part-whole is an ontological relation

First mistake of fantology:

All form is logical form

14

First-order logic

F(a)

R(a,b)

F(a) v R(a,b)

Either a F’s or a stands in R to b

15

Standard semantics

F stands for a propertya stands for an individual

properties belong to Platonic realm of forms

orproperties are sets of individuals for which

F(a) is true

16

Armstrong

Departs from fantology with his Aristotelian doctrine of universals as immanent to particulars

17

Fantology

The forms F(a) and R(a,b) are the basic clue to ontology

(Confusion of logical form and ontological form)

Armstrong recognizes that semantics and epistemology have no implications for ontology

18

... but

He is nonetheless a prisoner of fantological syntax

19

Fantology infects computer science, too

here I will concentrate on the role of fantology within analytical metaphysics

20

Fantology

Works very well in mathematics

Platonist theories of properties here are very attractive

21

Fantology

Fa

All generality belongs to the predicate‘a’ is a mere nameContrast this with the way scientists use names:

The electron has a negative chargeDNA-Binding Requirements of the Yeast Protein Rap1p as selected In Silico from Ribosomal Protein Gene Promoter Sequences

22

For extreme fantologists ‘a’ leaves no room for ontological complexity

Hence: reality is made of atoms

Hence: all probability is combinatoric

All true ontology is the ontology of ultimate universal furniture – the ontology of a future, perfected physics

Fantology cannot do justice to the existence of different levels of granularity of reality

Thus fantology is conducive to reductionism in philosophy

23

Fantology

Tends to make you believe in some future state of ‚total science‘

when the values of ‚F‘ and ‚a‘, all of them,will be revealed to the elect

(A science as a totality of propositions closed under logical consequence)

24

Armstrong

The ontology of the basic furniture of reality – must be expressible in F(a), R(a,b) form

Armstrong’s original definition of truthmaking:

the state of affairs that p makes q true :=p & necessarily(p q)

p ranges over truths of basic scienceq ranges over all truths

25

For the fantologist

“(F(a)”, “R(a,b)” … is the language for ontology

This language reflects the structure of reality

The fantologist sees reality as being made up of atoms plus abstract (1- and n-place) ‘properties’ or ‘attributes’

Truthmaker theory should set us free from this mistake

26

Fantology

Fa

The particular corresponds to a bare namenoumenal view of particulars (distinction

between thin and thick particulars)aversion to idea of substances as spatially

extended and spatially located

27

Fantology

Fa

noumenal view of particularsCf. Wittgenstein’s Tractatus (doctrine of

simples)

28

Fantalogy

FaQuine’s distinction between ontology

and ideologyphysical objects do not instantiate universals; they are just occupied regions of spacetime predicates are just ideology (no singular terms for universals)

29

Fantology


All necessity is logical necessity

Cf. Wittgenstein‘s doctrine of the independence of states of affairs

30

Fantology

Fa

To understand properties is to understand predication

(effectively in terms of functional application à la Frege)

31

Contrast Aristotle

Predication in the category of substance:

John is a man, Henry is an ox

Predication in the category of accident:

John is hungry, Henry is asleep

32

For Fantology

no predication in the category of substance (or the two types of predication are confused)

Armstrong: property universals are all we need

no need for kind universals

(Armstrong’s four-dimensionalism implies that there are no substances)

33

There is only one form of states of affairs

Fa

if there was predication in the category of substance, this would mess up Armstrong’s doctrine of states of affairs

34

Armstrong’s own view

State of affairs = Substance + universals

Substances are the locus of particularity

Universals explain invariance/similarity

(Both particulars and universals are abstractions from states of affairs)

35

Fantology

Fa

yields

the form of the basic ingredients of reality

Thick particulars: a + F + G + H + …

Thin particulars: a (‘irreducible particularity’)

36

For Armstrong

tropes are a bad theory for understanding states of affairs

(for understanding how the basic ingredients of reality are joined together)

For Armstrong tropes are congealed states of affairs

(Propositions of the form ‘Fa’ are the key to basic reality)

37

Fantology

Fa:

This should be the form of laws of nature (things + universal powers)

(not, for instance, differential equations)

Therefore, again, a noumenal view of science

Armstrong not able to name even one example of a really existing univeral

or of a really existing particular

Compare again Wittgenstein

38

Fantology

leads not only to Armstrong’s atoms + properties view of the basic ingredients of reality

but also to trope bundle views(where the a is deleted, and the F, G, H…

are seen as having particularity)Compare: Leibniz’s monadology (each

monad is a bundle of concepts)

39

Fantology

Fa

No clear way to deal with time

Armstrong talks not of processes but of particulars gaining or losing properties

But gaining and losing are themselves processes

40

Booleanism

if F stands for a property and G stands for a property

then

F&G stands for a property

FvG stands for a property

not-F stands for a property

FG stands for a property

and so on

41

Strong Booleanism

There is a complete lattice of properties:

self-identity

FvG

F G

F&G

non-self-identity

42

Strong Booleanism

There is a complete lattice of properties:

self-identity

FvG

not-F F G not-G

F&G

non-self-identity

43

Booleanism

responsible, among other things, for Russell’s paradox

Armstrong free from Booleanism

With his sparse theory of properties

44

That Lewis and Armstrong

arrived at their sparse view of properties against the solid wall of fantological Booleanist orthodoxy

is a miracle of modern intellectual historyanalogous to a 5 stone weakling climbing

up to breathe the free air at the top of Mount Everest with 1000 ton weights attached to his feet

45

leading them back, on this point,

to where Aristotelians were from the very beginning

46

Fantology

(given its roots in mathematics)

has no satisfactory way of dealing with time

hence leads to banishment of time from the ontology

(as in Armstrong’s four-dimensionalism)

47

A better view

In order to do justice to time we need to recognize both properties and processes

better: do not use the word ‘property’ at all, talk rather of

SPQR entities (both universals and instances)

and ofprocess-universals and process-instances

48

SPQR

states, powers, qualities, roles,

functions, dispositions, plans, shapes …

Plus

Processes = the expressions, realizations of all of these things in time

49

The (Aristotelian) Ontological Sextet

Substances SPQR entities Processes

UniversalsSubstance-universals

SQPR-universals,

Process-types

ParticularsIndividual

Substances

SPQR-instances (Tropes…)

Process-tokens

50

Armstrong´s view:


Universals Properties

Particulars Particulars

51

The trope view:


Universals

ParticularsTropes, bundles

52

The set-theoretical view:


Universals Sets

Particulars Elements

53

Armstrong

Property universals are all we needNo need to distinguish kind universals

No need to distinguish predications in the category of

substance from predications in the category of accident

54




SQPR-universals,

Process-types

ParticularsIndividual

Substances


Process-tokens

55

Gene Ontology

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

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

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

56

Fantology implies a poor treatment of relations

R(a,b)

in terms of adicity

What is the adicity of your headache (A relation between your consciousness and various processes taking place in an around your brain) ?

57

Fantology implies a neglect of environments

John kisses Mary

always in some environment

(= roughly, in some spatial region: a room, a car …)

Spatial regions are, like substances, three-dimensional endurants

58

Fantology leads you to talk nonsense about family

resemblances

59

Fantology

emphasizes the linguistic over the perceptual/physiognomic

(the digitalized over the analogue)

60

The limitations of fantology

lead one into the temptations of possible world metaphysics,

and other similar fantasies

61

Fantology leads one to talk nonsense about possible worlds

Definition: A possible world W is a pair (L,D) consisting of a set of first-order propositions L and a set of ground-level assertions D. …

Informally, the set L is called the laws of W, and the set D is called the database of W. Other informal terms might be used: L may be called the set of axioms or database constraints for W.

(John Sowa)

62




SQPR-universals,

Process-types

Particulars

Individual Substances

(including environments)


Process-tokens

63

The set-theoretical view:


Universals Sets

Particulars Elements

64

Fantology

is a form of linguistic Kantianism

Semantic Fantology

is a form of set-theoretical Kantianism

The [knowable] world = the [set-theoretic] model of a formal theory

65

Arguments against Set Theory

Lesniewski’s Argument: Even set theorists do not understand their own creations; thus they do not know how one important family of sets (the set of real numbers, for example) relates in size to other sets (the set of natural numbers, for example).

Still no generally accepted correct axiomatization of set theory,

Questions re Axiom of Choice, etc.

66

Set theory is Booleanism unremediated

Booleanism without any remediating features whatsoever

67

There are skew partitions (true) of the same reality

for example reflecting different granularities of analysis. If we identify entities in the world with sets, we cannot do justice to the identity of one and the same object as partitioned on different levels.

Mereology, in contrast, can allow the simultaneous truth of:

An organism is a totality of cells.An organism is a totality of molecules.

France is the totality of its 7 regions.France is the totality of its 116 provinces.

68

Dominance of set-theoretic ontology as an account of classes

means that there is no analytic-philosophical treatment of multi-variate statistical classification

in spite of the fact that this is the major approach to classification in all sorts of natural and social sciences

69

The application of set theory to a subject-matter

presupposes the isolation of some basic level of Urelemente, which make possible the simulation of the structures appearing on higher levels by means of sets of successively higher types.

70

But there is no such basic level of Urelemente in many spheres to which we might wish to direct ontological analysis, and in many spheres there is no unidirectional (upward) growth of complexity generated by simple combination.

71

Set theory reduces all complexity to combination or unification

Set theory is a general theory of the structures which arise when objects are conceived as being united together ad libitum on successively higher levels, each object serving as member or element of objects on the next higher level.

72

Set theory is of course of considerable mathematical interest

It is however an open question whether there is any theoretical interest attached to the possibility of such ad libitum unification from the perspective of ontology.

For the concrete varieties of complexity which in fact confront us are subject always in their construction to quite subtle sorts of constraints, constraints which vary from context to context.

73

Set theory

allows unrestricted (Boolean) combinations

therefore gives as far more objects than we need

{all red things, the number 6}

74

Sets are abstract entities

Sets are timeless (they do not change)

Thus a philosopher who countenances them in his ground-floor ontology has already renounced the advantages of a theory which is committed only to changing realia.

He is thereby left with the problem of connecting up the abstracta he countenances with the real entities with which they are in different ways associated.

75

Against Set Theory as a Vehicle for Semantics

There are some who would argue that we can understand a theory (for example in logic) only when we have given a set-theoretic semantics for that theory.(This is rather like saying that we can understand French only when we have translated it into English.)And how, on this basis, can we understand the language of set theory itself?

76

Truth for empirical sentences

has classically been understood in terms of a correspondence relation (i.e. of some sort of isomorphism) between a judgment or assertion on the one hand and a certain portion of reality on the other. But reality evidently does not come ready-parcelled into judgment-shaped portions Hence practitioners of logical semantics have treated not of truth as such (understood as truth to an autonomous reality), but of truth in a model, where the model is a specially constructed set-theoretic reality-surrogate.

77

Other problems

If sets don't change, then a set-theoretical ontology cannot do justice the causal-historical continuous orderSince sets divide the world into elements (points) this implies a certain unfaithfulness to boundary phenomena/continuaCan’t do justice to gradations/prototypes

78

Mereology can deal more adequately with real-world

collections

Consider the collection of trees that is a certain forst.

What is its cardinality?

Are two trees that share a common root system one or two?

79

Mereology can deal more adequately with fields

(e.g. in quantum field theory)

since it does not presuppose the isolation of urelemente/atoms at the bottom of a structural hierarchy

80

The standard set-theoretic account of the continuum

initiated by Cantor and Dedekind and contained in all standard textbooks of the theory of sets, will be inadequate for at least the following reasons:

81

The experienced continuum

does not sustain the sorts of cardinal number constructions imposed by the Dedekindian approach.

The experienced continuum is not isomorphic to any real-number structure;

standard mathematical oppositions, such as that between a dense and a continuous series, here find no application.

82

Set theory can yield at best a model

of the experienced continuum and similar structures, not a theory of these structures themselves (for the latter are after all not sets).

83

The experienced continuum

is in every case a concrete, changing phenomenon, a phenomenon existing in time, a whole which can gain and lose parts.

84

The application of set theory

to a subject-domain presupposes the isolation of some basic level of Urelemente in such a way as to make possible a simulation of all structures appearing on higher levels by means of sets of successively higher types.

85

Theory of the continuum

Set theory: out of unextended building blocks an extended whole can somehow be constructed.

But the experienced continuum is not organized out of particles or atoms,

rather, the wholes, including the medium of space, come before the parts which these wholes might contain and which might be distinguished on various levels within them.

86

Set theory leads to paradoxes

In mereology, paradoxes do not arise, since every collection is part of itself, and there cannot be a collection that is not a part of itself

87

The alternative to fantology

must take the spatiality and materiality and modular complexity of substances seriously

Mereology plus Granularity plus theory of spatial extension

‘a’ refers to something that is complex

88

Mereology

allows a nicer treatment of both plurals and mass nouns than set theory

(but mereology, too, has problems dealing with time,

and with granularity)

89

Mereology is much simpler than set theory

Whereas set theory has two distinct operators: element-of and subset-of,

mereology has only one basic operator: part-of

90

Mereology makes no distinction between an individual and a

singleton set

nor between different ways of building up collections by level of nesting:

{a,b,c} is identical to {a, {{{b}}, {c}}}.

Nelson Goodman: "No distinction of individuals without distinction of content."

91

How are the 6 categories of entity related together?

Via FORMAL RELATIONS

such as instantiation, part-whole, expression (between a function and a

process) …

92

A better syntax

variables x, y, z … range over

universals and particulars in all 6 categories

predicates stand only for FORMAL relations such as instantiates, part-of, connected-to, is-a-boundary-of, is-a-niche-for, etc.

FORMAL relations are not extra ingredients of being

(compare jigsaw puzzle pieces and the relations between them)

93

This suggests a new syntax:

=(x,y)Part(x,y)Inst(x,y)Dep(x,y)Isa(x,y)

John is wise: Inst(John, wisdom)John is a man: Isa(John, man)

94

Compare the syntax of set theory

(x,y)

one (formal) predicate

95

Compare the syntax of set theory

Basic Formal Ontology (BFO) has the syntax of set theory but with a PLURALITY of formal relations

Note that logic gives us no clue as to what these are

(they must include: location in space, location at a time …)

96

Compare the syntax of description logics

isa(x,y)

one formal predicate

97

Compare the syntax of description logics

isameans:

is an instance ofis a sub-class of (is subsumed by)

sometimes also:may be ais a part of

(all symbolized by means of a single relational constant)

98

New syntax:

=(x,y)

Part(x,y)

Inst(x,y)

Dep(x,y)

Compare Davidson’s treatment of events

Does(John,e)

99

Fantology


To understand how the world hangs together you need to understand

... and, or, not, all, some ...

No. You need formal-ontological relations like partial identity, spatial location, temporal location, instantiation, ...

100

But what ARE the formal relations?

Clue:

Anatomy vs. Physiology

SNAP vs. SPAN

Synchronic vs. diachronic ontology

101

Different ontological perspectives

SNAP vs SPAN

Universals vs. Particulars

Different levels of granularity:

molecular, cellular, organism ...

102

A hypothesis (first rough version)

Formal relations are those relations which are not captured by either SNAP or SPAN because they traverse the SNAP-SPAN dividethey glue SNAP and SPAN entities together

103


Formal relations are those relations which are not captured by either an inventory of universals or an inventory of particularsbecause they traverse the universal-particular dividethey glue universals and particulars together

---- above all instantiation

104


Formal relations are those relations which are not captured by an ontology on any single level of granularitybecause they traverse the granular dividethey glue together entities on different levels of granularity

--- above all parthood

105

This generates a first list of formal relations,

e.g. dependence,

but we find some of these relations also within SNAP or within SNAP

106

The idea (modified version)

Formal relations are the relations that hold SNAP and SPAN entities/ontologies togetherand analogous relations… they come for free, they do not add anything to being = they are links between categories

107

Example:Ontological Dependence

(SPAN, SNAP): process->substance

The erosion of the rock necessitates the existence of the rock

(SNAP, SNAP): SPQR->substance

The token redness of the sand necessitates the existence of the sand

108

Generating a typology

Two main types of formal relations:

inter-ontological („transcendental“): obtain between entities of different ontologies

intra-ontological: obtain between entities of the same ontology (intra-SNAP, intra-SPAN)

109

Three parameters:

- the arity of the relation

- the types of the relata, expressed as an ordered list, called the signature of the relation

- the formal nature of the relation

110

Principal Signatures

In the binary case:

SNAP-SNAP - (SNAPi, SNAPi), i = i

- (SNAPi, SNAPi), i < j, i > j

SPAN-SPAN

SNAP-SPANSPAN-SNAP

111

Transtemporal relations

Examples:

Genidentity

(transtemporal generalization of identity/part-whole)

Successive causality

112

Genidentity

Also SPAN-SPAN? Is there a form of genidentity among processes?

The such-as-to-have-come-forth-from relation.

Signature: SNAPi-SNAPj

Cut a chunk of matter in two, the sum of the remaining pieces is genidentical to the chunk before cutting

113

Successive Causality

SNAP-SPAN: Agent causationA substance produces causally a process

SPAN-SPAN: Process causationOne process causes another process

SPAN-SNAP: Causal repercussionA process results in the modification of a substance (always mediated by process causation)

SNAP-SNAP: Causal originOne substance is the causal origin of another (mediated by other types of causal relations)

114


SNAP-SPAN: Agent causation

SPAN-SPAN: Process causation

SPAN-SNAP: Causal repercussion

SNAP-SNAP: Causal origin

do not apply on all levels of granularity

115

Our main target: Temporally extended relations

Participation(holds between a substance and a process such as an action or a life or history)

Realization(holds between SPQR… entities and their SPAN expressions)

116

Substance->Process

PARTICIPATION(a species of dependence)

117

Participation (SNAP-SPAN)

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

A runner participates in a race

An organ participates in a sickness

118

Axes of variation

activity/passivity (agentive)

direct/mediated

benefactor/malefactor (conducive to existence) [MEDICINE]

119

SNAP-SPAN

Participation

Perpetration (+agentive)

Initiation

Perpetuation

Termination

Influence

Facilitation

Hindrance

Mediation

Patiency(-agentive)

120

Substances

Mesoscopic reality is

divided at its natural joints

into substances:

animals, bones, rocks, potatoes, brains

121

The Ontology of Substances

Substances form natural kinds

(universals, species + genera)

122

Processes

Processes merge into one another

Process kinds merge into one another

… few clean joints either between instances or between types

123

Processes

t i m e

124

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

125

Substances and processes

t i m

e

process

demand different sorts of inventories

126

Substances demand 3-D partonomies

space

127

Processes demand 4D-partonomies

t i m e

128

Processes

a whistling, a blushing, a speech

a run, the warming of this stone

129

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

130

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

131

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?

132

The Four-Dimensionalist Ontology (SPAN)

t i m e

133

The Time-Stamped Ontology (SNAP)

t1

t3t2

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

134

SNAP and SPAN

Substances+SPQR, and processesContinuants, and occurrentsEndurants, and perdurants

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

135

Fourdimensionalism denies this

– time is just another dimension, analogous to the three spatial dimensions

– only processes exist

– substances are analyzed away as worms/fibers within the four-dimensional process plenum

– there is no change

136

There are no substances

Bill Clinton does not exist

Rather: there exists within the four-dimensional plenum a continuous succession of processes which are similar in Billclintonizing way

137

Fourdimensionalism

is right in everything it says

But incomplete

138

It needs to be supplemented

Cf. Quantum mechanics: particle vs. wave ontologies

139

Two Orthogonal, Complementary Perspectives

SNAP and SPAN

140

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

141

Axiom

Part-relations never traverse the SNAP-SPAN divide

No process is ever part of a substanceand vice versaNo quality is ever part of a process and

vice versaProcess and function belong to two

different orders of being

142

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

143

SNAP vs. SPAN

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

2. SPAN: a four-dimensionalist ontology of processes

144

You are a substance

Your life is a process

You are 3-dimensional

Your life is 4-dimensional

145

Three kinds of SNAP entities

1. Substances

2. SPQR… entities

3. Spatial regions, contexts, niches, environments

146

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

147

relational SPQR… entities

John Mary

love

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

148

SNAP entities

provide the principles of individuation/segmentation for SPAN entities

No change without some THING or QUALITY which changes

identity-based change

149

Processes, too, are dependent on substances

One-place vs. relational processes

One-place processes:

getting warmer

getting hungrier

150

Examples of relational processes

kissings, thumps, conversations,

dances,

Such relational processes

join their carriers together into collectives of greater or lesser duration

151

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)

152

SNAP: Entities existing in toto at a time

155

SNAP

156

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

157


158


159

Relations between SNAP and SPAN

SNAP-entities participate in processes

they have lives, histories

160

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

161


function

role

plan

disposition

therapy

disease

SNAP

162


expression

exercise

execution

realization

application

course

SPAN

163

Special role of formal relations

Only they are represented by predicates in the first-order logic representation of our ontology

But what are formal relations?

164

Different ontological perspectives

SNAP vs SPAN

Universals vs. Particulars

Different levels of granularity:

molecular, cellular, organism ...

165


Formal relations are those relations which are not captured by either SNAP or SPAN because they traverse the SNAP-SPAN dividethey glue SNAP and SPAN entities together

166


Formal relations are those relations which are not captured by either an inventory of universals or an inventory of particularsbecause they traverse the universal-particular dividethey glue universals and particulars together

---- above all instantiation

167


Formal relations are those relations which are not captured by an ontology on any single level of granularitybecause they traverse the granular dividethey glue together entities on different levels of granularity

--- above all parthood

168

This generates a first list of formal relations,

e.g. dependence,

but we find some of these relations also within SNAP or within SNAP

169

The idea (modified version)

Formal relations are the relations that hold SNAP and SPAN entities/ontologies togetherand analogous relations… they come for free, they do not add anything to being = they are links between categories

170

Example:Ontological Dependence

(SPAN, SNAP): process->substance

The erosion of the rock necessitates the existence of the rock

(SNAP, SNAP): SPQR->substance

The token redness of the sand necessitates the existence of the sand

171

Generating a typology

Two main types of formal relations:

inter-ontological („transcendental“): obtain between entities of different ontologies

intra-ontological: obtain between entities of the same ontology (intra-SNAP, intra-SPAN)

172

Three parameters:

- the arity of the relation

- the types of the relata, expressed as an ordered list, called the signature of the relation

- the formal nature of the relation

173

Principal Signatures

In the binary case:

SNAP-SNAP - (SNAPi, SNAPi), i = i

- (SNAPi, SNAPi), i < j, i > j

SPAN-SPAN

SNAP-SPANSPAN-SNAP

174

Transtemporal relations

Examples:

Genidentity

(transtemporal generalization of identity/part-whole)

Successive causality

175

Genidentity

Also SPAN-SPAN? Is there a form of genidentity among processes?

The such-as-to-have-come-forth-from relation.

Signature: SNAPi-SNAPj

Cut a chunk of matter in two, the sum of the remaining pieces is genidentical to the chunk before cutting

176


SNAP-SPAN: Agent causationA substance produces causally a process

SPAN-SPAN: Process causationOne process causes another process

SPAN-SNAP: Causal repercussionA process results in the modification of a substance (always mediated by process causation)

SNAP-SNAP: Causal originOne substance is the causal origin of another (mediated by other types of causal relations)

177


SNAP-SPAN: Agent causation

SPAN-SPAN: Process causation

SPAN-SNAP: Causal repercussion

SNAP-SNAP: Causal origin

do not apply on all levels of granularity

178

Our main target: Temporally extended relations

Participation(holds between a substance and a process such as an action or a life or history)

Realization(holds between SPQR… entities and their SPAN expressions)

179

Substance->Process

PARTICIPATION(a species of dependence)

180

Participation (SNAP-SPAN)

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

A runner participates in a race

An organ participates in a sickness

181

Axes of variation

activity/passivity (agentive)

direct/mediated

benefactor/malefactor (conducive to existence) [MEDICINE]

182

SNAP-SPAN

Participation


Initiation

Perpetuation

Termination

Influence

Facilitation

Hindrance

Mediation

Patiency(-agentive)

183

Perpetration

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

The referee fires the starting-pistol

The captain gives the order

184

Initiation

A substance initiates a process:

The referee starts the race

The attorney initiates the process of appeal

185

Perpetuation

A substance sustains a process:

The charged filament perpetuates the emission of light

The organism perpetuates the process of metabolism

186

Termination

A substance terminates a process:

The operator terminates the projection of the film

The judge terminates the imprisonment of the pardoned convict

187

Influence

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

The hilly countryside affects the movement of the troopsThe politicians influence the course of the war

188

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

189

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

190

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

191

Patiency

Dual of agentive participation

John kisses [Mary] (John agent)

Mary is kissed [by John] (Mary patient)

192

Signatures of meta-relations

SNAP Component SPAN Component

Substances

SPQR…

Space Regions

Processuals

Processes

Events

Space-Time Regions

193



Substances

SPQR…

Space Regions

Processuals

Processes

Events

Space-Time Regions

194



Substances

SPQR…

Space Regions

Processuals

Processes

Events

Space-Time Regions

195



Substances

SPQR…

Space Regions

Processuals

Processes

Events

Space-Time Regions

196

2nd Family

REALIZATION

197



Substances

SPQR…

Spatial Regions

Processuals

Processes

Events

Space-Time Regions

participation

realization

198

Realization (SPQR->process)

The most general relation between a dependent (SPQR…) entity and a process

The power to legislate is realized through the passing of a law

The role of antibiotics in treating infections is via the killing of bacteria

199

Realization (SNAP-SPAN)

the execution of a plan, algorithm

the expression of a function

the exercise of a role

the realization of a disposition

200


plan

function

role

disposition

algorithm

SNAP

201


execution

expression

exercise

realization

application

course

SPAN

202

Material examples:

performance of a symphonyprojection of a filmexpression of an emotionutterance of a sentenceapplication of a therapycourse of a diseaseincrease of temperature

203

SNAP->SPAN

Participation

Substance -> Process

Realization

SPQR -> Process

204

SPAN -> SNAP

Involvement

205

SPAN -> SNAP

Involvement

Creation

Sustaining in being

Destruction

DemarcationBlurring

Degradation

206

Involvement

process -> substance(sometimes the converse of participation):

Races involve racers

(but not always):

Wars involve civilians

207

Creation

A process brings into being a substance:

The declaration of independence creates the new state

The work of the potter creates the vase

208

Sustaining in being

A process sustains in being a substance:

The circulation of the blood sustains the body

Levying taxes sustains the army

209

Degradation

A process has negative effects upon a substance

Eating sugar contributes to the deterioration of your teeth.

The flow of water erodes the rock

210

Destruction

A process puts a substance out of existence

The explosion destroys the car

The falling of the vase on the floor breaks it

211

Demarcation

A process creates (fiat or bona fide) boundaries of substances.

The tracing of the area by the surgeon defines a boundary, the incision performed by the surgeon yet another one

212

Blurring

A process destroys boundaries of substances:

The military stand-off creates the no man's land

The successful transplant obliterates the boundary between original and grafted tissue

213

SNAP-SPAN

Participation


Initiation

Perpetuation

Termination

Influence

Facilitation

Hindrance

Mediation

Patiency(-agentive)

214

SPAN-SNAP

Involvement

Creation

Sustenance

Destruction

Continuation

DegradationDestruction

Creation

DemarcationBlurring

Qualitative projection

Degradation

215

The idea (a closer approximation)

Formal relations are those relations which are not captured by either the SNAP or the SPAN ontologyeither because they traverse the SNAP-SPAN divideor because they traverse the granular divide

216

Types of Formal Relation

IntracategorialMereological (part)Topological (connected, temporally precedes)Dependency (e.g. functional ?)

IntercategorialInherence (quality of)Location Participation (agent)Dependency (of process on substance)

TranscendentalsIdentity

217

A case study

Disputes about properties

Cf. D.M. Armstrong

Universals vs. Tropes

Substance/attribute vs. bundles

218

Contemporary Bundle views

Bundle views 1: bearers of predication are bundles of universals (particularity is ‘constructed’)

Bundle views 2: nuclear tropes (adding up to thick particulars) + contingent tropes (reflecting contingent predications)

219

Four alternative positions

Substance-Attribute plus Universal Properties

Bundles with Universal Properties

Substance-Attribute plus Tropes

Bundles with Tropes

220

Armstrong’s own view

Substance/attribute + universals

Substances are the locus of particularity

Universals explain invariance/similarity

Plus

States of affairs

(Both particulars and universals are abstractions from states of affairs)

221

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

222

Aristotle’s 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

223



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

224



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

225



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

226



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

227

Refining the Ontological Square


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

228


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

229


Substantial Moments (Dependent)


Movement

Action

Substances

Collectives

Undetached parts


Powers

Functions

Qualities

Shapes

Occ

urre

nts

Con

tinua

nts

230




Movement

Action Processes?

Substances

Collectives

Undetached parts


Powers

Functions

Qualities

Shapes

Moments?

Occ

urre

nts

Con

tinua

nts

231



John‘s reddening

John‘s blushing

John‘s bruising

4-D

Substances

Collectives

Undetached parts


John‘s redness

John‘s blush

John‘s bruise

3-D

Occ

urre

nts

Con

tinua

nts

232



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

233

A Refined Ontological Square


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

234



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

235

Some philosophers

accept only part of the Aristotelian multi-categorial ontology

236

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


Attributes

F, G, R

Individuals

a, b, c

this, that

Uni

vers

alP

artic

ular

237

Bicategorial NominalismSubstantial Accidental

First substance

this man

this cat

this ox

First accident

this headache

this sun-tan

this dread

Uni

vers

alP

artic

ular

238

Process Metaphysics


Events

Processes

“Everything is flux”

Uni

vers

alP

artic

ular

1 vt the language of set theory is a folwut language

Documents

b slide

true slide

attractive slide

logical form slide

folwut language slide

fantology fa

good thing slide

analytical metaphysics