depicting reality

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Depicting Reality

Barry Smithhttp://ontology.buffalo.edu/smith

David Armstrong

Universals and Scientific Realism

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Armstrong’s Fantology

The spreadsheet ontology

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

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

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F G H I J K L M N O P Q R S T U Va x x x x xb x x x x xcdefghijk

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F G H I J K L M N O P Q R S T U Va x x x x xb x x x x xc x x x x xdefghijk

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F G H I J K L M N O P Q R S T U Va x x x x xb x x x x xc x x x x xd x xefghijk

and so on …

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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

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FantologyThe syntax of first-order predicate logic is a

mirror of reality‘Fa’ (or ‘Rab’) is the key to ontological

structure(Fantology a special case of linguistic

Kantianism: the structure of language is they key to the structure of [knowable] reality)

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

This language reflects the structure of realityThe fantologist sees reality as being made up of atoms plus abstract (1- and n-place) ‘properties’ or ‘attributes’

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Fantology infects computer science, too

(Modern forms of this in the world of OWL, where we might talk of “Fology”)

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Formal Ontology vs. Formal Logic (Husserl)

Formal ontology deals with the interconnections of thingswith objects and properties, parts and wholes, relations and collectivesFormal logic deals with the interconnections of truthswith consistency and validity, or and not

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Formal Ontology vs. Formal Logic

Formal ontology deals with formal ontological structuresFormal logic deals with formal logical structures

‘formal’ = obtain in all material spheres of reality

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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

First principle of fantology

all form is logical form

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pace Russell, Wittgenstein, Armstrong …

where entails is a logical relation,part-whole is an ontological relation

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Standard FOL semantics

‘F’ stands for a property‘a’ stands for an individual

properties belong to Platonic realm of forms

orproperties are sets of individuals for which

‘F(a)’ is true

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Armstrong

Departs from fantology in some ways (for example with his Aristotelian doctrine of universals as immanent to particulars)

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... but

He is still a prisoner of fantological syntax

… the forms F(a) and R(a,b) are still the basic key to ontology

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Fantology

Works very well in mathematicsPlatonist theories of properties are here

very attractive

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Second Principle of Fantology

“All generality belongs to the predicateˮ

The ‘a’ in ‘Fa’ is a mere nameContrast this with the way scientists use names:

The electron has a negative charge

DNA-Binding Requirements of the Yeast Protein Rap1p as selected In Silico from Ribosomal Protein Gene Promoter Sequences

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Third Principle of Fantology

“Individuals are mereologically simpleˮ

F G H I J K L M N O P Q R S T U Va x x x x xb x x x x xc x x x x xdefg

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‘a’ leaves no room for ontological complexity

Hence: reality is made of atomsHence: all probability is combinatoricAll 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

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Fantology

Armstrongʼs spreadsheet idea rests on a belief in some future state of ‘total (perfected) scienceʼ (see also Peirce)

when the values of ‘Fʼ and ‘aʼ will be revealed to the elect

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

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Fantology

Fa yields the form of the basic ingredients of reality

Thick particulars: a + F + G + H + …Thin particulars: a (‘irreducible

particularity’)

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Fantology: Some optional elements

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

(Fantology useless e.g. for biomedical ontology)

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Fantology

Fa

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

simples)

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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)

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Fantology

All form is logical formAll necessity is logical necessityCf. Wittgenstein‘s doctrine of the

independence of states of affairs

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Fantology

Fa

To understand properties is to understand predication

(effectively in terms of functional application à la Frege)

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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

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Fourth Principle of Fantology

“There is no predication in the category of substance”

(Alternatively: the two types of predication are confused)

ArmstrongThere are only property universals

negatively charged (of electrons)phosphorylated (of proteins)

etc.Thus no need for kind universals

electronprotein

etc.

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Armstrong’s own view

State of affairs = Substance + universalsSubstances are the locus of particularityUniversals explain invariance/similarity

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

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No tropes

For Armstrong, tropes are congealed states of affairs

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

‘a’ refers always to substances (objects, things)

‘F’ refers always to Platonically conceived universals

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FantologyFa, Gb x(Fx Gx)This should be the form of laws of nature (not,

for instance, differential equations)Therefore, again, a noumenal view of scienceArmstrong not able to name even one example

of a really existing univeral or of a really existing particular

Compare Wittgenstein

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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)

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Fantology

(given its roots in mathematics) has no satisfactory way of dealing with

timehence leads to banishment of time from

the ontology (as in Armstrong’s four-dimensionalism)

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Fifth Principle of Fantology: Booleanism

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

then F&G stands for a propertyFvG stands for a propertynot-F stands for a propertyFG stands for a propertyand so on

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Strong BooleanismThere is a complete lattice of properties:

self-identity

FvG

F G

F&G

non-self-identity

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Strong BooleanismThere is a complete lattice of properties:

self-identity

FvG

not-F F G not-G

F&G

non-self-identity

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Booleanism

responsible, among other things, for Russell’s paradox

Armstrong free from BooleanismWith his sparse theory of properties

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Gene OntologyCellular 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 Dependent Continuants

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

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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) ?

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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

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Fantology leads you to talk nonsense about family

resemblances

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Fantology

emphasizes the linguistic over the perceptual/physiognomic

(the digitalized over the analogue)

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The limitations of fantology

lead one into the temptations of possible world metaphysics,

and other similar fantasies

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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)

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A better view

In order to do justice to time we need to recognize both properties and processes (cf. Davidson’s views on events)

property-universals and property-instances (tropes) (dependent continuants)

process-universals and process-instances (occurrents)

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Dependent Continuants

states, powers, qualities, roles, functions, dispositions, plans, shapes …

PlusProcesses = the expressions,

realizations of all of these things in time (Occurrents)

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The (Aristotelian) Ontological Sextet

Substances Qualities, Roles, Functions, …. Processes

UniversalsSubstance-universals

Dependent Continuant-universals,

Process-universals

ParticularsIndividual

Substances

Dependent Continuant-instances

Process-instances

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Armstrong´s view:


Universals Properties

Particulars Particulars

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The tropist view:


Universals

Particulars Tropes, bundles

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The set-theoretical view:

Substances Qualities, Functions, Roles … Processes

Universals Sets

Particulars Elements

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Process Metaphysics


UniversalsEverything

is flux

Particulars

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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

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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

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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.

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Set theory is Booleanism unremediated

Booleanism without any remediating features whatsoever

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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.

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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

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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.

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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.

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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.

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Set theory is of course of considerable mathematical interestIt 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.

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Set theory

allows unrestricted (Boolean) combinations

therefore gives as far more objects than we need

{all red things, the number 6}

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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.

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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?

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Truth for empirical sentenceshas 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.

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Problems with set theory

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

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Mereology can deal more adequately with real-world

collectionsConsider the collection of trees that is a

certain forest. What is its cardinality? Are two trees that share a common root

system one or two?

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Mereology can deal more adequately with fields

(e.g. in quantum field theory)since it does not presuppose the isolation

of atoms at the bottom of a structural hierarchy

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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:

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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.

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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).

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The experienced continuum

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

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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.

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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.

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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

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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

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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)

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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

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Mereology makes no distinction between an individual and a

singleton setnor 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."

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How are the 6 categories of entity related together?

Via FORMAL RELATIONSsuch as instantiation, part-whole,

expression (between a function and a process) …

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A better syntax

variables x, y, z … range overuniversals and particulars in all 6 categoriespredicates 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)

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This suggests a new syntax:=(x,y)

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

John is a man: Inst(John, man)John’s headache depends on John:

Dep(John’s headache, John)

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Compare the syntax of set theory

(x,y)

one (formal) predicate

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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 …)

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Compare the syntax of description logics

isa(x,y)

one formal predicate

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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)

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New syntax:

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

Compare Davidson’s treatment of eventsDoes(John,e)

Aristotelian Ontological Sextet

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Fantology

All form is logical formTo 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, ...

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But what ARE the formal relations?

Clue:

Anatomy vs. PhysiologySNAP vs. SPAN

Synchronic vs. diachronic ontology

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Different ontological perspectives

SNAP vs SPANUniversals vs. ParticularsDifferent levels of granularity:

molecular, cellular, organism ...

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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

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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

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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

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This generates a first list of formal relations, e.g. dependence,but we find some of these relations also within SNAP or within SNAP

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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

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Example:Ontological Dependence

processsubstanceThe erosion of the rock necessitates the existence of the rock

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

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Generating a typology

Two main types of formal relations:inter-ontological („transcendental“): obtain

between entities of different ontologiesintra-ontological: obtain between entities

of the same ontology (intra-SNAP, intra-SPAN)

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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

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Principal SignaturesIn the binary case:

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

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

SPAN-SPAN

SNAP-SPANSPAN-SNAP

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Transtemporal relations

Examples:Genidentity

(transtemporal generalization of identity/part-whole)

Successive causality

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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

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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)

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SNAP-SPAN: Agent causation

SPAN-SPAN: Process causation

SPAN-SNAP: Causal repercussion

SNAP-SNAP: Causal origin

do not apply on all levels of granularity

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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 dependent continuants and their realizations in processes)

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Substance->Process

PARTICIPATION(a species of dependence)

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Participation (SNAP-SPAN)A substance (SNAP) participates in a

process (SPAN)

A runner participates in a race

An organ participates in a sickness

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Axes of variation

activity/passivity (agentive)

direct/mediated

benefactor/malefactor (conducive to existence) [MEDICINE]

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SNAP-SPAN

Participation

Perpetration (+agentive)

InitiationPerpetuation

Termination

Influence

Facilitation

Hindrance

Mediation

Patiency(-agentive)

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Substances

Mesoscopic reality is divided at its natural joints into substances: animals, bones, rocks, potatoes, brains

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The Ontology of Substances

Substances form natural kinds (universals, species + genera)

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Processes

Processes merge into one anotherProcess kinds merge into one another

… few clean joints either between instances or between types

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Processes

t i m e

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Nouns and verbs

Substances 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

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Substances and processes

t i m

e

process

demand different sorts of inventories

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Substances demand 3-D partonomies

space

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Processes demand 4D-partonomies

t i m e

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Processes

a whistling, a blushing, a speech a run, the warming of this stone

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Processes may have temporal parts

The first 5 minutes of my headache is a temporal part of my headacheThe first game of the match is a temporal part of the whole match

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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

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Substances and processes form two distinct orders of being

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

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The Four-Dimensionalist Ontology (SPAN)

t i m e

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The Time-Stamped Ontology (SNAP)

t1

t3t2

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

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SNAP and SPAN

Substances+(Qualities, Functions, Roles …), and Processes

Continuants and Occurrents

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

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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

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There are no substances

Bill Clinton does not existRather: there exists within the four-

dimensional plenum a continuous succession of processes which are similar in Billclintonizing way

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Fourdimensionalism

is right in everything it says

But incomplete

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It needs to be supplemented

Cf. Quantum mechanics: particle vs. wave ontologies

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Two Orthogonal, Complementary Perspectives

SNAP and SPAN

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SNAP and SPAN

the tumor and its growththe surgeon and the operation

the virus and its spreadthe temperature and its risethe disease and its course

the therapy and its application

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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

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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

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SNAP vs. SPAN

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

2. SPAN: a four-dimensionalist ontology of processes

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You are a substance

Your life is a process

You are 3-dimensionalYour life is 4-dimensional

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Three kinds of SNAP entities

1. Substances2. Qualities, functions, roles3. Spatial regions, contexts,

niches, environments

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one-place qualities, functions, roles

tropes, individual properties (‘abstract particulars’)

a blush my knowledge of French the whiteness of this cheese the warmth of this stone

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relational quality

John Mary

love

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

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SNAP entities

provide the principles of individuation/segmentation for SPAN entities

No change without some THING or QUALITY which changes

identity-based change

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Processes, too, are dependent on substances

One-place vs. relational processes

One-place processes:getting warmergetting hungrier

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Examples of relational processes

kissings, thumps, conversations, dances, Such relational processes

join their carriers together into collectives of greater or lesser duration

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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)

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SNAP: Entities existing in toto at a time

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SNAP

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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

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Relations between SNAP and SPAN

SNAP-entities participate in processes

they have lives, histories

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Realizable Dependent Continuants (Functions, Dispositions, Roles, …)

and their Realizations

the expression of a functionthe exercise of a rolethe execution of a planthe realization of a disposition

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Realizable entities

promisedebttendencyplandispositiontherapydisease

Dependent Continuants

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Realizable entities and their realizations

expression exercise execution realization applicationcourse

processes

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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?

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Different ontological perspectives

SNAP vs SPANUniversals vs. ParticularsDifferent levels of granularity:

molecular, cellular, organism ...

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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

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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

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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

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This generates a first list of formal relations, e.g. dependence,but we find some of these relations also within SNAP or within SNAP

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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

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Example:Ontological Dependence

(occurrent, independent continuant): process substanceThe erosion of the rock necessitates the existence of the rock

(dependent continuant, independent continuant): quality substance The token redness of the ball necessitates the existence of the ball

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Generating a typology

Two main types of formal relations:inter-ontological („transcendental“): obtain

between entities of different ontologiesintra-ontological: obtain between entities

of the same ontology (intra-SNAP, intra-SPAN)

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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

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Principal SignaturesIn the binary case:

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

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

SPAN-SPAN

SNAP-SPANSPAN-SNAP

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Transtemporal relations

Examples:Genidentity

(transtemporal generalization of identity/part-whole)

Successive causality

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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

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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)

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SNAP-SPAN: Agent causation

SPAN-SPAN: Process causation

SPAN-SNAP: Causal repercussion

SNAP-SNAP: Causal origin

do not apply on all levels of granularity

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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 functions, dispositions, roles … and their occurrent expressions or manifestations)

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Substance->Process

PARTICIPATION(a species of dependence)

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Participation (SNAP-SPAN)A substance (SNAP) participates in a

process (SPAN)

A runner participates in a race

An organ participates in a sickness

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Axes of variation

activity/passivity (agentive)

direct/mediated

benefactor/malefactor (conducive to existence) [MEDICINE]

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SNAP-SPAN

Participation



Termination

Influence

Facilitation

Hindrance

Mediation

Patiency(-agentive)

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Perpetration

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

The referee fires the starting-pistol

The captain gives the order

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Initiation

A substance initiates a process:

The referee starts the race

The attorney initiates the process of appeal

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Perpetuation

A substance sustains a process:

The charged filament perpetuates the emission of light

The organism perpetuates the process of metabolism

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Termination

A substance terminates a process:

The operator terminates the projection of the film

The judge terminates the imprisonment of the pardoned convict

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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

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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

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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

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MediationA substance plays an indirect role in the

unfolding of a process relating other participants:

The Norwegians mediate the discussions between the warring parties

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Patiency

Dual of agentive participation

John kisses [Mary] (John agent)Mary is kissed [by John] (Mary patient)

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Signatures of meta-relations

SNAP Component SPAN Component

Substances

Spatial Regions

Processuals

Processes

Events

Space-Time Regions

DependentContinuants…

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Substances


Space Regions

Processuals

Processes

Events

Space-Time Regions

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Substances

Space Regions

Processuals

Processes

Events

Space-Time Regions


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Substances

Space Regions

Processuals

Processes

Events

Space-Time Regions


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2nd Family

REALIZATION

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Substances

Spatial Regions

Processuals

Processes

Events

Space-Time Regions

participation

realizationDependentContinuants…

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Realization (function, role ... ->process)

A relation between a dependent continuant 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

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Realization (SNAP-SPAN)

the execution of a plan, algorithm

the expression of a functionthe exercise of a rolethe realization of a disposition

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Material examples:

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

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SNAP->SPAN

ParticipationSubstance Process

RealizationRole Process

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SPAN -> SNAP

Involvement

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SPAN -> SNAP

Involvement

Creation

Sustaining in being

DestructionDemarcation

BlurringDegradation

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Involvement

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

Races involve racers

(but not always):

Wars involve civilians

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Creation

A process brings into being a substance:

The declaration of independence creates the new state

The work of the potter creates the vase

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Sustaining in being

A process sustains in being a substance:

The circulation of the blood sustains the body

Levying taxes sustains the army

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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

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Destruction

A process puts a substance out of existence

The explosion destroys the car

The falling of the vase on the floor breaks it

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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

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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

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SNAP-SPAN

Participation



Termination

Influence

Facilitation

Hindrance

Mediation

Patiency(-agentive)

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SPAN-SNAP

Involvement

Creation

Sustenance

Destruction

ContinuationDegradation

Destruction

Creation

DemarcationBlurring

Qualitative projection

Degradation

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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

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Types of Formal RelationIntracategorial

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

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

TranscendentalsIdentity

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A case study

Disputes about propertiesCf. D.M. ArmstrongUniversals vs. TropesSubstance/attribute vs. bundles

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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)

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Four alternative positions

Substance-Attribute plus Universal Properties

Bundles with Universal Properties

Substance-Attribute plus Tropes

Bundles with Tropes

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Armstrong’s own view

Substance/attribute + universalsSubstances are the locus of particularityUniversals explain invariance/similarity

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

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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

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Aristotle’s Ontological SquareSubstantial Accidental

Second substance man cat ox

Second accident headache sun-tan dread

First substance this man this cat this ox

First accident this headache this sun-tan this dread

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Refining the Ontological SquareSubstantial Accidental





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Refining the Ontological SquareSubstantial Dependent Entities

Exercise of power Exercise of functionMovementAction

SubstancesCollectivesUndetached partsSubstantial boundaries

PowersFunctionsQualitiesShapes

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Refining the Ontological Square

Substantial Moments (Dependent)

Exercise of power Exercise of functionMovementAction


PowersFunctionsQualitiesShapes

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Exercise of power Exercise of functionMovementAction Processes?


PowersFunctionsQualitiesShapes Moments?

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John‘s reddeningJohn‘s blushingJohn‘s bruising

4-DSubstancesCollectivesUndetached partsSubstantial boundaries

John‘s rednessJohn‘s blushJohn‘s bruise

3-D

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4-D (perduring)Stuff(Blood, Snow, Tissue)MixturesHoles


3-D (enduring)

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A Refined Ontological SquareSubstantial Dependent Entities


4-D (perduring)Stuff(Blood, Snow, Tissue)MixturesHoles


3-D (enduring)

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Some philosophers

accept only part of the Aristotelian multi-categorial ontology

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

Substantial Accidental

Attributes F, G, R

Individuals a, b, c this, that

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Bicategorial NominalismSubstantial Accidental



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Process MetaphysicsSubstantial Accidental

EventsProcesses

“Everything is flux”

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UniversalsSubstance-universals

Dependent Continuant-universals

Process-universals

ParticularsIndividual

Substances


Process-instances

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SubstancesQualities, Functions, Roles …

Processes

Universals Substance-universals

Dependent Continuant-universals,

Process-types

Particulars

Individual Substances(including

environments)


Process-tokens

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The set-theoretical view:


Universals Sets

Particulars Elements

241

The OWL view:


Universals Classes

Particulars Individuals

depicting reality

Documents

combinatoricall true

collectivesformal logic

peanoin logic

ontological relation

forms fa

fantologist fa

structure of knowable

structure of language