The language of set theory is a FOLWUT language VT The language of set theory is a FOLWUT language

Against Fantology: The Case of Properties Barry Smith http://ifomis.de Ontologie Eins Null

Armstrong’s spreadsheet ontology

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

F G H I J K L M N O P Q R S T U V a x b c d e f g h i j k

F G H I J K L M N O P Q R S T U V a x b c d e f g h i j k

F G H I J K L M N O P Q R S T U V a x b c d e f g h i j k

F G H I J K L M N O P Q R S T U V a x b c d e f g h i j k and so on …

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)

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

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

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

But Russell, Wittgenstein, Armstrong … Entails is a logical relation Part-whole is an ontological relation First mistake of fantology: All form is logical form

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

Standard semantics F stands for a property a stands for an individual properties belong to Platonic realm of forms or properties are sets of individuals for which F(a) is true

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

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

... but He is nonetheless a prisoner of fantological syntax

Fantology infects computer science, too here I will concentrate on the role of fantology within analytical metaphysics

Fantology Works very well in mathematics Platonist theories of properties here are very attractive

Fantology Fa All generality belongs to the predicate ‘a’ is a mere name Contrast 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

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

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)

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 science q ranges over all truths

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

Fantology Fa The particular corresponds to a bare name noumenal view of particulars (distinction between thin and thick particulars) aversion to idea of substances as spatially extended and spatially located

Fantology Fa noumenal view of particulars Cf. Wittgenstein’s Tractatus (doctrine of simples)

Fantalogy Fa Quine’s distinction between ontology and ideology physical objects do not instantiate universals; they are just occupied regions of spacetime predicates are just ideology (no singular terms for universals)

Fantology All form is logical form All necessity is logical necessity Cf. Wittgenstein‘s doctrine of the independence of states of affairs

Fantology Fa To understand properties is to understand predication (effectively in terms of functional application à la Frege)

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

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)

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

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)

Fantology Fa yields the form of the basic ingredients of reality Thick particulars: a + F + G + H + … Thin particulars: a (‘irreducible particularity’)

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)

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

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)

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

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 FG stands for a property and so on

Strong Booleanism There is a complete lattice of properties: self-identity FvG F G F&G non-self-identity

Strong Booleanism There is a complete lattice of properties: self-identity FvG not-F F G not-G F&G non-self-identity

Booleanism responsible, among other things, for Russell’s paradox Armstrong free from Booleanism With his sparse theory of properties

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 history analogous 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

leading them back, on this point, to where Aristotelians were from the very beginning

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)

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 of process-universals and process-instances

SPQR states, powers, qualities, roles, functions, dispositions, plans, shapes … Plus Processes = the expressions, realizations of all of these things in time

The (Aristotelian) Ontological Sextet Substances SPQR entities Processes Universals Substance-universals SQPR-universals, Process-types Particulars Individual Substances SPQR-instances (Tropes…) Process-tokens

Armstrong´s view: Properties Substances SPQR entities Processes Universals Properties Particulars

The trope view: Tropes, bundles Substances SPQR entities Processes Universals Particulars Tropes, bundles

The set-theoretical view: Substances SPQR entities Processes Universals Sets Particulars Elements

Armstrong Property universals are all we need No need to distinguish kind universals No need to distinguish predications in the category of substance from predications in the category of accident

The (Aristotelian) Ontological Sextet Substances SPQR entities Processes Universals Substance-universals SQPR-universals, Process-types Particulars Individual Substances SPQR-instances (Tropes…) Process-tokens

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

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) ?

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

Fantology leads you to talk nonsense about family resemblances

Fantology emphasizes the linguistic over the perceptual/physiognomic (the digitalized over the analogue)

The limitations of fantology lead one into the temptations of possible world metaphysics, and other similar fantasies

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)

The (Aristotelian) Ontological Sextet Substances SPQR entities Processes Universals Substance-universals SQPR-universals, Process-types Particulars Individual Substances (including environments) SPQR-instances (Tropes…) Process-tokens

The set-theoretical view: Substances SPQR entities Processes Universals Sets Particulars Elements

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

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.

Set theory is Booleanism unremediated Booleanism without any remediating features whatsoever

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.

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

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.

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.

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.

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.

Set theory allows unrestricted (Boolean) combinations therefore gives as far more objects than we need {all red things, the number 6}

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.

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?

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.

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

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?

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

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:

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.

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).

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

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.

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.

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

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

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)

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

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."

How are the 6 categories of entity related together? Via FORMAL RELATIONS such as instantiation, part-whole, expression (between a function and a process) …

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)

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)

Compare the syntax of set theory (x,y) one (formal) predicate

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 …)

Compare the syntax of description logics isa(x,y) one formal predicate

Compare the syntax of description logics isa means: is an instance of is a sub-class of (is subsumed by) sometimes also: may be a is a part of (all symbolized by means of a single relational constant)

Compare Davidson’s treatment of events New syntax: =(x,y) Part(x,y) Inst(x,y) Dep(x,y) Compare Davidson’s treatment of events Does(John,e)

Fantology All form is logical form 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, ...

But what ARE the formal relations? Clue: Anatomy vs. Physiology SNAP vs. SPAN Synchronic vs. diachronic ontology

Different ontological perspectives SNAP vs SPAN Universals vs. Particulars Different levels of granularity: molecular, cellular, organism ...

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 divide they glue SNAP and SPAN entities together

A hypothesis (first rough version) Formal relations are those relations which are not captured by either an inventory of universals or an inventory of particulars because they traverse the universal-particular divide they glue universals and particulars together ---- above all instantiation

A hypothesis (first rough version) Formal relations are those relations which are not captured by an ontology on any single level of granularity because they traverse the granular divide they glue together entities on different levels of granularity --- above all parthood

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

The idea (modified version) Formal relations are the relations that hold SNAP and SPAN entities/ontologies together and analogous relations … they come for free, they do not add anything to being = they are links between categories

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

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)

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

Principal Signatures In the binary case: SNAP-SNAP - (SNAPi, SNAPi), i = i - (SNAPi, SNAPi), i < j, i > j SPAN-SPAN SNAP-SPAN SPAN-SNAP

Transtemporal relations Examples: Genidentity (transtemporal generalization of identity/part-whole) Successive causality

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

Successive Causality SPAN-SPAN: Process causation One process causes another process SPAN-SNAP: Causal repercussion A process results in the modification of a substance (always mediated by process causation) SNAP-SPAN: Agent causation A substance produces causally a process SNAP-SNAP: Causal origin One substance is the causal origin of another (mediated by other types of causal relations)

do not apply on all levels of granularity Successive Causality SPAN-SPAN: Process causation SPAN-SNAP: Causal repercussion SNAP-SPAN: Agent causation SNAP-SNAP: Causal origin do not apply on all levels of granularity

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)

Substance->Process PARTICIPATION (a species of dependence)

Participation (SNAP-SPAN) A substance (SNAP) participates in a process (SPAN) A runner participates in a race An organ participates in a sickness

Axes of variation direct/mediated benefactor/malefactor activity/passivity (agentive) direct/mediated benefactor/malefactor (conducive to existence) [MEDICINE]

SNAP-SPAN Participation Perpetration (+agentive) Influence Patiency Initiation Termination Facilitation Perpetuation Hindrance Mediation

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

The Ontology of Substances Substances form natural kinds (universals, species + genera)

Processes Processes merge into one another Process kinds merge into one another … few clean joints either between instances or between types

Processes t i m e

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

Substances and processes t i m e process demand different sorts of inventories

Substances demand 3-D partonomies space

Processes demand 4D-partonomies t i m e

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

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

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

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?

The Four-Dimensionalist Ontology (SPAN) t i m e

The Time-Stamped Ontology (SNAP) here time exists outside the ontology, as an index or time-stamp

SNAP and SPAN Substances+SPQR, 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

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

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

is right in everything it says Fourdimensionalism is right in everything it says But incomplete

It needs to be supplemented Cf. Quantum mechanics: particle vs. wave ontologies

Two Orthogonal, Complementary Perspectives SNAP and SPAN

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

Axiom Part-relations never traverse the SNAP-SPAN divide No process is ever part of a substance and vice versa No quality is ever part of a process and vice versa Process and function belong to two different orders of being

SNAP and SPAN SNAP 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

SNAP vs. SPAN SNAP: a SNAPshot ontology of endurants existing at a time SPAN: a four-dimensionalist ontology of processes

Your life is 4-dimensional You are a substance Your life is a process You are 3-dimensional Your life is 4-dimensional

Three kinds of SNAP entities Substances SPQR… entities Spatial regions, contexts, niches, environments

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

relational SPQR… entities John Mary love stand in relations of one-sided dependence to a plurality of substances simultaneously

SNAP entities provide the principles of individuation/segmentation for SPAN entities No change without some THING or QUALITY which changes identity-based change

Processes, too, are dependent on substances One-place vs. relational processes One-place processes: getting warmer getting hungrier

Examples of relational processes kissings, thumps, conversations, dances, Such relational processes join their carriers together into collectives of greater or lesser duration

SNAP and SPAN ontologies are partial only Each is a window on that dimension of reality which is visible through the given ontology (Realist perspectivalism)

SNAP: Entities existing in toto at a time

SNAP

SPAN: Entities extended in time

SPAN: Entities extended in time

SPAN: Entities extended in time

Relations between SNAP and SPAN SNAP-entities participate in processes they have lives, histories

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

SPQR… entities and their SPAN realizations SNAP function role plan disposition therapy disease

SPQR… entities and their SPAN realizations expression exercise execution realization application course SPAN

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?

Different ontological perspectives SNAP vs SPAN Universals vs. Particulars Different levels of granularity: molecular, cellular, organism ...

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 divide they glue SNAP and SPAN entities together

A hypothesis (first rough version) Formal relations are those relations which are not captured by either an inventory of universals or an inventory of particulars because they traverse the universal-particular divide they glue universals and particulars together ---- above all instantiation

A hypothesis (first rough version) Formal relations are those relations which are not captured by an ontology on any single level of granularity because they traverse the granular divide they glue together entities on different levels of granularity --- above all parthood

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

The idea (modified version) Formal relations are the relations that hold SNAP and SPAN entities/ontologies together and analogous relations … they come for free, they do not add anything to being = they are links between categories

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

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)

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

Principal Signatures In the binary case: SNAP-SNAP - (SNAPi, SNAPi), i = i - (SNAPi, SNAPi), i < j, i > j SPAN-SPAN SNAP-SPAN SPAN-SNAP

Transtemporal relations Examples: Genidentity (transtemporal generalization of identity/part-whole) Successive causality

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

Successive Causality SPAN-SPAN: Process causation One process causes another process SPAN-SNAP: Causal repercussion A process results in the modification of a substance (always mediated by process causation) SNAP-SPAN: Agent causation A substance produces causally a process SNAP-SNAP: Causal origin One substance is the causal origin of another (mediated by other types of causal relations)

do not apply on all levels of granularity Successive Causality SPAN-SPAN: Process causation SPAN-SNAP: Causal repercussion SNAP-SPAN: Agent causation SNAP-SNAP: Causal origin do not apply on all levels of granularity

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)

Substance->Process PARTICIPATION (a species of dependence)

Participation (SNAP-SPAN) A substance (SNAP) participates in a process (SPAN) A runner participates in a race An organ participates in a sickness

Axes of variation direct/mediated benefactor/malefactor activity/passivity (agentive) direct/mediated benefactor/malefactor (conducive to existence) [MEDICINE]

SNAP-SPAN Participation Perpetration (+agentive) Influence Patiency Initiation Termination Facilitation Perpetuation Hindrance Mediation

Perpetration A substance perpetrates an action (direct and agentive participation in a process): The referee fires the starting-pistol The captain gives the order

Initiation A substance initiates a process: The referee starts the race The attorney initiates the process of appeal

Perpetuation A substance sustains a process: The charged filament perpetuates the emission of light The organism perpetuates the process of metabolism

Termination A substance terminates a process: The operator terminates the projection of the film The judge terminates the imprisonment of the pardoned convict

Influence A substance (or its quality) has an effect on a process The hilly countryside affects the movement of the troops The politicians influence the course of the war

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

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

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

Patiency Dual of agentive participation John kisses [Mary] (John agent) Mary is kissed [by John] (Mary patient)

Signatures of meta-relations SNAP Component SPAN Component Substances Processuals Processes This slide unfolds step-wise. SPQR… Events Space Regions Space-Time Regions

Signatures of meta-relations SNAP Component SPAN Component Substances Processuals Processes This slide unfolds step-wise. SPQR… Events Space Regions Space-Time Regions

Signatures of meta-relations SNAP Component SPAN Component Substances Processuals Processes This slide unfolds step-wise. SPQR… Events Space Regions Space-Time Regions

Signatures of meta-relations SNAP Component SPAN Component Substances Processuals Processes This slide unfolds step-wise. SPQR… Events Space Regions Space-Time Regions

2nd Family REALIZATION

Signatures of meta-relations SNAP Component SPAN Component participation Substances Processuals realization Processes This slide unfolds step-wise. SPQR… Events Spatial Regions Space-Time Regions

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

Realization (SNAP-SPAN) the execution of a plan, algorithm the expression of a function the exercise of a role the realization of a disposition

SPQR… entities and their SPAN realizations plan function role disposition algorithm SNAP

SPQR… entities and their SPAN realizations execution expression exercise realization application course SPAN

Material examples: performance of a symphony projection of a film expression of an emotion utterance of a sentence application of a therapy course of a disease increase of temperature

Substance -> Process SNAP->SPAN Participation Substance -> Process Realization SPQR -> Process

SPAN -> SNAP Involvement

SPAN -> SNAP Involvement Creation Sustaining in being Degradation Destruction Blurring Demarcation

Involvement process -> substance (sometimes the converse of participation): Races involve racers (but not always): Wars involve civilians

Creation A process brings into being a substance: The declaration of independence creates the new state The work of the potter creates the vase

Sustaining in being A process sustains in being a substance: The circulation of the blood sustains the body Levying taxes sustains the army

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

Destruction A process puts a substance out of existence The explosion destroys the car The falling of the vase on the floor breaks it

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

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

SNAP-SPAN Participation Perpetration (+agentive) Influence Patiency Initiation Termination Facilitation Perpetuation Hindrance Mediation

SPAN-SNAP Qualitative projection Creation Involvement Continuation Destruction Degradation Creation Sustenance Degradation Destruction Blurring Demarcation

The idea (a closer approximation) Formal relations are those relations which are not captured by either the SNAP or the SPAN ontology either because they traverse the SNAP-SPAN divide or because they traverse the granular divide

Types of Formal Relation Intracategorial Mereological (part) Topological (connected, temporally precedes) Dependency (e.g. functional ?) Intercategorial Inherence (quality of) Location Participation (agent) Dependency (of process on substance) Transcendentals Identity

A case study Disputes about properties Cf. D.M. Armstrong Universals vs. Tropes Substance/attribute vs. bundles

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)

Four alternative positions Substance-Attribute plus Universal Properties Bundles with Universal Properties Substance-Attribute plus Tropes Bundles with Tropes

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)

Not in a Subject Substantial In a Subject Accidental Said of a Subject Universal, General, Type Second Substances man, horse, mammal Non-substantial Universals whiteness, knowledge Not said of a Subject Particular, Individual, Token First Substances this individual man, this horse this mind, this body Individual Accidents whiteness, knowledge of grammar

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 Universal Particular

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 Universal Particular

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 Universal Particular

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 Universal Particular

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 Universal Particular

Refining the Ontological Square Substantial Accidental Second substance man cat ox Second accident headache sun-tan dread First substance this man this cat this ox First accident this headache this sun-tan this dread Universal Particular

Refining the Ontological Square Substantial Dependent Entities Exercise of power Exercise of function Movement Action Substances Collectives Undetached parts Substantial boundaries Powers Functions Qualities Shapes Occurrents Continuants

Refining the Ontological Square Substantial Moments (Dependent) Exercise of power Exercise of function Movement Action Substances Collectives Undetached parts Substantial boundaries Powers Functions Qualities Shapes Occurrents Continuants

Refining the Ontological Square Substantial Dependent Entities Exercise of power Exercise of function Movement Action Processes? Substances Collectives Undetached parts Substantial boundaries Powers Functions Qualities Shapes Moments? Occurrents Continuants

Refining the Ontological Square Substantial Dependent Entities John‘s reddening John‘s blushing John‘s bruising 4-D Substances Collectives Undetached parts Substantial boundaries John‘s redness John‘s blush John‘s bruise 3-D Occurrents Continuants

Refining the Ontological Square Substantial Dependent Entities John‘s reddening John‘s blushing John‘s bruising 4-D (perduring) Stuff (Blood, Snow, Tissue) Mixtures Holes John‘s redness John‘s blush John‘s bruise 3-D (enduring) Occurrents Continuants

A Refined Ontological Square Substantial Dependent Entities John‘s reddening John‘s blushing John‘s bruising 4-D (perduring) Stuff (Blood, Snow, Tissue) Mixtures Holes John‘s redness John‘s blush John‘s bruise 3-D (enduring) Occurrents Continuants

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 Universal Particular

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

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

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

Process Metaphysics Substantial Accidental Universal Particular Events Processes “Everything is flux” Universal Particular