SNAP and SPAN Barry Smith

Institute for Formal Ontology and Medical Information Science http://ifomis.de Institute for Formal Ontology and Medical Information Science Faculty of Medicine University of Leipzig

Reality

Reality

Reality

Reality is complicated

What is the best language to describe this complexity?

formalized + domain-independent Formal ontology formalized + domain-independent

Formal Ontology Examples of categories: Substance, Process, Agent, Property, Relation, Location, Spatial Region Part-of, Boundary-of

= regional or domain-specific Material Ontology = regional or domain-specific e.g. GeO Examples of categories: River, Mountain, Country, Desert … Resides-In, Is-to-the-West-of

Realist Perspectivalism There is a multiplicity of ontological perspectives on reality, all equally veridical i.e. transparent to reality vs. Eliminativism: “Only my preferred perspective on reality is veridical”

Need for different perspectives Double counting: 3 apples on the table 7 x 1016 molecules at spatial locations L1, L2 and L3 Not one ontology, but a multiplicity of complementary ontologies Cf. Quantum mechanics: particle vs. wave ontologies

Cardinal Perspectives Formal vs. Material Micro- vs. Meso- vs. Macro SNAP vs. SPAN

A Network of Domain Ontologies BFO = Basic Formal Ontology

A Network of Domain Ontologies

A Network of Domain Ontologies

A Network of Domain Ontologies

A Network of Domain Ontologies

A Network of Domain Ontologies

AgrO PsychO

Cardinal Perspectives Formal vs. Material Ontologies Granularity (Micro vs. Meso vs. Macro) SNAP vs. SPAN

Ontological Zooming  

Ontological Zooming medicine cell biology

Ontological Zooming both are transparent partitions of one and the same reality

Cardinal Perspectives Formal vs. Material Ontologies Granularity (Micro vs. Meso vs. Macro) Time: SNAP vs. SPAN

Ontology seeks an INVENTORY OF REALITY Relevance of ontology for information systems, e.g.: terminology standardization taxonomy standardization supports reasoning about reality

Semantic Web Ontoweb OWL DAML+OIL … these are standardized languages only – not themselves ontologies

Ontology research marked by ad hoc-ism

get real ontology right first IFOMIS Strategy get real ontology right first and then investigate ways in which this real ontology can be translated into computer-useable form later DO NOT ALLOW ISSUES OF COMPUTER-TRACTABILITY TO DETERMINE THE CONTENT OF THE ONTOLOGY IN ADVANCE

a language to map these Formal-ontological structures in reality

a directly depicting language ‘John’ ‘( ) is red’ Property Object Frege

Wittgenstein’s Tractatus Propositions States of affairs are pictures of

The Oil-Painting Principle in a directly depicting language all well-formed parts of a true formula are also true A new sort of mereological inference rule – the key to the idea of a directly depicting language – presupposes that parthood is determinate

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A directly depicting language may contain an analogue of conjunction p and q _______ p

but it can contain no negation p _______ p

and also no disjunction p or q ______ p

The idea of a directly depicting language suggests a new method of constituent ontology: to study a domain ontologically is to establish the parts of the domain and the interrelations between them

BFO Basic Formal Ontology = a formal ontological theory, expressed in a directly depicting language, of all parts of reality (a great mirror)

John lived in Atlanta for 25 years The Problem John lived in Atlanta for 25 years

John lived in Atlanta for 25 years The Problem John lived in Atlanta for 25 years substances, things, objects PARTHOOD NOT DETERMINATE

John lived in Atlanta for 25 years The Problem John lived in Atlanta for 25 years process state

Substances and processes exist in time in different ways

SNAP and SPAN Substances and processes Continuants and occurrents In preparing an inventory of reality we keep track of these two different categories of entities in two different ways

A Popular Solution

Fourdimensionalism – 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

Parts of processes (1) a c b a: scattered part b: temporal slice c: boundary

Parts of processes (2) a a: sub-process b b: phase

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

4-Dism –>There is no change That the water boils means: Not: the water is colder at one time and hotter at another time Rather: that one phase of the boiling process is cold and another hot as one part of a colored ribbon is red and another blue

The Parable of Little Tommy’s Christmas Present

Eliminativism a sort of adolescent rebellion a product of physics envy we must simplify reality for the sake of the software

Fourdimensionalism rests on a misunderstanding of physics (both of relativity theory and of quantum mechanics) and on a misunderstanding of the status of Newtonian physics

Confession Some of my best friends are fourdimensionalists Fourdimensionalism is right in everything it says But incomplete

Realist Perspectivalism There is a multiplicity of ontological perspectives on reality, all equally veridical = transparent to reality

Need for different perspectives Not one ontology, but a multiplicity of complementary ontologies Cf. Quantum mechanics: particle vs. wave ontologies

Two Orthogonal, Complementary Perspectives SNAP and SPAN

Substances and processes exist in time in different ways

Snapshot Video ontology ontology t i m e process substance

SNAP and SPAN Substances and processes Continuants and occurrents In preparing an inventory of reality we keep track of these two different categories of entities in two different ways

commodities and services anatomy and physiology SNAP and SPAN stocks and flows commodities and services product and process anatomy and physiology

SNAP and SPAN the lobster and its growth the nation and its history a population and its migration the ocean and its tide(s)

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

Substances vs. their lives SNAP vs. SPAN Substances vs. their lives

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

Change Adding SNAP to the fourdimensionalist perspective makes it possible to recognize the existence of change (SNAP entities are that which endure, thus providing identity through change) SNAP ontologies provide perspective points – landmarks in the flux – from which SPAN processes can be apprehended as changes

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

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

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

SPQR… entities States, powers, qualities, roles … Substances are independent SPQR entities are dependent on substances, they have a parasitic existence: a smile smiles only in a human face

Other SPQR… entities: functions, dispositions, plans, shapes SPQR… entities are all dependent on substances one-place SPQR entities: temperature, color, height

Substances and SPQR… entities Substances are the bearers or carriers of, SPQR… entities ‘inhere’ in their substances

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

Ontological Dependence Substances are that which can exist on their own SPQR… entities require a support from substances in order to exist Dependence can be specific or generic

Generic dependence of relational SPQR… entities legal systems languages (as systems of competences) religions (as systems of beliefs)

Ontological Dependence Substances are such that, while remaining numerically one and the same, they can admit contrary qualities at different times … I am sometimes hungry, sometimes not

Substances can also gain and lose parts … as an organism may gain and lose molecules

Dependence process a thought cannot exist without a thinker substance

Spatial regions, niches, environments Organisms evolve into environments SNAP Scientific Disciplines Atomic physics Cell biology Island biogeography

SPAN scientific disciplines Thermodynamics Wave Mechanics Physiology Also FIELD disciplines: Quantum Field Theory

each SNAP section through reality includes everything which exists (present tense)

each section through reality is to be conceived in presentist terms each section includes everything which exists at the corresponding now

mereology works without restriction in every instantaneous 3-D section through reality

Problem of identity over time for substances What is it in virtue of which John is identical from one SNAP ontology to the next?

Many SNAP Ontologies t3 t2 t1 here time exists outside the ontology, as an index or time-stamp

SNAP ontology = a sequence of snapshots

Examples of simple SNAP ontologies space

Examples of simple SNAP ontologies

Examples of simple SNAP ontologies

The SPAN Ontology t i m e

The SPAN ontology here time exists as part of the domain of the ontology

Processes demand 4D-partonomies t i m e

many smeered boundaries SNAP ontology many sharp boundaries SPAN ontology many smeered boundaries

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

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

boundaries are mostly fiat everything is flux t i m e

mereology works without restriction everywhere here t i m e clinical trial

Some clean joints derive from the fact that processes are dependent on substances (my headache is cleanly demarcated from your headache)

Some clean joints in realms of artefactual processes: weddings chess games dog shows ontology tutorials sharp divisions imputed via clocks, calendars

Clean joints also through language = fiat demarcations Quinean gerrymandering ontologies are attractive for processes not for substances Quine: there are no substances

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

Example: the Ontology of War needs both continuants (army, battle-group , materiel, morale, readiness, battlespace …) and occurrents (manoeuvre, campaign, supply, trajectory, death …)

Battalion moves from A to B t i m e invasion

Processes, like substances, are concrete denizens of reality My headache, like this lump of cheese, exists here and now, and both will cease to exist at some time in the future. But they exist in time in different ways

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

Three kinds of SNAP entities Substances SPQR… entities Spatial regions, Contexts, Niches

SNAP

SPAN: Entities extended in time

SPAN: Entities extended in time

SPAN: Entities extended in time

3-dimensional and 4-dimensional environments “Lobsters have evolved into environments marked by cyclical patterns of temperature change” The Afghan winter The window of opportunity for an invasion of Iraq

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

Participation SNAP-ti. SPAN substances x, y participate in process B time SPAN B time B x y substances x, y participate in process B x y SNAP-ti.

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 the application of a therapy the course of a disease

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

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

instruction and operation score and performance algorith and execution

provide the principles of individuation for SPAN entities SNAP entities provide the principles of individuation for SPAN entities

Movement to location y begins movement ends from location x

Creation process P initiates a, a's birth at t2 SNAP-t1 t2>t1 R SNAP-t2 process P initiates a, a's birth at t2 a's life overlaps process P

Some ontological consequences

Granularity parts of substances are always substances spatial region

Granularity parts of spatial regions are always spatial regions substance parts of spatial regions are always spatial regions

Granularity process parts of processes are always processes

Relations crossing the SNAP/SPAN border are never part-relations MORAL Relations crossing the SNAP/SPAN border are never part-relations

Relations crossing the SNAP/SPAN border are never part-relations substance John John’s life sustaining in existence physiological processes

problem cases traffic jam forest fire anthrax epidemic hurricane Maria waves shadows

forest fire: a process a pack of monkeys jumping from tree to tree the Olympic flame: a process or a thing? anthrax spores are little monkeys

hurricanes why do we give an entity a proper name? because it is 1) important, 2) such that we want to re-identify it when it reappears at a later time

How do we glue these two different sorts of entities together mereologically? How do we include them both in a single inventory of reality

How do we fit these two entities together within a single system of representations? within a directly depicting language?

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?

Main problem English swings back and forth between two distinct depictions of reality … imposing both 3-D partitions (yielding substances) and 4-D partitions (yielding processes) at the same time

Main problem There is a polymorphous ontological promiscuity of the English sentence, which is inherited also by the form ‘F(a)’ of standard predicate logic

Against Fantology For the fantologist “(F(a)”, “R(a,b)” … is the description language for ontology The fantologist sees reality as being made up of atoms plus abstract (1- and n-place) ‘properties’ or ‘attributes’ … confuses logical form with ontological form

Formalizing time F(a,b) at t F(a,b,t) F(a@t,b@t)

John lived in Atlanta for 25 years

F(a@t,b@t) – stage ontology Formalizing time F(a,b) at t – SNAP F(a,b,t) – Eternalism(?) F(a@t,b@t) – stage ontology

Two alternative basic ontologies both of which are able to sustain a directly depicting language plus a system of meta-relations for building bridges between the two ontologies via: dependence participation initiation etc.

Three views/partitions of the same reality

species, genera instances substance organism animal mammal cat frog siamese frog instances

common nouns proper names substance organism animal mammal cat pekinese mammal cat organism substance animal common nouns proper names Common nouns

types substance organism animal cat mammal siamese frog tokens

Accidents: Species and instances substance animal mammal human Irishman Accidents: Species and instances types this individual token man tokens

There are universals both among substances (man, mammal) and among processes (run, movement)

Substance universals pertain to what a thing is at all times at which it exists: cow man rock planet VW Golf

Note use of ‘substance’ in the sense of ‘thing’, ‘object’ count sense of substance vs. mass sense of substance (‘milk’, ‘gold’)

red hot suntanned spinning Quality universals pertain to how a thing is at some time at which it exists: red hot suntanned spinning Clintophobic Eurosceptic

Qualities, too, instantiate genera and species Thus quality universals form trees

quality color red scarlet R232, G54, B24

qualities too are distinguished as between tokens and types which is to say: between genera and species on the one hand, ... and instances on the other

Accidents: Species and instances quality color red scarlet R232, G54, B24 this individual accident of redness (this token redness – here, now)

One plus Nine Categories (AQL) quid? substance quale? quality quantum? quantity ad quid? relation ubi? place quando? time in quo situ? status/context in quo habitu? habitus quid agit? action quid patitur? passion

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 Events Processes “Everything is flux” Universal Particular

An adequate ontology of geography has to have three components: SNAP GeO SPAN GeO FIELD GeO

GeO

SNAP GeO

SPAN GeO

FIELD GeO

A good formal ontology must divide into two sub-ontologies: 1. a four-dimensionalist ontology (of processes) cf. Quine 2. a modified presentist ontology cf. Brentano, Aristotle, Chisholm (takes tense seriously)

These represent two views of the same rich and messy reality, the reality captured promiscuously by natural language sentences