SNAP and SPAN Barry Smith 1 http ifomis

SNAP and SPAN Barry Smith 1

http: //ifomis. de Institute for Formal Ontology and Medical Information Science Faculty of Medicine University of Leipzig 2

Reality 3

Reality 4

Reality 6

Reality is complicated 7

What is the best language to describe this complexity? 8

Formal ontology formalized + domain-independent 9

Formal Ontology Examples of categories: Substance, Process, Agent, Property, Relation, Location, Spatial Region Part-of, Boundary-of 10

Material Ontology = regional or domain-specific e. g. Ge. O Examples of categories: River, Mountain, Country, Desert … Resides-In, Is-to-the-West-of 11

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” 12

Need for different perspectives Double counting: 3 apples on the table 7 x 1016 molecules at spatial locations L 1, L 2 and L 3 Not one ontology, but a multiplicity of complementary ontologies Cf. Quantum mechanics: particle vs. wave ontologies 13

Cardinal Perspectives Formal vs. Material Micro- vs. Meso- vs. Macro SNAP vs. SPAN 14

A Network of Domain Ontologies BFO = Basic Formal Ontology 15

A Network of Domain Ontologies Med. O BFO 16

A Network of Domain Ontologies Med. O Ge. O BFO 17

A Network of Domain Ontologies Med. O Ge. O BFO Lex. O 18

A Network of Domain Ontologies Med. O Ge. O BFO Mil. O Lex. O 19

A Network of Domain Ontologies Med. O Ge. O Ec. O BFO Mil. O Lex. O 20

Agr. O Psych. O 21

Cardinal Perspectives Formal vs. Material Ontologies Granularity(Microvs. Mesovs. Macro) SNAP vs. SPAN 22

Ontological Zooming 23

Ontological Zooming medicine cell biology 24

Ontological Zooming both are transparent partitions of one and the same reality 25

Cardinal Perspectives Formal vs. Material Ontologies Granularity(Microvs. Mesovs. Macro) Time: SNAP vs. SPAN 26

Ontology seeks an INVENTORY OF REALITY Relevance of ontology for information systems, e. g. : terminology standardization taxonomy standardization supports reasoning about reality 27

Semantic Web Ontoweb OWL DAML+OIL … these are standardized languages only – not themselves ontologies 28

Ontology research marked by ad hoc-ism 29

IFOMIS Strategy get real ontology right first and then investigate ways in which this real ontology can be translated into computeruseable form later DO NOT ALLOW ISSUES OF COMPUTERTRACTABILITY TO DETERMINE THE CONTENT OF THE ONTOLOGY IN ADVANCE 30

a language to map these Formal-ontological structures in reality 31

a directly depicting language ‘John’ ‘( ) is red’ Object Property Frege 32

Wittgenstein’s Tractatus Propositions are pictures of States of affairs 33

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 34

A directly depicting language may contain an analogue of conjunction p and q _______ p 36

but it can contain no negation p _______ p 37

and also no disjunction p or q ______ p 38

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 39

BFO Basic Formal Ontology = a formal ontological theory, expressed in a directly depicting language, of all parts of reality (a great mirror) 40

The Problem John lived in Atlanta for 25 years 41

The Problem John lived in Atlanta for 25 years substances, things, objects PARTHOOD NOT DETERMINATE 42

The Problem John lived in Atlanta for 25 years process state 43

Substances and processes ti m e exist in time in different ways process substance 44

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 45

A Popular Solution 46

Fourdimensionalism – time is just another dimension, analogous to the three spatial dimensions – only processes exist – substances are analyzed away as worms/fibers within the fourdimensional process plenum 47

Parts of processes (1) a c a b a: scattered part b: temporal slice c: boundary 48

Parts of processes (2) a: sub-process b: phase a b 49

There are no substances Bill Clinton does not exist Rather: there exists within the fourdimensional plenum a continuous succession of processes which are similar in Billclintonizing way 50

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 another hot as one part of a colored ribbon is red another blue 51

The Parable of Little Tommy’s Christmas Present 52

Eliminativism 1. a sort of adolescent rebellion 2. a product of physics envy 3. we must simplify reality for the sake of the software 53

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 54

Confession Some of my best friends are fourdimensionalists Fourdimensionalism is right in everything it says But incomplete 55

Realist Perspectivalism There is a multiplicity of ontological perspectives on reality, all equally veridical = transparent to reality 56

Need for different perspectives Not one ontology, but a multiplicity of complementary ontologies Cf. Quantum mechanics: particle vs. wave ontologies 57

Two Orthogonal, Complementary Perspectives SNAP and SPAN 58

Substances and processes ti m e exist in time in different ways process substance 59

Video ontology ti m e Snapshot ontology process substance 60

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 61

SNAP and SPAN stocks and flows commodities and services product and process anatomy and physiology 62

SNAP and SPAN the lobster and its growth the nation and its history a population and its migration the ocean and its tide(s) 63

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 64

SNAP vs. SPAN 1. SNAP: a SNAPshot ontology of endurants existing at a time 2. SPAN: a four-dimensionalist ontology of processes 65

SNAP vs. SPAN Substances vs. their lives 66

You are a substance Your life is a process You are 3 -dimensional Your life is 4 -dimensional 67

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 68

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 69

How do you know whether an entity is SNAP or SPAN? 70

Three kinds of SNAP entities 1. Substances 2. SPQR… entities 3. Spatial regions, contexts, niches, environments 71

SPQR… entities States, powers, qualities, roles … Substances are independent SPQR entities are dependent on substances, they have a parasitic existence: a smiles only in a human face 72

Other SPQR… entities: functions, dispositions, plans, shapes SPQR… entities are all dependent on substances one-place SPQR entities: temperature, color, height 73

Substances and SPQR… entities Substances are the bearers or carriers of, SPQR… entities ‘inhere’ in their substances 74

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 75

relational SPQR… entities love John Mary stand in relations of one-sided dependence to a plurality of substances simultaneously 76

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 77

Generic dependence of relational SPQR… entities legal systems languages (as systems of competences) religions (as systems of beliefs) 78

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 79

Substances can also gain and lose parts … as an organism may gain and lose molecules 80

Dependence a thought process cannot exist without a thinker substance 81

Spatial regions, niches, environments Organisms evolve into environments SNAP Scientific Disciplines Atomic physics Cell biology Island biogeography 82

SPAN scientific disciplines Thermodynamics Wave Mechanics Physiology Also FIELD disciplines: Quantum Field Theory 83

each SNAP section through reality includes everything which exists (present tense) 84

each section through reality is to be conceived in presentist terms each section includes everything which exists at the corresponding now 85

mereology works without restriction in every instantaneous 3 -D section through reality 86

Problem of identity over time for substances What is it in virtue of which John is identical from one SNAP ontology to the next? 88

Many SNAP Ontologies t 3 t 2 t 1 here time exists outside the ontology, 89 as an index or time-stamp

SNAP ontology = a sequence of snapshots 90

Examples of simple SNAP ontologies space 91

Examples of simple SNAP ontologies 94

Examples of simple SNAP ontologies 95

The SPAN Ontology time 96

The SPAN ontology here time exists as part of the domain 97 of the ontology

Processes demand 4 D-partonomies time 98

SNAP ontology many sharp boundaries SPAN ontology many smeered boundaries 99

Substances Mesoscopic reality is divided at its natural joints into substances: animals, bones, rocks, potatoes 100

The Ontology of Substances form natural kinds (universals, species + genera) 101

Processes merge into one another Process kinds merge into one another … few clean joints either between instances or between types 102

boundaries are mostly fiat everything is flux time 103

mereology works without restriction everywhere clinical trial time 104

Some clean joints derive from the fact that processes are dependent on substances (my headache is cleanly demarcated from your headache) 105

Some clean joints in realms of artefactual processes: weddings chess games dog shows ontology tutorials sharp divisions imputed via clocks, calendars 106

Clean joints also through language = fiat demarcations Quinean gerrymandering ontologies are attractive for processes not for substances Quine: there are no substances 107

SNAP entities provide the principles of individuation/segmentation for SPAN entities No change without some THING or QUALITY which changes identity-based change 108

Processes, too, are dependent on substances One-place vs. relational processes One-place processes: getting warmer getting hungrier 109

Examples of relational processes kissings, thumps, conversations, dances, Such relational processes join their carriers together into collectives of greater or lesser duration 110

Example: the Ontology of War needs both continuants (army, battlegroup , materiel, morale, readiness, battlespace …) and occurrents (manoeuvre, campaign, supply, trajectory, death …) 111

Battalion moves from A to B invasion time 112

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 113

SNAP and SPAN ontologies are partial only Each is a window on that dimension of reality which is visible through the given ontology (Realistperspectivalism ) 114

SNAP: Entities existing in toto at a time 115

Three kinds of SNAP entities 1. Substances 2. SPQR… entities 3. Spatial regions, Contexts, Niches 116

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SNAP 119

SPAN: Entities extended in time 120

SPAN: Entities extended in time 121

SPAN: Entities extended in time 122

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 123

Relations between SNAP and SPAN SNAP-entities participate in processes they have lives, histories 124

Participation B x y time SNAP-ti. SPAN substances x, y participate in process B 125

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 126

SPQR… entities and their SPAN realizations function role plan disposition therapy disease SNAP 127

SPQR… entities and their SPAN realizations expression exercise execution realization application course SPAN 128

instruction and operation score and performance algorith and execution 129

SNAP entities provide the principles of individuation for SPAN entities 130

Movement to location y ends from location t n e m e v o m x begins 131

Creation process P initiates a, a's birth at t 2 a's life overlaps process P R t 2>t 1 SNAP-t 2 R t 1 SNAP-t 1 132

Some ontological consequences 133

Granularity spatial region substance parts of substances are always substances 134

Granularity spatial region substance parts of spatial regions are always spatial regions 135

Granularity process parts of processes are always processes 136

MORAL Relations crossing the SNAP/SPAN border are never part-relations 137

Relations crossing the SNAP/SPAN border are never part-relations substance John’s life sus tain ing in e xis ten ce physiological processes 138

problem cases traffic jam forest fire anthrax epidemic hurricane Maria waves shadows 139

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 140

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 141

How do we glue these two different sorts of entities together mereologically? How do we include them both in a single inventory of reality 142

How do we fit these two entities together within a single system of representations? within a directly depicting language? 143

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? 144

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 145

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 146

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 147

Formalizing time F(a, b) at t F(a, b, t) F(a@t, b@t) 148

John lived in Atlanta for 25 years 149

Formalizing time F(a, b) at t – SNAP F(a, b, t) – Eternalism(? ) F(a@t, b@t) – stage ontology 150

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. 151

Three views/partitions of the same reality 152

species, genera substance organism animal mammal cat siamese frog instances 153

common nouns substance Common nouns organism animal mammal cat pekinese proper names 154

types substance organism animal mammal cat siamese frog tokens 155

substance Accidents: Species and instances animal types mammal human Irishman this individual token man tokens 156

There are universals both among substances (man, mammal) and among processes (run, movement) 157

Substance universals pertain to what a thing is at all times at which it exists: cow man rock planet VW Golf 158

Note use of ‘substance’ in the sense of ‘thing’, ‘object’ count sense of substance vs. mass sense of substance (‘milk’, ‘gold’) 159

Quality universals pertain to how a thing is at some time at which it exists: red hot suntanned spinning Clintophobic Eurosceptic 160

Qualities, too, instantiate genera and species Thus quality universals form trees 161

quality color red scarlet R 232, G 54, B 24 162

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 163

Accidents: Species and instances quality color red scarlet R 232, G 54, B 24 this individual accident of redness (this token redness – here, now) 164

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 165

Not in a Subject Substantial In a Subject Accidental Said of a Second Substances Subject Universal, man, General, horse, Type mammal Non-substantial Universals Not said First Substances of a Subject this individual Particular, man, this horse Individual, this mind, this body Token Individual Accidents whiteness, knowledge this individual whiteness, knowledge of grammar 166

Particular Universal Aristotle’s Ontological Square Substantial Accidental Second substance man cat ox First substance this man this cat this ox Second accident headache sun-tan dread First accident this headache this sun-tan this dread 167

Particular Universal Refining the Ontological Square Substantial Accidental Second substance man cat ox First substance this man this cat this ox Second accident headache sun-tan dread First accident this headache this sun-tan this dread 172

Refining the Ontological Square Substantial Exercise of power Exercise of function Movement Action Occurrents Continuants Dependent Entities Substances Collectives Undetached parts Substantial boundaries Powers Functions Qualities Shapes 173

Refining the Ontological Square Substantial Exercise of power Exercise of function Movement Action Occurrents Continuants Moments (Dependent) Substances Collectives Undetached parts Substantial boundaries Powers Functions Qualities Shapes 174

Refining the Ontological Square Substantial Exercise of power Exercise of function Movement Action Processes? Occurrents Continuants Dependent Entities Substances Collectives Undetached parts Substantial boundaries Powers Functions Qualities Shapes Moments? 175

Refining the Ontological Square Continuants Occurrents Substantial Dependent Entities John‘s reddening John‘s blushing John‘s bruising 4 -D Substances John‘s redness Collectives John‘s blush Undetached parts John‘s bruise Substantial boundaries 3 -D 176

Refining the Ontological Square Substantial John‘s reddening John‘s blushing John‘s bruising Occurrents Continuants Dependent Entities 4 -D (perduring) Stuff (Blood, Snow, Tissue) Mixtures Holes John‘s redness John‘s blush John‘s bruise 3 -D (enduring) 177

A Refined Ontological Square Substantial John‘s reddening John‘s blushing John‘s bruising Occurrents Continuants Dependent Entities 4 -D (perduring) Stuff (Blood, Snow, Tissue) Mixtures Holes John‘s redness John‘s blush John‘s bruise 3 -D (enduring) 178

Some philosophers accept only part of the Aristotelian multi-categorial ontology 180

Standard Predicate Logic – F(a), R(a, b). . . Substantial Attributes F, G, R Universal Particular Accidental Individuals a, b, c this, that 181

Bicategorial Nominalism Accidental Particular Universal Substantial First substance this man this cat this ox First accident this headache this sun-tan this dread 182

Process Metaphysics Accidental Particular Universal Substantial Events Processes “Everything is flux” 183

An adequate ontology of geography has to have three components: SNAP Ge. O SPAN Ge. O FIELD Ge. O 184

Ge. O 185

SNAP Ge. O 186

SPAN Ge. O 187

FIELD Ge. O 188

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) 189