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SNAP and SPAN. Barry Smith . 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?. Formal ontology.

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snap and span

SNAP and SPAN

Barry Smith

http ifomis de
http://ifomis.de
  • Institute for Formal Ontology and Medical Information Science
  • Faculty of Medicine
  • University of Leipzig
reality7
Reality

is complicated

formal ontology
Formal ontology
  • formalized + domain-independent
formal ontology10
Formal Ontology
  • Examples of categories:
  • Substance, Process, Agent, Property, Relation, Location, Spatial Region
  • Part-of, Boundary-of
material ontology
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
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
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
Cardinal Perspectives
  • Formal vs. Material
  • Micro- vs. Meso- vs. Macro
  • SNAP vs. SPAN
a network of domain ontologies
A Network of Domain Ontologies

BFO = Basic Formal Ontology

slide21
AgrO
  • PsychO
cardinal perspectives22
Cardinal Perspectives

Formal vs. Material Ontologies

Granularity (Micro vs. Meso vs. Macro)

SNAP vs. SPAN

ontological zooming25
Ontological Zooming

both are transparent partitions of one and the same reality

cardinal perspectives26
Cardinal Perspectives

Formal vs. Material Ontologies

Granularity (Micro vs. Meso vs. Macro)

Time: SNAP vs. SPAN

ontology
Ontology
  • seeks an INVENTORY OF REALITY
  • Relevance of ontology for information systems, e.g.:
  • terminology standardization
  • taxonomy standardization
  • supports reasoning about reality
semantic web
Semantic Web
  • Ontoweb
  • OWL
  • DAML+OIL
  • these are standardized languages only – not themselves ontologies
ontology research
Ontology research
  • marked by ad hoc-ism
ifomis strategy
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
a language to map these
  • Formal-ontological structures in reality
a directly depicting language

Property

Object

a directly depicting language
  • ‘John’ ‘( ) is red’

Frege

wittgenstein s tractatus

are pictures of

Wittgenstein’s Tractatus
  • Propositions
  • States of affairs
the oil painting principle
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

a directly depicting language36
A directly depicting language
  • may contain an analogue of conjunction
  • p and q
  • _______
  • p
and also no disjunction
and also no disjunction
  • p or q
  • ______
  • p
the idea of a directly depicting language
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
slide40

BFO

  • Basic Formal Ontology
  • = a formal ontological theory, expressed in a directly depicting language, of all parts of reality
  • (a great mirror)
the problem
The Problem
  • John lived in Atlanta for 25 years
the problem42
The Problem
  • John lived in Atlanta for 25 years
  • substances, things, objects
  • PARTHOOD NOT DETERMINATE
the problem43
The Problem
  • John lived in Atlanta for 25 years
  • process
  • state
snap and span45
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
fourdimensionalism
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
slide48

a

c

b

a

a: scattered part

b: temporal slice

c: boundary

Parts of processes (1)

slide49

a: sub-process

b: phase

a

b

Parts of processes (2)

there are no substances
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
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
eliminativism
Eliminativism
  • a sort of adolescent rebellion
  • a product of physics envy
  • we must simplify reality for the sake of the software
fourdimensionalism54
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
Confession
  • Some of my best friends are fourdimensionalists
  • Fourdimensionalism is right in everything it says
  • But incomplete
realist perspectivalism56
Realist Perspectivalism

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

need for different perspectives57
Need for different perspectives
  • Not one ontology, but a multiplicity of complementary ontologies
  • Cf. Quantum mechanics: particle vs. wave ontologies
snap and span61
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
snap and span62
SNAP and SPAN
  • stocks and flows
  • commodities and services
  • product and process
  • anatomy and physiology
snap and span63
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 span64
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 vs. SPAN
  • SNAP: a SNAPshot ontology of endurants existing at a time
  • SPAN: a four-dimensionalist ontology of processes
snap vs span66
SNAP vs. SPAN
  • Substances vs. their lives
you are a substance
You are a substance
  • Your life is a process
  • You are 3-dimensional
  • Your life is 4-dimensional
change
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
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
three kinds of snap entities
Three kinds of SNAP entities
  • Substances
  • SPQR… entities
  • Spatial regions, contexts, niches, environments
spqr entities
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
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 and SPQR… entities
  • Substances are the bearers or carriers of,
  • SPQR… entities ‘inhere’ in their substances
one place spqr entities
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
slide76

love

John

Mary

  • relational SPQR… entities

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

ontological dependence
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
Generic dependence of relational SPQR… entities
  • legal systems
  • languages (as systems of competences)
  • religions (as systems of beliefs)
ontological dependence79
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
Substances
  • can also gain and lose parts
  • … as an organism may gain and lose molecules
dependence
Dependence

process

a thought

cannot exist without a thinker

substance

spatial regions niches environments
Spatial regions, niches, environments
  • Organisms evolve into environments
  • SNAP Scientific DisciplinesAtomic physics
  • Cell biology
  • Island biogeography
span scientific disciplines
SPAN scientific disciplines
  • Thermodynamics
  • Wave Mechanics
  • Physiology
  • Also FIELD disciplines:
  • Quantum Field Theory
problem of identity over time for substances
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
Many SNAP Ontologies

t3

t2

t1

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

the span ontology97
The SPAN ontology

here time exists as part of the domain of the ontology

snap ontology
SNAP ontology
  • many sharp boundaries
  • SPAN ontology
  • many smeered boundaries
substances100
Substances
  • Mesoscopic reality is
  • divided at its natural joints
  • into substances:
  • animals, bones, rocks, potatoes
the ontology of substances
The Ontology of Substances
  • Substances form natural kinds
  • (universals, species + genera)
processes
Processes
  • Processes merge into one another
  • Process kinds merge into one another
  • … few clean joints either between instances or between types
some clean joints
Some clean joints
  • derive from the fact that processes are dependent on substances
  • (my headache is cleanly demarcated from your headache)
some clean joints106
Some clean joints
  • in realms of artefactual processes:
  • weddings
  • chess games
  • dog shows
  • ontology tutorials
  • sharp divisions imputed via clocks, calendars
clean joints
Clean joints
  • also through language
  • = fiat demarcations
  • Quinean gerrymandering ontologies are attractive for processes
  • not for substances
  • Quine: there are no substances
snap entities
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
Processes, too, are dependent on substances
  • One-place vs. relational processes
  • One-place processes:
  • getting warmer
  • getting hungrier
examples of relational processes
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
Example: the Ontology of War
  • needs both continuants (army, battle-group , materiel, morale, readiness, battlespace …)
  • and occurrents (manoeuvre, campaign, supply, trajectory, death …)
processes like substances are concrete denizens of reality
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
slide114

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)
three kinds of snap entities116
Three kinds of SNAP entities
  • Substances
  • SPQR… entities
  • Spatial regions, Contexts, Niches
3 dimensional and 4 dimensional environments
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
Relations between SNAP and SPAN

SNAP-entities participate in processes

they have lives, histories

participation

B

B

x

x

y

y

time

time

SNAP-ti.

SPAN

substances x, y participate in process B

Participation
spqr entities and their span realizations
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 realizations127

SNAP

SPQR… entities and their SPAN realizations
  • function
  • role
  • plan
  • disposition
  • therapy
  • disease
spqr entities and their span realizations128
SPQR… entities and their SPAN realizations
  • expression
  • exercise
  • execution
  • realization
  • application
  • course

SPAN

slide129
instruction and operation
  • score and performance
  • algorith and execution
snap entities130
SNAP entities
  • provide the principles of individuation for SPAN entities
movement

to location

y

from location

movement

x

begins

Movement

ends

slide132

Creation

process P initiates a,

a\'s birth at t2

a\'s life overlaps process P

R

SNAP-t2

t2>t1

R

t1

SNAP-t1

granularity
Granularity

spatial region

substance

parts of substances are always substances

granularity135
Granularity

spatial region

substance

parts of spatial regions are always spatial regions

granularity136
Granularity

process

parts of processes are always processes

moral
MORAL
  • Relations crossing the SNAP/SPAN border are never part-relations
relations crossing the snap span border are never part relations

substance John

sustaining in existence

physiological processes

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

John’s life

problem cases
problem cases
  • traffic jam
  • forest fire
  • anthrax epidemic
  • hurricane Maria
  • waves
  • shadows
forest fire
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
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
slide142
How do we glue these two different sorts of entities together mereologically?
  • How do we include them both in a single inventory of reality
slide143

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 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
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 problem146
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
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 time150
Formalizing time
two alternative basic ontologies
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.
species genera

substance

organism

animal

cat

siamese

species, genera

mammal

frog

instances

common nouns

substance

organism

mammal

animal

cat

pekinese

common

nouns

proper names

Common nouns
types

substance

organism

animal

cat

siamese

types

mammal

frog

tokens

accidents species and instances

substance

animal

mammal

human

Irishman

this individual token man

Accidents: Species and instances

types

tokens

there are universals
There are universals
  • both among substances (man, mammal)
  • and among processes (run, movement)
substance universals
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
Note use of ‘substance’
  • in the sense of ‘thing’, ‘object’
  • count sense of substance vs.
  • mass sense of substance
  • (‘milk’, ‘gold’)
quality universals
Quality universals
  • pertain to how a thing is at some time at which it exists:

red hot suntanned spinning

ClintophobicEurosceptic

qualities too instantiate genera and species
Qualities, too, instantiate genera and species
  • Thus quality universals form trees
slide162

quality

color

red

scarlet

R232, G54, B24

qualities too are distinguished as between tokens and types
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 instances164
Accidents: Species and instances

quality

color

red

scarlet

R232, G54, B24

this individual accident of redness

(this token redness – here, now)

slide166

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 SubjectParticular, Individual,

Token

First Substances

this individual

man, this horse

this mind, this body

Individual Accidents

this individual

whiteness, knowledge

of grammar

refining the ontological square173
Refining the Ontological Square

Occurrents

Continuants

refining the ontological square174
Refining the Ontological Square

Occurrents

Continuants

refining the ontological square175
Refining the Ontological Square

Occurrents

Continuants

refining the ontological square176
Refining the Ontological Square

Occurrents

Continuants

refining the ontological square177
Refining the Ontological Square

Occurrents

Continuants

a refined ontological square
A Refined Ontological Square

Occurrents

Continuants

some philosophers
Some philosophers
  • accept only part of the Aristotelian multi-categorial ontology
bicategorial nominalism
Bicategorial Nominalism

Universal

Particular

process metaphysics
Process Metaphysics

Universal

Particular

slide184

An adequate ontology of geography has to have three components:

SNAP GeO

SPAN GeO

FIELD GeO

a good formal ontology
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
These represent two views
  • of the same rich and messy reality, the reality captured promiscuously by natural language sentences
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