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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 l.jpg

SNAP and SPAN

Barry Smith


Http ifomis de l.jpg
http://ifomis.de

  • Institute for Formal Ontology and Medical Information Science

  • Faculty of Medicine

  • University of Leipzig





Reality7 l.jpg
Reality

is complicated



Formal ontology l.jpg
Formal ontology

  • formalized + domain-independent


Formal ontology10 l.jpg
Formal Ontology

  • Examples of categories:

  • Substance, Process, Agent, Property, Relation, Location, Spatial Region

  • Part-of, Boundary-of


Material ontology l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
Cardinal Perspectives

  • Formal vs. Material

  • Micro- vs. Meso- vs. Macro

  • SNAP vs. SPAN


A network of domain ontologies l.jpg
A Network of Domain Ontologies

BFO = Basic Formal Ontology







Slide21 l.jpg


Cardinal perspectives22 l.jpg
Cardinal Perspectives

Formal vs. Material Ontologies

Granularity (Micro vs. Meso vs. Macro)

SNAP vs. SPAN



Ontological zooming24 l.jpg

medicine

cell biology

Ontological Zooming


Ontological zooming25 l.jpg
Ontological Zooming

both are transparent partitions of one and the same reality


Cardinal perspectives26 l.jpg
Cardinal Perspectives

Formal vs. Material Ontologies

Granularity (Micro vs. Meso vs. Macro)

Time: SNAP vs. SPAN


Ontology l.jpg
Ontology

  • seeks an INVENTORY OF REALITY

  • Relevance of ontology for information systems, e.g.:

  • terminology standardization

  • taxonomy standardization

  • supports reasoning about reality


Semantic web l.jpg
Semantic Web

  • Ontoweb

  • OWL

  • DAML+OIL

  • these are standardized languages only – not themselves ontologies


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Ontology research

  • marked by ad hoc-ism


Ifomis strategy l.jpg
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 l.jpg
a language to map these

  • Formal-ontological structures in reality


A directly depicting language l.jpg

Property

Object

a directly depicting language

  • ‘John’ ‘( ) is red’

Frege


Wittgenstein s tractatus l.jpg

are pictures of

Wittgenstein’s Tractatus

  • Propositions

  • States of affairs


The oil painting principle l.jpg
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 l.jpg
A directly depicting language

  • may contain an analogue of conjunction

  • p and q

  • _______

  • p



And also no disjunction l.jpg
and also no disjunction

  • p or q

  • ______

  • p


The idea of a directly depicting language l.jpg
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 l.jpg

BFO

  • Basic Formal Ontology

  • = a formal ontological theory, expressed in a directly depicting language, of all parts of reality

  • (a great mirror)


The problem l.jpg
The Problem

  • John lived in Atlanta for 25 years


The problem42 l.jpg
The Problem

  • John lived in Atlanta for 25 years

  • substances, things, objects

  • PARTHOOD NOT DETERMINATE


The problem43 l.jpg
The Problem

  • John lived in Atlanta for 25 years

  • process

  • state


Substances and processes exist in time in different ways l.jpg

t i m e

process

Substances and processesexist in time in different ways

substance


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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 l.jpg
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 l.jpg

a

c

b

a

a: scattered part

b: temporal slice

c: boundary

Parts of processes (1)


Slide49 l.jpg

a: sub-process

b: phase

a

b

Parts of processes (2)


There are no substances l.jpg
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 l.jpg
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 l.jpg
Eliminativism

  • a sort of adolescent rebellion

  • a product of physics envy

  • we must simplify reality for the sake of the software


Fourdimensionalism54 l.jpg
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 l.jpg
Confession

  • Some of my best friends are fourdimensionalists

  • Fourdimensionalism is right in everything it says

  • But incomplete


Realist perspectivalism56 l.jpg
Realist Perspectivalism

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


Need for different perspectives57 l.jpg
Need for different perspectives

  • Not one ontology, but a multiplicity of complementary ontologies

  • Cf. Quantum mechanics: particle vs. wave ontologies



Substances and processes exist in time in different ways59 l.jpg

t i m e

process

Substances and processesexist in time in different ways

substance


Snapshot video ontology ontology l.jpg

t i m e

process

Snapshot Video ontology ontology

substance


Snap and span61 l.jpg
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 l.jpg
SNAP and SPAN

  • stocks and flows

  • commodities and services

  • product and process

  • anatomy and physiology


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SNAP and SPAN

  • the lobster and its growth

  • the nation and its history

  • a population and its migration

  • the ocean and its tide(s)


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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 l.jpg
SNAP vs. SPAN

  • SNAP: a SNAPshot ontology of endurants existing at a time

  • SPAN: a four-dimensionalist ontology of processes


Snap vs span66 l.jpg
SNAP vs. SPAN

  • Substances vs. their lives


You are a substance l.jpg
You are a substance

  • Your life is a process

  • You are 3-dimensional

  • Your life is 4-dimensional


Change l.jpg
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 l.jpg
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 l.jpg
Three kinds of SNAP entities

  • Substances

  • SPQR… entities

  • Spatial regions, contexts, niches, environments


Spqr entities l.jpg
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 l.jpg
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 l.jpg
Substances and SPQR… entities

  • Substances are the bearers or carriers of,

  • SPQR… entities ‘inhere’ in their substances


One place spqr entities l.jpg
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 l.jpg

love

John

Mary

  • relational SPQR… entities

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


Ontological dependence l.jpg
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 l.jpg
Generic dependence of relational SPQR… entities

  • legal systems

  • languages (as systems of competences)

  • religions (as systems of beliefs)


Ontological dependence79 l.jpg
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 l.jpg
Substances

  • can also gain and lose parts

  • … as an organism may gain and lose molecules


Dependence l.jpg
Dependence

process

a thought

cannot exist without a thinker

substance


Spatial regions niches environments l.jpg
Spatial regions, niches, environments

  • Organisms evolve into environments

  • SNAP Scientific DisciplinesAtomic physics

  • Cell biology

  • Island biogeography


Span scientific disciplines l.jpg
SPAN scientific disciplines

  • Thermodynamics

  • Wave Mechanics

  • Physiology

  • Also FIELD disciplines:

  • Quantum Field Theory


Each snap section through reality l.jpg

includes everything which exists

(present tense)

each SNAP section through reality


Each section through reality is to be conceived in presentist terms l.jpg

each section includes everything which exists

at the corresponding now

each section through reality is to be conceived in presentist terms



Problem of identity over time for substances l.jpg
Problem of identity over time for substances 3-D section through reality

  • What is it in virtue of which John is identical from one SNAP ontology to the next?


Many snap ontologies l.jpg
Many SNAP Ontologies 3-D section through reality

t3

t2

t1

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


Snap ontology a sequence of snapshots l.jpg
SNAP ontology = a sequence of snapshots 3-D section through reality


Examples of simple snap ontologies l.jpg

space 3-D section through reality

Examples of simple SNAP ontologies


Slide94 l.jpg

Examples of simple SNAP ontologies 3-D section through reality


Examples of simple snap ontologies95 l.jpg
Examples of simple SNAP ontologies 3-D section through reality


The span ontology l.jpg

t i m e 3-D section through reality

The SPAN Ontology


The span ontology97 l.jpg
The SPAN ontology 3-D section through reality

here time exists as part of the domain of the ontology


Processes demand 4d partonomies l.jpg

t i m e 3-D section through reality

Processes demand 4D-partonomies


Snap ontology l.jpg
SNAP ontology 3-D section through reality

  • many sharp boundaries

  • SPAN ontology

  • many smeered boundaries


Substances100 l.jpg
Substances 3-D section through reality

  • Mesoscopic reality is

  • divided at its natural joints

  • into substances:

  • animals, bones, rocks, potatoes


The ontology of substances l.jpg
The Ontology of Substances 3-D section through reality

  • Substances form natural kinds

  • (universals, species + genera)


Processes l.jpg
Processes 3-D section through reality

  • Processes merge into one another

  • Process kinds merge into one another

  • … few clean joints either between instances or between types


Boundaries are mostly fiat l.jpg

t i m e 3-D section through reality

boundaries are mostly fiat

everything is flux


Mereology works without restriction everywhere here l.jpg

clinical trial 3-D section through reality

t i m e

mereology works without restriction everywhere here


Some clean joints l.jpg
Some clean joints 3-D section through reality

  • derive from the fact that processes are dependent on substances

  • (my headache is cleanly demarcated from your headache)


Some clean joints106 l.jpg
Some clean joints 3-D section through reality

  • in realms of artefactual processes:

  • weddings

  • chess games

  • dog shows

  • ontology tutorials

  • sharp divisions imputed via clocks, calendars


Clean joints l.jpg
Clean joints 3-D section through reality

  • also through language

  • = fiat demarcations

  • Quinean gerrymandering ontologies are attractive for processes

  • not for substances

  • Quine: there are no substances


Snap entities l.jpg
SNAP entities 3-D section through reality

  • 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 l.jpg
Processes, too, are dependent on substances 3-D section through reality

  • One-place vs. relational processes

  • One-place processes:

  • getting warmer

  • getting hungrier


Examples of relational processes l.jpg
Examples of relational processes 3-D section through reality

  • kissings, thumps, conversations,

  • dances,

  • Such relational processes

  • join their carriers together into collectives of greater or lesser duration


Example the ontology of war l.jpg
Example: the Ontology of War 3-D section through reality

  • needs both continuants (army, battle-group , materiel, morale, readiness, battlespace …)

  • and occurrents (manoeuvre, campaign, supply, trajectory, death …)


Battalion moves from a to b l.jpg

invasion 3-D section through reality

t i m e

Battalion moves from A to B


Processes like substances are concrete denizens of reality l.jpg
Processes, like substances, are concrete denizens of reality 3-D section through 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 l.jpg

SNAP and SPAN ontologies are partial only 3-D section through reality

Each is a window on that dimension of reality which is visible through the given ontology

  • (Realist perspectivalism)


Slide115 l.jpg

SNAP: Entities existing 3-D section through realityin toto at a time


Three kinds of snap entities116 l.jpg
Three kinds of 3-D section through realitySNAP entities

  • Substances

  • SPQR… entities

  • Spatial regions, Contexts, Niches


Slide119 l.jpg

SNAP 3-D section through reality


Span entities extended in time l.jpg
SPAN: Entities extended in time 3-D section through reality


Span entities extended in time121 l.jpg
SPAN: Entities extended in time 3-D section through reality


Span entities extended in time122 l.jpg
SPAN: Entities extended in time 3-D section through reality


3 dimensional and 4 dimensional environments l.jpg
3-dimensional and 4-dimensional environments 3-D section through reality

  • “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 l.jpg
Relations between SNAP and SPAN 3-D section through reality

SNAP-entities participate in processes

they have lives, histories


Participation l.jpg

B 3-D section through reality

B

x

x

y

y

time

time

SNAP-ti.

SPAN

substances x, y participate in process B

Participation


Spqr entities and their span realizations l.jpg
SPQR… entities and their SPAN realizations 3-D section through reality

  • 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 l.jpg

SNAP 3-D section through reality

SPQR… entities and their SPAN realizations

  • function

  • role

  • plan

  • disposition

  • therapy

  • disease


Spqr entities and their span realizations128 l.jpg
SPQR… entities and their SPAN realizations 3-D section through reality

  • expression

  • exercise

  • execution

  • realization

  • application

  • course

SPAN


Slide129 l.jpg

  • instruction 3-D section through reality and operation

  • score and performance

  • algorith and execution


Snap entities130 l.jpg
SNAP entities 3-D section through reality

  • provide the principles of individuation for SPAN entities


Movement l.jpg

to location 3-D section through reality

y

from location

movement

x

begins

Movement

ends


Slide132 l.jpg

Creation 3-D section through reality

process P initiates a,

a's birth at t2

a's life overlaps process P

R

SNAP-t2

t2>t1

R

t1

SNAP-t1


Some ontological consequences l.jpg
Some ontological consequences 3-D section through reality


Granularity l.jpg
Granularity 3-D section through reality

spatial region

substance

parts of substances are always substances


Granularity135 l.jpg
Granularity 3-D section through reality

spatial region

substance

parts of spatial regions are always spatial regions


Granularity136 l.jpg
Granularity 3-D section through reality

process

parts of processes are always processes


Moral l.jpg
MORAL 3-D section through reality

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


Relations crossing the snap span border are never part relations l.jpg

substance John 3-D section through reality

sustaining in existence

physiological processes

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

John’s life


Problem cases l.jpg
problem cases 3-D section through reality

  • traffic jam

  • forest fire

  • anthrax epidemic

  • hurricane Maria

  • waves

  • shadows


Forest fire l.jpg
forest fire: 3-D section through reality

  • 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 l.jpg
hurricanes 3-D section through reality

  • 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 l.jpg


Slide143 l.jpg


Substances and processes form two distinct orders of being l.jpg
Substances and processes form two distinct orders of being system of representations?

  • 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 l.jpg
Main problem system of representations?

  • 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 l.jpg
Main problem system of representations?

  • 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 l.jpg
Against Fantology system of representations?

  • 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 l.jpg
Formalizing time system of representations?

  • F(a,b) at t

  • F(a,b,t)

  • F([email protected],[email protected])


John lived in atlanta for 25 years l.jpg
John lived in Atlanta for 25 years system of representations?


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Formalizing time system of representations?

  • F(a,b) at t – SNAP

  • F(a,b,t) – Eternalism(?)

  • F([email protected],[email protected]) – stage ontology


Two alternative basic ontologies l.jpg
Two alternative basic ontologies system of representations?

  • 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 l.jpg
Three views/partitions of the same reality system of representations?


Species genera l.jpg

substance system of representations?

organism

animal

cat

siamese

species, genera

mammal

frog

instances


Common nouns l.jpg

substance system of representations?

organism

mammal

animal

cat

pekinese

common

nouns

proper names

Common nouns


Types l.jpg

substance system of representations?

organism

animal

cat

siamese

types

mammal

frog

tokens


Accidents species and instances l.jpg

substance system of representations?

animal

mammal

human

Irishman

this individual token man

Accidents: Species and instances

types

tokens


There are universals l.jpg
There are universals system of representations?

  • both among substances (man, mammal)

  • and among processes (run, movement)


Substance universals l.jpg
Substance universals system of representations?

  • pertain to what a thing is at all times at which it exists:

cow man rock planet

VW Golf


Note use of substance l.jpg
Note use of ‘substance’ system of representations?

  • in the sense of ‘thing’, ‘object’

  • count sense of substance vs.

  • mass sense of substance

  • (‘milk’, ‘gold’)


Quality universals l.jpg
Quality universals system of representations?

  • pertain to how a thing is at some time at which it exists:

red hot suntanned spinning

ClintophobicEurosceptic


Qualities too instantiate genera and species l.jpg
Qualities, too, instantiate genera and species system of representations?

  • Thus quality universals form trees


Slide162 l.jpg

quality system of representations?

color

red

scarlet

R232, G54, B24


Qualities too are distinguished as between tokens and types l.jpg
qualities too are distinguished as between system of representations?tokens and types

  • which is to say: between genera and species on the one hand,

  • ... and instances on the other


Accidents species and instances164 l.jpg
Accidents system of representations?: 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 l.jpg
One plus Nine Categories (AQL) system of representations?


Slide166 l.jpg

Not in a Subject system of representations?

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


Aristotle s ontological square l.jpg
Aristotle system of representations?’s Ontological Square

Universal

Particular


Aristotle s ontological square168 l.jpg
Aristotle system of representations?’s Ontological Square

Universal

Particular


Aristotle s ontological square169 l.jpg
Aristotle system of representations?’s Ontological Square

Universal

Particular


Aristotle s ontological square170 l.jpg
Aristotle system of representations?’s Ontological Square

Universal

Particular


Aristotle s ontological square171 l.jpg
Aristotle system of representations?’s Ontological Square

Universal

Particular


Refining the ontological square l.jpg
Refining the Ontological Square system of representations?

Universal

Particular


Refining the ontological square173 l.jpg
Refining the Ontological Square system of representations?

Occurrents

Continuants


Refining the ontological square174 l.jpg
Refining the Ontological Square system of representations?

Occurrents

Continuants


Refining the ontological square175 l.jpg
Refining the Ontological Square system of representations?

Occurrents

Continuants


Refining the ontological square176 l.jpg
Refining the Ontological Square system of representations?

Occurrents

Continuants


Refining the ontological square177 l.jpg
Refining the Ontological Square system of representations?

Occurrents

Continuants


A refined ontological square l.jpg
A Refined Ontological Square system of representations?

Occurrents

Continuants


Aristotle s ontological square179 l.jpg
Aristotle system of representations?’s Ontological Square

Universal

Particular


Some philosophers l.jpg
Some philosophers system of representations?

  • accept only part of the Aristotelian multi-categorial ontology


Standard predicate logic f a r a b l.jpg
Standard Predicate Logic – F(a), R(a,b) ... system of representations?

Universal

Particular


Bicategorial nominalism l.jpg
Bicategorial system of representations?Nominalism

Universal

Particular


Process metaphysics l.jpg
Process Metaphysics system of representations?

Universal

Particular


Slide184 l.jpg

An adequate ontology of geography has to have three components:

SNAP GeO

SPAN GeO

FIELD GeO


Slide185 l.jpg
GeO components:


Snap geo l.jpg
SNAP GeO components:


Span geo l.jpg
SPAN GeO components:


Field geo l.jpg
FIELD GeO components:


A good formal ontology l.jpg
A good formal ontology components:

  • 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 l.jpg
These represent two views components:

  • of the same rich and messy reality, the reality captured promiscuously by natural language sentences


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