1 Part 3 Tools of Ontology: Universals, Partitions.

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Part 3

Tools of Ontology:

Universals, Partitions

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Porphyrian Hierarchy

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Linnaean Hierarchy

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Medical Diagnostic Hierarchy

a hierarchy in the realm of processes

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Species-genus hierarchies

capture the way the world is (Aristotelian realism)

– they depict the invariant structures/patterns/regularities in reality

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or: species-genus hierarchies

may capture the way the world should be

– by depicting the structures/patterns/regularities in the realm of standards, ideal cases, recipes

(cf. a hierarchy of medical therapies)

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Anglocentric (Aristotelian) Realism

The general terms of TEE (or many of them),

including terms like ‘Coca Cola’,

correspond to universals (species and genera, invariant patterns) in reality

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Two distinct realms of being

universals particulars

general individual

types tokens

species instances

essence fact

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siamese

mammal

cat

organism

substancespecies, genera

animal

instances

frog

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Common nouns

pekinese

mammal

cat

organism

substance

animal

common nouns

proper names

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siamese

mammal

cat

organism

substancetypes

animal

tokens

frog

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Accidents: Species and instances

substance

animal

mammal

human

Irishman

types

tokensthis individual token man

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There are universals

both among substances (man, mammal)

and among moments (run, movement)

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Substance universals

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

cow man rock planetVW Golf

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Note use of ‘substance’

in the sense of ‘thing’, ‘object’

count sense of substance vs.

mass sense of substance

(‘milk’, ‘gold’)

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Moment universals

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

red hot suntanned spinningClintophobic Eurosceptic

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Moments, too, instantiate genera and species

Thus moment universals form trees

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quality

color

red

scarlet

R232, G54, B24

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moments 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

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Accidents: Species and instances

quality

color

red

scarlet

R232, G54, B24

this individual accident of redness (this token redness – here, now)

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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

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Not in a SubjectSubstantial

In a SubjectAccidental

Said of a SubjectUniversal, 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

this individual whiteness, knowledge of grammar

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Aristotle’s Ontological SquareSubstantial 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

Uni

vers

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artic

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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

Uni

vers

alP

artic

ular

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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

Uni

vers

alP

artic

ular

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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

Uni

vers

alP

artic

ular

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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

Uni

vers

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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

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Substantial Dependent Entities

Exercise of power Exercise of function

Movement

Action

Substances

Collectives

Undetached parts

Substantial boundaries

Powers

Functions

Qualities

Shapes

Occ

urre

nts

Con

tinua

nts

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Substantial Moments (Dependent)


Movement

Action

Substances

Collectives

Undetached parts


Powers

Functions

Qualities

Shapes

Occ

urre

nts

Con

tinua

nts

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Movement

Action Processes?

Substances

Collectives

Undetached parts


Powers

Functions

Qualities

Shapes

Moments?

Occ

urre

nts

Con

tinua

nts

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John‘s reddening

John‘s blushing

John‘s bruising

4-DSubstances

Collectives

Undetached parts


John‘s redness

John‘s blush

John‘s bruise

3-D

Occ

urre

nts

Con

tinua

nts

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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)

Occ

urre

nts

Con

tinua

nts

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A Refined Ontological SquareSubstantial 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)

Occ

urre

nts

Con

tinua

nts

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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

Uni

vers

alP

artic

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Some philosophers

accept only part of the Aristotelian multi-categorial ontology

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Standard Predicate Logic – F(a), R(a,b) ...


Attributes

F, G, R

Individuals

a, b, c

this, that

Uni

vers

alP

artic

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Bicategorial Nominalism


First substance

this man

this cat

this ox

First accident

this headache

this sun-tan

this dread

Uni

vers

alP

artic

ular

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Process MetaphysicsSubstantial Accidental

Events

Processes

“Everything is flux”

Uni

vers

alP

artic

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Problems arise for such partial ontologies

arise only if they come along with the claim to be complete

(reductionists are nearly always correct in what they hold to exist --

but incorrect when they hold that nothing else exists)

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Reductionism

is like holding that only maps of some one specific scale (say 1:10,000) are true representations of reality

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Basic Formal Ontology

BFO is neutral with regard to mental/intentional entities

BFO is neutral with regard to sets/classes

… ontology is like every other science a work in progress

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Species-genusgenus trees can be represented also as map-like partitions

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From Species to Genera

canary

animal

bird

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From Species to Genera

animal

bird

canarycanary

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Species Genera as Tree

canary

animal

bird fish

ostrich

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Species-Genera as Map/Partition

animal

bird

canary

ostrich

fish

canary

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Tree and Map-Partitions Together

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‘Granularity’ in two senses:

depth of a tree hierarchy

resolution of a map-like partition

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There are many different species-genus hierarchies

many different ways to cut through the complex thicket of invariant patterns in reality

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Recall the distinct temporal partitions of reality as a whole

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Coarse-grained Partition

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Fine-Grained Partition

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??

?

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Ontological Zooming

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Universe/Periodic Table

animal

bird

canary

ostrich

fishfolk biology

partition of DNA space

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Universe/Periodic Table

animal

bird

canary

ostrich

fish

both are transparent partitions of one and the same reality

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France

RegionsDepartments

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Perspectivalism

Perspectivalism

Different partitions may represent cuts through the same reality which are skew to each other

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An organism is a totality of molecules

An organism is a totality of cells

An organism is a single unitary substance

... all of these express veridical partitions

An organism is a totality of atoms

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all express partitions which are transparent,

at different levels of granularity,

to the same reality beyond

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Ontology

like cartography

must work with maps at different scales and with maps picking out different dimensions of invariants

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inspired in part by spatial ontologies developed in Geographic Information Science

Cf. Th. Bittner

map layers

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If Aristotelian realism is right

then there are very many map-like

partitions, at different scales,

which are all transparent to the reality beyond

the mistake arises when one supposes

that only one of these partitions is veridical

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There are not only map-like partitions of reality into spatial chunks

but also distinct partitions of reality into universals

-- mutually compatible ways of providing inventories of universals

(among proteins, among cells, among organisms …)

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Varieties of granular partitions

Partonomies: inventories of the parts of individual entities

Maps: partonomies of space

Taxonomies: inventories of the universals covering a given domain of reality

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come with a labelling and an address system

Partitions

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Lake Tahoe Land Cover

two mutually dependent partitions

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Cerebral Cortex

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Mouse Chromosome 5

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Periodic TablePeriodic Table of Chemical Elements

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Set theory is one possible partition of reality

is it a transparent partition?

or a useful tool of mathematics?

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Partonomies and taxonomies can be combined

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79

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but should not be confused

is-a overloading

ulcer

parts of ulcer types of ulcer phases of ulcer

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Artefactual universalshave crisp borderlines

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birds

ostrich

Natural universals have non-crisp borderlines

sparrow

marked by borderline cases

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Natural universals have a kernel/penumbra structure

kernel of focal

instances

penumbra of borderline cases

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Prototypicality amongsub-categories

some sub-species of a given genus are more typical, standard, than others

canary is more typical than ostrich

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instances

There is prototypicality among instances too

albino frogalbino frog

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Types of boundaries in the realm of universal partitions

Fiat vs. bona fide

Crisp vs. non-crisp

Natural vs. artefactual

Continuous vs. non-continuous

…

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The Ontology of Holes

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Places are holes

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Temple at Corinth

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Pipe

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The Ontology of Places

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Varieties of Controlled Airspace

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Places

For Aristotle there are no empty places

The place of a substance is the interior boundary of the surrounding body

(for example the interior boundary of the surrounding water where it meets a fish’s skin)

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Places

For Aristotle a place is a hole filled by a substance

The place occupied by you is the boundary of the surrounding air where it meets your body

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A more adequate ontology:

Places are holes

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Places are holes

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A hole in the groundSolid physical boundaries at the floor and walls

but with a fiat lid:

hole

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Holes, too, involve two kinds of boundaries

bona fide boundaries which exist independently of our demarcating acts

fiat boundaries which exist only because we put them there

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niches, environments are holes

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Ontology of Environments

Gibson: affordancesgeometry of surface layout

1 Part 3 Tools of Ontology: Universals, Partitions.

Documents

b24 slide

reality slide

gold slide

partitions slide

movement slide

passion slide

linnaean hierarchy slide

porphyrian hierarchy