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

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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

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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

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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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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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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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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

Occ

urre

nts

Con

tinua

nts

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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

Occ

urre

nts

Con

tinua

nts

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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?

Occ

urre

nts

Con

tinua

nts

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Refining the Ontological Square

Substantial Dependent Entities

John‘s reddening

John‘s blushing

John‘s bruising

4-DSubstances

Collectives

Undetached parts

Substantial boundaries

John‘s redness

John‘s blush

John‘s bruise

3-D

Occ

urre

nts

Con

tinua

nts

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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)

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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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

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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) ...

Substantial Accidental

Attributes

F, G, R

Individuals

a, b, c

this, that

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Bicategorial Nominalism

Substantial Accidental

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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Process MetaphysicsSubstantial Accidental

Events

Processes

“Everything is flux”

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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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Basic Formal Ontology

??

?

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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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Basic Formal Ontology

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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Partonomies and taxonomies can be combined

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Partonomies and taxonomies can be combined

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Partonomies and taxonomies can be combined

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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