1 introduction to ontology barry smith. 2 aristotle author of the categories aristotle
TRANSCRIPT
1
Introduction to Ontology
Barry Smith
2
Aristotle
author of The Categories
Aristotle
3
From Species to Genera
canary
animal
bird
4
Species Genera as Tree
canary
animal
bird fish
ostrich
5
Species-genusgenus trees can be represented also as map-like partitions
6
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
10
If Aristotelian realism is right,
then such partitions are transparent to the reality beyond
11
Tree and Map/Partition
12
Alberti’s Grid
c.1450
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Coarse-grained Partition
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Fine-Grained Partition
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Scientific theories
comprehend in their underlying category systems veridical partitions of reality
often there are many veridical partitions of reality,
cross-cutting each other,
differing only in nuances)
16
Question:
what other sorts of partitions have this feature of transparency?
the partitions of common sense (folk biology, folk physics, folk psychology ...)
Answer:
17
Aristotle
the ontologist of common-sense reality
Aristotle
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The world we grasp in natural language
= the world as apprehended via that conceptualization we call common sense
= the normal environment (the niche) shared by children and adults in everyday perceiving and acting
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The world of mothers, milk, and mice ...
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The Empty Mask (Magritte)
mama
mouse
milk
Mount Washington
21
our common-sense partition of the world of common sense is transparent
(common sense, like science, is [mostly*] true)
mothers exist ...
* “mostly” because of the problem of vagueness
22
What is common-sense reality?
the mesoscopic space of everyday human action and perception
– a space centered on objects organized into hierarchies of species and genera
... and subject to prototypicality
23
but more:
24
in addition to objects (substances),
which pertain to what a thing is at all times at which it exists:
cow man rock planet
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the common-sense world contains also accidents
which pertain to how a thing is at some time at which it exists:
red hot suntanned spinning
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An accident
= what holds of a substance per accidens
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= relations of inherence(one-sided existential dependence)
John
hunger
Substances are the bearers of accidents
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Both substances and accidents
instantiate universals at higher and lower levels of generality
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siamese
mammal
cat
organism
substancespecies, genera
animal
instances
frog
30
Common nouns
pekinese
mammal
cat
organism
substance
animal
common nouns
proper names
31
siamese
mammal
cat
organism
substancetypes
animal
tokens
frog
32
Our clarification
accidents to be divided into
two large and essential distinct families of
QUALITIES
and
PROCESSES
33
There are universals
both among substances (man, mammal)
and among qualities (hot, red)
and among processes (run, movement)
There are universals also among spatial regions (triangle, room, cockpit)
and among spatio-temporal regions (orbit)
34
Substance universals
pertain to what a thing is at all times at which it exists:
cow human rock planetVW Golf
35
Quality universals
pertain to how a thing is at some time at which it exists:
red hot suntanned spinningClintophobic Eurosceptic
36
Process universals
reflect invariants in the spatiotemporal world taken as an atemporal whole
football match
course of disease
exercise of function
(course of) therapy
37
Processes and qualities, too, instantiate genera and species
Thus process and quality universals form trees
38
Accidents: Species and instances
quality
color
red
scarlet
R232, G54, B24
this individual accident of redness (this token redness – here, now)
39
Substances have slots
which are filled by qualities
(by specific values)
(determinables vs. determinates)
40
substance
Substances are the bearers of accidents
accidentsBearers
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substance
Substances are the bearers of accidents
accidents
John = relations of inherence(one-sided existential dependence)
Bearers
hunger
42
s
substance
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Substance + Accident = State of Affairs
setting into relief
States of Affair
s
44
instances
Prototypicality among instances too
albino frogalbino frog
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Aristotle 1.0
an ontology recognizing:substance tokensaccident tokenssubstance typesaccident types
46
Aristotle 1.0
in fact however we need more than this
What is missing from Aristotle 1.0 asan ontology of common-sense reality?
47
Is everything in common-sense reality either a substance or an accident?
48
well, what about artefacts ?
49
Standard Aristotelian theory of artefacts:
artefacts are mereological sums of substances
50
Positive and negative parts
positivepart
negativepartor hole
(made of matter)
(not made of matter)
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quid? substance quantum? quantity quale? qualityad quid? relationubi? placequando? timein quo situ? status/contextin quo habitu? habitusquid agit? actionquid patitur? passion
Nine Accidental Categories
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Places
For Aristotle 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)
53
What is missing from Aristotle?
Gibson: affordancesniches
Barker: behavior settings
54
The metaphysics of holes
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Aristotle 1.5
an ontology ofsubstances + accidents+ holes (and other entities not made of matter)+ fiat and bona fide boundaries+ artefacts and environments
is true
56
folk biology
Aristotelian folk biology, folk physics, folk psychology, etc., are true of the common-sense world as it currently exists
(they have nothing to offer regarding its pre-history, its long term evolution, its position in the cosmos)
57
They have not much to offer, either, by way of good explanatory theories of the entities in their respective domains,
but they are transparent to those domainsnonetheless
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Both scientific partitions and common-sense partitions
are based on reference-systems which have survived rigorous empirical tests
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The $64000 Question
How do those parts and dimensions of reality which we call the common-sense world
... relate to those parts and dimensions of reality which are studied by science?
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Granularity
61
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
63
many transparent partitions
at different levels of granularity
will operate with species-genus hierarchies
and with an ontology of substances (objects) and accidents (attributes, processes)
along the lines described by Aristotle
64
relative hylomorphism
substances and accidents reappear in the microscopic and macroscopic worlds of e.g. molecular biology and astronomy
(Aristotelian ontological zooming)
65
we do not assert
that every level of granularity is structured in substance-accident form -- perhaps there are pure process levels, perhaps there are levels structured as fields
66
Perspectivalism
PerspectivalismDifferent partitions may represent cuts through the same reality which are skew to each other
67
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
69
Coarse-grained Partition
what happens when a fringe instance arises ?
70
Coarse-grained Partition
what happens when a fringe instance arises ?
Aristotle 1.0: you shrug your shoulders
71
Aristotle 2000:you go out to find a finer grained partition which will recognize the phenomenon in question as prototypical
72
Gene Ontology
Molecular Function Ontology: tasks performed by individual gene products; examples: transcription factor, DNA helicase
Biological Process Ontology: broad biological goals accomplished by ordered assemblies of molecular functions; examples: mitosis, purine metabolism
Cellular Component Ontology: subcellular structures, locations, and macromolecular complexes;examples: nucleus, telomere
73
Example from Molecular Function Ontology
hormone ; GO:0005179
%digestive hormone ; GO:0046659 %peptide hormone ; GO:0005180 %adrenocorticotropin ; GO:0017043 %glycopeptide hormone ; GO:0005181 %follicle-stimulating hormone ; GO:0016913
% = IS A
74
as tree (joined by is a links):
hormone
digestive hormone peptide hormone
adrenocorticotropin glycopeptide hormone
follicle-stimulating hormone
75
Problem: There exist multiple databases
genomic cellular
structural phenotypic
… and even for each specific type of information, e.g. DNA sequence data, there exist several databases of different scope and organisation
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What is a gene?
GDB: a gene is a DNA fragment that can be transcribed and translated into a protein
Genbank: a gene is a DNA region of biological interest with a name and that carries a genetic trait or phenotype
(from Schulze-Kremer)
77
Application ontology
cannot solve the problems of database integration
There can be no mechanical solution to the problems of data fusion in a domain
like medicine
78
Applications ontology:
… grew out of work in AI and in knowledge representation
Ontologies are applications running in real time
79
Applications ontology:
ontologies are inside the computer
thus subject to severe constraints on expressive power
(effectively the expressive power of description logic)
80
Applications ontology cannot solve the data-fusion problem
because of its roots in knowledge mining
81
different conceptual systems
82
need not interconnect at all
83
because of the limits of knowledge mining
84
we cannot make incompatible concept-systems interconnect
just by looking at concepts, or knowledge – we need some tertium quid
85
What is needed
in some sort of wider common framework which is sufficiently rich and nuanced to allow concept systems deriving from different sources to be hand-callibrated
86
What is needed
is not an applications ontology
but
a reference ontology
(something like old-fashioned metaphysics)
87
Reference Ontology
… grew out of logic and analytic metaphysics
An ontology is a theory of the relevant domain of entities
Ontology is outside the computer
seeks maximal expressiveness and adequacy to reality
willing to sacrifice computational tractability for the sake of representational adequacy
88
Reference Ontology
a theory of the tertium quid
– called
reality –needed to hand-callibrate
database/terminology systems
89
Methodology
Get ontology right first
(realism; descriptive adequacy; rather powerful logic);
solve tractability problems later
90
The Reference Ontology Community
IFOMIS (Leipzig) Laboratory for Applied Ontology (Trento/Rome,
Turin)Foundational Ontology Project (Leeds)Ontology Works (Baltimore)Ontek Corporation (Buffalo/Leeds)LandC (Belgium/Philadelphia)(CYC?)
91
Domains of Current Work in Reference Ontology
IFOMIS Leipzig: MedicineLaboratory for Applied Ontology
Trento/Rome: Ontology of Cognition/Language Turin: Law
Foundational Ontology Project (Leeds): Space, PhysicsOntology Works (Baltimore): Genetics, Molecular BiologyOntek Corporation (Buffalo/Leeds): Biological SystematicsLandC (Belgium/Philadelphia): Medical NLP(? CYC : Everything ?)
92
GDB: a gene is a DNA fragment that can be transcribed and translated into a protein
Genbank: a gene is a DNA region of biological interest with a name and that carries a genetic trait or phenotype
(from Schulze-Kremer)
93
Ontology
Note that terms like ‘fragment’, ‘region’, ‘name’, ‘carry’, ‘trait’, ‘type’
… along with terms like ‘part’, ‘whole’, ‘function’, ‘substance’, ‘inhere’ …
are ontological terms in the sense of traditional (philosophical) ontology
94
Three types of reference ontology
1) formal ontology = framework for rigorous definition of the highly general concepts – such as object, event, whole, part – employed in every domain
2) domain ontology, a top-level system with a few highly general concepts, applies formal ontology to a particular domain, such as genetics or medicine
3) terminology-based ontology, a very large system embracing many concepts and inter-concept relations
95
So what is the ontology of blood?
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We cannot solve this problem just by looking at concepts (by engaging in further
acts of knowledge mining)
97
concept systems may be simply incommensurable
98
the problem can only be solved
by taking the world itself into account
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By looking not at concepts, representations,
and their semantic models
but rather at organisms acting in the world
and standing at different levels in a range of different sorts of relations to the world
100
We then recognize
that the same object can be apprehended at different levels of granularity:
at the perceptual level blood is a liquid (?)
at the cellular level blood is a tissue
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This implies a view of ontology
not as a theory of concepts
but as a theory of reality
But how is this possible?
How can we get beyond our concepts?
answer: ontology must be maximally opportunistic
it must relate not to beliefs, concepts, syntactic strings but to the world itself
102
“Maximally opportunistic”
means:
look at concepts and beliefs critically
and always in the context of a wider view which includes independent ways to access the objects themselves
at different levels of granularity
and taking account of tacit knowledge of those features of reality of which the domain experts are not consciously aware
103
“Maximally opportunistic”
means:
look not at what the expert says
but at what the expert does
Experts have expertise = knowing how
Ontologists can have windows on reality, by focusing on categories, and can extract some form of knowing that
Gibsonianism: experts don’t know what the ontologist knows
104
Ontology must be maximally opportunistic
This means:
don’t just look at beliefs
look at the objects themselves
from every possible direction,
formal and informal
scientific and non-scientific …
105
Maximally opportunistic
means:look at the same objects at different levels of granularity:
106
Second step: select out the good conceptualizations
these have a reasonable chance of being integrated together into a single ontological system
• based on tested principles• robust• conform to natural science
107
Ontology
like cartography
must work with maps at different scales
108
Medical ontologies
at different levels of granularity:
cell ontology
drug ontology
protein ontology
gene ontology
anatomical ontology
epidemiological ontology
Rigidly hierachical, modular organization – with many things which can go wrong
109
There are many compatible map-like partitions
many maps at different scales,
all transparent to the reality beyond
110
Partitions should be cuts through reality
a good medical ontology should NOT be compatible with the conceptualization of disease as:
caused by evil spirits and demons and cured by golems
111
Three main sorts of partitions
1. substances and their parts
2. qualities/functions/roles
3. processes
in addition:
spatial regions/niches
spatio-temporal regions
112
1. Substances and their parts
Patterned parts (carved out by fiat)
chess board
football pitch
Broca’s Region
nervous system
113
2. Functions
function of a screwdriver
tied to processes
= generalized four-dimensional shapes (carved out by fiat)
contextual dependence
function of the heart
function of the circulatory system
114
Once we understand functions
we can also understand malfunctions:
broken screwdriver
defective heart
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Application to Bodily Systems
Immune system, digestive system …
are complex substances paradigm: skeleton
carved out by fiat from the whole organism in terms of their functions
engaging in specific types of processes
116
Mereotopologies: Fiat and Bona Fide Boundaries
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A substance has a complete physical boundary
The latter is a special sort of part of a substance
… a boundary part
something like a maximally thin extremal slice
118
interiorsubstance
boundary
119
A substance takes up space.
A substance occupies a place or topoid (which enjoys an analogous completeness or rounded-offness)
A substance enjoys a place at a time
120
A substance has spatial parts
… perhaps also holes
121
Each substance is such as to have divisible bulk:
it can in principle be divided into separate spatially extended substances
122
By virtue of their divisible bulk
substances compete for space:
(unlike shadows and holes)
no two substances can occupy the same spatial region at the same time.
123
Substances vs. Collectives
Collectives = unified aggregates: families, jazz bands, empires
Collectives are real constituents of reality (contra sets)
but still they are not additional constituents, over and above the substances which are their parts.
124
Collectives inherit some, but not all, of the ontological marks of substances
They can admit contrary moments at different times.
125
Collectives,
like substances,
may gain and lose parts or members
may undergo other sorts of changes through time.
126
Qualities and processes, too, may form collectives
a musical chord is a collective of individual tones
football matches, wars, plagues are collectives of actions involving human beings
127
Collectives/heaps
are the duals of undetached parts
Both involve fiat boundaries
128
Substances, Undetached Parts and Heaps
Substances are unities.
They enjoy a natural completeness
in contrast to their undetached parts (arms, legs)
and to heaps or aggregates
… these are topological distinctions
129
substance
undetached part
collective of substances
130
special sorts of undetached parts
ulcers
tumors
lesions
…
131
Fiat boundaries
physical (bona fide) boundary
fiat boundary
132
Holes, too, involve fiat boundaries
133
A hole in the ground
Solid physical boundaries at the floor and walls
but with a lid that is not made of matter:
hole
134
Holes 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
135
Examples
of bona fide boundaries:
an animal’s skin, the surface of the planet
of fiat boundaries:
the boundaries of postal districts and census tracts
136
Mountain
bona fide upper boundaries with a fiat base:
137
where does the mountain start ?
... a mountain is not a substance
138
nose
...and it’s not an accident, either
139
Examples
of bona fide boundaries:
an animal’s skin, the surface of the planet
of fiat boundaries:
the boundaries of postal districts and census tracts
140
Mountain
bona fide upper boundaries with a fiat base:
141
Architects Plan for a House
fiat upper boundaries with a bona fide base:
142
where does the mountain start ?
... a mountain is not a substance
143
nose
...and it’s not a process, either
144
One-place qualities and processes
depend on one substance
(as a headache depends upon a head)
145
Relational qualities and processes
John Mary
kiss
stand in relations of one-sided dependence to a plurality of substances simultaneously
146
Examples of relational qualities and processes
kisses, thumps, conversations,
dances, legal systems
Such real relational entities
join their carriers together into collectives of greater or lesser duration
147
Basic Formal Ontology
mereotopologydependencegranularity/partition theory SNAP/SPANaction/participationplans/functions/executionssystems/modularitycausality/powers/dispositionsenvironments/nichesnormativity
148
Medical Beingmereotopology: anatomy with holes, layers
dependence
granularity/partition theory: molecules, genes, cells …
SNAP/SPAN: anatomy, physiology …
action/participation: doctor, patient, drug …
plans/functions/executions: therapy, application of therapy …
causality/powers/dispositions: prevention
environment: environmental influences on disease
normativity: health, disease, ‘normal’ liver
149
Bodily Systems
e.g.nervous systemrespiratory systemimmune system
How do these systems relate together?(a medico-ontological analogue of the
mind-body problem)WHAT IS A SYSTEM? Fiat object?
150
The ontologist’s job
is not to mimic or replace or usurp sciencenot to discover statistical or functional laws
it is to establish the categories involved in given domains of reality and the relations between themvia: taxonomiesand: partonomiesand by addressing NORMATIVE ISSUES such as: what holds in the standard case
151
Rules for Good Ontology
These are rules of thumb:
They represent ideals to be approximated to in practice
(and often come with trade-offs)
152
Naturalness
A good ontology should include in its basic category scheme only those categories which are instantiated by entities in reality (it should reflect nature at its joints)
153
A good first test:
the categories in question should be reflected in Technically Extended English
= English as extended by the various technical vocabularies of medical and scientific disciplines
154
Basic categoriesare reflected by morphologically simple terms:
dogpainfootbloodhungerhotreddiabetes
155
Ontology
like cartography
must work with maps at different scales and with maps picking out different dimensions of invariants
156
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
157
Rule: Respect Granularity
spatial region qualitysubstance
parts of spatial regions are always spatial regions
158
Respect Granularity
spatial region qualitysubstance
parts of substances are always substances
159
Relations crossing the SNAP/SPAN border are not part-relations
John’s lifesubstance John
physiological processes
sustaining in existence
160
Rule: Representations
A representation is never identical with the object which it is a representation of
161
Rule: Fallibilism
Ontologists are seeking principles that are true of reality,
but this does not mean that they have special powers for discovering the truth.
Ontology is, like physics or chemistry, part of a piecemeal, on-going process of exploration, hypothesis-formation, testing and revision.
162
Fallibilism
Ontological claims advanced as true today may well be rejected tomorrow in light of further discoveries or of new and better arguments
Ontology is like a small window on reality which, in fits and starts, gets bigger and more refined as we proceed
163
Rule: Adequatism
A good ontology should be adequatist:
its taxonomies and partonomies should comprehend the entities in reality at all levels of aggregation,
from the microphysical to the cosmological,
and including also the middle world (the mesocosmos) of human-scale entities in between. Adequatists: Aristotle, Ingarden, Chisholm; Johansson, Smith
164
Rules Governing Taxonomies
Every (coherent, tested) ontology for a given domain at a given level of granularity
should be representable as a tree in the mathematical sense
Problem cases: shapes, colors ?
165
Natural scientific classifications are principled
166
Principled classifications satisfy the no-diamonds rule:
A E
F G
B C D
HGood Bad
167
Counterexample in the realm of artifacts ?
urban structures
buildings car parks
multi-story car-parks
168
Eliminating counter-examples
urban structures
buildings parking areas
multi-story car-parks
“Ontoclean”
169
Tree structure
Higher nodes within the tree represent more general universals, lower nodes represent less general universals.
170
Branches connecting nodes represent the relations of inclusion of a lower category in a higher:
man is included in mammal
mammal is included in animal
and so on.
171
An Ontology (Taxonomy) should be Principled
Suppose that in counting off the cars passing beneath you on the highway, your checklist includes one box labeled red cars and another box labeled Chevrolets.The resultant inventory will be unprincipled; you will almost certainly be guilty of counting some cars twice. Unprincipled = the two modes of classification belong to two distinct classifications made for two distinct purposes
172
An Ontology (Taxonomy) should be Principled
Principled = Constructed for a single purpose
Principled = Generative (recursive?)
Principled = Double-counting clearly marked
Principled = SNAP-SPAN opposition reflected (so mereological determinateness is guaranteed)
Principled = Clear rules when a new category must be admitted
What else?
CYC is not principled
173
Well-formedness rule
Each tree is unified
in the sense that it has a single top-most or maximal node, representing the maximum category
comprehending all the categories represented by the nodes lower down the tree
174
Why trees?
A taxonomy (ontology) with two maximal nodes would be in need of completion by some extra, higher-level node representing the union of these two maxima.
Otherwise it would not be one taxonomy at all, but rather two separate taxonomies (e.g. SNAP and SPAN)
175
‘Entity’
= label for the highest-level category of ontology.
Everything which exists is an entity
Alternative top-level terms favored by different ontologists: ‘thing,’ ‘object,’ ‘item,’ ‘element,’ ‘existent.’
Use of ‘entity’ is dangerous (see Frege)
176
Rule: Aim for Exhaustiveness
The chemical classification of the noble gases is exhausted by:
Helium, Neon, Argon, Krypton, Xenon and Radon.
…normally very hard to achieve
177
Relations can also hold across granularities
Microbial processes in the human body sustain the human body in existence
Neurophysiological processes in the brain cause and provide the substratum for cognitive processes
178
Substances
Mesoscopic reality is
divided at its natural joints
into substances:
animals, bones, rocks, potatoes
179
The Ontology of Substances
Substances form natural kinds
(universals, species + genera)
180
Processes
Processes merge into one another
Process kinds merge into one another
… few clean joints either between instances or between types
181
Processes
t i m e
182
Nouns and verbs
Substances and processes
Continuants and occurrents
Endurants and perdurants
In preparing an inventory of reality
we keep track of these two different categories of entities in two different ways
183
Natural language
glues them together indiscriminately
substance
t i m
e
process
184
Substances and processes
t i m
e
process
demand different sorts of inventories
185
Substances demand 3-D partonomies
space
186
Moments demand 4D-partonomies
t i m e
187
Processes
a whistling, a blushing, a speech
a run, the warming of this stone
188
Processes may have temporal parts
The first 5 minutes of my headache is a temporal part of my headache
The first game of the match is a temporal part of the whole match
189
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 moment which is my life
190
How do we glue these two different sorts of entities together mereologically?
How do we include them both in a single inventory of reality?
191
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?
192
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
193
Main problem
There is a polymorphous ontological promiscuity of the English sentence,
which is inherited also by the form ‘F(a)’
194
The Four-Dimensionalist Ontology
t i m e
195
boundaries are mostly fiat
t i m e
everything is flux
196
mereology works without restriction everywhere here
t i m e
clinical trial
197
The Time-Stamped Ontology
t1
t3t2
here time exists outside the ontology, as an index or time-stamp
198
mereology works without restriction in every 3-D SNAPti ontology
199
Ontological Dependence
Substances are that which can exist on their own
Processes require a support from substances in order to exist
This holds for qualities, too
200
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
201
Substances
can also gain and lose parts
… as an organism may gain and lose molecules
202
SNAP and SPAN
Substances+qualities and processesContinuants and occurrents
In preparing an inventory of realitywe keep track of these two different categories of entities in two different ways
203
Need for different perspectives
Not one ontology, but a multiplicity of complementary ontologies
Cf. Quantum mechanics: particle vs. wave ontologies
204
Two Orthogonal, Complementary Perspectives
SNAP and SPAN
205
SNAP and SPAN
the tumor and its growth
the surgeon and the operation
the virus and its spread
the temperature and its rise
the disease and its course
the therapy and its application
206
SNAP and SPANSNAP 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
207
SNAP vs. SPAN
1. SNAP: a SNAPshot ontology of endurants existing at a time
2. SPAN: a four-dimensionalist ontology of processes
208
You are a substance
Your life is a process
You are 3-dimensional
Your life is 4-dimensional
209
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
210
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
211
How do you know whether an entity is SNAP or SPAN?
212
Three kinds of SNAP entities
1. Substances
2. SPQR… entities
3. Spatial regions, contexts, niches, environments
213
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
214
Other SPQR… entities:
functions, dispositions, plans, shapes
SPQR… entities are all dependent on substances
one-place SPQR entities: temperature, color, height
215
Substances and SPQR… entities
Substances are the bearers or carriers of,
SPQR… entities ‘inhere’ in their substances
216
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
217
relational SPQR… entities
John Mary
love
stand in relations of one-sided dependence to a plurality of substances simultaneously
218
Ontological Dependence
Substances are that which can exist on their own
SPQR… entities require a support from substances in order to exist
219
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
220
SNAP ontology
many sharp boundaries
SPAN ontologymany smeered boundaries
many fiat boundaries
(more scope for gerrymandering – why?)
221
Processes, too, are dependent on substances
One-place vs. relational processes
One-place processes:
getting warmer
getting hungrier
222
Examples of relational processes
kissings, thumps, conversations,
dances,
Such relational processes
join their carriers together into collectives of greater or lesser duration
223
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
224
Each is a window on that dimension of reality which is visible through the given ontology
SNAP and SPAN ontologies are partial only
(Realist perspectivalism)
225
SNAP: Entities existing in toto at a time
226
Three kinds of SNAP entities
1. Substances
2. SPQR… entities
3. Spatial regions, Contexts, Niches
227
228
229
SNAP
230
SPAN: Entities extended in time
SPANEntity extended in time
Portion of Spacetime
Fiat part of process *First phase of a clinical trial
Spacetime worm of 3 + Tdimensions
occupied by life of organism
Temporal interval *projection of organism’s life
onto temporal dimension
Aggregate of processes *Clinical trial
Process[±Relational]
Circulation of blood,secretion of hormones,course of disease, life
Processual Entity[Exists in space and time, unfolds
in time phase by phase]
Temporal boundary ofprocess *
onset of disease, death
231
SPAN: Entities extended in time
232
SPAN: Entities extended in time
233
Relations between SNAP and SPAN
SNAP-entities participate in processes
they have lives, histories
234
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
235
SPQR… entities and their SPAN realizations
function
role
plan
disposition
therapy
disease
SNAP
236
SPQR… entities and their SPAN realizations
expression
exercise
execution
realization
application
course
SPAN
237
SNAP and SPAN
space
space-time
substances
SPQR entities (including functions)
processes
238
Gene Ontology
Cellular Component Ontology: subcellular structures, locations, and macromolecular complexes;examples: nucleus, telomere SNAP-INDEPENDENT
Molecular Function Ontology: tasks performed by individual gene products; examples: transcription factor, DNA helicase SNAP-DEPENDENT (SPQR)
Biological Process Ontology: broad biological goals accomplished by ordered assemblies of molecular functions; examples: mitosis, purine metabolism SPAN
239
Substance->Process
PARTICIPATION(a species of dependence)
240
Participation (SNAP-SPAN)
A substance (SNAP) participates in a process (SPAN)
A runner participates in a race
A voter participates in an election
241
Axes of variation
activity/passivity (agentive)
direct/mediated
benefactor/malefactor (conducive to existence) [MEDICINE]
242
SNAP-SPAN
Participation
Perpetration (+agentive)
Initiation
Perpetuation
Termination
Influence
Facilitation
Hindrance
Mediation
Patiency(-agentive)
243
Perpetration
A substance perpetrates an action (direct and agentive participation in a process):
The referee fires the starting-pistol
The captain gives the order
244
Initiation
A substance initiates a process:
The referee starts the race
The attorney initiates the process of appeal
245
Perpetuation
A substance sustains a process:
The singer sings the song
The charged filament perpetuates the emission of light
246
Termination
A substance terminates a process:
The operator terminates the projection of the film
The judge terminates the imprisonment of the pardoned convict
247
Influence
A substance (or its quality) has an effect on a process
The steepness of the slope affects the movement of the troopsThe politicians influence the course of the war
248
Facilitation
A substance plays a secondary role in a process (for example by participating in a part or layer of the process)
The catalyst provides the chemical conditions for the reaction
The traffic-police facilitate our rapid progress to the airport
249
Hindrance, prevention
A substance has a negative effect on the unfolding of a process (by participating in other processes)
The drug hinders the progression of the disease
The strikers prevent the airplane from departing
250
Mediation
A substance plays an indirect role in the unfolding of a process relating other participants:
The Norwegians mediate the discussions between the warring parties
251
Patiency
Dual of agentive participation
John kisses [Mary] (John agent)
Mary is kissed [by John] (Mary patient)
252
Signatures of meta-relations
SNAP Component SPAN Component
Substances
SPQR…
Space Regions
Processuals
Processes
Events
Space-Time Regions
253
2nd Family
REALIZATION
254
Signatures of meta-relations
SNAP Component SPAN Component
Substances
SPQR…
Spatial Regions
Processuals
Processes
Events
Space-Time Regions
participation
realization
255
Realization (SNAP-SPAN)
the execution of a plan, algorithm
the expression of a function
the exercise of a role
the realization of a disposition
256
SPQR… entities and their SPAN realizations
plan
function
role
disposition
algorithm
SNAP
257
SPQR… entities and their SPAN realizations
execution
expression
exercise
realization
application
course
SPAN
258
SNAP->SPAN
Participation
Substance -> Process
Realization
SPQR -> Process
259
Ecological Ontology: Niches, Environments, Contexts
260
Formal Ontology
atomism vs. holism
set theory
mereology
261
Environments a Neglected Major Category in the History of Ontology
Substances
States, Qualities, Powers, Roles …
Processes
-- environments missing from Aristotle, from DOLCE, from entity-relationship models
262
environmentplaceniche
habitatsetting
holespatial region
interior
263
Applications of these concepts
in biology, ecologyin anthropologyin lawin politicsin medicinein embryology
264
A Theory of Contexts, Settings, Environments for Social Acts
Searle:
X counts as Y in context C
What kinds of entities are social contexts?
265
The Idea: Contexts can be Nested One Inside Another
Many settings occur in assemblies:
A unit in the middle range of a nesting structure is simultaneously both circumjacent and interjacent,
both whole and part, both entity and environment. (Roger Barker)
266
Human body
Compare the hierarchical organization of the human body into organs, cells, …
modular organization – with many things which can go wrong
267
Large-scale social organizations
are organized as rigidly hierarchical, modular nesting structures, with many things which can go wrong
268
Ecological Niche Concepts
niche as particular place or subdivision of an environment that an organism or population occupies (TOKEN)
vs.
niche as function of an organism or population within an ecological community (TYPE)
269
Eltonthe ‘niche’ of an animal means its place in the biotic environment, its relations to food and enemies. [...] When an ecologist says ‘there goes a badger’ he should include in his thoughts some definite idea of the animal’s place in the community to which it belongs, just as if he had said ‘there goes the vicar’ (Elton 1927, pp. 63f.)
270
The Niche as Hypervolume
temperature
hum
idity
foli
age
den
sity
271
The Niche as Hypervolume
temperature
hum
idity
foli
age
den
sity
272
The Niche as Hypervolume
temperature
hum
idity
foli
age
den
sity
273
The Niche as Hypervolume
temperature
hum
idity
foli
age
den
sity
274
Hypervolume niche is a location in an attribute space
defined by a specific constellation of environmental variables such as degree of slope, exposure to sunlight, soil fertility, foliage density...… John found his niche as a mid-level accounts manager in a small-town bank …
275
But every hypervolume niche must be realized in some specific spatial
location
Niche type must be tokenized in space
or better: it must be tokenized in space-time
276
Niche Construction
Lewontin: niches normally arise in symbiosis with the activities of organisms or groups of organisms;
they are not already there, like vacant rooms in a gigantic evolutionary hotel, awaiting organisms who would evolve into them.
“ecosystem engineering”
maintenance of niches (screwdrivers, paintings)
277
Armchair Ontology
278
Positive and negative parts
positivepart
negativepartor hole
(made of matter)
(not made of matter)
279
Artifacts and Holes
280
niches, environments are holes
281
Places are holes
282
Armchair Ontology
artefacts and niches
the niche-tenant relation
vacant niches
283
Double Hole Structure
Medium (filling the environing hole)
Tenant (occupying the central hole)
Retainer (a boundary of some surrounding structure)
284
The Structure of Niches
media and retainers
the medium of the bear’s niche is a
circumscribed body of air
285
Two Types of Boundary
Fiat boundary Physical boundary
286
Four Basic Niche Types
1 2 3 4
1: a womb;2: a snail’s shell; 3: the niche of a pasturing cow; 4: the niche around a buzzard
287
Types of Niches
a pond, a nest, a cave, a hut, an air-conditioned apartment building
the history of evolution as a history of the development of niches
288
all vacant niches must have a retainerdependence of niche on tenant(s) the armchair nichetransforming niches of type 2 into niches of type 1
289
Four Basic Niche Types
1 2 3 4
1: a house;2: a snail’s shell; 3: the niche of a pasturing cow; 4: the earth’s atmosphere
290
stationary niches
1: your office when the door is closed; 2: a rabbit hole; 3: a seat at Yankee stadium; 4: the Klingon Empire
291
The Ontology of Niches
Niches are in some ways like the interiors of substances
Two concepts of spaceship:John is in the spaceshipThe embryo is in the uterusThe yoghurt is in the refrigerator
Niches and quasi-nichesSubstances and quasi-substances
292
Two concepts of spaceship
John is in LondonJohn saw London from the air London London
IBM IBM
John admired her carJohn was sitting in her car
A is part of B vs. A is in the interior of B as a tenant is in its niche
293
Two concepts of uterus
Issue of parts of the human body
Cavities
Need for Layered Mereotopology
294
The Ontology of Niches
Niches are endurants
(SNAP entities)
295
mobile niches
296
Four Basic Mobile Niche Types
1 2 3 4
1: a womb;2: a snail’s shell; 3: the niche of a pasturing cow; 4: the niche around a buzzard
297
Recall
Lewontin’s ecological engineering
298
niches on different (granularity) levels of the food chain
a. at the bottom of the hiearchy is the saprophytic chain, in which micro-organisms live on dead organic matter;
b. above this is the primary relation between animals and the plants they consume;
c. above this is the predator chain, in which animals of one sort eat smaller animals of another sort;
d. crosscutting all of these is the parasite chain, in which a smaller organism consumes part of a larger host organism.
299
Token Science
selection theory is concerned with phenomena at the level of populations; it is ‘concerned with what properties are selected for and against in a population. We do not describe single organisms and their physical constituents one by one.’ genotypes vs. genotokens
niche theory and set theory
300
Fiat Boundaries
fish and bird niches as volumes of space
demarcatory vs. behavioral fiat boundaries
trade-off between security/comfort and freedom of movement
301
Apertures, Mouths, and Sphincters
security vs. freedom of movement plantsbarnacles and snails fish and birdsskin or hide
302
Security vs. Freedom
the mouth of the bear, the threshold of your office
freedom of movement and fiat boundaries (of niches and of organisms)
the alimentary canal: hole or part ?
303
Double Hole Structure
Medium (filling the environing hole)
Tenant (occupying the central hole)
Retainer (a boundary of some surrounding structure)
304
The Medium for Life
a medium is a medium only relative to a given type of niche
a medium requires either a retainer (in the case of a vacant niche) or a tenant (in the case of an occupied niche)
when a tenant leaves its niche the gap left by the tenant is filled immediately by the surrounding mediumMichelangelo’s Davidexamples of media: air, smoke, water
305
Mixed Media
mixed media (including radioactive impurities, as well as as vitamins, amino acids, salts, and sugars)
Scrooge, crowds, plastic balls
every medium is maximal
what does the job of filling out the niche whose medium is made of air or water? Answer: bodies of vacuum
306
Lexical Semantics
the fruit is in the bowlthe bird is in the nestthe lion is in the cagethe pencil is in the cupthe fish is in the riverthe river is in the valleythe water is in the lakethe car is in the garagethe fetus is in the cavity in the uterine liningthe colony of whooping crane is in its breeding grounds
307
Lexical Semantics
‘She swam across the bay in which the submarine was buried and which supplied oysters for the local population.’
308
The niche around the sleeping bear
There are relations of spatial overlap which do not imply corresponding relations of mereological overlap.
Niches are bounded not just spatially, and not just via physical material (the walls of the cave), but also via thresholds in quality-continua (for instance, temperature).
309
Hence:
distinct niches, may occupy the same spatial region.
Hence need for Layered Mereotopology
(The niche of the fly overlaps with the niche of the horse,
but the two are on different layers)
310
Vagueness
A niche for an entity y may have proper parts that are not niches for y
What of the outer boundaries of niches?
Indoor vs. outdoor niches (fog)
311
Ecological subjects
A niche for a sum y+z is not ipso facto a niche for each of the summed parts.
y+z = John’s head the head plus the rest of John’s body
Not every entity has its own niche. Those which do are natural units
(Compare Aristotle’s theory of places)
312
Defining Substance
A substance (body, thing) is a maximally connected tenant, a tenant which is such that no larger connected tenant includes it as a proper part.
You are a substance, but your heart is only a connected tenant within your interior.
A group is a tenant including substances as proper parts.
313
Extending Mereology
mereology, formalized in terms of the single primitive relation: part of
mereotopology, obtained by adding extra primitive relation boundary for
theory of location, obtained by adding extra primitive relation located at
formal ecology, obtained by adding extra primitive relation niche for
314
AimTo define structural properties such
as: open, closed, connected, compact, spatial coincidence, integrity, aggregate, boundary
315
Primitives
mereological predicate:
P(x, y) (read: “x is part of y”)
topological predicate:
B(x, y) (“x is a boundary for y”),
locational predicate:
L(x, y) (“x is located at y”)
316
Defined TermsD1 O(x, y)=df z (P(z, x) P(z, y))overlap
D2 xx =df xy (O(y, x) z (z O(z, y))) sum
D3 x+y =df z (P(z, x) P(z, y)) sum of x and y
D4 x–y =df z (P(z, x) O(z, y)) difference
D5 l(x) =df x(L(y, x)) location of x
317
Defined Terms
D6 b(x) =df z B(z, x) boundary of x
D7 i(x) =df x–b(x) interior of x
D8 c(x) =df x+b(x) closure of x
D9 Cl(x) =df x=c(x) closedness
D10 Rg(x) =df c(x) = c(i(x)) i(x) = i(c(x))
regularity
318
Defined Terms
D11 C(x, y) =df O(x, y) O(c(x), y) O(x, c(y))
connection
D12 EC(x, y) =df C(x, y) O(x, y)
external connection
D13 IP(x, y) =df P(x, y) z(B(z, y) O(x, z))
interior parthood
D14 Cn(x) =df yz (x=y+z C(y, z))
self-connectedness
319
Some theorems:
T1 B(x, y) B(x, –y).
T2 B(x, y) B(y, z) B(x, z).
T3 P(x, y) B(y, z) B(x, z).
320
niche predicates
N(x, y), read: “x is a niche for y”.
N(x), read: “x is a niche”. This could be defined in terms of the binary predicate, but only if every niche has a tenant
‘N(x, y)’ and ‘N(x)’, where ‘’ ranges over organism-types.
321
medium and retainer
M(x, y)
“x is a medium for y”
R(x, y)
“x is a retainer for y”
322
free niche
D15 N*(x, y) =df N(x, y) zR(z, x) free niche for y
D16 N*(x) =df N(x) zR(z, x)
Every niche is either a free niche, in this sense, or else it has a retainer—
which will imply that it has a solid physical boundary for at least a portion of its exterior surface.
323
further definitions
D17 t(x) =df y N(x, y) tenant of x
D18 r(x) =df z R(z, x) retainer of x
D19 m(x) =df z M(z, x) medium of x
324
The Axioms for N
A1 N(x, y) O(l(x), l(y)) disjointness
A2 N(x, y) IP(l(y), l(x+y)) spatial containment
A3 N(x, y) C(x, y) connection of niche
A4 N(x, y) Cl(y) closure of tenant
A5 N(x, y) Cn(x) connectedness of niche
A6 N(x, y) Rg(y) regularity of tenant
A7 N(x, y) Rg(x) regularity of niche
A8 N(x, y) N(x, z) y = z functionality
325
Every occupied niche is a niche.
A9 yN(x, y) N(x)
326
There are no vacant fiat niches
A10 N*(x) yN(x, y)
Every fiat niche is a niche for something.
327
Media and retainers
A11 M(x, y) N(y)
A12 R(x, y) N(y)
Media are media of niches
Retainers are retainers of niches.
328
Parts
A13 M(x, y) P(z, x) M(z, y)A14 R(x, y) P(z, x) R(z, y)
The parts of a medium for a given niche are themselves media for that niche and the parts of a retainer are themselves retainers.
A15 N(x) x = z(M(z, x) R(z, x))
Niches have no parts other than media and retainers.
329
Retainers and boundaries
A16 R(z, x) B(z, x)
Retainers are boundaries of niches (though not all boundaries of niches are retainers).
A17 N(x) zM(z, x)
Every niche has a medium (though a niche may lack a retainer).
A18 m(x) = m(y) x = y
No two niches have the same medium (though we leave it open whether two niches can have the same retainer).
330
Retainers and tenants
A19 N(x, y) R(z, x) C(z, y)
Retainers and tenants are not connected to each other, i.e., they do not share any physical parts or boundaries (for they are in every case separated by a medium.)
A20 M(z, x) R(w, x) EC(l(z), l(w))
The location of a retainer is externally connected (i.e., connected without overlap) to the location of the medium.
331
Axioms
A2' N(x, y) IP(l(y), l(m(x) + y))It is the medium of an occupied niche that
surrounds the tenant.
A3' N(x, y) C(m(x), y)It is the medium of an occupied niche that is
connected to the tenant. This actually follows from A3 in view of A19.
332
Axioms
A5' N(x) Cn(m(x))The medium of a niche is self-connected (though it
need not be compact, i.e., fill the entire environing hole: consider the bat flying in the bear’s cave).
A7' N(x) Rg(m(x))The medium of a niche is regular.
333
Theorems
T1 N(x) y(N(x, y) R(y, x))Every niche has either a tenant or a retainer. This is
a consequence of A10.
T2 M(x, y) z(N(y, z) R(z, y))Every medium requires either a tenant or a retainer.
This follows from T1 via A12.
334
Theorems
T3 M(z, x) P(z, x)
T4 R(z, x) P(z, x) Media and retainers are parts of niches. More
generally:
T5 M(x, y) P(z, x) P(z, y)
T6 R(x, y) P(z, x) P(z, y) All parts of a medium and all parts of a retainer are
parts of the relevant niche.
335
Theorems
T7 N(x, y) M(y, x)
T8 N(x, y) R(y, x)The tenant of a niche is neither a medium nor a
retainer thereof.
T9 M(z, x) R(w, x) EC(z, w)
The retainer of a niche is externally connected to the medium.
T10 R(z, x) B(z, m(x))
Retainers are boundaries of media.
336
Against multiplication of niches
T11 R(x, y) N(y – x)
A niche minus (part of) its retainer is not a niche.
This excludes the possibility that the difference between two niches might lie entirely in their retainers, which would result in an undue multiplication of niches with what are putatively the same boundaries.
337
Open Problems
X1 N(x, y) N(x', y') N(x + x', y + y') Mereological summing of niches is never additive.
cats whose niches come together to form a new, fused niche: the new niche is not just the mereological sum of the two separate niches;
for even assuming that the fiat boundaries of the two niches survive the fusion and continue to exist within the interior of the new niche, they are still not a part of it but are rather extrinsic to it.
338
Open Problems
X2 M(x, y) B(z, x) R(z, y) B(z, t(x))The boundaries of a medium are either retainers of the niche or boundaries of the tenant.
This would only be true if ‘B’ were understood as standing for physical boundaries, and only if one assumed that a medium has no holes except for the central holes occupied by the tenants.
(But consider again the bat in the bear’s cave, or a cage floating in the sea through which fish can swim.)
339
Open Problems
X3 M(x, y) B(z, x) EC(z, x)A medium never contains its own physical boundaries.
X4 B(b(m(x)), x)
Any boundary of the medium of a niche is a boundary of the niche itself.
This is false if we consider that the medium need not fill the environing hole completely. (The bat flying in the cave would not be part of the medium of the bear’s niche, yet the surface of the bat would not be part of the retainer either.)
340
The Ecological Psychology of J. J. Gibson and Roger Barker
341
Affordances
“The affordances of the environment are what it offers the animal, what it provides or furnishes, either for good or evil.”
James J. Gibson, The Ecological Approach to Visual Perception
342
Organisms are tuning forks
They have evolved to resonate automatically and directly to those quality regions in their niche which are relevant for survival
-- perception is a form of automatic resonation-- cognitive beings resonate to speech acts and
to linguistic records-- cognitive beings resonate deontically
343
affordances: positive and negative features of the environment:
permissions and prohibitions
344
Gibson’s theory of surface layout
Niches = systems of barriers, openings, pathways to which organisms are specifically attuned,
Include: temperature gradients, patterns of movement of air or water molecules, electro-chemical signals guiding the movements of micro-organisms
But also: traffic signs, instructions posted on notice boards or displayed on the computer screen
345
Niches
are in many ways analogous to substances
346
Marks of (bodily) substance
i. Rounded-offness
ii. Occupies space
iii. Complete boundary
iv. May have substantial parts (nesting)
v. May be included in larger substances
vi. Has a life (manifests contrary accidents at different times)
347
Corresponding Marks of Niches
(i) A niche enjoys a certain natural completeness or rounded-offness,
being neither too small nor too large
—in contrast to the arbitrary undetached parts of environmental settings and to arbitrary heaps or aggregates of environmental settings.
348
(ii) A niche takes up space,
it occupies a physical-temporal locale,
and is such as to have spatial parts.
Within this physical-temporal locale is a privileged locus—a hole—
into which the tenant or occupant of the setting fits exactly.
349
(iii) A niche
has an outer boundary:
there are objects which fall clearly within it,
and other objects which fall clearly outside it.
(The boundary itself need not be crisp.)
350
(iv) A niche
may have actual parts which are also environmental settings(hierarchical nesting)
351
(v) A niche
may be a proper part of larger, circumcluding niche.
352
(vi) A niche has a life
is now warm, now cold
now at peace, now at war ….
now expanding, now contracting
353
Marks of (bodily) substance
i. Rounded-offness
ii. Occupies space
iii. Complete boundary
iv. May have substantial parts (nesting)
v. May be included in larger substances
vi. Has a life; is now warm, now cold
354
Where are Niches?Concrete Entity
[Exists in Space and Time]Concrete Entity
[Exists in Space and Time]
Entity in 3-D Ontology[Endure. No Temporal Parts]
Entity in 3-D Ontology[Endure. No Temporal Parts]
Entity in 4-D Ontology[Perdure. Unfold in Time]Entity in 4-D Ontology
[Perdure. Unfold in Time]
Processual EntityProcessual EntitySpatio-Temporal Region
Dim = T, T+0, T+1, T+2, T+3Spatio-Temporal Region
Dim = T, T+0, T+1, T+2, T+3
Spatial Regionof Dimension 0,1,2,3
Spatial Regionof Dimension 0,1,2,3 Dependent EntityDependent Entity
Independent EntityIndependent Entity
Quality (Your Redness, My Tallness)[Form Quality Regions/Scales]
Quality (Your Redness, My Tallness)[Form Quality Regions/Scales]
Role, Function, PowerHave realizations (called: Processes)
Role, Function, PowerHave realizations (called: Processes)
Substance[maximally connected causal unity]
Substance[maximally connected causal unity]
Boundary of Substance *Fiat or Bona Fide or MixedBoundary of Substance *
Fiat or Bona Fide or Mixed
Aggregate of Substances * (includes masses of stuff? liquids?)
Aggregate of Substances * (includes masses of stuff? liquids?)
Fiat Part of Substance * Nose, Ear, Mountain
Fiat Part of Substance * Nose, Ear, Mountain
Process [Has Unity]Clinical trial; exercise of role
Process [Has Unity]Clinical trial; exercise of role
Fiat Part of Process*Fiat Part of Process*
Aggregate of Processes*Aggregate of Processes*
Instantaneous Temporal Boundary of Process (= Ingarden’s 'Event’)*
Instantaneous Temporal Boundary of Process (= Ingarden’s 'Event’)*
Quasi-ProcessJohn’s Youth. John’s Life
Quasi-ProcessJohn’s Youth. John’s Life
Quasi-Quality Prices, Values, Obligations
Quasi-Quality Prices, Values, Obligations
Quasi-SubstanceChurch, College, Corporation
Quasi-SubstanceChurch, College, Corporation
Quasi-Role/Function/PowerThe Functions of the PresidentQuasi-Role/Function/Power
The Functions of the President
355
Where are Places?Concrete Entity
[Exists in Space and Time]Concrete Entity
[Exists in Space and Time]
Entity in 3-D Ontology[Endure. No Temporal Parts]
Entity in 3-D Ontology[Endure. No Temporal Parts]
Entity in 4-D Ontology[Perdure. Unfold in Time]Entity in 4-D Ontology
[Perdure. Unfold in Time]
Processual EntityProcessual EntitySpatio-Temporal Region
Dim = T, T+0, T+1, T+2, T+3Spatio-Temporal Region
Dim = T, T+0, T+1, T+2, T+3
Spatial Regionof Dimension
0,1,2,3
Spatial Regionof Dimension
0,1,2,3
Dependent EntityDependent Entity
Independent EntityIndependent Entity
356
Types of PlacesConcrete Entity
[Exists in Space and Time]Concrete Entity
[Exists in Space and Time]
Entity in 3-D Ontology[Endure. No Temporal Parts]
Entity in 3-D Ontology[Endure. No Temporal Parts]
Entity in 4-D Ontology[Perdure. Unfold in Time]Entity in 4-D Ontology
[Perdure. Unfold in Time]
Processual EntityProcessual EntitySpatio-Temporal Region
Dim = T, T+0, T+1, T+2, T+3Spatio-Temporal Region
Dim = T, T+0, T+1, T+2, T+3
Generalized Spatial Regionof Dimension
0,1,2,3
Generalized Spatial Regionof Dimension
0,1,2,3
Dependent EntityDependent Entity
Independent EntityIndependent Entity
StationaryStationaryMobileMobile
357
Ecological Psychology
Gibson: Perception
:: Roger Barker: Society
Barker’s
Ecological Ontology of Social Reality
358
Barker on Unity of Social Reality
“The conceptual incommensurability of phenomena which is such an obstacle to the unification of the sciences does not appear to trouble nature’s units.
Within the larger units, things and events from conceptually more and more alien sciences are incorporated and regulated.”
359
Barker on Unity of Social Reality
“As far as our behaviour is concerned, … even the most radical diversity of kinds and categories need not prevent integration”
360
Roger Barker: Niche as Behavioral Setting
Niches are recurrent settings which serve as the environments for our everyday activities:
my swimming pool,
your table in the cafeteria,
the 5pm train to Long Island.
361
Behavior Settings
Each behavior setting is associated with certain standing patterns of behavior.
These standing patterns of behavior present everywhere in the domain of medical treatment
(and correspondingly also in the domain of unstructured patient records)
362
Settings, for Barker,
are natural units in no way imposed by an investigator.
To laymen they are as objective as rivers and forests
— they are parts of the objective environment that are experienced as directly as rain and sandy beaches are experienced. (Barker 1968, p. 11)
363
SettingsEach setting has a boundary which separates an organized internal (foreground) pattern from a differing external (background) pattern.
364
Nesting
Many settings occur in assemblies:
A unit in the middle range of a nesting structure is simultaneously both circumjacent and interjacent,
both whole and part,
both entity and environment.
365
Unity of Behaviour and Ecological Setting
A physical-behavioural unit is a unit: its parts are unified together, but not through any similarity or community of substance.
366
The Systematic Mutual Fittingness of Behaviour and Ecological Setting
The behaviour and the physical objects … are intertwined in such a way as to form a pattern that is by no means random: there is a relation of harmonious fit between the standard patterns of behaviour occurring within the unit and the pattern of its physical components.
Compare the way in which the processes in the body are constrained by the hierarchical organization of body, organs, cells …
367
The Systematic Mutual Fittingness of Behaviour and Ecological Setting
(The seats in the lecture hall face the speaker.
The speaker addresses his remarks out towards the audience.
The boundary of the football field is, leaving aside certain predetermined exceptions, the boundary of the game.)
368
Non-transposability
This mutual fittingness of behaviour and physical environment extends to the fine, interior structure of behaviour in a way which will imply a radical nontransposability of standing patterns of behaviour from one environment to another.
The physical or historical or ceremonial conditions obtaining in particular settings are in addition as essential for some kinds of behaviour as are persons with the requisite authority, motives and skills.
369
Power and Authority
There are various forces which help to bring about and to sustain this mutual fittingness and thus to constitute the unity of the physical-behavioural unit through time. Forces which flow in the direction from setting to behaviour include physical constraints exercised by hedges, walls or corridors or by persons with sticks; they include social forces manifested in the authority of the teacher, in threats, promises, warnings;
370
The Unifying Effects of the Physical Environment
they include the physiological effects of climate, the need for food and water; and they include the effects of perceived physiognomic features of the environment
(open spaces seduce children, a businesslike atmosphere encourages businesslike behaviour).
371
Mutual Fittingness
can be reinforced by learning, and also by a process of selection of the persons involved, whether this be one of self-selection (of children who remain in Sunday school class in light of their ability to conform to the corresponding standing patterns of behaviour), or of externally imposed mental or physical entrance tests.
372
Behaviour shapes Setting
Influences which flow from behaviour to setting, include all those ways in which a succession of separate and uncoordinated actions can have unintended consequences in the form of new types of actions and new, modified types of settings in the future (as the passage of many feet causes pathways to form in the hillside).
373
Settings shape Persons
Each person has many strengths, many intelligences, many social maturities, many speeds, many degrees of liberality and conservativeness, and many moralities, depending in large part on the particular contexts of the person’s behavior.
For example, the same person who displays marked obtusiveness when confronted with a mechanical problem may show impressive skill and adroitness in dealing with social situations.
374
Aurel Kolnai
a human society
… comprehends the same individual over and over again in line with his various social affiliations …
375
Daily life
= passage through a succession of physical-behavioural units which are as much a part of the furniture of reality as are garden-variety continuants and occurrents (such as you and me). Physical-behavioural units have parts.And they have consequences:contracts signed, orders issued, judgments passed, medals awarded.
376
Where are behavior settings?
SPANEntity extended in time
Portion of Spacetime
Fiat part of process *First phase of a clinical trial
Spacetime worm of 3 + Tdimensions
occupied by life of organism
Temporal interval *projection of organism’s life
onto temporal dimension
Aggregate of processes *Clinical trial
Process[±Relational]
Circulation of blood,secretion of hormones,course of disease, life
Processual Entity[Exists in space and time, unfolds
in time phase by phase]
Temporal boundary ofprocess *
onset of disease, death
spatio-temporal volumes
377
4-dimensional environments
Lobsters have evolved into environments marked by cyclical patterns of temperature change
Tudor EnglandThe Afghan winterThe window of opportunity for an
invasion of IraqThe surgical ward during early
morning
378
1
SPANEntity extended in time
Portion of Spacetime
Fiat part of process *First phase of a clinical trial
Spacetime worm of 3 + Tdimensions
occupied by life of organism
Temporal interval *projection of organism’s life
onto temporal dimension
Aggregate of processes *Clinical trial
Process[±Relational]
Circulation of blood,secretion of hormones,course of disease, life
Processual Entity[Exists in space and time, unfolds
in time phase by phase]
Temporal boundary ofprocess *
onset of disease, death
spatio-temporal volumes
standardizedpatterns of
behavior
379
The Theory of Granular Partitions
380
A Simple Partition
381
382
383
A partition can be more or less refined
A partition can be more or less refined
384
385
386
Partition
A partition is the drawing of a (typically complex) fiat boundary over a certain domain
387GrGr
388
A partition is transparent
It leaves the world exactly as it is
389Artist’s Grid
390
Label/Address System
A partition typically comes with labels and/or an address system
391
Montana
Montana
392
Cerebral Cortex
393
Mouse Chromosome Five
394
A partition can comprehend the whole of reality
395
Universe
396
It can do this in different ways
397
Periodic Table
398
Perspectivalism
PerspectivalismDifferent partitions may represent cuts through the same reality which are skew to each other
399
Universe/Periodic Table
400
Partitions can sometimes create objects
fiat objects = objects determined by partitions
401
Kansas
402
= objects which exist independently of our partitions
(objects with bona fide boundaries)
bona fide objects
403
404
California Land Cover
405Artist’s Grid
406
a partition is transparent (veridical)
= its fiat boundaries correspond at least to fiat boundaries on the side of the objects in its domain
if we are lucky they correspond to bona fide boundaries (JOINTS OF REALITY)
407
Tibble’s Tail
fiat boundary
408
Partitions are artefacts of our cognition
= of our referring, perceiving, classifying, mapping activity
409
and they always have a certain granularity
when I see an apple my partition does not recognize the molecules in the apple
410
Alberti’s Grid
411
Sets belong not to the realm of objects but to the realm of partitions
Sets are not objects in reality, but mathematical tools for talking about reality
412
Idealism
the road to idealism
propositions,sets,
noemata, ...
413
Goodman: Many worlds
Me: Many partitions
414
we have all been looking in the wrong direction
415
Dürer Reverse
416
Intentionality
417
Intentionality
418
corrected
content, meaningrepresentations
419
The mistaken view
420
The correct view
set-like structures belong here
421
Alberti’s Grid
422
Not propositional attitudes
but object attitudes
the attitudes mediated by partitions
(thus relatively coarse-grained)
423
Defining
Sets are (at best) special cases of partitions
Cells are to partitions as singletons are to sets
424
Objects and cells
objects are located in cells as guests are located in hotel rooms:
LA(x, z)
the analogue of the relation between an element and its singleton
425
an object x is recognized by a partition A:
x A := z (LA(x, z))
there is some cell in A in which x is located
426
Set as List Partition
A set is a list partition (a set is, roughly, a partition minus labels and address system)
The elements exist within the set withoutorder or location—they can be permuted at will and the set remains identical
427
Partitions better than sets
Partitions are
better than sets
428
David Lewis on Sets
Set theory rests on one central relation: the relation between element and singleton.
Sets are mereological fusions of their singletons (Lewis, Parts of Classes, 1991)
429
Cantor’s Hell
... the relation between an element and its singleton is “enveloped in mystery” (Lewis, Parts of Classes)
430
Cantor’s Hell
... the relation between an element and its singleton is “enveloped in mystery” (Lewis, Parts of Classes)
... the relation between an element and its singleton is “enveloped in mystery” (Lewis, Parts of Classes)
431
MysteryLewis:
... since all classes are fusions of singletons, and nothing over and above the singletons they’re made of, our utter ignorance about the nature of the singletons amounts to utter ignorance about the nature of classes generally.
432
An object can be located in a cell within a partition in any number of ways:
– object x exemplifies kind K
– object x possesses property P
– object x falls under concept C
– object x is in location L
433
The theory of partitionsis a theory of foregrounding,
of setting into relief
434
You use the name ‘Mont Blanc’ to refer to a certain mountain
You see Mont Blanc from a distance
In either case your attentions serve to foreground a certain portion of reality
Setting into Relief
435
You use the name ‘Mont Blanc’ to refer to a certain mountain
You see Mont Blanc from a distance
In either case your attentions serve to foreground a certain portion of reality
Setting into Relief
436
You use the name ‘Mont Blanc’ to refer to a certain mountain
You see Mont Blanc from a distance
In either case your attentions serve to foreground a certain portion of reality
Setting into Relief
437
You use the name ‘Mont Blanc’ to refer to a certain mountain
You see Mont Blanc from a distance
In either case your attentions serve to foreground a certain portion of reality
Setting into Relief
438
Foreground/Background
439
The Problem of the Many
There is no single answer to the question as to what it is to which the term ‘Mont Blanc’ refers. Many parcels of reality are equally deserving of the name ‘Mont Blanc’
– Think of its foothills and glaciers, and the fragments of moistened rock gradually peeling away from its exterior; think of all the rabbits crawling over its surface
440Mont Blanc from Lake Annecy
441
The world itself is not vague
Rather, many of the terms we use to refer to objects in reality are such that, when we use these terms, we stand to the corresponding parcels of reality in a relation that is one-to-many rather than one-to-one.
Something similar applies also when we perceive objects in reality.
442
Many but almost one
David Lewis:
There are always outlying particles, questionable parts of things, not definitely included and not definitely not included.
443
GranularityCognitive acts of Setting into Relief: the Source of Partitions
Partititions: the Source of Granularity
Granularity: the Source of Vagueness
444
Objects and cells
x A := z (LA(x, z)
there is some cell in A and x is located in that cell
Recall:object x is recognized by partition A
445
John
446
Tracing Over
Granularity: if x is recognized by a partition A, and y is part of x, it does not follow that y is recognized by A.
When you think of John on the baseball field, then the cells in John’s arm and the fly next to his ear belong to the portion of the world that does not fall under the beam of your referential searchlight.
They are traced over.
447
(Recall Husserl’s theory of Abschattungen)
(Ship of Theseus: different partitions of the same unterliegende sachliche
Tatbestandsmaterial)
448
John
449
Granularity the source of vagueness
... your partition does not recognize parts beneath a certain size.
This is why your partition is compatible with a range of possible views as to the ultimate constituents of the objects included in its foreground domain
450
Granularity the source of vagueness
It is the coarse-grainedness of our partitions which allows us to ignore questions as to the lower-level constituents of the objects foregrounded by our uses of singular terms.
This in its turn is what allows such objects to be specified vaguely
Our attentions are focused on those matters which lie above whatever is the pertinent granularity threshold.
451
Mont Blanc from Chatel
452
Mont Blanc (Tricot)
453
Bill Clinton is one person
– these are both supertrue
Mont Blanc is one mountain
454
they are trueh
no matter which of the many aggregates of matter you assign as precisified referent
455
Bill Clinton is one person
– both are true on the appropriate level of granularity(our normal, common-sense ontology is in perfect order as it stands)
Mont Blanc is one mountain
456
Standard Supervaluationism
A sentence is supertrue if and only if it is true under all precisifications. A sentence is superfalse if and only if it is false under all precisifications.
A sentence which is true under some ways of precisifying and false under others is said to fall down a supervaluational truth-value gap. Its truth-value is indeterminate.
457
Are those rabbits part of Mont Blanc?
458
Example of Gaps
On Standard Supervaluationism
Rabbits are part of Mont Blanc
falls down a supertruth-value gap
459
Different Contexts
In a perceptual context it is supertrue that these rabbits are part of Mont Blanc
In a normal context of explicit assertion it is superfalse that these rabbits are part of Mont Blanc
In a real estate context in a hunting community it is supertrue that these rabbits are part of that mountain
460
So, even with
Rabbits are part of Mont Blanc,
there are no gaps.
Are there any naturally occurring contextswith gaps?
461
Supervaluationism Contextualized
We pay attention in different ways and to different things in different contexts
So: the range of available precisified referents and the degree and the type of vagueness by which referring terms are affected will be dependent on context.
462
Supervaluationism Contextualized
The range of admissible precisifications depends on context
The evaluations of supervaluationism should be applied not to sentences taken in the abstract but to judgments taken in their concrete real-world contexts
463
No gapsThe everyday judgments made in everyday contexts do not fall down supervaluational truth-value gaps
because the sentences which might serve as vehicles for such judgments are in normal contexts not judgeable
464
Gaps and GlutsConsider:
Rabbits are part of Mont Blancis in a normal context unjudgeable
Compare:Sakhalin Island is both Japanese and
not Japanese
465
Problem cases
An artist is commissioned to paint a picture of Jesus Christ and uses himself as a model. Consider the judgment:
‘This is an image of Jesus Christ’
466
No gaps
Just as sentences with truth-value gaps are unjudgeable, so also are sentences with truth-value gluts. (Solution, here, to the liar paradox.
Pragmatic approach to problematic cases (e.g. liar paradox) ontologically clarified by contextualized supervaluationism
467
Normal contexts
including normal institutional contexts have immune systems which protect them against problematic utterances
such utterances are not taken seriously as expressing judgments
468
Judgments
exist only as occurring episodes within natural contexts
... thus they are partly determined by the immune systems which natural contexts standardly possess
469
Judgments and Evolution
Most naturally occurring contexts possess immune systems because those which did not would have been eliminated in the struggle for survival.
But the semantics hereby implied has nothing to do with pragmatic eliminations of objective truth normally favored by proponents of evoluationary epistemology
470
Contextualized Supervaluationism
A judgment p is supertrue if and only if:
(T1) it successfully imposes in its context C a partition of reality assigning to its constituent singular terms corresponding families of precisified aggregates, and
(T2) the corresponding families of aggregates are such that p is true however we select individuals from the many candidate precisifications.
471
Supertruth and superfalsehood are not symmetrical:
A judgment p is superfalse if and only if
either:
(F0) it fails to impose in its context C a partition of reality in which families of aggregates corresponding to its constituent singular referring terms are recognized,
472
Falsehood
or both:
(F1) the judgment successfully imposes in its context C a partition of reality assigning to its constituent singular terms corresponding families of precisified aggregates, and
(F2) the corresponding families of aggregates are such that p is false however we select individuals from the many candidate precisifications.
473
Pragmatic presupposition failure:
In case (F0), p fails to reach the starting gate for purposes of supervaluation
Consider: „Karol Wojtyła is more intelligent than the present Pope“
474
Lake Constance
No international treaty establishes where the borders of Switzerland, Germany, and Austria in or around Lake Constance lie.
Switzerland takes the view that the border runs through the middle of the Lake.
Austria and Germany take the view that all three countries have shared sovereignty over the whole Lake.
475
Lake Constance
If you buy a ticket to cross the lake by ferry in a Swiss railway station your ticket will take you only as far as the Swiss border (= only as far as the middle of the lake)
476
but for all normal contextsconcerning
fishing rights,
taxation,
shipping,
death at sea, etc., there are treaties regulating how decisions are to be made (with built in immune-systems guarding against problematic utterances)
477
Lake Constance
an ontological black hole in the middle of Europe
478
Lake Constance (D, CH, A)
SwitzerlandAustria
Germany
479
That Water is in SwitzerlandYou point to a certain kilometer-wide volume of water in the center of the Lake, and you assert:
[Q] That water is in Switzerland.
Does [Q] assert a truth on some precisifications and a falsehood on others?
480
No
By criterion (F0) above, [Q] is simply (super)false.
Whoever uses [Q] to make a judgment in the context of currently operative international law is making the same sort of radical mistake as is someone who judges that Karol Wojtyła is more intelligent than the present Pope.
481
Reaching the Starting GateIn both cases reality is not such as to sustain a partition of the needed sort.
The relevant judgment does not even reach the starting gate as concerns our ability to evaluate its truth and falsehood via assignments of specific portions of reality to its constituent singular terms.
482
Partitions do not care
Our ordinary judgments, including our ordinary scientific judgments, have determinate truth-values
because the partitions they impose upon reality do not care about the small (molecule-sized) differences between different precisified referents.
483
Again:
Enduring types of (social, legal, administrative, planning) contexts have immune systems to prevent the appearance of the sort of problematic vagueness that is marked by gaps and gluts
484
No Gaps‘Bald’, ‘cat’, ‘dead’, ‘mountain’ are all vague
But corresponding (normal) judgments nonetheless have determinate truth-values.
There are (on one way of precisifying ‘normal’ in the above) no truth-value gaps
485
philosophical contexts are not normal
486
DOWN
WITH
PHILOSOPHY !
487
An ontology
is a canonical representation of the types of entities in a given domain and of the types of relations between these entities:
holy grail of a single benchmark ontology, which would make all databases intertranslatable
an ontological Esperanto
488
Ontological Zooming
489
Universe/Periodic Table
animal
bird
canary
ostrich
fishfolk biology
partition of DNA space
490
Universe/Periodic Table
animal
bird
canary
ostrich
fish
both are transparent partitions of one and the same reality
491
492
Ontology
like cartography
must work with maps at different scales and with maps picking out different dimensions of invariants
493
If ontological realism is rightthen 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
494
There are not only map-like partitions of reality into material (spatial) chunks
but also distinct partitions of reality into universals (genera, categories, kinds, types)
mutually compatible ways of providing inventories of universals
(among proteins, among cells, among organisms …)
and distinct ways of partitioning the temporal dimension of processes
495
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
496
One example of ‘folk’ partition
WordNet[1] developed at the University of Princeton defines concepts as clusters of terms called synsets. Wordnet consists of some 100,000 synsets
organized hierarchically via:A concept represented by the synset {x, x, …} is
said to be a hyponym of the concept represented by the synset {y, y,…} if native speakers of English accept sentences constructed from such frames as « An x is a kind of y ».
497
A Formal Theory of Granular Partitions
Thomas Bittner and Barry Smith
http://ontology.buffalo.edu/smith/articles/partitions.pdf
498
The Parable of the Two Tables
from Arthur Eddington, The Nature of the Physical World (1928)
Table No. 1 = the ordinary solid table made of wood
Table No. 2 = the scientific table
499
The Parable of the Two Tables
‘My scientific table is mostly emptiness. Sparsely scattered in that emptiness are numerous electric charges rushing about with great speed; but their combined bulk amounts to less than a billionth of the bulk of the table itself.’
500
Eddington:
Only the scientific table exists.
501
The Parable of the Two Tables
Both of the tables exist – in the same place: in fact they are the same table but pictured in maps of different scales
the job of the theory of granular partitions is to do justice to this identity in (granular) difference
502
Towards a Theory of Intentionality / Reference / Cognitive Directedness
GRANULAR PARTITIONS: THE SECOND DIMENSION
503
Intentional directedness
… is effected via partitions
we reach out to objects because partitions are transparent
504
Applications
Theory of selectivity of cognition (including natural language cognition)
Theory of granularity (medical data, genetic data)
Theory of transformations between partitions of the same reality (SNOMED, UMLS …)
505
THE END
THE END