1 truth and categorization barry smith
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Truth and CategorizationBarry Smith
http://ontology.buffalo.edu
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A categorization
is a sorting,
a dividing,
a partitioning of reality,
or of a certain portion of reality
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All categorizations are partial
(we are finite beings)
But nearly all categorizations are true, correct, veridical
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Borges’ Chinese Encyclopedia
• animals which belong to the emperor• embalmed animals• sirens• fabulous animals• wild dogs• which are painted with a fine camelhair brush• which have broken the water-pitcher• which look like flies from a distiance
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A Simple Partition
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A partition can be more or less refined
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Partition
A partition is the drawing of a (typically complex) fiat boundary over a certain domain
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GrGr
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Partitions are artefacts of our cognition
= of our categorizing, sorting, classifying, naming, listing, referring, perceiving, mapping activity
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A partition is transparent
It leaves the world exactly as it is
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Artist’s Grid
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Label/Address System
A partition typically comes with labels and/or an address system
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Dewey Decimal Classification
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Dewey Decimal Classification
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All transparent partitions are equal
... but some are more equal than others
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There are many, competing criteria for quality of partitions:
completeness
naturalness
principledness
…
(Borges’ Chinese Encyclopedia violates them all)
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Some partitions support reliable predictions
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Mouse Chromosome Five
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Some do not …
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DER
(masculine)
moon
lake
atom
DIE
(feminine)
sea
sun
earth
DAS
(neuter)
girl
firedangerous thing
The der-die-das Partition
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The Empty Mask (Magritte)
mama
mouse
milk
Mount Washington
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Mothers exist
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The common sense partitions of folk physics, folk psychology, folk biology, are all transparent to reality
Aristotelianism for today:
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... rook bishop pawn knight ...
John Paul George Ringo
... up down charm strange ...
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Even the partitions of reductionists are transparent
The objects admitted by the nominalist, the process-metaphysician, the physicalist, truly do exist.
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Reductionists err only when they add ‘and nothing else exists’
(as if one were to insist that only maps of exactly one preferred scale can be true of reality)
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are our scientific partitions truly transparent to an independent reality ?
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... what about quantum mechanics ?
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Refinement
a partition can be refined or coarsened by adding or subtracting from its constituent cell-divisions
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Manipulation of partitions
• refinement
• coarsening
• gluing
• restricting
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Enlargement of a partition
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The realist’s ideal
A total partition of the universe, a super-partition (a God’s eye view) satisfying:
“Every element of the physical reality has a counterpart in the physical theory.”
(Einstein-Podolsky-Rosen 1935)
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A universal partition
why not just take the product of all partitions covering each successive domain and glue them all together ?
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Ontological Problem
In the quantum domain not all transparent partitions are consistent
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But still:
In relation to the mesoscopic and macroscopic realms sense realism holds with unrestricted validity
Indeed we can derive the truths of folk physics rigorously from quantum mechanical laws
we do this by moving from finer-grained to coarser-grained histories
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A partition can comprehend the whole of reality
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Universe
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It can do this in different ways
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The Spinoza Partition
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Periodic Table
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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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(You can cut the cheese in different ways)
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Universe/Periodic Table
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Partitions have different granularity
just as maps have different scales
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Partitions can have empty cells
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0 1 2 3 4 …
Partition of people in this room according to: number of years spent in jail
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Partition of people in this room according to: number of days spent in jail
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Therefore a good theory of
partitions needs more than
one empty set.
(We can err in many ways.)
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Partitions can sometimes create objects
fiat objects = objects created by partitions
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Tibble’s Tail
fiat boundary
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Canada
Que
bec
Canada
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Kansas
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= objects which exist independently of our partitions
(objects with bona fide boundaries)
bona fide objects
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globe
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Some partitions involve both types of boundaries
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Cerebral Cortex
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California Land Cover
Reciprocal partitions
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a partition is transparent (veridical)
1. its fiat boundaries correspond at least to fiat boundaries on the side of the objects in its domain
2. if we are lucky they correspond to bona fide boundaries (JOINTS OF REALITY)
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In case 1. our partition/categorization is a discretization of a continuum
In case 2. our partition/categorization captures discrete divisions on the sides of the objects
In both cases our partitions are transparent
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What is a partition?
a way of successfully projecting a system of cells upon reality
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These are different ways in which cells can be projected successfully onto reality
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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 spatial location L
– object x is in measurement-band B
contrast the meager resources of set theory
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Intentional directedness
… is effected via partitions
we reach out to objects because partitions are transparent
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and they always have a certain granularity
when I see an apple my partition does not recognize the molecules in the apple
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This is a mistake
propositions,sets, noemata,
meanings, models,
concepts, senses, ...
content does not belong in the target position
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Intentionality
this is the correct view
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corrected
content, meaningrepresentations are transparent – they are like spectacles
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Intentionality
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AGAINST “PROPOSITIONAL ATTITUDES”
Examples of pseudo-problems in philosophy:
what are ‘meanings’?
what are the identity criteria for meanings?
where is the ‘realm of meanings’?
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The worst example of a pseudo-problem in the history of philosophy:
How can we ever transcend the realm of meanings / contents / ideas / sensations / noemata and reach out to the realm of objects in themselves ?
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Intentional directedness
… is effected via partitions
we reach out to objects because partitions are transparent
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1 2 3 4
Counting requires partitions
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Frege: “Numbers belong to the realm of concepts”
Smith: Numbers belong to the realm of partitions
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Measurement belongs to the realm of partitions
... -20-10 -10 0 0 10 10 20 ...
massivelyincreased... normal increased chronic ...
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Sets belong to the realm of partitions
Sets are not objects in reality, but mathematical tools for talking about reality
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Another mistake:
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The correct view
set-like structures belong here
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Defining
Sets are (at best) special cases of partitions
Cells are to partitions as singletons are to sets
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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
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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
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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)
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Cantor’s Hell
... the relation between an element and its singleton is
“enveloped in mystery”
(Lewis, Parts of Classes)
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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)
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Partitions better than sets
Partitions are
as we can see
better than sets
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Mystery
Lewis:
... 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.
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The ‚mystery‘ of set theory arises from supposing that sets are objects
This is the root, also, of Frege’s problem in the Grundgesetze
This is the root of the catastrophic high- rise projects of post-Cantorian set theory
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Demolition
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Cantor’s Hell
arises because set theory confuses
the fiat boundaries generated by our partitions (e.g. by our setting certain phenomena into relief in terms of the ‘real numbers’)
with bona fide boundaries possessed by special objects (the sets)
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How do partitions, classifications, categories relate to reality
via intentionality (via the projections of conscious subjects)
partitions, classifications, categories are cognitive artefacts
but they are transparent to what exists on the side of objects in reality
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An (Irregular) Partition
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A Portion of Reality
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Cartographic Hooks
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A Map
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A Sentence
Blanche is shaking hands with Mary
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A Portion of Reality
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Semantic Hooks
Blanche is shaking hands with Mary
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A Sentence
Blanche is shaking hands with Mary
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Wittgenstein‘s Tractatus on Projection
3.12 ... the proposition is the propositional sign in its projective relation to the world
3.13 to the proposition belongs everything which belongs to the projection; not however that which is projected
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Satz und Sachverhalt
a r b
language
world
names
simple objects
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Satz und Sachverhalt
a r b
language
world
cells(in coarse-grained partitions)
simpleand complex objects
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Satz und Sachverhalt
a r b
language
world
projection
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Satz und Sachverhalt
a r b
Semantic Projection
„ John is kissing Mary “
John this kiss Mary
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Truth is a free lunch
Truth is easy easy to come by, even for
small children; easy to explain (if you avoid
Kant and other bad philosophy)
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Falsehood: A Realist Theory
Falsehood is not: successful conformity with some non-existing state of affairs
... it is the failure of an attempted conformity, resting on either
1. failure of projection, or2. failure of coordination
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Satz und Sachverhalt
a r b
Projection Failure
„John is kissing Mary“
John Mary
nothing here
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Nothing
really nothing
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Satz und Sachverhalt
a r b
Projection Failure
„John is kissing Mary“
John Mary
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Coordination Failure
a r b„John is kissing Mary“
Mary this kiss John
Coordination Failure
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Realist Semantics
We begin with a theory of propositions as articulated pictures of reality
The theory of truth comes along as a free lunch
We then show how to deal with the two kinds of failure which constitute falsehood
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THE END
THE END