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Semantik für Realisten
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1. Die Welt ist alles was der Fall ist.
Das, was nicht der Fall ist, gehört nicht zur Welt.
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5.6 Die Grenzen meiner Sprache bedeuten die Grenzen meiner Welt.
Falschheiten (das, was nicht der Fall ist) kann ich in meiner Sprache nicht zum Ausdruck bringen.
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Wittgensteins Lösung
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2. Was der Fall ist, die Tatsache, ist das Bestehen von Sachverhalten.
Sachverhalte können also bestehen oder nicht bestehen.
Es gibt also nicht nur die Welt, sondern auch zusätzliche Bereiche (von möglichen Welten, nicht-bestehenden Sachverhalten udgl.)
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2.01 Der Sachverhalt ist eine Verbindung von Gegenständen (Sachen, Dingen).
Dies gilt eigentlich nur von bestehenden Sachverhalten.
Wie vermeiden wir nicht-bestehende Sachverhalte?
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Wittgensteins Bildtheorie der Sprache
2.1 Wir machen uns Bilder der Tatsachen.
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Das propositionale Bild als ein Komplex von Namen
3.14 Das Satzzeichen besteht darin, dass sich seine Elemente, die Wörter, in ihm auf bestimmte Art und Weise voneinander verhalten.
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Satz
a r b
4.22 Der Elementarsatz besteht aus Namen.Er ist ein Zusammenhang, eine Verkettung, von Namen.
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Satz und Sachverhalt
a r b
language
world
names
simple objects
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Der Satz als Bild eines Sachverhalts
3.21 Der Konfiguration der einfachen Zeichen im Satzzeichen entspricht die Konfiguration der Gegenstände in der Sachlage.
3.22 Der Name vertritt im Satz der Gegenstand.
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Satz und Sachverhalt
a r b
language
world
projection
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Die Projektion
3.12 ... der Satz ist das Satzzeichen in seiner projektiven Beziehung zur Welt.
3.13 Zum Satz gehört alles, was zur Projektion gehört; aber nicht das Projizierte.
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Semantic Projection
„ Blanche is shaking hands with Claire “
Ein Satz
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A Map
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Satz und Sachverhalt
a r b
Semantic Projection
„ John kisses Mary “
John this kiss Mary
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Falsehood
2.21 Das Bild stimmt mit der Wirklichkeit überein oder nicht; es ist richtig oder unrichtig, wahr oder falsch.
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Satz und Sachverhalt
a r b
Falsehood
„John kisses Mary“
John Maryprojection
fails
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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, or
2. failure of coordination
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4.25 Ist der Elementarsatz wahr, so besteht der Sachverhalt; ist der Elementarsatz falsch, so besteht der Sachverhalt nicht.
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Satz und Sachverhalt
a r b
Projection Failure
„John kisses 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 kisses Mary“
John Mary
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Coordination Failure
a r b„John kisses 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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Semantic Projection„ Blanche is shaking hands with Claire “
Semantic Projection
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Optical Projection
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Cartographic Hooks
Cartographic Projection
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Semantic ProjectionThe Problem of Vagueness
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Semantic Projection
„ Blanche is shaking hands with Claire “
The Problem of Vagueness
what is thisentity called ashaking of hands?
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The Problem of Vagueness
Wittgenstein solved this problem by presupposing that the world is made up of absolute simples and that only in relation to configurations of absolute simples can language picture reality.
Can the semantic realist find a better solution?
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The basic machinery of realist semantics
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A Simple Partition
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A partition can be more or less refined
A partition can be more or less refined
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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 or coordinate system
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Cerebral Cortex
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Mouse Chromosome Five
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Partitions are artefacts of our cognition
= of our referring, perceiving, classifying, mapping activity
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Partitions always have a certain granularity:
when I see an apple my partition does not recognize the molecules in the apple
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A partition is transparent
= it corresponds to a true propositional picture in the sense of the Tractatus
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Intentionality
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Intentionality
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CartographicHooks
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an object x is recognized by a partition:
= there is some cell in which x is located
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The theory of partitionsis a theory of foregrounding,of setting into relief
Cf. L. Talmy, The Windowing of Attention in Language
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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
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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
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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
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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
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Hertz
4.04 Am Satz muss gerade soviel zu unterscheiden sein, als an der Sachlage die er darstellt. Die beiden müssen die gleiche logische (mathematische) Mannigfaltigkeit besitzen.
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Wittgenstein: a sentence can picture a complex in reality only if the two have the same logical-mathematical multiplicity.
Have we solved this problem of logical-mathematical multiplicity?
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Cartographic Hooks
Cartographic Projection
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Foreground/Background
our partition does not allow us torecognize objects beneath a certain size
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Have we solved the problem of logical-mathematical multiplicity?
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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
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Mont Blanc from Chatel
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Mont Blanc (Tricot)
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The world itself is not vague
Rather, there are for any given referring term different equally good ways to demarcate its referent from out of the surrounding messy reality
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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.
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Many but almost oneDavid Lewis:
There are always outlying particles, questionable parts of things, not definitely included and not definitely not included.
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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 the partition A.
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John
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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.
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John
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Granularity
Cognitive acts of Setting into Relief: the Source of Partitions
Partititions: the Source of Granularity
Granularity: the Source of Vagueness
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John
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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
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Granularity the source of vaguenessIt 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.
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Reference can be successful even though our referring terms are vague
Satz und Sachverhalta r b
projection
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Reference can be successful even though our referring terms are vague
Satz und Sachverhalta r b
alternative crisp aggregates of matter
projection is a one-to-many function
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Bill Clinton is one person
Mont Blanc is one mountain
Consider:
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these are both trueno matter which of the many aggregates of matter we assign as precisified referent of the corresponding terms
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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
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John is kissing Mary
Blanche is shaking hands with Claire
and the same applies to:
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The world is messyHow to solve the problem of vagueness?
Supervaluationism:
we need to distinguish between truth and supertruth
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Definition of precisification
a precisification is an acceptable way of projecting from a term to a crisp aggregate of matter
(to Bill Clinton with these hairs in his ear, to Bill Clinton without those hairs in his ear, and so on)
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For each term
there is a range of admissible precisified references
(some with bits of hair, some without; some with bits of food, some without)
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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.
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but ...
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semantic realism has no room for truth-value gaps
4.25 Ist der Elementarsatz wahr, so besteht der Sachverhalt; ist der Elementarsatz falsch, so besteht der Sachverhalt nicht.
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Mont Blanc (Tricot)look for the rabbits
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Are those rabbits part of Mont Blanc?
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Mont Blanc (Tricot)
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Example of Gaps
On Standard Supervaluationism
Rabbits are part of Mont Blanc
falls down a supertruth-value gap
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Rabbits
Some precisifications contain rabbits as parts
Some precisifications do not contain rabbits as parts
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Can we do better?
Well consider that there are different contexts involved
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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
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The hunter says: These rabbits are
part of my mountain
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But now, if we stick to some one given context, then even with
Rabbits are part of Mont Blanc,
there are no gaps.
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Hypothesis:
projection always within some given context
there are no naturallyoccurring contexts with gaps
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Supervaluationism Contextualized
We pay attention in different ways and to different things in different contexts
So: the range of available precisified referents is dependent on context.
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Supervaluationism Contextualized
Thus the evaluations of supervaluationism should be applied not to sentences taken in the abstract but to judgments taken in their concrete real-world contexts
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No gaps
The everyday judgments made in everyday contexts do not fall down supervaluational truth-value gaps
This is so, because the sentences which might serve as vehicles for such judgments are in normal contexts not judgeable
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Unjudgeability
Consider:
Rabbits are part of Mont Blanc
is in the normal contexts occupied by you and me unjudgeable
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Normal contexts
(including normal institutional contexts) have immune systems which protect them against problematic utterances
such utterances are not taken seriously as expressing judgments
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Judgments and Evolution
Most naturally occurring contexts possess immune systems because those which did not would have been eliminated in the struggle for survival.
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Contextualized Supervaluationism
A judgment p is supertrue if and only if:
• (T1) the judgment successfully projects, in its context C, upon corresponding families of precisifications, and
• (T2) the corresponding families of precisifications are such that p is true whichever precisification we select.
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Supertruth and superfalsehood are not symmetrical:
A judgment p is superfalse if and only if
either:
• (F0) it fails to project, in its context C, upon anything in the world corresponding to its constituent singular referring terms,
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Falsehoodor both:
• (F1) the judgment successfully projects, in its context C, upon corresponding families of precisifications, and
• (F2) the corresponding families of precisifications are such that p is false whichever precisification we select.
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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“
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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.
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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)
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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)
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Lake Constance
an ontological black hole in the middle of Europe
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Lake Constance (D, CH, A)
SwitzerlandAustria
Germany
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That Water is in Switzerland
You 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?
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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.
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Reaching the Starting Gate
In 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.
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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.
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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
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The philosophical contexts invented by philosophers interested in the logic of vagueness are not normal
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DOWN
WITH
PHILOSOPHY !
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THE END
THE END
