5 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.)
6 2.01 Der Sachverhalt ist eine Verbindung von Gegenständen (Sachen, Dingen). Dies gilt eigentlich nur von bestehenden Sachverhalten. Wie vermeiden wir nicht- bestehende Sachverhalte?
7 Wittgensteins Bildtheorie der Sprache 2.1 Wir machen uns Bilder der Tatsachen.
8 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.
9 Satz arb 4.22 Der Elementarsatz besteht aus Namen. Er ist ein Zusammenhang, eine Verkettung, von Namen.
10 Satz und Sachverhalt arb language world names simple objects
11 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.
12 Satz und Sachverhalt arb language world projection
13 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.
14 Semantic Projection Blanche is shaking hands with Claire Ein Satz
16 Satz und Sachverhalt arb Semantic Projection John kisses Mary John this kiss Mary
17 Falsehood 2.21 Das Bild stimmt mit der Wirklichkeit überein oder nicht; es ist richtig oder unrichtig, wahr oder falsch.
18 Satz und Sachverhalt arb Falsehood John kisses Mary John Mary projection fails
19 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
20 4.25 Ist der Elementarsatz wahr, so besteht der Sachverhalt; ist der Elementarsatz falsch, so besteht der Sachverhalt nicht.
21 Satz und Sachverhalt arb Projection Failure John kisses Mary John Mary nothing here
23 Satz und Sachverhalt arb Projection Failure John kisses Mary John Mary
24 Coordination Failure arb John kisses Mary Mary this kiss John Coordination Failure
25 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
26 Semantic Projection Blanche is shaking hands with Claire Semantic Projection
29 Semantic Projection The Problem of Vagueness
30 Semantic Projection Blanche is shaking hands with Claire The Problem of Vagueness what is this entity called a shaking of hands?
31 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?
58 Foreground/Background our partition does not allow us to recognize objects beneath a certain size
59 Have we solved the problem of logical-mathematical multiplicity?
60 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
63 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
64 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.
65 Many but almost one David Lewis: There are always outlying particles, questionable parts of things, not definitely included and not definitely not included.
66 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.
68 When you think of John on the baseball field, then the cells in Johns 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.
72 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
73 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.
74 Reference can be successful even though our referring terms are vague Satz und Sachverhalt arb projection
75 Reference can be successful even though our referring terms are vague Satz und Sachverhalt arb alternative crisp aggregates of matter projection is a one-to-many function
76 Bill Clinton is one person Mont Blanc is one mountain Consider:
77 these are both true no matter which of the many aggregates of matter we assign as precisified referent of the corresponding terms
78 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
79 John is kissing Mary Blanche is shaking hands with Claire and the same applies to:
80 The world is messy How to solve the problem of vagueness? Supervaluationism: we need to distinguish between truth and supertruth
81 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)
82 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)
83 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.
89 Example of Gaps On Standard Supervaluationism Rabbits are part of Mont Blanc falls down a supertruth-value gap
90 Rabbits Some precisifications contain rabbits as parts Some precisifications do not contain rabbits as parts
91 Can we do better? Well consider that there are different contexts involved
92 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
93 The hunter says: These rabbits are part of my mountain
94 But now, if we stick to some one given context, then even with Rabbits are part of Mont Blanc, there are no gaps.
95 Hypothesis: projection always within some given context there are no naturally occurring contexts with gaps
96 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.
97 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
98 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
99 Unjudgeability Consider: Rabbits are part of Mont Blanc is in the normal contexts occupied by you and me unjudgeable
100 Normal contexts (including normal institutional contexts) have immune systems which protect them against problematic utterances such utterances are not taken seriously as expressing judgments
101 Judgments and Evolution Most naturally occurring contexts possess immune systems because those which did not would have been eliminated in the struggle for survival.
102 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.
103 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,
104 Falsehood or 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.
105 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
106 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.
107 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)
108 but for all normal contexts concerning 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)
109 Lake Constance an ontological black hole in the middle of Europe
110 Lake Constance (D, CH, A) Switzerland Austria Germany
111 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?
112 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.
113 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.
114 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.
115 No Gaps Bald, cat, dead, mountain are all vague But corresponding (normal) judgments nonetheless have determinate truth- values. There are (on one way of precisifyingnormal in the above) no truth-value gaps
116 The philosophical contexts invented by philosophers interested in the logic of vagueness are not normal