Glüer II 22
Truth theory/Davidson: the defined T-predicate (truth predicate) in the metalanguage can be translated back into the object language and the state before the elimination of the true can be restored.
>
Truth predicate, >
Object language, >
Metalanguage.
Object language and metalanguage should contain the predicate true.
>
Homophony.
Davidson, however, can evade the dilemma by not giving a definition. He calls it a definition of truth in Tarski's style, hereafter referred to as T-theory.
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Rorty IV (a) 22
True/Tarski: the equivalences between the two sides of the T-sentences do not correspond to any causal relationship.
>
Tarski scheme, >
Equivalence.
Davidson: there is no way to subdivide the true sentences so that on the one hand they express "factual", while on the other side they do not express anything.
Cf. >
Correspondence, >
Correspondence theory.
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Berka I 396
Truth/Tarski: we start from the classical correspondence theory.
I 399
We interpret truth like this: we want to see all sentences as valid, which correspond to the Tarski scheme - these are partial definitions of the concept of truth. - Objectively applicable: is the truth definition, if we are able, to prove all the mentioned partial definitions on the basis of the meta language.
(1)
1. A.Tarski, „Grundlegung der wissenschaftlichen Semantik“, in: Actes du Congrès International de Philosophie Scientifique, Paris 1935, Vol. III, ASI 390, Paris 1936, pp. 1-8
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Berka I 475
Truth-Definition/truth/Tarski: wrong: to assume that a true statement is nothing more than a provable sentence. - This is purely structural.
Problem: No truth-definition must contradict the sentence definition.
N.B.: but this has no validity in the field of provable sentences. - E.g. There may be two contradictory statements that are not provable. - All provable statements are indeed content-wise true. Nevertheless the truth definition must also contain the non-provable sentences.
>
Provability, >
Definitions.
Berka I 482
Definition true statement/Tarski: x is a true statement, notation
x ε Wr iff. x ε AS
(meaningful statement) and if every infinite sequence of classes satisfies x.
>
Satisfaction/Tarski.
That does not deliver a truth criterion.
>
Truth criterion.
No problem: nevertheless the sense of
x ε Wr
(x belongs to the class of true statements) gets understandable and unambiguous.
I 486
Relative Truth/accuracy in the range/Tarski: plays a much greater role than the (Hilbertian) concept of absolute truth, which was previously mentioned - then we modify Definition 22 (recursive fulfillment) and 23 (truth).
As derived terms we will introduce the term of the statement that
a) in a domain of individuals with k elements is correct and
b) of the statement that is true in every domain of individuals.
(2)
2. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol. 1, Lemberg 1935
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Horwich I 111
Truth/Tarski: is a property of sentences - but in the explanation we refer to "facts". - ((s) Quotation marks by Tarski).
>
Facts.
Horwich I 124
Truth/true/eliminability/Tarski: truth cannot be eliminated with generalizations if we want to say that all true sentences have a certain property.
E.g. All consequences of true sentences are true.
Also not eliminable: in particular statements of the form "x is true": E.g. the first sentence that Plato wrote, is true.
Because we do not have enough historical knowledge.
(3)
((s) The designation "the first sentence..." is here the name of the sentence. This cannot be converted into the sentence itself.
Eliminability: from definition is quite different from that of redundancy.)
>
Elimination, >
Eliminability, cf. >
Redundancy theory.
3. A. Tarski, The semantic Conceptions of Truth, Philosophy and Phenomenological Research 4, pp. 341-75
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Skirbekk I 156
Definition Truth/Tarski: a statement is true when it is satisfied by all objects, otherwise false.
Skirbekk I 158
Truth/Tarski: with our definition, we can prove the (semantic, not the logical) sentence of contradiction and the sentence definition. - The propositional logic does not include the term true at all.
Truth almost never coincides with provability.
All provable statements are true, but there are true statements that cannot be proved. - Such disciplines are consistent but incomplete.
>
Incompleteness/Gödel). There is even a pair of contradictory statements, neither of which is provable.
(4)
4. A.Tarski, „Die semantische Konzeption der Wahrheit und die Grundlagen der Semantik“ (1944) in: G. Skirbekk (ed.) Wahrheitstheorien, Frankfurt 1996
