Semantic Theory of Truth as a Correspondence Theory
As I earlier indicated that STT is the correspondence theory of truth in modern setting. Presumably, this qualification can be justified either by appealing to (SDT) or by reference to (TE).
The latter option seems fairly correct and justified by Tarski's own explanations. In particular, his famous example that the sentence(i) ‘snow is white' is true if and only if snow is white, points out that because (i) says that snow is white and it is so as this sentence says, (i) is true. What about the intuitive content of (TD)? We have two possibilities, firstly, that it is a mathematical trick, and, secondly, that (SDT) brings some intuitions concerning the correspondence theory of truth. Clearly, sequences of objects cannot be identifies with facts. Moreover, the satisfaction by the empty sequence appears as an artificial construction (see Tarski 1933, p. 195; page-reference to Tarski 1956). On the other hand, if (SDT) is a special case of the definition of satisfaction and the latter is based on explicit intuitions, it suggests that perhaps some philosophical intuitions are behind (SDT) as well. I am inclined to take this option. That an open formula is satisfied or not by an object, depends of valuation of free variables. Such valuations are irrelevant in the case of sentences, because they do not contain free variables. Consequently, every infinite sequence of objects can be ascribed to bound variables or individual constants. As far as the second case is concerned, we can eliminate individual constants via identity and existential quantification or say that if V(a) = o, every infinite sequence of objects with o as the first member, satisfies the formula Pa, if o satisfies this formula. The same can be expressed by saying that the empty sequence satisfies a sentence, because no free variables occur in it. What remains? The answer is that being true depends on how L is interpreted and, metaphorically speaking, how things are in M associated with L interpreted by V. And it precisely expresses what is established by the T-scheme. Informally speaking, truth depends on the domain sentences say about. If one wants connects this explanations with facts, we could perhaps say that a given sentence A of L cannot be demonstrated as false in M if it is the satisfaction by the empty sequence (or by all infinite sequences or by one infinites sequence) excludes, provided that V is fixed. Putting this in other words, if A is true, no fact defined on M can be A-falsifier.
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