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Semantic Categories | Tarski | Berka I 498 Def Semantic Category/meaning category/Husserl/Tarski: 1. two expressions belong to the same meaning category when its first propositional function is one that contains any of these phrases. 2. When no function that contains one of these expressions loses the character of a propositional function if this expression is substituted by the other - ( reflexive, transitive, symmetric). Example of Category propositional function: e.g. names of individuals - e.g. variables. >Propositional functions, >Variables, >Proper names, >Meaning categories. I 499 Def Main Principle of semantic categories/Tarski: in everyday language a single case seems to satisfy the propositional function which is preserved while replacing the expression. >Everyday language. Meaning category/Tarski: here not for compound expressions but only for variables - Decisive is the mere form. Wit of the Main Principle: we want that substitution always results in new statements, we can use as variables only expressions of the same semantic category. >Inserting, >Substitution, >Abstraction/Tarski. I 500 It follows that no character can be a functor of two functions at the same time that can have a different number of arguments or two such functions (even if they have the same number of arguments) in which two of their relevant arguments belong to different meaning categories. >Uniqueness, >Unambiguity, >Functors. I 520 Bound variables have no influence on the semantic type.(1) >Bound variables. 1. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol. 1, Lemberg 1935 |
Tarski I A. Tarski Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
That | Cresswell | II 30 That/attribution of propositional attitudes/Cresswell: "that" should be a function that is applied to the referents of the partial expressions. Value: of this function is then the structure (>Structure = >Sense). Argument/(s): here reference of the parts of the complement sentence. Reference/that-clause/Cresswell: (very similar to Frege): the reference of the that-clause is the sense (the mode of being given) of the complement sentence (of the sentence that follows the "that"). That/meaning: if it is a function, it is a triple or quadruple ... - II 69 Notation/Cresswell: D: Range D0: refers to the set of all sets of possible worlds D1: to the universe of things >Semantic categories/meaning categories D(0/1): is a class of (one-digit) functions of things (elements of D1) on sets of possible worlds (Elements of D0), etc. |
Cr I M. J. Cresswell Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988 Cr II M. J. Cresswell Structured Meanings Cambridge Mass. 1984 |
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