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The author or concept searched is found in the following 6 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Arithmetics | Waismann | I 50 Arithmetics/Waisman: arithmetics is based on logic. In doing so, one makes strong use of terms of the set theory, or the class calculus. The assertion that mathematics is only a >"part of logic" includes two theses, which are not always clearly separated: (A) The basic concepts of arithmetic can be traced back by definition to purely logical ones. (B) The principles of arithmetic can be deduced by means of proof from purely logical propositions. >Basic concepts, >Propositions, >Definitions, Definability. |
Waismann I F. Waismann Einführung in das mathematische Denken Darmstadt 1996 Waismann II F. Waismann Logik, Sprache, Philosophie Stuttgart 1976 |
| Calculus | Tarski | Berka I 505 Calculus of classes/Tarski: satisfaction by sequences of objects.(1) >Sequences/Tarski, >Satisfaction/Tarski, >Satisfiability/Tarski, >Truth/Tarski, >Class calculus. 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 |
| Criteria | Tarski | Horwich I 130 Truth criterion/criteria/Tarski: we will probably never find a critoron for truth. - But equally not for most other concepts including physics.(1) >Truth criterion, >Definition/criterion. 1. A. Tarski, The semantic Conceptions of Truth, Philosophy and Phenomenological Research 4, pp. 341-75 Skirbekk I 177 Criterion of truth/Tarski: there is no tuth criterion that shows that there is no wrong record of an empirical theory. ((s) The criterion cnnot be found in the sttements - these are different.) Tarski: Common feature of true propositions: truth, not a criterion as blackness of the coal and whiteness of the snow.(2) Cf. >Truth/Quine. 2. A.Tarski, „Die semantische Konzeption der Wahrheit und die Grundlagen der Semantik“ (1944) in: G. Skirbekk (ed.) Wahrheitstheorien, Frankfurt 1996 Berka I 492 Truth/criterion/structural/Tarski: a structural truth-criterion allows each statement of the language to effectively allocate a statement that is equivalent to them, which, if it is not quantitative, is obviously true or obviously wrong. That works in the class calculus. A structural characteristic of true statements possible if it can be shown that the class of individuals is infinite. ((s) Because then accuracy/provability coincide). >general criterion of truth. >Definitions/Tarski, >Correctness, >Provability. I 502 Criterion of truth/structural/Tarski: is given to us in that we find that the concept of the true statement (from §3) and the one of the provable theorem (due to the matrix method) are of the same scope. >Term scope. Problem: this is only true for simple languages - (i.e. with only a single semantic category E.g. only individuals).(3) >Semantic categories. 3. 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 Horwich I P. Horwich (Ed.) Theories of Truth Aldershot 1994 Skirbekk I G. Skirbekk (Hg) Wahrheitstheorien In Wahrheitstheorien, Gunnar Skirbekk Frankfurt 1977 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Method | Tarski | Berka I 401 Consistent-proof/Gödel: cannot be performed if the meta language does not contain variables of higher type. >Metalanguage, >Expressivity, cf. >Type theory. Undecidability: Undecidability is eliminated when one enriches the examined theory (object language) with variables of higher type.(1) >Decidability. 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 --- I 462 Meta language/Tarski: is our real examination object. ((s) because of the application conditions of the truth concept). I 464 Meta language/Tarski: 2nd category of expressions: specific terms of structural-descriptive character. >Structural-descriptive name. Names of specific signs and expressions of the class calculus, names of classes names of sequences of such expressions and of structural relations between them, Any expression of the considered language (object language) one can allocate - on the one hand an individual name of this expression, and - on the other hand an expression that is the translation of this expression in the meta language. That is decisive for the construction of the truth-definition. >Truth definition/Tarski. I 464 Name/translation/meta language/object language/Tarski: difference: an expression of the object language can in the meta language a) be given a name, or b) be a translation. Berka I 525 Morphology/Tarski: our meta language includes here the entire object language - that is, for us only logical expressions of the general class theory. - That is, only structural-descriptive terms. >Homophony. So we have the morphology of the language, that is, even the concept of inference is traced back. I 526 Thus we have justified the logic of this studied science as a part of the morphology.(2) >Description levels, >Semantic closure. 2. 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 |
| Satisfiability | Tarski | Berka I 482 Satisfiability/Tarski: depends only on those terms of the sequence from which (with respect to their indices) correspond to the free variables of propositional functions. >Sequences/Tarski, >Propositional functions. In the case of a statement (without free variables) the satisfiability does not depend on the properties of the links. >Statements. Each infinite sequence of class satisfies a given true statement - (because it does not contain free variables). >Free variables, >Bound variables. False statement: satisfied by no sequence - variant: satisfiability by finite sequences: according to this view, only the empty sequence satisfies a true statement (because this one has no variables). Berka I 483 Satisfiability/sequences/statements/Tarski: (here: by finite sequences): E.g. the statement (not propositional function) L1U2l1,2. i.e. "PxlNPxllNIxlxll" according to Definition 22 (satisfiability) satisfies the propositional function L1,2 those and only those sequences f of classes for which f1 Being satisfied/satisfiability/Tarski: previously ambiguous because of relations of different linking numbers or between object and classes, or areas of different semantic categories - therefore actually an infinite number of different satisfiability-concepts - Problem: then no uniform method for construction of the concept of the true statement - solution: recourse to the class calculus: Satisfiability by succession of objects.(1) >Truth definition, >Truth theory, >Class calculus. 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 |
| Ultimate Justification | Waismann | I 50 Ultimate justification/foundation/Mathematics/Waismann: The question of the last anchorage has not been solved with these researches, but merely pushed back further. A justification is unsuitable with the help of arithmetic; we have already reached the last clues of the arithmetic deduction. But such a possibility seems to arise when one looks beyond arithmetic: this leads to the third standpoint. >Foundation. Arithmetic/Waismann: is based on logic. In doing so, one makes strong use of terms of the set theory, or the class calculus. The assertion that mathematics is only a >"part of logic" includes two theses, which are not always clearly separated: A) The basic concepts of arithmetic can be traced back to purely logical ones by definition B) The principles of arithmetic can be deduced from evidence from purely logical propositions. >Logic, >Proof, >Empiricism. I 51 It looks like the sets of logic are tautologies. (Wittgenstein in 1921 introduced the concept of tautology). >Tautology. WaismannVsFrege: Frege was completely lacking the insight that the whole logic becomes meaningless, because he did not understand the nature of logic at all. In Frege's opinion, logic should be a descriptive science, such as mechanics. And to the question of what it describes, he replied: the relations between ideal objects, such as "and", "or", "if", etc. Platonic conception of a realm of uncreated structures. >Platonism, >G. Frege. |
Waismann I F. Waismann Einführung in das mathematische Denken Darmstadt 1996 Waismann II F. Waismann Logik, Sprache, Philosophie Stuttgart 1976 |
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