|Tautology, philosophy: A tautology is a statement that is constructed in such a way that it cannot be wrong, because its elements are repeated either affirmatively or negatively, or an exhaustive enumeration of possibilities is spread between which no decision is made. For example, A = A; If A, then A; A or non-A. Tautologies are not informative. See also certainty, information, knowledge, logic, validity, universality, contradiction, truth values, interpretation._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
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Tautologies / Mates : depend on the meaning of "and", "not", " if .... then ", etc. , but not the meaning of " all ", " some ", " people ", " mortal" , etc. - ( i.e. only from the logical constants , not of the quantifiers ) - on the other hand: analyticity of a syllogism depends on the meaning of "all" , "some"
Tautology / Mates : can not be an atomic statement - because this also may not be valid - I 119 there are valid statements that are not to be tautological - E.g. "(x ) Fx > Fa " - there are inferences that are not tautological - in derivatives only tautological inferences are needed - Def tautology : valid statement whose validity does not depend on the quantifiers .
Tautology / propositional calculus / Mates : since all statements of p.c. ( propositional calculus ) are quantifier-free , they are tautological, if they are valid - that carries over to their inserting results - still no decision procedure , if there is tautology - I 127 a Taut. is the same as a consequence of any set of propositions ._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
Elementare Logik Göttingen 1969