Philosophy Dictionary of ArgumentsHome
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| Inserting: In a formula, elements can be replaced by others, making the formula simpler or more complex. Thus, variables can in turn be replaced by other formulas, or vice versa. See also Fine-grained/coarse-grained, Logical formulas, Formulas._____________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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Logic Texts on Inserting - Dictionary of Arguments
II 133 Insertion/substitution/identity/truth preservation: Logical equivalence is (...) a weakening of the identity of statements. Logically equivalent statements are not the same in all properties, but only in logical terms. If one statement is logically true, so is the other and vice versa. If a certain statement follows logically from one, then it follows logically from the other and vice versa. >Substitution, >Substitution (Insertion), >Equivalence, >Logical truth. Insertion Theorem: Let FA be a propositional logical formula which contains a partial form A. Let FB be a formula which results from FA when A is replaced by a propositional formula B, (not necessarily everywhere). If A is now ≡ B, then FA ≡ FB applies. II 134 Logically equivalent formulas have the same inference sets. Logically equivalent formulas can be inferred from the same prerequisites. Redundancy Theory/Hoyningen-Huene: therefore, in propositional logic one does not really have to distinguish between "A" and "It is true that A". (In propositional logic such properties are abstracted from). >Redundancy theory, >Propositional logic._____________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. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Logic Texts Me I Albert Menne Folgerichtig Denken Darmstadt 1988 HH II Hoyningen-Huene Formale Logik, Stuttgart 1998 Re III Stephen Read Philosophie der Logik Hamburg 1997 Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 |
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> Counter arguments in relation to Inserting
Ed. Martin Schulz, access date 2024-04-29