Philosophy Dictionary of ArgumentsHome
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| Functional calculus: The Functional Calculus in logic is a way of applying mathematical functions to logical operators. It is used to extend the expressiveness of logical languages and to reason about complex relationships between propositions. For example, a functional calculus can be used to define new logical operators, such as the modal operators of necessity and possibility, or the temporal operators of past and future. See also Operators, Functions, Propositions, Modal operator, Modal logic, Possibility, Necessity._____________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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Karel Berka on Functional Calculus - Dictionary of Arguments
Berka I 119 Extended function calculus/Hilbert: Extended function calculus is used to express the existence of the opposite of a statement. E.g. For every statement X there is a statement Y, so that at least one and only one is true. This saves the constraint of content representation. >Formalism, >Statements, >Validity, >Satisfiability. I 120 Then we can ask for a criterion for the correctness of formulas with arbitrary combinations of all- and existential quantifiers. >Universal quantification, >Existential quantification, >Quantification. Then there is the principal possibility of decidability about the provability of a mathematical theorem. >Decidability, >Provability, >Proofs. Narrow function calculus: The narrow function calculus is sufficient for the formalization of logical reasoning. >Formalization. Berka I 337 Function calculus/Hilbert/Ackermann: here (in contrast to the propositional calculus) the decision problem is still unsolved and difficult. - But for certain simple cases a procedure could be given. Simplest case: only function variable with one argument. >Decision problem, >Propositional calculus. I 337 Functional calculus: here the following circumstance has to be considered in particular: the generality or satisfiability of a logical expression may depend on how large the number of objects in the individual domain is. >Individual domain, >Domain._____________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. |
Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
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> Counter arguments against Berka
> Counter arguments in relation to Functional Calculus
