Economics Dictionary of ArgumentsHome
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| Correctness, Logik: is a property of systems or calculi, not of conclusions. A system is correct when all the statements provable in it are true. The system is complete when all valid statements in it are also provable. Completeness and correctness are complementary; they are complementing each other to adequacy. (R. Stuhlmann-Laeisz, Philosophische Logik, Paderborn, 2002).
B. Correctness, accuracy, philosophy contrary to the concept of truth, the concept of accuracy refers to an implicitly or explicitly presupposed rule system, which is fulfilled or not fulfilled. While truth is something that is attributed or denied to sentences, accuracy is rather applied to actions - also verbal acting - as well as to illustrations. Unlike truth, accuracy allows gradations. See also truth, truth conditions, indeterminacy, systems, theory, fulfillment, satisfiability._____________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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Alfred Tarski on Correctness - Dictionary of Arguments
Berka I 489 Correctness/domain/Tarski: according to the sentences 14-16 (or Lemma I) there is for each natural number k such a statement that is true in any area with k elements and in any area of the other thickness. In contrast: Every statementthat is true in an infinite range is also true in any other infinite domain. Properties/classes: so we conclude that the object language allows us to express such a property of classes of individuals, such as the existence of exactly k elements. There is no means for designating any specific type of infinity (e.g. countability) and we cannot distinguish by means of a single or a finite number of statements... I 490 ...two such properties of classes such as finiteness, infinity from each other. >Infinity. I 491 Truth (in the domain): depends on the scope in the finite case, not in the infinite. I 491 Correctness in the doamin/provability/Tarski: if we add the statement a (every nonempty class contains a singleton class as a part) to the axiom system correctness and provability will be coextensive terms. >Provability. N.B.: this does not work in the logical algebra, because here a is not satisfied in all interpretations. I 516 "In every correct domain"/Tarski: this term stands according to the extent in the middle between the provable sentence and the true statement, but is narrower than the class of all true statements generally. It does not contain statements whose validity depends on how big the total number of individuals is.(1) 1. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol 1, Lemberg 1935_____________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. |
Tarski I A. Tarski Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
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> Counter arguments against Tarski
> Counter arguments in relation to Correctness
