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Frases de Alfred Tarski

Alfred Tarski foi um lógico, matemático e filósofo polonês. Emigrou para os Estados Unidos em 1939, onde tornou-se cidadão naturalizado em 1945, foi professor de matemática da Universidade da Califórnia em Berkeley, de 1942 até sua morte.Escreveu, dentre outras áreas, sobre topologia, geometria, teoria da mensuração, axiomatização da álgebra e geometria, fundamentação da semântica, lógica matemática, teoria dos conjuntos, metamatemática, e, especialmente, sobre teoria dos modelos, teoria semântica da verdade, álgebra abstrata e lógica algébrica. Seu trabalho possui grande relevância filosófica. É considerado um dos maiores lógicos da história, junto de Aristóteles, Frege e Kurt Gödel. Tarski descrevia-se como "um matemático ". Na filosofia, ganha destaque especialmente por suas caracterizações matemáticas dos conceitos de verdade, constante lógica e consequência lógica para sentenças de linguagens formalizadas clássicas. Já na matemática e na filosofia, sua fama deve-se principalmente a seus impressionantes trabalhos sobre teoria dos conjuntos, teoria dos modelos e álgebra, incluindo resultados e desenvolvimentos como o paradoxo de Banach-Tarski, o teorema da indefinibilidade da verdade, a integralidade e decibilidade da álgebra e da geometria elementar, e as noções de cardinal, ordinal, relação e álgebra cilíndrica. Wikipedia  

✵ 14. Janeiro 1901 – 26. Outubro 1983
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Alfred Tarski frases e citações

“Não há dúvida de que o conhecimento da lógica é de considerável importância prática para todos os que desejam pensar e inferir corretamente.”

Alfred Tarski

There can be no doubt that the knowledge of logic is of considerable practical importance for everyone who desires to think and infer correctly.
Introduction to Logic and to the Methodology of Deductive Sciences. - Olaf Helmer (trad.) - p. 109 - (ed. 2013) ISBN-13: 978-1614275404

Conhecimento

Alfred Tarski: Frases em inglês

“For reasons mentioned at the beginning of this section, we cannot offer here a precise structural definition of semantical category and will content ourselves with the following approximate formulation: two expressions belong to the same semantical category if (I) there is a sentential function which contains one of these expressions, and if (2) no sentential function which contains one of these expressions ceases to be a sentential function if this expression is replaced in it by the other. It follows from this that the relation of belonging to the same category is reflective, symmetrical and transitive. By applying the principle of abstraction, all the expressions of the language which are parts of sentential functions can be divided into mutually exclusive classes, for two expressions are put into one and the same class if and only if they belong to the same semantical category, and each of these classes is called a semantical category. Among the simplest examples of semantical categories it suffices to mention the category of the sentential functions, together with the categories which include respectively the names of individuals, of classes of individuals, of two-termed relations between individuals, and so on. Variables (or expressions with variables) which represent names of the given categories likewise belong to the same category.”

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Alfred Tarski

Fonte: The Semantic Conception of Truth (1952), p. 45; as cited in: Schaff (1962) pp. 36-37.

“It is perhaps worth while saying that semantics as conceived in this paper (and in former papers of the author) is a sober and modest discipline which has no pretensions to being a universal patent-medicine for all the ills and diseases of mankind, whether imaginary or real. You will not find in semantics any remedy for decayed teeth or illusions of grandeur or class conflicts. Nor is semantics a device for establishing that everyone except the speaker and his friends is speaking nonsense.”

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Alfred Tarski

Fonte: The Semantic Conception of Truth (1952), p. 17; as cited in: Adam Schaff (1962). Introduction to semantics, p. 90.

“If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes.”

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Alfred Tarski

Fonte: The Semantic Conception of Truth (1952), p. 41.

“Logic is justly considered the basis of all other sciences, even if only for the reason that in every argument we employ concepts taken from the field of logic, and that ever correct inference proceeds in accordance with its laws.”

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Alfred Tarski

Introduction to Logic: and to the Methodology of Deductive Sciences. (1941/2013) Tr. Olaf Helmer, pp. 108-110.

“There can be no doubt that the knowledge of logic is of considerable practical importance for everyone who desires to think and infer correctly.”

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Alfred Tarski

Introduction to Logic: and to the Methodology of Deductive Sciences. (1941/2013) Tr. Olaf Helmer, p. 109.

“The present article is almost wholly devoted to a single problem—the definition of truth. Its task is to construct—with reference to a given language—a materially adequate and formally correct definition of the term 'true sentence. This problem, which belongs to the classical problems of philosophy, raises considerable difficulties. For although the meaning of the term 'true sentence' in colloquial language seems to be quite clear and intelligible, all attempts to define this meaning more precisely have hitherto been fruitless, and many investigations in which this term has been used and which started with apparently evident premisses have often led to paradoxes and antinomies (for which, however, a more or less satisfactory solution has been found). The concept of truth shares in this respect the fate of other analogous concepts in the domain of the semantics of language.”

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Alfred Tarski

"The Concept of Truth in Formalized Languages" (1931) in Logic, Semantics, Metamathematics: Papers from 1923 to 1938 (1956) Tr. J. H. Woodger.