Reviews - J. H. Woodger. Translator's preface. Logic, semantics, metamathematics, papers from 1923 to 1938.Oxford at the Clarendon Press, London1956, pp. vii–ix. - Alfred Tarski. Author's acknowledgments.Logic, semantics, metamathematics, papers from 1923 to 1938.Oxford at the Clarendon Press, London1956, pp. xi–xii. - Alfred Tarski. On the primitive term of logistic. Modified English translation based on 2852–4. Logic, semantics, metamathematics, papers from 1923 to 1938.Oxford at the Clarendon Press, London1956, pp. 1–23. - Alfred Tarski. Foundations of the geometry of solids.Logic, semantics, metamathematics, papers from 1923 to 1938.Oxford at the Clarendon Press, London1956, pp. 24–29. (Translated, with additions, from Księga Pamiątkowa Pierwszego Polskiego Zjazdu Matematycznego, supplement to Annales de la Société Polonaise de Mathématique, Cracow 1929, pp. 29-33.) - Alfred Tarski. On some fundamental concepts of metamathematics. English translation of 2857. Logic, semantics, metamathematics, papers from 1923 to 1938.Oxford at the Clarendon Press, London1956, 30–37. - Jan Łukasiewicz and Alfred Tarski. Investigations into the sentential calculus. English translation of 4077, with added footnotes. Logic, semantics, metamathematics, papers from 1923 to 1938.Oxford at the Clarendon Press, London1956, pp. 38–59. - Alfred Tarski. Fundamental concepts of the methodology of the deductive sciences. English translation of 2858, with added footnotes. Logic, semantics, metamathematics, papers from 1923 to 1938.Oxford at the Clarendon Press, London1956, pp. 60–109. - Alfred Tarski. On definable sets of real numbers. English translation of 28510, with additions in the text by the author as well as added footnotes. Logic, semantics, metamathematics, papers from 1923 to 1938.Oxford at the Clarendon Press, London1956, pp. 110–142. - Kazimierz Kuratowski and Alfred Tarski. Logical operations and projective sets. English translation of 4321, with added footnotes. Logic, semantics, metamathematics, papers from 1923 to 1938.Oxford at the Clarendon Press, London1956, pp. 143–151. - Alfred Tarski. The concept of truth in formalized languages. English translation of 28516, with added footnotes. Logic, semantics, metamathematics, papers from 1923 to 1938.Oxford at the Clarendon Press, London1956, pp. 152–278.

1969 ◽  
Vol 34 (1) ◽  
pp. 99-106 ◽  
Author(s):  
W. A. Pogorzelski ◽  
S. J. Surma
Keyword(s):  
English Translation ◽  
Real Numbers ◽  
Sentential Calculus ◽  
Alfred Tarski ◽  
Primitive Term ◽  
Logical Operations ◽  
Definable Sets ◽  
Concept Of Truth

Philosophical implications of Tarski's work

1988 ◽  
Vol 53 (1) ◽  
pp. 80-91 ◽  
Author(s):  
Patrick Suppes
Keyword(s):  
United States ◽  
English Translation ◽  
The United States ◽  
International Congress ◽  
Unity Of Science ◽  
Scientific Philosophy ◽  
Philosophical Texts ◽  
Concept Of Truth ◽  
Almost All ◽  
Philosophical Questions

In his published work and even more in conversations, Tarski emphasized what he thought were important philosophical aspects of his work. The English translation of his more philosophical papers [56m] was dedicated to his teacher Tadeusz Kotarbiński, and in informal discussions of philosophy he often referred to the influence of Kotarbiński. Also, the influence of Leśniewski, his dissertation adviser, is evident in his early papers. Moreover, some of his important papers of the 1930s were initially given to philosophical audiences. For example, the famous monograph on the concept of truth ([33m], [35b]) was first given as two lectures to the Logic Section of the Philosophical Society in Warsaw in 1930. Second, his paper [33], which introduced the concepts of ω-consistency and ω-completeness as well as the rule of infinite induction, was first given at the Second Conference of the Polish Philosophical Society in Warsaw in 1927. Also [35c] was based upon an address given in 1934 to the conference for the Unity of Science in Prague; [36] and [36a] summarize an address given at the International Congress of Scientific Philosophy in Paris in 1935. The article [44a] was published in a philosophical journal and widely reprinted in philosophical texts. This list is of course not exhaustive but only representative of Tarski's philosophical interactions as reflected in lectures given to philosophical audiences, which were later embodied in substantial papers. After 1945 almost all of Tarski's publications and presentations are mathematical in character with one or two minor exceptions. This division, occurring about 1945, does not, however, indicate a loss of interest in philosophical questions but is a result of Tarski's moving to the Department of Mathematics at Berkeley. There he assumed an important role in the development of logic within mathematics in the United States.

sets of reals

1997 ◽  
Vol 62 (4) ◽  
pp. 1379-1428 ◽  
Author(s):  
Joan Bagaria ◽  
W. Hugh Woodin
Keyword(s):  
Set Theory ◽  
Real Numbers ◽  
Borel Sets ◽  
Definable Sets ◽  
Analytic Sets ◽  
Basic Facts ◽  
Continuous Images

Some of the most striking results in modern set theory have emerged from the study of simply-definable sets of real numbers. Indeed, simple questions like: what are the posible cardinalities?, are they measurable?, do they have the property of Baire?, etc., cannot be answered in ZFC.When one restricts the attention to the analytic sets, i.e., the continuous images of Borel sets, then ZFC does provide an answer to these questions. But this is no longer true for the projective sets, i.e., all the sets of reals that can be obtained from the Borel sets by taking continuous images and complements. In this paper we shall concentrate on particular projective classes, the , and using forcing constructions we will produce models of ZFC where, for some n, all , sets have some specified property. For the definition and basic facts about the projective classes , and , as well as the Kleene (or lightface) classes , and , we refer the reader to Moschovakis [19].The first part of the paper is about measure and category. Early in this century, Luzin [16] and Luzin-Sierpiński [17] showed that all analytic (i.e., ) sets of reals are Lebesgue measurable and have the property of Baire.

Truth, Interpretation, and Meaning

2010 ◽  
Author(s):  
Scott Soames
Keyword(s):  
Logical Consequence ◽  
Formal Languages ◽  
Donald Davidson ◽  
Semantic Model ◽  
Semantic Approach ◽  
Alfred Tarski ◽  
Concept Of Truth ◽  
And Mathematics ◽  
Definition Of

This chapter begins by discussing the work of Alfred Tarski. In the 1930s, Tarski published two articles that became classics. In “The Concept of Truth in Formalized Languages” (1935) he defined truth for formal languages of logic and mathematics. In “On the Concept of Logical Consequence” (1936) he used that definition to give what is essentially the modern “semantic” (model-theoretic) definition of logical consequence. In addition to their evident significance for logic and metamathematics, these results have come to play an important role in the study of meaning. The chapter then discusses Rudolf Carnap's embrace of truth-theoretic semantics and the semantic approach of Donald Davidson.

Computational logic

1949 ◽  
Vol 14 (3) ◽  
pp. 167-172 ◽  
Author(s):  
Nathan P. Levin
Keyword(s):  
Computational Logic ◽  
Elementary Algebra ◽  
Sentential Calculus ◽  
Primitive Term ◽  
Arbitrary Sign ◽  
Image Position ◽  
Binary Combination

We make certain notational conventions. These are referred to as CL (Computational Logic). The relation of interchangeability is introduced as the basic connection between logical formulas. This approach lends perspicuity to the results of sentential calculus. With its technical devices CL is able to rephrase logical theorems in rather succinct manner. Our exposition tries to steer a middle course between informality and strict rigor.It is felt that the method of CL offers advantages for the teaching of logic. Proofs are algorithmic and resemble those of elementary algebra. All inferences are reversible and practically non-tentative.Sign is a primitive term of CL. Its denning property is a capacity for entering into binary combination with other signs, or with itself, according to this convention:x and y are signs if, and only if, (x y) is a sign. Bracketing is looked upon as an operation on signs in terms of which other operations are definable. The practice of some authors in classifying brackets under the heading of symbols, seems to us questionable; for unlike symbols or signs brackets are never used to denote anything. Brackets enter into the composition of signs, not to denote a grouping, but rather to exhibit it, in the manner of a diagram.An unending list of letters, with or without subscripts,serve to denote arbitrary signs. An arbitrary sign may or may not have other signs as parts. The numeral “2” is used as a constant. Bracketing abbreviation is as follows:and so on. Outermost brackets will ordinarily be omitted. This kind of bracketing may be termed left-associative. For convenience, these bracketing conventions are crystallized into a rule.

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