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Which Mathematical Logic is the Logic of Mathematics?
Logica Universalis, 2012The main tool of the arithmetization and logization of analysis in the history of nineteenth century mathematics was an informal logic of quantifiers in the guise of the “epsilon–delta” technique. Mathematicians slowly worked out the problems encountered in using it, but logicians from Frege on did not understand it let alone formalize it, and instead ...
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Mathematical Logic: Mathematics of Logic or Logic of Mathematics
2020This brief historical survey is written from a logical point of view. It is a rational reconstruction of the genesis of some interrelations between formal logic and mathematics. We examine how mathematical logic was conceived: as the abstract mathematics of logic or as the logic of mathematical practice.
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Science, 1966
Publisher Summary The purpose of this chapter is to regard a language as a set of primitive symbols and formation rules and—in some sense that it is not necessary to make definite—meanings for the expressions of the language. \The chapter concerns an old question relative to which developments have come to a conclusion or at least a pause.
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Publisher Summary The purpose of this chapter is to regard a language as a set of primitive symbols and formation rules and—in some sense that it is not necessary to make definite—meanings for the expressions of the language. \The chapter concerns an old question relative to which developments have come to a conclusion or at least a pause.
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The mathematical logic of life
Origins of Life, 1984Protein synthesis can be likened to a particular coded information storage, transmission and execution system. Noise, error or mutations are the essential phenomena to which a living organism is subjected. Genetic coding aims at preserving the integrity of a structure under aggression from the surroundings.
G. Cullmann, J. M. Labouygues
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Nature, 1973
What is Mathematical Logic? By J. N. Crossley, C. J. Ash, C. J. Brickhill, J. C. Stillwell and N. H. Williams. Pp. ix + 82. (Oxford University: London and New York, November 1972). £1.40 cloth; 70p paper.
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What is Mathematical Logic? By J. N. Crossley, C. J. Ash, C. J. Brickhill, J. C. Stillwell and N. H. Williams. Pp. ix + 82. (Oxford University: London and New York, November 1972). £1.40 cloth; 70p paper.
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Descriptions in mathematical logic
Studia Logica, 1984After a discussion of the different treatments in the literature of vacuous descriptions, the notion of descriptor is slightly generalized to function descriptor Ⅎy→(x), so as to form partial functions φ = Ⅎy→(x).A→(x, y) which satisfy ∀→xz(z = φx→ ↔ ∀y(A(x→, y) ↔ y = z)).
Gerard R. Renardel, null de Lavalette
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Visualization in Logic and Mathematics
2005In the last two decades there has been renewed interest in visualization in logic and mathematics. Visualization is usually understood in different ways but for the purposes of this article I will take a rather broad conception of visualization to include both visualization by means of mental images as well as visualizations by means of computer ...
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Philosophy, 1928
It is often said to-day that mathematics is nothing but an extension or development of logic; indeed, the identity of logic and pure mathematics is alleged so confidently by persons whose mathematical attainments entitle them to consideration when they talk about the subject-matter of mathematics, as to be in danger of being ranked with the truths that
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It is often said to-day that mathematics is nothing but an extension or development of logic; indeed, the identity of logic and pure mathematics is alleged so confidently by persons whose mathematical attainments entitle them to consideration when they talk about the subject-matter of mathematics, as to be in danger of being ranked with the truths that
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2018
It is Frege, not Boole, who is the father of modern logic. What exactly is modern about modern logic? Why did Frege develop it? The answers given here are these. Modern logic is both comprehensive and fully formal. The comprehensiveness in question is the sufficiency for the purposes of mathematics.
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It is Frege, not Boole, who is the father of modern logic. What exactly is modern about modern logic? Why did Frege develop it? The answers given here are these. Modern logic is both comprehensive and fully formal. The comprehensiveness in question is the sufficiency for the purposes of mathematics.
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