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Descriptions in mathematical logic
Studia Logica, 1984If A(x) is a predicate satisfied by exactly one x, then we write Ix.A(x) for that object x. The operator I is called a descriptor. The author reviews the various treatments of descriptors in the literature, pointing out that the problem each treatment faces is ''what to do with Ix.A(x) when \(\exists !xA(x)\) is not (yet) known''. The obvious answer is
Gerard R. Renardel, null de Lavalette
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IF logic and the foundations of mathematics
Synthese, 2001One of the properties of independence friendly (IF) first-order logic as discussed, e.g., by \textit{J. Hintikka} in his ``The principles of mathematics revisited'' [Cambridge University Press, Cambridge (1996; Zbl 0869.03003)] is that ``it defines its own truth-predicate in certain models, like for instance, in the standard model \(N\) of PA'' (p. 40).
Tapani Hyttinen, Gabriel Sandu
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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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Physics and mathematical logic [PDF]
Il Nuovo Cimento, 1955 The possibility of application of mathematical logic to the investigation of physical problems is discussed; the basic elements of mathematical logic are introduced and examples are given.
A. Gamba, U. Farinelli
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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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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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