symbolic logic

[sim′bäl·ik ′läj·ik]

(mathematics)

The formal study of symbolism and its use in the foundations of mathematical logic.

symbolic logic

(logic)

The discipline that treats formal logic by means of a formalised artificial language or symbolic calculus, whose purpose is to avoid the ambiguities and logical inadequacies of natural language.

This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Symbolic Logic

a synonym for “mathematical logic.” In the words of P. S. Poretskii, mathematical logic is “logic in subject and mathematics in methodology.” According to A. Church, it is logic studied through the construction of formalized languages.

The term “symbolic logic” draws attention to the special nature of the basic elements of the formalized languages used in the mathematical method of studying logic. These elements are not the words employed in everyday discourse, even if such words are used in some special meanings. Instead, the elements are symbols that are selected (or constructed from previously selected symbols) and interpreted in a definite way specific to the given logical situation. In general, this way has no relation to any “traditional” usage, understanding, or functions of the symbols in other contexts.

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References in periodicals archive

Skinner had been interested in the history and philosophy of science from his graduate student days, as reflected, for example, in the work of Mach and Poincare, but he never subscribed to the formal symbolic logic of logical empiricism.

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Utilizing the new symbolic logic systematically synthesized by Frege and his definition of the natural numbers in term s of classes of classes, the first three volumes set out to axiomatize logic and to show how arithmetic could be deduced from the proposed system.

ALFRED NORTH WHITEHEAD

Delany's Analytics of Attention." I found it difficult to concentrate my own attention on the technical details of his argument, but anyone possessing a passing acquaintance with symbolic logic should have no trouble with it.

Ash of Stars: On the Writing of Samuel R. Delany

This new system of logic described the relationship of symbols to each other, or symbolic logic. The importance of the work by Whitehead and Russell lay in the fact that it did not reject the centuries of work by philosophers since Aristotle, but refined it through mathematics to a degree of precision never before seen.

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Despite this fact, Britain provided us with a great philosopher, namely Bertrand Russell, who specialized in the purest forms of science and scholarship in areas such as symbolic logic, philosophy of mathematics, and the theory of knowledge.

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On the contrary, Robinson delighted in showing that symbolic logic could be used within mathematics to positive, creative effect (p.

Abraham Robinson: The Creation of Nonstandard Analysis: A Personal and Mathematical Odyssey

It is "surprising" how many people take a "belletristic view," Jameson comments, making "the assumption, which they would never make in the area of nuclear physics, linguistics, symbolic logic, or urbanism, that such [cultural] problems can still be laid out with all the leisurely elegance of a coffee-table magazine."

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In 1847 he published The Mathematical Analysis of Logic, thus founding what might be called Boolean algebra or symbolic logic. This was later to be of much use in studying the rigorous foundations of mathematics and, eventually, in programming computers.

Symbolic logic

Paulos, who teaches freshmen as well as graduate stu- dents, is a recognized expert in symbolic logic, computer languages, and artificial intelligence.

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