mathematical logic


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mathematical logic:

see symbolic logicsymbolic logic
or mathematical logic,
formalized system of deductive logic, employing abstract symbols for the various aspects of natural language. Symbolic logic draws on the concepts and techniques of mathematics, notably set theory, and in turn has contributed to
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.

Mathematical Logic

 

a branch of logic that makes use of mathematical methods.

The use of formal languages with an exact syntax and precise semantics that unambiguously define the meaning of formulas is characteristic of mathematical logic. The need for such a logic arose in the early 20th century in connection with the intensive development of the foundations of mathematics, the emergence of set theory in which antinomies had been discovered, the refinement of the concept of an algorithm, as well as with other profound and fundamental problems of mathematical science. The importance of mathematical logic for science as a whole, however, is not exhausted by its mathematical applications, since all sciences require good reasoning and methods of proof. This is why mathematical logic can rightfully be called logic in its most recent development.

A. A. MARKOV

mathematical logic

[¦math·ə¦mad·ə·kəl ′läj·ik]
(mathematics)
The study of mathematical theories from the viewpoint of model theory, recursive function theory, proof theory, and set theory.
References in periodicals archive ?
The absence of the subjective factor, understood as "emotional chaos," the isolation and the compulsion of desire is a necessary effect of the development of mathematical logic by the fact that the unconscious cannot be formalized in a digital model.
According to the textbooks of mathematical logic, the interpreted theory is a structure and not a theory.
Ordinary mathematics is well removed from logic, in that the work to formulate most mathematical proofs in the terms of mathematical logic would be overwhelming, and would introduce more potential errors and problems than it would remove.
Relationship between variable parameters and the original introduced through mathematical logic relations.
Cohen succeeds in showing that this rhetoric of humility has roots in the hopes of George Boole (1815-1864) and Augustus De Morgan (1806-1871) to use mathematical logic in the service of true religion.
To such understanding of the relationship between logic and mathematics, which results from the creation of mathematical logic, one can come from the following opposition.
They have become the Arsenal of the Championship; joyful to watch and capable of creating the kind of triangles that defy mathematical logic.
But from the point of pure logic--and also taking into consideration the fact that logical formulae and logical concepts do not themselves evolve--there is a constancy in logic, both in mathematical logic and formal logic and one can make a logical criticism of the prevalent understanding of evolution based on reductionism.
The results published by Kurt Godel during the decade 1929-1939 transformed completely mathematical logic.
I think that this criticism doesn't realise that your novel is, to use the language of mathematical logic, a novel of a higher logical type than the standard narrative (or reflective) novel.
Chiang takes a philosophical approach to predictive situations: the breakdown of mathematical logic, the link between naming and existence, the transformation of time.
Russell's mathematical statement of this paradox implied that there could be no truth in mathematics, since mathematical logic was flawed at a basic level.

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