Sentence examples for mathematical logic was from inspiring English sources

In Poland mathematical logic was considered to be an autonomous science, not a part of mathematics or philosophy.

Boole's work on mathematical logic was criticized and ignored by his contemporaries, except for an American logician, Charles Sanders Peirce.

One main achievement of early mathematical logic was precisely to show how to characterize notions of derivability and validity in terms of concepts of standard mathematics.

The special controversy between Ernst Schröder and Gottlob Frege which was at the root of the later distinction between two kinds of modern logic, the algebra of logic and the Frege-style mathematical logic, was centered on the question how far the Leibnizian heritage was present in the respective variations of logic.

Quine's set theory New Foundations (abbreviated NF), proposed in 1937 in his paper "New foundations for mathematical logic", is also based on a procedure for identifying the objects in successive types in order to obtain an untyped theory.

But the major breakthrough came in 1960 when it occurred to the mathematical logician Abraham Robinson (1918 1974) that "the concepts and methods of contemporary Mathematical Logic are capable of providing a suitable framework for the development of the Differential and Integral Calculus by means of infinitely small and infinitely large numbers".

The algebra of logic, as an explicit algebraic system showing the underlying mathematical structure of logic, was introduced by George Boole (1815 1864) in his book The Mathematical Analysis of Logic (1847).

Whereas mathematical fuzzy logic is truth-functional, Williamson (1994, 97) holds that "the nature of vagueness is not captured by any approach that generalizes truth-functionality".

In mathematical logic, it is suggested that problems that are essentially the same must be resolved by the same means, and similar paradoxes should be resolved by similar means.

Informed by mathematical logic, it was highly practical, rich in terms of its ideas, and lacked any over-elaborate decoration.

Although he made eminent contributions to deductive, or mathematical, logic, Peirce was a student primarily of "the logic of science"—i.e., of induction and of what he referred to as "retroduction," or "abduction," the forming and accepting on probation of a hypothesis to explain surprising facts.