The Meaning of the Word "Implication"

Paper Summary:

This paper summarizes, analyzes, and critiques John Corcoran's work, in which he puts the different definitions of the word "implications" into distinct, well-defined, recognizable contexts. The paper reviews Corcoran's work from the perspectives of history, logic, philosophy, and linguistics.

From the Paper:

"In his paper, Corcoran lists several "implication" phrases in common English usage which presuppose that the premise "A" is true and that validates the conclusion B. Corcoran also critiques the philosopher/mathematician Frege in that Frege's thesis on logic is constrained by his instincts. Corcoran avers that Frege included pure logic in his thinking and did not make room for deduction as a major contributor to the concept of implication. "Frege's strategy was to show that no appeal to intuition is required for the derivation of the theorems of number theory. This in turn required that he show that the latter are derivable using only rules of inference, axioms, and definitions that are purely analytic principles of logic(Ref)" which he did not."

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