Peirce and Logic

Seemingly unrecognized in American academic Philosophy is the fact that Peirce, also the father of Semiology and Pragmatism, was at least is seminal as is Frege in the development of Modern Logic. A fundamental insight of Peirce's is that while Logic studies the drawing of Inference, Mathematics is an exemplary drawer of Inference. His Logic is, therefore, a refinement of Mathematics, without the latter being a branch of the former. More specifically, the main elements of his Logic are Mathematical, a project already initiated by especially Boole, who derives the Logical connectives Negation, Conjunction, and Disjunction from the Mathematical notions Negative, Multiplication, and Addition. But Peirce makes the more significant leap, linking the new Logic to the Aristotelian, by deriving Implication from Less Than, All from Multiplication, and Some from Addition. Though Frege's innovations slightly predated him, Peirce's independently-developed notation is plainly the one adopted by subsequent Logicians. Peirce also explains how Mathematics can be abstract without being a reification of processes such as counting--it is implicitly hypothetical, namely 'a+b=c' means 'if b of any unit is added to a of the same unit, then there will result a total of c of that unit'. Hence, to Peirce, Mathematics is Pragmatic, i. e. operational, in a dynamic sense. Dewey, therefore, draws the appropriate conclusion from Peirce's conceptions of the nature of Mathematics, and of the relation of Mathematics to Logics, by defining Logic as a Theory of Inquiry, specifically of experimental inquiry, the predominant type of knowledge-acquisition of this era. Hence, Pragmatism manages to integrate Logic with practical activity without diminishing its abstract nature. Many American academic Philosophers not only regard Russell as the greatest contemporary Philosopher, but are barely familiar with Peirce. But if comprehensiveness of systematic vision is the criterion of greatness, Russell is the lesser of the two.