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Numerically Exceptive Logic

A Reduction of the Classical Syllogism


Wallace A. Murphree

The thesis of this important new direction in classical logic is that the syllogism is an inherently numerical form of entailment - a position in direct opposition to the perennial view. In the book the author shows both that the propositions of classical logic make implicit numerical claims, and also that alternative numerical values can be substituted for these implicit ones to yield a logic whose quantifiers are infinitely flexible. A significant aspect of this work is the development of a «schematic» which clearly exhibits the validity or invalidity of each categorical argument, whether it be classically or numerically extended.