The Principle Of Excluded Middle Then And Now: Aristotle And Principia Mathematica

Andrews Doull, Floy (1996) The Principle Of Excluded Middle Then And Now: Aristotle And Principia Mathematica. Animus, 1. pp. 53-66. ISSN 1209-0689

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Abstract

The prevailing truth-functional logic of the twentieth century, it is argued, is incapable of expressing the subtlety and richness of Aristotle's Principle of Excluded Middle, and hence cannot but misinterpret it. Furthermore, the manner in which truth-functional logic expresses its own Principle of Excluded Middle is less than satisfactory in its application to mathematics. Finally, there are glimpses of the "realism" which is the metaphysics demanded by twentieth century logic, with the remarkable consequent that Classical logic is a particularly inept instrument to analyze those philosophies which stand opposed to the "realism" it demands.

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