A Brief History of Logic

The Preface of George Englebretsen’s book Something To Reckon With: The Logic of Terms gives a brief history of logic. Major topics are Aristotle’s categorical (term) logic and criticisms of it, mathematical logic introduced by Gottlob Frege, Fred Sommers’ new term logic, and the skirmishes between advocates of term and mathematical logic. Of course, the aim of mathematical logic is to explain the logic of mathematical reasoning, whereas term logic, especially that of Fred Sommers, is to explain the logic of natural (everyday) language.

Fred Sommers wrote the Forward of Englebretsen’s book. I had thought that a contradictory statement said something about its utterer, and still do, but Sommers gives a different perspective.  “Note that a contradictory sentence such as ‘some man is not a man’ transcribes as a sentence of the form ‘+X+(-X)’, which literally says nothing.”  The notation he used is his.

I read the book a few years ago and plan to reread it. The way statements expressed in Sommers’ logical syntax combine arithmetically is very cool.