Quote: get the law of contradiction from x^2=x

Quotation

Let us write [x^2=x] in the form x-x^2=0, whence we have x(1-x)=0; ... Let us, for simplicity of conception, give to the symbol x the particular interpretation of men, then 1-x will represent the class of "not-men". ... Now let the meaning of the symbol x be extended from the representing of "men," to that of any class of beings characterized by the possession of any quality whatever; and the equation (1) will then express that it is impossible for a being to possess a quality and not to possess that quality at the same time. But this is identically that "principle of contradiction" which Aristotle has described as the fundamental axiom of all philosophy. "It is impossible that the same quality should both belong and not belong to the same thing...This is the most certain of all principles...Wherefore they who demonstrate refer to this as an ultimate opinion. For it is by nature the source of all the other axioms. [Aristotle, Metaphysica, III 3.]   Google-1   Google-2

Published before 1923

Additional Titles

Quote: the law of contradiction is the most certain of all principles and the basis of logic

Related Topics

Topic: logic (84 items)