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The law of contradiction, after all, is not enforceable; if it were the jails would overflow.

The certainty afforded in the law of Identity in positive form, in the law of Contradiction in negative form, in the law of Excluded Middle in the form of an opposition, and in the law of Sufficient Reason in conditional form, is based upon Causality, Community of Species, or Totality.

Agreement with this view violates the law of contradiction; denial of it implies that two moments can be immediately adjacent.

Considering the important place assigned by philosophers and logicians to the law of contradiction, the remark will naturally be resented by many of the older schools of philosophy, and especially by Kantians, that “in spite of its fame we have found few occasions for its use.”

It follows from the logical law of contradiction that the proof of the existence theorem proves also the consistency of the axioms.