Three traditional laws of logic

It is to Aristotle to fully understand the importance of three principles of our reasoning: the law of identity, non-contradiction and excluded middle.

1. The law of identity states that given A, A=A. This principle is not formally present in Aristotelian writings, but from Parmenide (VI-V century BC) to stoics (III century BC) to Duns Scotus (13th century) it is the logical version of the fact that, during a reasoning, the meaning of the terms must remain constant.

2. The law of non-contradiction states that in a statement one can not assert and deny a subject’s predicate at the same time and in the same sense. Aristotle expresses this as follows: “It is impossible that the same attribute at the same time belong to and not belong to the same object and in the same relationship” (Metaphysics IV, 1005b, 19-20).

3. The law of the excluded middle states that in a two-value system, True and False, a statement is either true or false: a third possibility is excluded. This is a useful principle to infer a conclusion, say A, demonstrating that its opposite (non-A) is contradictory. They are of this kind the Reductio ad absurdum demonstrations.