Category:Aristotelian Logic

Aristotelian logic is a system of logic which is based upon the philosophy of Aristotle. It forms the cornerstone of the entirety of "classical" logic.

It was Aristotle who, in particular, introduced the following two axioms of logic:

The Law of the Excluded Middle (LEM)

All statements have a truth value of either true or false:

$\vdash p \lor \neg p$

Otherwise known as:

• (Principium) tertium non datur, Latin for third not given, that is, a third possibility is not possible;
• Principium tertii exclusi, the Principle of the Excluded Third (PET).

Principle of Non-Contradiction (PNC)

A statement can not be both true and not true at the same time.

$\vdash \neg \left({p \land \neg p}\right)$

Otherwise known as:

• Principium contradictionis, Latin for principle of contradiction;
• Law of Contradiction.

Thus, a logical system which includes both of these principles is known as Aristotelian logic.