NON-CONTRADICTION PRINCIPLE

1. In logic

In logic, the principle of non-contradiction prohibits the affirmation of contradictory propositions. In other words:

— The conjunction “P and not-P” is a contradiction, and, as such, is a self-destructive proposition, that is necessarily false.
— The disjunction “P or not-P” is necessarily true.

One of the two propositions P or not-P must be true, both cannot be true at the same time. The same thing cannot both be and not be. This principle is considered  as a law of thought in classical logic and an axiom in contemporary logic. A logical system that respects the principle of non-contradiction contains no antinomies and  is said to be consistent.

Negation — Using the truth table method, the negation operator is defined as follows:

This table expresses the principle of the excluded middle. It reads:

Line 1: ‘if P is true, then not-P is false’.
Line 2: ‘if P is false, then not-P is true’.

2. In natural language

The application of the non-contradiction principle to everyday language is complex, because:
— It presupposes that P is either unambiguously true or false, not far from true or practically false, true or not according to the circumstances.
— There are natural language utterances that cannot be said to be either true or false, such as « Come back tomorrow! » or « I promise to come back tomorrow. »

Many forms of argument appeal to the principle of non-contradiction , albeit under different names. See ad hominem; dialectic; contradiction; consistency.

The principle of non-contradiction applies not only to logical and argumentative discourse, but to any kind of discourse. Inconsistent narratives or descriptions for example, are rejected as such.

According to the basic rule of Aristotelian dialectic, any discourse that leads to a contradiction is irrational and must be abandoned. Hegelian dialectics sees the motor of history in the ongoing treatment of contradictions. Cynical politicians can invoke Hegel to hide their opportunism:

Stalin’s speech on the Five-Year Plan serves as a passionate apology for contradiction as a “vital value” and an “instrument of struggle”. One of Lenin’s great strengths was his ability never to feel imprisonned by what he had preached as true the day before. Mussolini’s famous words “Let us beware of the deadly trap of coherence” could be endorsed by anyone intending to work within unpredictable currents they cannot.
Julien Benda, [The Betrayal of the Intellectuals], [1927][1]

Affirming of a paradox as an oxymoron enables one to endure the contradiction: “O wound without scar!”. Rather than being deemed absurd or fallacious and dismissed, such a paradoxical assertion triggers a search for the deeper, symbolic meaning of the words wound and scar used in this context.
This interpretive approach goes a step further than hastily dismissing it as a  “fallacy”.

[1] Julien Benda, La Trahison des Clercs, [1927]. Excerpt from the preface to the 1946 edition. Paris: Grasset, 1975, pp. 78-79.