# 1. In logic

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

— The conjunction “**P** and **not-P**” expresses a contradiction, and, as such, is a self-destructing statement, which is necessarily *false*.

— The disjunction “**P** or **not-P**” is necessarily *true*.

One of the two propositions **P** and **not-P** must be true, both cannot be true simultaneously. The same thing cannot *be* and *not be*. This principle is considered by classical logic as a *law of thought*, and as an *axiom* by contemporary logicians. A logical system respecting the principle of non-contradiction does not contain any *antinomies*; it is said to be *consistent*.

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

P |
¬ P |

T | F |

F | T |

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

line 1: “when P is true, then not-P is false”

line 2: “when 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 plainly true or false, not *far from true* or *practically false*, not true or not *according to the circumstances*.

Many argumentative forms appeal to the non-contradiction principle, albeit under different names: S. *Ad Hominem*; Dialectic; Contradiction; Consistency

The non-contradiction principle applies not only to logical, argumentative discourse, but also to any kind of discourse; inconsistent *narrations* or *descriptions* for example, are rejected as such.

According to the basic Aristotelian dialectical rule, any discourse resulting in a contradiction is irrational and must be abandoned. Hegelian dialectic sees in the ongoing treatment of contradictions the motor of History. The cynical politician can lay claim to Hegel to hide his opportunism:

Stalin’s speech on the five-year plan serves as an ardent apology for contradiction as a “*vital value*” and an “*instrument of struggle*”. One of Lenin’s great strengths was his ability never to feel a prisoner of what he had preached as true the day before […] Mussolini’s famous word “*Let us beware of the mortal trap of coherence*” could be signed by all those who intend to pursue a work within currents they cannot foresee.

Julien Benda, [*The Betrayal of the Intellectuals*], [1927][1]

The affirmation of a paradox as an *oxymoron* makes it possible to withstand the contradiction: “*O wound without scar!*”. Such paradoxical assertion is not seen as absurd or fallacious and eliminated as such, but triggers a quest to identify the deeper, symbolic meaning of the words *wound* and *scar* used in this context.

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