A set of propositions is inconsistent iff the proposition P and not P is in the deductive closure of the set.

In`con*sist"ent (?), a. [Pref. in- not + consistent: cf. F. inconsistant.]

1.

Not consistent; showing inconsistency; irreconcilable; discordant; at variance, esp. as regards character, sentiment, or action; incompatible; incongruous; contradictory.

Compositions of this nature . . . show that wisdom and virtue are far from being inconsistent with politeness and good humor. Addison.

2.

Not exhibiting uniformity of sentiment, steadiness to principle, etc.; unequal; fickle; changeable.

Ah, how unjust to nature, and himself, Is thoughtless, thankless, inconsistent man. Young.

Syn. -- Incompatible; incongruous; irreconcilable; discordant; repugnant; contradictory. -- Inconsistent, Incongruous, Incompatible. Things are incongruous when they are not suited to each other, so that their union is unbecoming; inconsistent when they are opposed to each other, so as render it improper or wrong; incompatible when they can not coexist, and it is therefore impossible to unite them. Habitual levity of mind is incongruous with the profession of a clergyman; it is inconsistent with his ordination vows; it is incompatible with his permanent usefulness. Incongruity attaches to the modes and qualities of things; incompatibility attaches to their essential attributes; inconsistency attaches to the actions, sentiments, etc., of men.

 

© Webster 1913.

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