Dictionary Meaning and Definition on 'Inconsistent'
- displaying a lack of consistency; "inconsistent statements"; "inconsistent with the roadmap" [ant: consistent]
- not capable of being made consistent or harmonious; "inconsistent accounts"
- not in agreement [syn: discrepant]
- Inconsistent \In`con*sist"ent\, a. [Pref. in- not + consistent:
cf. F. inconsistant.]
- Not consistent; showing inconsistency; irreconcilable; discordant; at variance, esp. as regards character, sentiment, or action; incompatible; incongruous; contradictory.
Wikipedia Meaning and Definition on 'Inconsistent'
In logic, a consistent theory is one that does not contain a contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent if it has a model; this is the sense used in traditional Aristotelian logic, although in contemporary mathematical logic the term satisfiable is used instead. The syntactic definition states that a theory is consistent if there is no formula P such that both P and its negation are provable from the axioms of the theory under its associated deductive system.
If these semantic and syntactic definitions are equivalent for a particular logic, the logic is complete.. Stronger logics, such as second-order logic, are not complete.
A consistency proof is a mathematical proof that a particular theory is consistent. The early development of mathematical proof theory was driven by the desire to provide finitary consistency proofs for all of mathematics as part of Hilbert's program. Hilbert's program was strongly impacted by incompleteness theorems, which showed that sufficiently strong proof theories cannot prove their own consistency (provided that they are in fact consistent).[See more about Inconsistent at Dictionary 3.0 Encyclopedia]
Words and phrases related to 'Inconsistent'
'Inconsistent' in famous quotation sentence
* Let tears flow of their own accord their flowing is not inconsistent with inward peace and harmony. - Seneca
* Absurdity. A statement or belief manifestly inconsistent with one's own opinion. - Ambrose Gwinett Bierce
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