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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Inconsistent Sample Sentences in News
- Why Successful People Are Inconsistent
This wasn’t your usual advice, and I found it interesting to read and interesting how familiar it felt as I read each next line. The post was all about “changing your mind.” The way I would describe the overall theme, is “inconsistency.” Read more on this news related to 'Inconsistent'
- Legal group faults Pakistan's top judge as inconsistent
By Katharine Houreld ISLAMABAD (Reuters) - Pakistan's flamboyant chief justice has strengthened human rights but his inconsistent choice of cases has left the Supreme Court vulnerable to accusations of partisan intervention, a global group of 60 eminent judges and lawyers said on Thursday. Chief Justice Iftikhar Chaudhry - due to step down on December 12 - spe Read more on this news related to 'Inconsistent'
- Jeff Seidel: Inconsistent Lions can't hold onto ball -- or a lead
Assume the position. Face the wall. Now, bang your head into it. Don't worry. You will get used to it. That's what it's like to watch the Lions. It's painful. Miserable. Frustrating. Exasperating. With moments of fleeting excitement and joy. Then again, that could be delirium setting in. Read more on this news related to 'Inconsistent'