What does inconsistency mean?

Definitions for inconsistency
ˌɪn kənˈsɪs tən siin·con·sis·ten·cy

This dictionary definitions page includes all the possible meanings, example usage and translations of the word inconsistency.

Princeton's WordNet

  1. incompatibility, mutual exclusiveness, inconsistency, repugnancenoun

    the relation between propositions that cannot both be true at the same time

  2. inconsistencynoun

    the quality of being inconsistent and lacking a harmonious uniformity among things or parts

Wiktionary

  1. inconsistencynoun

    The state of being inconsistent

  2. inconsistencynoun

    an incompatibility between two propositions that cannot both be true

Samuel Johnson's Dictionary

  1. Inconsistence, Inconsistencynoun

    Etymology: from inconsistent.

    There is a perfect inconsistency between that which is of debt, and that which is of free gift. Robert South, Sermons.

    Mutability of temper, and inconsistency with ourselves, is the greatest weakness of human nature. Addison.

    If a man would register all his opinions upon love, politicks, religion and learning, what a bundle of inconsistencies and contradictions would appear at last? Jonathan Swift.

Wikipedia

  1. inconsistency

    In classical deductive logic, a consistent theory is one that does not lead to a logical 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, i.e., there exists an interpretation under which all formulas in the theory are true. This is the sense used in traditional Aristotelian logic, although in contemporary mathematical logic the term satisfiable is used instead. The syntactic definition states a theory T {\displaystyle T} is consistent if there is no formula φ {\displaystyle \varphi } such that both φ {\displaystyle \varphi } and its negation ¬ φ {\displaystyle \lnot \varphi } are elements of the set of consequences of T {\displaystyle T} . Let A {\displaystyle A} be a set of closed sentences (informally "axioms") and ⟨ A ⟩ {\displaystyle \langle A\rangle } the set of closed sentences provable from A {\displaystyle A} under some (specified, possibly implicitly) formal deductive system. The set of axioms A {\displaystyle A} is consistent when φ , ¬ φ ∈ ⟨ A ⟩ {\displaystyle \varphi ,\lnot \varphi \in \langle A\rangle } for no formula φ {\displaystyle \varphi } .If there exists a deductive system for which these semantic and syntactic definitions are equivalent for any theory formulated in a particular deductive logic, the logic is called complete. The completeness of the sentential calculus was proved by Paul Bernays in 1918 and Emil Post in 1921, while the completeness of predicate calculus was proved by Kurt Gödel in 1930, and consistency proofs for arithmetics restricted with respect to the induction axiom schema were proved by Ackermann (1924), von Neumann (1927) and Herbrand (1931). 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 the incompleteness theorems, which showed that sufficiently strong proof theories cannot prove their own consistency (provided that they are in fact consistent). Although consistency can be proved by means of model theory, it is often done in a purely syntactical way, without any need to reference some model of the logic. The cut-elimination (or equivalently the normalization of the underlying calculus if there is one) implies the consistency of the calculus: since there is no cut-free proof of falsity, there is no contradiction in general.

ChatGPT

  1. inconsistency

    Inconsistency refers to the state or condition of lacking coherence, uniformity, or stability. It could be defined as disagreement, discrepancy, or contradiction among elements in a system, situation, statement, or behavior. An inconsistency might suggest unreliability, changing without reason, or an error or mistake in a set of data, information, or outcomes. It is essentially the opposite of consistency or harmony.

Webster Dictionary

  1. Inconsistencynoun

    the quality or state of being inconsistent; discordance in respect to sentiment or action; such contrariety between two things that both can not exist or be true together; disagreement; incompatibility

  2. Inconsistencynoun

    absurdity in argument ore narration; incoherence or irreconcilability in the parts of a statement, argument, or narration; that which is inconsistent

  3. Inconsistencynoun

    want of stability or uniformity; unsteadiness; changeableness; variableness

  4. Etymology: [Cf. F. inconsistance.]

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Numerology

  1. Chaldean Numerology

    The numerical value of inconsistency in Chaldean Numerology is: 1

  2. Pythagorean Numerology

    The numerical value of inconsistency in Pythagorean Numerology is: 7

Examples of inconsistency in a Sentence

  1. Hiromi Yamaoka:

    Any inconsistency in rules among countries creates a loophole that renders the rules ineffective.

  2. Comptroller Manuel Galindo on Wednesday:

    Anti-corruption laws consider (omissions in wealth declarations) an inconsistency, or a concealment which quickly and without any (legal) process results in an administrative ban for 12 months.

  3. James Russell Lowell:

    This imputation of inconsistency is one to which every sound politician and every honest thinker must sooner or later subject himself. The foolish and the dead alone never change their opinion.

  4. Brian Battle:

    There's been inconsistency out of the White House as to what the (trade) policy actually is, we're all just waiting and tapping our foot to see the actual policy.

  5. Bruce Rauner:

    We are intent on avoiding wrongful convictions and the injustice of inconsistency.

Popularity rank by frequency of use

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"inconsistency." Definitions.net. STANDS4 LLC, 2024. Web. 22 May 2024. <https://www.definitions.net/definition/inconsistency>.

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