Tautology (redirected from Circular explanation)

tautology

In logic, a statement that cannot be denied without inconsistency. Thus, “All bachelors are either male or not male” is held to assert, with regard to anything whatsoever that is a bachelor, that it is male or it is not male. In the propositional calculus, even complicated symbolic expressions such as [(A ⊃ B) ∧ (C ⊃ ¬ B)] ⊃ (C ⊃ ¬ A) can be shown to be tautologies by displaying in a truth table every possible combination of T (true) and F (false) of its arguments A, B, C. A tautology can be purely formal (a statement form rather than a statement), and in some usages only such formal truths are tautologies.

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tautology

Logic a statement that is always true, esp a truth-functional expression that takes the value true for all combinations of values of its components, as in either the sun is out or the sun is not out

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(logic)

tautology - A proposition which is always true. Compare: paradox. The Linguistic Smarandache Tautologies,.

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Tautology 

(1) The repetition of the same word or of words close in meaning: also, an example of such repetition. Examples are iasnee iasnogo (“completely obvious”; literally, “clearer than clear”) and plachet, slezami zalivaetsia (“she weeps, dissolved in tears”). In poetic language, especially in oral folk poetry, tautology is used to intensify emotional effect. An example in the bylina (epic folk song) about Nightingale the Robber is Pod Chernigovom silushki chernym-cherno, I Chernym-cherno, chernei vorona (“Near Chernigov the troops looked black as could be [literally, ‘black-black’], / Black as could be, blacker than a raven”). Poets often use tautology and tautological rhymes; an example is Pushkin’s Vot na bereg vyshli gosti, / Tsar’ Saltan zovet ikh v gosti (“The visitors disembarked, / Tsar Saltan invited them to visit”).

A number of tautological word groups are widely used in colloquial speech, for example, tselikom i polnost’iu (“wholly and completely”), k segodniashnemu dniu (“by today”; literally, “by today’s day”) and den’-den’skoi (“the livelong day”). Unnecessary repetitions in speech sometimes testify to a speaker’s limited command of language. Tautology is a type of pleonasm.

T. V. VENTTSEL’

(2) In logic, an extreme example of the logical fallacy of the unwarranted premise (Latin petitio principii), namely, the definition or proof of something by the same thing (Latin idem per idem). In two-valued classical logic the term “tautology,” like the term “law of logic,” refers to reliable, always true, or identically true formulas that remain constant in relation to their constituent variables, that is, in relation to the world’s actual state of affairs. In this type of logic, according to G. W. von Leibniz, tautologies are truths in all possible worlds, eternal truths, essential truths, and truths by virtue of the postulates of classical logic. An example of this type of tautology is the law of the excluded middle.

In many-valued logic, a tautology is a formula which in any set from an accepted universal system of values for variables retains the same distinctive value. This type of tautology is used in proofs of independence.

REFERENCES

Wittgenstein, L. Logiko-filosofskii traktat. Moscow, 1958. (Translated from German.)
Church, A. Vvedenie v matematicheskuiu logiku, vol. 1. Moscow, 1960. (Translated from English.)

M. M. NOVOSELOV