tautology


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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

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

tautology

(logic)
A proposition which is always true.

Compare: paradox.

The Linguistic Smarandache Tautologies,.
References in periodicals archive ?
(22) These are all points that Joel Feinberg misses in his discussion of psychological egoism and tautology in his "Psychological Egoism," in Reason and Responsibility, ed.
Nevertheless, what interested us here is not the anthropological perspective, used in television, but the implications of the second item from above, of the tautology display-reality, namely duplication of reality.
The results obtained were promising as the runtime monitor developed for the subject was able to handle all of the tautology based SQLIAs.
To illustrate this extremity, Wittgenstein calls to mind the simple tautology "It is raining or not raining." This tells us nothing, for after hearing it, we have no idea whether we need an umbrella (4.461).
The contradictory of a Liar cannot itself be a Liar, for a Liar is contradictory (on Bradwardine's account) and so its contradictory must be a tautology.
"I say, old fellow," you probe, "Is this the road to Pear Tree Cottage?" He cautiously tamps down the dottle in his pipe with a horny thumb while he thinks about it, then replies: "This is the road to Pear Tree Cottage or this is not the road to Pear Tree Cottage." (Actually, he replies in the vernacular, saying "Could be, could be not." But his elliptical paraphrase is equivalent to the original tautology.) Either version of his utterance is resolutely unhelpful; and that is the sad fact about tautologies.
There is a numerous class of readers who imagine that the same words cannot be repeated without tautology; this is a great error: virtual tautology is much oftener produced by using different words when the meaning is the same.
I have referred before to the tautology involved in the phrase "climate change".
According to this analysis, if the material implication from a sentence "p" to the sentence "q" is a tautology, then the fact q is a consequence of the fact p and the other way around.
Moreover, to the extent that America is a society hostile to unions, discovering that workers are reluctant to join them is nothing more than stating a tautology. Finally, what these two case studies reveal is how important were the activities of the two respective employers, and the drawn out procedural problems unions experience with working their way through the legislative processes which govern such campaigns, in hindering their ability to organise workers.
Another concern is the logical status of the Darwinian principle of natural selection, often referred to as "survival of the fittest." If it is asked who are the "fittest," the only properly Darwinian answer is "those who survive." But then this principle would seem to be a mere tautology without empirical content, and so unfalsifiable.
It's not rocket science - the way people speak today is enough to get traditionalists fuming, from idiotic idioms to terrible tautology, according to a new book.