What is "tautology"

Tautology \Tau*tol"o*gy\, n. [L. tautologia, Gr. ?: cf. F. tautologie.] (Rhet.) A repetition of the same meaning in different words; needless repetition of an idea in different words or phrases; a representation of anything as the cause, condition, or consequence of itself, as in the following lines:

The dawn is overcast, the morning lowers, And heavily in clouds brings on the day.
--Addison.

Syn: Repetition.

Usage: Tautology, Repetition. There may be frequent repetitions (as in legal instruments) which are warranted either by necessity or convenience; but tautology is always a fault, being a sameness of expression which adds nothing to the sense or the sound.

1570s, from Late Latin tautologia "representation of the same thing in other words," from Greek tautologia, from tautologos "repeating what has been said," from tauto "the same" (contraction of to auto, with to "the" + auto, see auto-) + -logos "saying," related to legein "to say" (see lecture (n.)). Related: Tautological.

n. 1 (context uncountable English) redundant use of words 2 (context countable English) An expression that features tautology. 3 (context countable logic English) A statement that is true for all values of its variables

1. n. (logic) a statement that is necessarily true; "the statement `he is brave or he is not brave' is a tautology"

2. useless repetition; "to say that something is `adequate enough' is a tautology"

Tautology may refer to:

• Tautology (rhetoric), a self-reinforcing pretense of significant truth
• Tautology (grammar), the use of redundant words
• Tautology (logic), a universal truth in formal logic
• Tautology (rule of inference), a rule of replacement for logical expressions
• Tautonym, a species name composed of a repeated word, or one identical to the genus name

In logic, a tautology (from the Greek word ταυτολογία) is a formula that is true in every possible interpretation.

Philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921. (It had been used earlier to refer to rhetorical tautologies, and continues to be used in that alternative sense.) A formula is satisfiable if it is true under at least one interpretation, and thus a tautology is a formula whose negation is unsatisfiable. Unsatisfiable statements, both through negation and affirmation, are known formally as contradictions. A formula that is neither a tautology nor a contradiction is said to be logically contingent. Such a formula can be made either true or false based on the values assigned to its propositional variables. The double turnstile notation $\vDash S$ is used to indicate that S is a tautology. Tautology is sometimes symbolized by "Vpq", and contradiction by "Opq". The tee symbol ⊤ is sometimes used to denote an arbitrary tautology, with the dual symbol ⊥ ( falsum) representing an arbitrary contradiction; in any symbolism, a tautology may be substituted for the truth value " true," as symbolized, for instance, by "1."

Tautologies are a key concept in propositional logic, where a tautology is defined as a propositional formula that is true under any possible Boolean valuation of its propositional variables. A key property of tautologies in propositional logic is that an effective method exists for testing whether a given formula is always satisfied (or, equivalently, whether its negation is unsatisfiable).

The definition of tautology can be extended to sentences in predicate logic, which may contain quantifiers, unlike sentences of propositional logic. In propositional logic, there is no distinction between a tautology and a logically valid formula. In the context of predicate logic, many authors define a tautology to be a sentence that can be obtained by taking a tautology of propositional logic and uniformly replacing each propositional variable by a first-order formula (one formula per propositional variable). The set of such formulas is a proper subset of the set of logically valid sentences of predicate logic (which are the sentences that are true in every model).

In rhetoric, a tautology (from Greek ταὐτός, "the same" and λόγος, "word/idea") is a logical argument constructed in such a way, generally by repeating the same concept or assertion using different phrasing or terminology, that the proposition as stated is logically irrefutable, while obscuring the lack of evidence or valid reasoning supporting the stated conclusion. (A rhetorical tautology should not be confused with a tautology in propositional logic.)

In propositional logic, tautology is one of two commonly used rules of replacement. The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs. They are:

The principle of idempotency of disjunction:

and the principle of idempotency of conjunction:

Where " ⇔ " is a metalogical symbol representing "can be replaced in a logical proof with."

In grammar, a tautology (from Greek tauto, "the same" and logos, "word"/"idea") is an unnecessary repetition of meaning, using more than one word effectively to say the same thing (often originally from different languages). It is considered a fault of style and was defined by A Dictionary of Modern English Usage ( Fowler) as "saying the same thing twice", when it is not apparently necessary to repeat the entire meaning of a phrase. "Fatal murder" is an example of a tautology. If a part of the meaning is repeated in such a way that it appears as unintentional, or clumsy, then it may be described as tautological. On the other hand, a repetition of meaning that improves the style of a piece of speech or writing is not necessarily tautological.

Intentional repetition of meaning intends to amplify or emphasize a particular, usually significant, fact about what is being discussed. For example, a gift is, by definition, free of charge; using the phrase "free gift" might emphasize that there are no hidden conditions or fine print, be it the expectation of money or reciprocation, or that the gift is being given by volition.

This is related to the rhetorical device of hendiadys, where one concept is expressed through the use of two, for example "goblets and gold" meaning wealth, or "this day and age" meaning the present time (meaning "now"). Superficially these expressions may seem tautological, but they are stylistically sound because the repeated meaning is just a way to emphasise the same idea.

The use of tautologies is, however, usually unintentional. They often hinder reader comprehension and undermine the writer's credibility. As Kallan explains, "Mental telepathy, planned conspiracies, and small dwarfs, for example, convey the possibility of physical telepathy, spontaneous conspiracies, and giant dwarfs." (Kallan)

Fowler offers that some tautologies derive from historic processes. One example of this is that when the Bible was translated into Anglo-Saxon, Norman French was still common among the aristocracy, so expressions like "save and except" were translated both for the commoners and the aristocrats; although in this case both "save" and "except" have a French or Latin origin.

Fowler makes a similar case for double negatives; in Old English they intensified the expression, did not negate it back to being a positive, and plenty of examples exist in writings before the eighteenth century, such as Shakespeare. In Modern French, for example, the "ne-pas" formation is essentially a double negative,as also is the Russian form, "Ya ne vizhu nichevo" (literally I don't see nothing). and in many other Western European latinate languages the same applies, with "ni" or "no", mutatis mutandis, emphasising instead of negating the initial negative. In common French, the "ne" is quite typically dropped, as it was believed to have been in Vulgar Latin.

Parallelism is not tautology, but rather a particular stylistic device. Much Old Testament poetry is based on parallelism: the "same thing" said twice, but in slightly different ways (Fowler puts it as pleonasm). However, modern biblical study emphasizes that there are subtle distinctions and developments between the two lines, such that they are usually not truly the "same thing." Parallelism can be found wherever there is poetry in the Bible: Psalms, the Books of the Prophets, and in other areas as well.