Tautology

Tautology refers to a use of redundant language in speech or writing, or, put simply, "saying the same thing twice".

Within the study of logic, a tautology is a statement that is true by its own definition.

Tautology

Tautology, often regarded as a fault of style, was defined by Fowler as "saying the same thing twice". In fact, it is not necessary for the entire meaning of a phrase to be repeated; 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 tautology. On the other hand, a repetition of meaning which improves the style of a piece of speech or writing is not usually described as tautology, although it may be a logical tautology. Below is a discussion of various patterns of semantic repetition and to what extent they are tautologies.

The Concise Oxford Dictionary defines tautology as "the saying of the same thing twice over in different words". In the spirit of pedantry, it should be noted that this statement is itself tautological (maybe intentionally, see below); by using the word "same", it is already implied that the thing has a plural value, so there is no need for the word "twice". It could also be argued that the word "over" is redundant in this context. The definition could instead read "the saying of something twice in different words" or "the saying of the same thing in different words".

Examples of tautology

The British supermarket Tesco sells a brand of the herb lemon thyme which it describes as having an "aromatic aroma". Non-cognate synonyms may also produce a tautology; "three-part trilogy" is tautologous because a trilogy, by definition, has three parts. Other examples of tautology include the phrases "helpful assistance" or "new innovation".

Repetitions of meaning in mixed language phrases

Exact repetitions of meaning sometimes occur when multiple languages are used together, such as "The La Brea Tar Pits" (the The tar tar pits), "Sierra Nevada Mountains" (Snowy Mountains mountains), "Shiba Inu dog" (small dog dog), "cheese quesadilla" (cheese cheese item), Mount Fujiyama (Mount Fuji mountain), "Lake Tahoe" (Lake Lake) "Pizza Pie" (circle circle), "Chai Tea" (Tea Tea), "Table Mesa" (Table Table), or East Timor (east east). The tautological status of these phrases is subjective, since they are only perceived as tautologous by people who understand enough of both languages to realize the redundancy.

Repetition of an abbreviated word

In some cases an acronym or abbreviation is commonly used in conjunction with a word which is actually part of the abbreviation. Examples are "ATM machine", "PIN number", "PAT testing", "HTML language", "VIN number", "LCD display", "HIV virus","SIN number" (in Canada), "NIC card", "Gigaflops per second", "RAS syndrome" or "E3 expo". These are tautologies, although many of them pass unnoticed.

Intentional repetition of meaning

A repetition of meaning may be intended to amplify or emphasize a certain aspect of the thing being discussed: for example, a gift is by definition free of charge, but one might talk about a "free gift" to emphasize that there are no hidden obligations, financial or otherwise, or that the gift is being given out of free will. 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" to mean the present time. Superficially these expressions may seem tautologous, but they are stylistically sound because the repeated meaning is merely a stylized way to express a single unified concept.

Pop culture examples of tautology

The late comedian Alan King used to tell this story: His lawyer asked him if he had ever drawn up a will. Alan said "No". The lawyer, in shock and horror, said, "If you died without a will, you would die intestate!" Alan looked up the word and found that it means "to die without a will". "In other words, if I die without a will, then I'll die without a will. This legal pearl cost me $500!"

United States President George W. Bush, before the Unity Journalists of Color convention on August 6, 2004, is quoted as saying, "Tribal sovereignty means that, it's sovereign. You're a -- you've been given sovereignty, and you're viewed as a sovereign entity. And, therefore, the relationship between the federal government and tribes is one between sovereign entities." [[1]]

One Dilbert cartoon takes this subject to a humorous extreme. Dilbert says he is working on a project that is known as "TTP". When asked what "TTP" stands for, Dilbert responds that it means "The TTP Project". This is not strictly a tautology, but a recursive acronym. Other examples of recursive acronyms, are GNU and PHP.

Tautologies in the study of logic

A logical tautology is a statement containing more than one sub-statement, that is true regardless of the truth values of its parts. For example, the statement "Either all crows are black, or not all of them are," is a tautology, because it is true no matter what color crows are. Expressing this formally, as a proposition with X representing "All crows are black" would give $X\lor \lnot X$ which is identically true because regardless of whether or not X is true, one of the disjuncts would be true, making the whole thing true.

A statement that is always false regardless of the truth values of its parts is known as a contradiction.

In propositional logic, the symbol $\models$ may be placed before a sentence to indicate that it is a tautology. Also, the symbol $\top$ is sometimes used as a "generic" tautology (in contexts where any old tautology will do).

In predicate logic, a distinction is often made between tautologies and validities. From this perspective, a statement is called a tautology only if it is a tautology in propositional logic (that is, when everything in the scope of a quantifier is viewed as a black box). So for example the statment

(\forall x)(x=5)\lor \lnot (\forall x)(x=5)

is a tautology, but the statement

(\forall x){\big (}(x=5)\lor \lnot (x=5){\big )}

is not a tautology, even though it is true in every possible interpretation and is thus a validity. This distinction is not always observed.

Discovering tautologies

The simplest way to discover tautologies in propositional logic is to use truth tables. However, as the number of variables involved increases, the size of the truth table increases in powers of 2, making it less favourable for four variable or greater tautologies, at which point simplification and algebra become more useful.

External links

Tautology

Examples of tautology

Repetitions of meaning in mixed language phrases

Repetition of an abbreviated word

Intentional repetition of meaning

Pop culture examples of tautology

Tautologies in the study of logic

Discovering tautologies

See also

External links