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core definition

A tautology is a proposition that is true by definition (such as 'all mothers are female') or one in which the same thing is said twice in different words (e.g. 'they followed one after the other in succession').

explanatory context

Tautology can be extended to refer to a whole argument. In which case the outcome of the tautological argument will logically always be true irrespective of the truth or falsity of the propositions. A simple example is 'either all grass is green or it is isn't. A more complex example is represented symbolically by: (p or q) or not-p, where it doesn't matter what combination of true or false are assigned to p and q the outcome will be true.


Tautologies are true because of the nature of the logical operators, independently of the veracity of the propositions made about the real world. This has lead to tautologies as being seen as vacuous, saying nothing, and as irrelevent to developing knowledge about the world.

analytical review

Stanford Encyclopedia of Philosophy (2017) explains the analytic/synthetic distinction thus:

Tautology, in logic, a statement so framed that it cannot be denied without inconsistency. Thus, "All humans are mammals" is held to assert with regard to anything whatsoever that either it is not a human or it is a mammal. But that universal "truth" follows not from any facts noted about real humans but only from the actual use of human and mammal and is thus purely a matter of definition.

In the propositional calculus, a logic in which whole propositions are related by such connectives as ⊃ ("if…then"), · ("and"), ∼ ("not"), and ∨ ("or"), even complicated 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 truth-values—T (true) and F (false)—of its arguments A, B, C and after reckoning out by a mechanical process the truth-value of the entire formula, noting that, for every such combination, the formula is T. The test is effective because, in any particular case, the total number of different assignments of truth-values to the variables is finite, and the calculation of the truth-value of the entire formula can be carried out separately for each assignment of truth-values.

The notion of tautology in the propositional calculus was first developed in the early 20th century by the American philosopher Charles Sanders Peirce, the founder of the school of pragmatism and a major logician. The term itself, however, was introduced by the Austrian-born British philosopher  Ludwig Wittgenstein, who argued in the Logisch-philosophische Abhandlung (1921; Tractatus Logico-Philosophicus, 1922) that all necessary propositions are tautologies and that there is, therefore, a sense in which all necessary propositions say the same thing—viz, nothing at all....

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Encyclopaedia Britannica, 2019, 'Tautology', updated 28 May 2019, available at, accessed 15 June 2019.

copyright Lee Harvey 2012–2020

