Tautology
TAUTOLOGY
TAUTOLOGY is the empty (needless) repetition of a word or a sentence, which is altogether the same either in respect to the sound, or even in respect to the sense. See Gnom. on Act 23:6, note on .-Rom 7:13, note on .
Fuente: Gnomon Technical Terms
Tautology
As a syntactical term of the propositional calculus this is defined in the article on logic, formal (q.v.). Wittgenstein and Ramsey proposed to extend the concept of a tautology to disciplines involving quantifiers, by interpreting a quantified expression as a multiple (possibly infinite) conjunction or disjunction; under this extension, however, it no longer remains true that the test of a tautology is effective.
The name law of tautology is given to either of the two dually related theorems of the propositional calculus,
[p ? p] = p,
pp = p,
or either of the two corresponding dually related theorems of the algebra of classes,
a ? a,
a n a.
Whitehead and Russell reserve the name principle of tautology for the theorem of the propositional calculus, [p ? p] ? p, but use law of tautology in the above senses. — A.C.
L. Wittgenstein, Tractatus Logico-Philosophicus, New York and London, 1922. F. P. Ramsey, The foundations of mathematics, Proceedings of the London Mathematical Society, ser. 2, vol. 25 (1926), pp. 338-384; reprinted in his book of the same title, New York and London, 1931.