6.1203 In order to recognize an expression as a tautology, in cases where

no generality-sign occurs in it, one can employ the following intuitive

method: instead of 'p', 'q', 'r', etc. I write 'TpF', 'TqF', 'TrF', etc.

Truth-combinations I express by means of brackets, e.g. and I use lines to

express the correlation of the truth or falsity of the whole proposition

with the truth-combinations of its truth-arguments, in the following way So

this sign, for instance, would represent the proposition p z q. Now, by way

of example, I wish to examine the proposition P(p .Pp) (the law of

contradiction) in order to determine whether it is a tautology. In our

notation the form 'PE' is written as and the form 'E . n' as Hence the

proposition P(p . Pp). reads as follows If we here substitute 'p' for 'q'

and examine how the outermost T and F are connected with the innermost

ones, the result will be that the truth of the whole proposition is

correlated with all the truth-combinations of its argument, and its falsity

with none of the truth-combinations.

- -- Wittgenstein, Ludwig