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