Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/167

Rh  If for example two propositions "p" and "q" give a tautology in the connexion "p⊃a", then it is clear that "q" follows from "p".

E.g. that "q" follows from "p⊃q.p" we see from these two propositions themselves, but we can also show it by combining them to "p⊃q.p:⊃:q" and then showing that this is a tautology.

This throws light on the question why logical propositions can no more be empirically confirmed than they can be empirically refuted. Not only must a proposition of logic be incapable of being contradicted by any possible experience, but it must also be incapable of being confirmed by any such.

It now becomes clear why we often feel as though "logical truths" must be "postulated" by us. We can in fact postulate them in so far as we can postulate an adequate notation.

It also becomes clear why logic has been called the theory of forms and of inference.

It is clear that the laws of logic cannot themselves obey further logical laws.

(There is not, as Russell supposed, for every "type" a special law of contradiction; but one is sufficient, since it is not applied to itself.)

The mark of logical propositions is not their general validity.

To be general is only to be accidentally valid for all things. An ungeneralized proposition can be tautologous just as well as a generalized one.

Logical general validity, we could call essential as opposed to accidental general validity, e.g. of the proposition "all men are mortal". Propositions like Russell's "axiom of reducibility" are not Rh