6.122

Home
Su
1.
2.
3.
4.
5.
6.

 

Whence it follows that we can get on without logical propositions, for we can recognize in an adequate notation the formal properties of the propositions by mere inspection.

6.1221 If for example two propositions "p" and "q" give a tautology in the connexion "p  HOOK  q", then it is clear that q follows from p.

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

6.1222    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.

6.1223    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.

6.1224    It also becomes clear why logic has been called the theory of forms and of inference.