C q' we write, for example,
'p|q. |. p|q', and instead of 'Pp', 'p|p' (p|q = neither p nor q), then
the inner connexion becomes obvious. (The possibility of inference from
(x). fx to fa shows that the symbol (x). fx itself has generality in
it.)

5.132 If p follows from q, I can make an inference from q to p, deduce
p from q. The nature of the inference can be gathered only from the two
propositions. They themselves are the only possible justification of
the inference. 'Laws of inference', which are supposed to justify
inferences, as in the works of Frege and Russell, have no sense, and
would be superfluous.

5.133 All deductions are made a priori.

5.134 One elementary proposition cannot be deduced form another.

5.135 There is no possible way of making an inference form the existence
of one situation to the existence of another, entirely different
situation.

5.136 There is no causal nexus to justify such an inference.

5.1361 We cannot infer the events of the future from those of the
present. Belief in the causal nexus is superstition.

5.1362 The freedom of the will consists in the impossibility of knowing
actions that still lie in the future. We could know them only if
causality were an inner necessity like that of logical inference.--The
connexion between knowledge and what is known is that of logical
necessity. ('A knows that p is the case', has no sense if p is a
tautology.)

5.1363 If the truth of a proposition does not follow from the fact that
it is self-evident to us, then its self-evidence in no way justifies our
belief in its truth.

5.14 If one proposition follows from another, then the latter says more
than the former, and the former less than the latter.

5.141 If p follows from q and q from p, then they are one and same
proposition.

5.142 A tautology follows from all propositions: it says nothing.

5.143 Contradiction is that common factor of propositions which no
proposition has in common with another. Tautology is the common factor
of all propositions that have nothing in common with one another.
Contradiction, one might say, vanishes outside all propositions:
tautology vanishes inside them. Contradiction is the outer limit of
propositions: tautology is the unsubstantial point at their centre.

5.15 If Tr is the number of the truth-grounds of a proposition 'r', and
if Trs is the number of the truth-grounds of a proposition 's' that are
at the same time tru