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.

6.121 The propositions of logic demonstrate the logical properties of propositions by combining them so as to form propositions that say nothing.  This method could also be called a zero-method.  In a logical proposition, propositions are brought into equilibrium with one another, and the state of equilibrium then indicates what the logical constitution of these propositions must be.

6.122 It follows from this that we can actually do without logical propositions; for in a suitable notation we can in fact recognize the formal properties of propositions by mere inspection of the propositions themselves.

6.1221 If, for example, two propositions ‘p’ and ‘q’ in the combination ’p z q’ yield a tautology, then it is clear that q follows from p.  For example, we see from the two propositions themselves that ‘q’ follows from ‘p z q . p’, but it is also possible to show it in this way:  we combine them to form ‘p z q . p :z:  q’, and then show that this is a tautology.

6.1222 This throws some light on the question why logical propositions cannot be confirmed by experience any more than they can be refuted by it.  Not only must a proposition of logic be irrefutable by any possible experience, but it must also be unconfirmable by any possible experience.

6.1223 Now it becomes clear why people have often felt as if it were for us to ’postulate ’ the ‘truths of logic’.  The reason is that we can postulate them in so far as we can postulate an adequate notation.

6.1224 It also becomes clear now why logic was called the theory of forms and of inference.

6.123 Clearly the laws of logic cannot in their turn be subject to laws of logic. (There is not, as Russell thought, a special law of contradiction for each ‘type’; one law is enough, since it is not applied to itself.)

6.1231 The mark of a logical proposition is not general validity.  To be general means no more than to be accidentally valid for all things.  An ungeneralized proposition can be tautological just as well as a generalized one.

6.1232 The general validity of logic might be called essential, in contrast with the accidental general validity of such propositions as ’All men are mortal’.  Propositions like Russell’s ‘axiom of reducibility’ are not logical propositions, and this explains our feeling that, even if they were true, their truth could only be the result of a fortunate accident.

6.1233 It is possible to imagine a world in which the axiom of reducibility is not valid.  It is clear, however, that logic has nothing to do with the question whether our world really is like that or not.