5.453 All numbers in logic stand in need of justification.  Or rather, it must become evident that there are no numbers in logic.  There are no pre-eminent numbers.

5.454 In logic there is no co-ordinate status, and there can be no classification.  In logic there can be no distinction between the general and the specific.

5.4541 The solutions of the problems of logic must be simple, since they set the standard of simplicity.  Men have always had a presentiment that there must be a realm in which the answers to questions are symmetrically combined—­a priori—­to form a self-contained system.  A realm subject to the law:  Simplex sigillum veri.

5.46 If we introduced logical signs properly, then we should also have introduced at the same time the sense of all combinations of them; i.e. not only ‘p C q’ but ‘P(p C q)’ as well, etc. etc.  We should also have introduced at the same time the effect of all possible combinations of brackets.  And thus it would have been made clear that the real general primitive signs are not ’ p C q’, ‘(dx) . fx’, etc. but the most general form of their combinations.

5.461 Though it seems unimportant, it is in fact significant that the pseudo-relations of logic, such as C and z, need brackets—­unlike real relations.  Indeed, the use of brackets with these apparently primitive signs is itself an indication that they are not primitive signs.  And surely no one is going to believe brackets have an independent meaning. 5.4611 Signs for logical operations are punctuation-marks,

5.47 It is clear that whatever we can say in advance about the form of all propositions, we must be able to say all at once .  An elementary proposition really contains all logical operations in itself.  For ‘fa’ says the same thing as ‘(dx) . fx . x = a’ Wherever there is compositeness, argument and function are present, and where these are present, we already have all the logical constants.  One could say that the sole logical constant was what all propositions, by their very nature, had in common with one another.  But that is the general propositional form.

5.471 The general propositional form is the essence of a proposition.

5.4711 To give the essence of a proposition means to give the essence of all description, and thus the essence of the world.

5.472 The description of the most general propositional form is the description of the one and only general primitive sign in logic.

5.473 Logic must look after itself.  If a sign is possible , then it is also capable of signifying.  Whatever is possible in logic is also permitted.  (The reason why ‘Socrates is identical’ means nothing is that there is no property called ‘identical’.  The proposition is nonsensical because we have failed to make an arbitrary determination, and not because the symbol, in itself, would be illegitimate.) In a certain sense, we cannot make mistakes in logic.