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.
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