se 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.
5.4731 Self-evidence, which Russell talked about so much, can become
dispensable in logic, only because language itself prevents every
logical mistake.--What makes logic a priori is the impossibility of
illogical thought.
5.4732 We cannot give a sign the wrong sense.
5,47321 Occam's maxim is, of course, not an arbitra
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