Thursday, October 11, 2007

4.466 To a definite logical combination of symbols corresponds a definite logical combination of their meanings [Bedeutungen]; every arbitrary combination corresponds only to unconnected symbols.

That is to say, propositions that are true for every state of things cannot after all be combinations of symbols, because otherwise only definite combinations of objects could correspond to them.

(And there is no logical combination to which no combination of objects corresponds.)

Tautology and contradiction are the limiting cases of the combination of symbols, namely their dissolution.

So tautologies and contradictions are not, after all (├╝berhaupt), combinations of signs. Everything in between is a combination, but at the limits, these bindings become undone. So we need to re-think, if not take back, 4.4611. But is that enough? What sense can we now make of these “limiting cases” as limits of anything? And then what do we mean by “everything in between”?

I have changed “signs” to ‘symbols” here in line with p. 60 of Letters to Ogden.

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