4.463 Truth-conditions define the room to move [Spielraum – literally “play space”] left to the facts by a proposition.
(A proposition, a picture, a model, are in a negative sense like a solid body that restricts the free movement of others; in a positive sense [they are] like a space limited by solid substance wherein there is room for a body.)
Tautology leaves to reality the whole – endless – logical space; contradiction fills the whole of logical space and leaves reality not a point. Neither of them, therefore, can determine reality in any way.
Odd to say that a contradiction fills logical space, taking up every point, as if there were room for a contradiction in logical space. To say it belongs to the symbolism is, I suppose, to say just this. But in that sense tautology too is within logical space, yet Wittgenstein denies this here. So what is he saying?
Cf. Notebooks November 14th 1914.
4 comments:
I think 'logical space' here just means the space of possible realities, not space of possible logical forms, or however it is you're interpreting it.
Thanks.
Yes, I agree that 'logical space' means the space of possible realities. What I'm puzzled by is more Wittgenstein's way of expressing his point. "Contradiction fills the whole of logical space" sounds very odd to my ears. Maybe 'blocks' would work better than 'fills'.
I think it 'fills' the space because it states that all possible realities hold (p and not-p, for example). Whereas a tautology says nothing about which possible reality holds. A tautology provides no information; a contradiction provides too much.
Yes, that makes sense. Thanks.
It (what Wittgenstein writes) still strikes me as an odd way to put the point, but I probably shouldn't worry about that.
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