I’m no ambassador to anything, but this says it all, folks, it aids me quite well.
Response: of course it doesn’t! Which is why (P & (P->Q))->Q is also meaningless. TVAA goes on to say,
I think the hidden assumption here is that if it is a symbol that can be manipulated (used) then it must represent (note I don’t say represent something; we don’t care whether anything exists or not). But this is the very thing I am arguing: a symbol that is able to be manipulated does not necessarily represent. And then to say: logic doesn’t represent; it is meaningless; these symbols (the symbols of logic) do not represent.
Jerevan notes,
[cutting and pasting + laziness = removed emphasis]That’s fine. I would agree to this, as well, as words like “pain” have no reference (RE: previous discussions we’ve had).
Wittgenstein’s tactic (in the dogmatic Tractutus) was this: the world is the totality of facts, and facts are determined by logic. This means that logic is the limit of knowledge, and in a breathtakingly literal way. One couldn’t even say it was the edge, for that implied something was beyond logic, and if logic determines facts, this, too, would be a fact, and so logic would be able to say what was beyond it. Which is nonsense. So logic can then have no sense, it can’t represent anything, because if it did then what it represents is nonsense. The only way to escape the paradox is to remove meaning from logic. (I do not do his argument justice here; everyone interested in logic really should read this book.)
My tactic does not depend on declaring logic as “that which declares facts”, because it doesn’t. We use it for that, but the act of declaring facts is ours, not logic’s. Black holes, some say, pinch off matter from spacetime. Logic is pinched off from sensible speech. I should be able to use logic even in a world where I both have and don’t have eggs for breakfast simultaneously, contrary to Math Geek’s comment. Take the topology of Klein Bottles, or Mobius Strips, for example. Even in first-year calculus one can demonstrate a mathematical beast that has a finite volume but infinite surface area (or maybe it was the other way around, I can’t remember any longer).
Chess would not become more meaningful if we used it to plan real-world battles. The meaning is in those boys dying out there, in those other boys killing out there.
If I am asleep and it is raining, and in my dream I dream of rain, and even if we show a causal connection between the two (say, by monitoring brain activity in some great scientific way), were I to say in my dream, “It is raining,” those words aren’t meaningful. [This isn’t meant to claim that logic is a dream or even a pure fancy, by the way.]