Page 80. (Via.)
"I also emphasize that, when I insert the Platonic output of a computation as a latent node in a causal diagram, I am not making a philosophical claim about computations having Platonic existence. I am just trying to produce a good approximation of reality that is faithful in its predictions and useful in its advice."Technically speaking to solve the problem you not only need the givens, but need to assume or be given the rules of logic themselves.
Isn't 678 * 987 equal to 669,186 regardless of how well the calculators are constructed, regardless of electronic glitches or damage in transit?
The normal thing to say is that it is equal to 669,186 regardless of any facts about the physical world. My answer is that logic and arithmetic are facts about the physical world. Arithmetic works because it ultimately describes physics, which means physics described it long before we did.
If the calculator doesn't display 669,186 I can conclude it is broken. There's the calculation it is doing and then the calculation it is (platonically?) supposed to be doing, and they're different.
Imagine I dump 987 piles of sand into one sandbox, each exactly 678 grains. If my subsequent fully vetted count isn't nearly 670,000, then either I'm not creating an analogue of multiplication, or multiplication doesn't work the way I think it does. For the former, my experiment design is broken, because physics doesn't work the way I think it does. For the latter, multiplication doesn't work the way I think it does, which means my understanding of physics is broken. Either way, not the sand's fault.
Thing is, in such a world, would it have ever occurred to me that the answer might be nearly 670,000? I submit: no. Even if it occurs to you that your world might be fundamentally different, it is impossible to work out how.
Verification: try describe a world where A=A is false. A!=A. What does a thing look like when it doesn't look like itself? If that works, maybe you can tell me what multiplication might have looked like if it wasn't what we've got. Or, what an alternate world would have instead of multiplication. If you try to tell me these things are platonically impossible, then I'll ask you how it knows it is supposed to be impossible. What stops it?
Things like this are probably impossible to prove. It questions questioning itself; it tries to verify verification. You need some framework to hang arguments off of, and here I am wondering how to get a grasp of the framework. A hand, trying to grab itself.
Which itself interests me. If I'm trying to make a hand grasp itself, how do I get the answer 'no' at all? Shouldn't my brain just crash?