To me, by far the most satisfying solution is a full-fledged Platonic acknowledgement that numbers are indeed just “out there” and that they are directly accessible to our intuitions. I embrace this view for (at least) three reasons: A. After a lifetime of thinking about numbers, it feels right to me. B. Pretty much every one else who spends his/her life thinking about numbers has come to the same conclusion. C. It seems enormouosly more plausible to me that numbes are “just out there” than that physical objects are “just out there”, partly because there is in fact a unique system of (standard) natural numbers, whereas the properties of the physical universe appear to be far more contingent and therefore unnecessary.
But the set of all possible minds is so vast that the fact that numbers feel real to us feels to my mind as extremely weak evidence that numbers are real.
I think (it’s not my post) that it’s supposed to be evidence that numbers are real because the set of all possible minds is vast. Because there are so many possible minds, it’s unlikely that a mind chosen randomly from that set would have similar intuitions about numbers to mine. It’s even more unlikely that a third mind would also have those intuitions. Yet, for some reason, this vastly unlikely thing happens anyway. This implies that there is some reason which is responsible for all the minds feeling the same way. One such reason would be “the intuition is correct, and the minds have correctly figured it out”.
(Other possible reasons could be “all the minds are biased in the same way” or some other reason unrelated to truth of the idea, but nobody’s saying it’s proof, it’s just evidence.)
Though the number of possible minds is vast, I think the likelihood of two minds sharing an intuitive concept of number is high, because minds (or perhaps I should say consciousnesses) process information sequentially. Perhaps it is akin to the shared perception of rhythm, which is not limited to human minds. I suppose you have already seen it, but this video is amazing: the dancing cockattoo.
Landsburg writes:
But the set of all possible minds is so vast that the fact that numbers feel real to us feels to my mind as extremely weak evidence that numbers are real.
I think (it’s not my post) that it’s supposed to be evidence that numbers are real because the set of all possible minds is vast. Because there are so many possible minds, it’s unlikely that a mind chosen randomly from that set would have similar intuitions about numbers to mine. It’s even more unlikely that a third mind would also have those intuitions. Yet, for some reason, this vastly unlikely thing happens anyway. This implies that there is some reason which is responsible for all the minds feeling the same way. One such reason would be “the intuition is correct, and the minds have correctly figured it out”.
(Other possible reasons could be “all the minds are biased in the same way” or some other reason unrelated to truth of the idea, but nobody’s saying it’s proof, it’s just evidence.)
Though the number of possible minds is vast, I think the likelihood of two minds sharing an intuitive concept of number is high, because minds (or perhaps I should say consciousnesses) process information sequentially. Perhaps it is akin to the shared perception of rhythm, which is not limited to human minds. I suppose you have already seen it, but this video is amazing: the dancing cockattoo.