3 ms·

Isn’t that an infinite regress problem?

• JadeNB 12y ago
  > Isn’t that an infinite regress problem? I can certainly see the sense in which it might be said to be, but I think that's not the sense in which the term is originally meant. I tried to come up with an explanation of why I think they were meaningfully different by an appeal to mathematical analogy, but I'm not sure that it's convincing. Fermat argued as follows: a positive integer solution to `x^4 + y^4 = z^4` could always be converted into a smaller such solution, and you can't produce ever-smaller positive integers forever, so there weren't any such solutions in the first place. I'd say that this is clearly an infinite regress (though it was actually called infinite descent). On the other hand, consider the problem of subtracting 1. In the system of ordinary (not-necessarily-positive) integers, this leads to a (non-paradoxical) infinite regress; whereas, in the system of integers modulo some fixed positive integer, it leads to a (non-paradoxical) circularity (where repeatedly subtracting 1 from a number will eventually yield that number itself). I think that it is reasonable to call these different phenomena.