The logical induction criterion requires that, in the limit, all logical inductors assign probability 0 to Fermat’s last theorem being false. Conditioning on an event with probability 0 is ill-defined, so we have no formal guarantee that these conditional probabilities are well-behaved.
From what I understand, an LI need not assign probability 0 to Fermat’s last theorem at any finite time. She might give it price 2−n on day n. In practice I don’t know if the LI constructed according to the paper will ever assign price 0 to it. For all I know that would depend on the particular enumerations of traders and rationals used.
So if she never assigns price 0 except in the limit, we could condition on FLT being false at any finite time, and mayybe we could even consider the limit of those conditionings?
From what I understand, an LI need not assign probability 0 to Fermat’s last theorem at any finite time. She might give it price 2−n on day n. In practice I don’t know if the LI constructed according to the paper will ever assign price 0 to it. For all I know that would depend on the particular enumerations of traders and rationals used.
So if she never assigns price 0 except in the limit, we could condition on FLT being false at any finite time, and mayybe we could even consider the limit of those conditionings?
I’d, uh, be surprised if this works.