There is a reason we consider infinities only as limits of sequences of finite quantities.

Suppose you tried to sum the log-odds evidence of the infinite scientist that the pond has more big fish. Well, some of them have positive evidence (summing to positive infinity), some have negative evidence (summing to negative infinity), and you can, by choosing the order of summation, get any result you want (up to some granularity) between negative and positive infinity.

You don't need anthropomorphic tricks to make things weird if you have actual infinities in the problem.