[HIST 2297] Never Say Never

In my History and Philosophy of Science course, we are reading Samir Okasha’s Philosophy of Science: A Very Short Introduction. It’s an excellent introductory book of philosophy of science. 

During class discussions, a question came up about the following passage. Okasha (2002, p. 91) writes:

Kuhn’s insistence that there is no algorithm for theory choice in science is almost certainly correct. For no-one has ever succeeded in producing such an algorithm. Lots of philosophers and scientists have made plausible suggestions about what to look for in theories—simplicity, broadness of scope, close fit with the data, and so on. But these suggestions fall far short of providing a true algorithm, as Kuhn knew well.

Here, Okasha seems to argue as follows: 

1. No one has ever succeeded in producing an algorithm for theory choice in science. 
2. Therefore, no one will ever succeed in producing an algorithm for theory choice in science. (There is no such algorithm.)

My students and I were discussing whether the fact that no one has been able to accomplish something (e.g., producing an algorithm for theory choice) is a good reason to believe that it cannot be accomplished.

Surely, the fact that no one has been able to square the circle is a good reason to think that it cannot be done. But that is because squaring the circle is logically impossible. But producing an algorithm for theory choice doesn’t seem to be logically impossible. So, is the fact that no one has been able to come up with one thus far a good reason to believe that it cannot be done (or, more strongly, that there is no such algorithm)? 

How many failed attempts to accomplish something—which is not logically impossible—justify the conclusion that that thing cannot be accomplished?