Some statisticians claim that the surest way to increase the

The passage first presents a claim that some statisticians make: "the surest way to increase the overall correctness of the total set of one’s beliefs is: never change that set, except by rejecting a belief when given adequate evidence against it" (in other words, "don't add any beliefs; rather, only remove beliefs when given adequate evidence against them).

The author then prefaces the argument with, "if this were the only rule one followed.." (and that rule is, "never change that set, except by rejecting a belief when given adequate evidence against it."). Therefore, the author's argument is only concerned with what would happen if that were the only rule one followed (ie if one were to only remove beliefs and never add new beliefs). If someone were to "accept new beliefs when presented with some kinds of evidence" (as stated in choice B), then that person would NOT be adhering only to that rule (since they would be ADDING to the set of beliefs). So the author does not neglect the "possibility that even while following the statisticians’ rule, one might also accept new beliefs when presented with some kinds of evidence"; rather, the author specifically states that the argument does not apply in those situations. Thus, B can be eliminated.

Now let's consider choice A... both the author and the statisticians would agree that, "if this were the only rule one followed... then, over time, one could only have fewer and fewer beliefs". The statisticians claim that this is the "surest way to increase the overall correctness of the total set of one’s beliefs"; however, the author concludes that "the statisticians’ claim must be mistaken", since "we need many beliefs in order to survive". But the statisticians only claim that following that rule will increase the overall correctness of the total set of one's beliefs; they never claim that following that rule will or will not hinder one's ability to survive. For example, imagine a person with 100 beliefs who only follows the rule presented in the passage and ends up rejecting 95 of those beliefs. This may in fact hinder that person's ability to survive, but if the few remaining beliefs are all correct, then the statisticians claim would still be correct and the author's argument would fail. In other words, the statisticians claim is only concerned with the correctness of the total set of one's belief, not with how those beliefs (or lack thereof) affect one's ability to survive. Choice A accurately identifies this weakness in the author's argument.