Theory of inquiry

Abstract

works on a proof and submits the results at t2.There are no problems with her proof.In fact, it is perfectly sound.Who should get the reward for settling that THEOREM?It is intuitively clear that the answer is: the second mathematician.Since the first mathematician's work contained an error, he did not settle that THEOREM.Crucially, between the three live candidates in the literature, only K-AIM can secure this result.To see why, note that the case of the first mathematician is a textbook example of a Gettier case: he has a belief that THEOREM, which is both justified and true, but falls short of knowledge.Since he has a justified true belief, both T-AIM and J-AIM predict that he has attained the aim of inquiry into whether THEOREM holds.And since he was the first to do so, by Reward Entitlement, these views are firmly committed to the claim that he is entitled to the big prize.But, of course, that's the wrong result.In contrast, K-AIM predicts the right result.Since his belief is gettiered, he does not know.So, by K-AIM, he has not attained the aim of the inquiry into whether THEOREM and so isn't entitled to the prize.The second mathematician, in contrast, does come to know the answer.In conjunction with Reward Entitlement, K-AIM predicts, correctly, that she should get the prize.By the same token, there is reason to believe that K-AIM is correct way of unpacking the aim of inquiry, rather than T-AIM or J-AIM. 2Let's move on to the second argument.One can be committed to attaining successes in AAs.One way in which one can be released from any commitment one may have towards attaining the aim of an AA is by actually pulling off the feat, i.e. by attaining the relevant success.This gives us the following first crucial thesis about AAs:Commitment Release If, at t, one attains the aim of a given AA, then, at t, one is released from all commitments towards attaining this aim. Now consider the following case:The Hire You are a private detective.I have contracted you to find out whether (MURDER =) someone in my family is the murderer of my wife.The first suspect you investigate is my uncle who, let us suppose, has a particularly