A Couple More Cases

CASE 1: (due to Jay Allman)

Prof. Nitpick teaches an undergraduate class in propositional/predicate logic. On Monday, he gives a homework assignment which requires his students to evaluate a completed proof, marking whether each step of the proof follows from a previous step (or steps) via the rule cited in that step's justification.

That night, Shirley Knott, who is a competent student in the class, carefully evaluates the proof, and she decides that one of the steps misapplies the rule of universal generalization. So she marks the proof as being invalid. She is correct that the proof makes this mistake, and she is justified in believing the proof is invalid because she has carefully checked each step against her (carefully taken) notes about how the rules are supposed to be applied.

On Tuesday, Shirley compares her homework with that of her boyfriend, Randy McGlib. Randy is a careless student and not very good at logic, but he has a radiant (and completely unjustified) confidence in his own logical abilities, and he has far more confidence in his abilities than Shirley has in her own. Randy thinks the proof makes no errors, and he soon convinces Shirley that she was wrong. So she gives up her belief that the proof is invalid and decides that it is valid, going so far as to alter her own notes on the rule of universal generalization to bring them into line with her new (and faulty) understanding of the invalid proof.

On Monday night, did Shirley know that the proof was invalid?

CASE 2:

Mr. Nickfit, a smoker, has been considering the question of whether or not smoking causes cancer. He was told by his doctor that it does. He has also read (and understood) some authoritative meta-analyses of the evidence in professional medical journals which support the claim. On balance, therefore, Mr. Nickfit has some fairly good evidence (probably far better than you or I) that smoking causes cancer. In addition, Mr. Nickfit understands that this evidence supports the claim that smoking causes cancer and comes to believe as a result that smoking causes cancer. Suppose further that smoking does cause cancer. So, Mr. Nickfit has a justified true belief that smoking causes cancer.

Suppose, however, that Mr. Nickfit is currently so disposed that fairly weak counterevidence to the contrary will result in his changing his belief (i.e., believing that smoking doesn’t cause cancer). Think of the case as one in which Nickfit correctly uses his evidence to justify his belief while nevertheless being confused in various ways about how justification works. Specifically, he understands that his evidence gives him a reason to believe that smoking causes cancer; what he fails to understand is that this evidence ought to continue to compel him to believe that smoking causes cancer even in the face of relatively weak counterevidence. In some sense, Mr. Nickfit fails to make use of a rational diachronic update procedure on his evidence.

Does Mr. Nickfit know that smoking causes cancer?

Comments

[j.s.]

Nice cases! For now, just a vote ... I'll try to comment later. First case: surely, Shirley knows on Monday. Second case: I need some clarification on Nickfit's situation. Is it the case that he -- at the time we are considering his situation -- only has very strong evidence in favor of his current belief, inter alia, he has -- at the time we are considering him -- no countervailing evidence, and that he WOULD be likely to change his belief were he to have any countervailing evidence, even if the countervailing evidence is very weak?

[marc]

Clarification on the first case. I agree with Joe that if the example is construed simply as a case of coercian (independent of her grasp of the relevant concepts), then it is clear that Shirley knows on Monday. However, if we understand the case as one in which Shirley's flip-flop is determined by her weak grasp of universal generalization (e.g., if we suppose that she would never have behaved as she did with existential generalization because she has mastered that rule), then it is not so clear to me that she knows on Monday.

[j.s.]

Thanks for the clarification, Marc. Could I ask for a follow-up on the clarification? In the initial description of the case, you described Shirley as justified in her belief. Is the clarificatory description of Shirley as having a "weak grasp of universal generalization" compatible with her being justified in so believing?

[marc]

I think so. Consider Burge-style cases in which an individual incompletely or incorrectly grasps, say, the concept of arthritis. In such cases, we would still want to say that the individual knows (and, hence, is justified in believing) many things concerning arthritis. For example, the individual knows that arthritis causes the pain in his joints. So I don't think that even out-and-out misunderstanding of a concept precludes knowledge.

I guess I am further committed to the claim that a deficient understanding of a concept doesn't imply instability of belief--but I /think/ that is ok. I don't see any reason to say that the arthritis patient's belief is unstable even though he misunderstands the concept of arthritis. Nevertheless, I do think that the nature of one's grasp of a concept may contribute to instability.

Incidentally, I have been pretty vague about what stability amounts to in this discussion--relying on an intuitive grasp of the idea. I do want to point out, however, that I take stability to have both a temporal and a modal characteristic. The first case involves temporal instability; the second, modal instability.

[modeling women]

You are being so honest. I like your personality.