Knowledge and the Gettier Problem P2

This is part 2 of Knowledge and the Gettier Problem. This addresses some of the things left in the comments section, so read that as well.

I have to agree with Graham in that the problem lies with justification for the propositions. It is, in a sense, logically spurious, but I think that statement alone doesn't address the possibility of whether "a man with 10 cents in his pocket will get the job" and "Jones owns a Ford or Brown is in Barcelona" should be considered knowledge IF Jones actually got the job or if Jones actually owned a Ford (and, in my opinion, I think they should be considered knowledge--to say otherwise would be neglecting the fact that logical operations are truth preserving). I started writing this before the comments came in so it might seem to backtrack a little bit, but here it is. Oh, and I apologize that this is somewhat incomplete... I've just lost the will to go on.

My first intuition upon first learning of this problem was that the justification condition of JTB conditions was the culprit. One option is to say that Smith was not actually justified in believing P1 (in both cases). In case 1, Smith was justified only to the extent that one can be justified by someone else's claim. But how is this different than believing pi has infinitely many decimal places without a pattern when told that it is so by a mathematician? Or how about when we are taught that Australia is a continent southeast of Asia by our 7th grade geography teacher? We most certainly would ignore claims made by the compulsive liar or delusional schizophrenic, but we also consider both of these cases to have reliable, and thereby justifiable, sources of knowledge. Even if we ascribe such reliability to the hiring manager (besides, the hiring manager really was telling the truth!), the problem remains. If you want to say that we in fact don't gain knowledge when told facts by others and we gain knowledge only when we ourselves verify that a belief is in fact true, then I will have to say that I don't know that the world is round and that the sun is the center of our solar system and so on. But wait, aren't all of these knowledge? I think the contradictions that we arrive to by considering other people as unviable sources of justification lets us safely rule this one out since we are appealing to the common-sense notion of knowledge.

But what about justification of facts that could change? I think this might answer an aspect of John's concerns with this problem. Imagine that I am outside and it is raining. I hope that you would at least grant that my belief "it is raining" is a JTB (if you don't, you have issues that can't be resolved here, or anywhere else for that matter). Say that I find shelter in a sound-proof shed with no windows or other means of seeing or hearing the outside. When I go inside, you would say that my means of justification have been removed, but does my knowledge that it is raining cease to be knowledge? Common-sense tells us that believing in the proposition "it is raining" is still knowledge even when immediate justifications have been removed, as evidenced by the fact that we often ask people "is it still raining" and expect that their knowledge of weather outside to be sound. Even if you claim that knowledge stripped of immediate justification is somehow lesser knowledge than one who has immediate justifications, I don't think you can reasonably argue that it is no longer knowledge (though you can say that someone inside who claims to know that "it is raining" is actually claiming to know only that "I believe it is raining"... and so on and so on... and I don't know if I want to explore this here, at least not in this post). What you can say, though, is that the knowledge is valid only within a reasonable range: I don't expect "it is raining" to count as knowledge if the last justification for it was removed 2-3 days ago. Ultimately, the predictive powers of knowledge are limited, but I think we all have to agree that, by common-sense knowledge, that some predictive propositions are knowledge (whatever the extent of their predictive powers may be).

Anyway, I'd like to focus on the logical intricacies of this problem rather than the metaphysical, sense-datum, intentionality, etc., issues--I think any investigation into the nature of belief or truth will ultimately summon questions in the aforementioned fields, which ultimately don't have definitive answers (we really just need to take the 'leap of faith' in believing that our experiences are causally related to an objective world--or at least consistent with something like it).

Let's first consider the logical steps that we take from going from P1 to Pn. In case 1, we take the instantiation of someone and make an existential claim. Consider we have the following:

Q1-Bessy is a cow.

Given this, we can make the existential claim that:

Q2-There exists a cow.

If Q1 is true and we are justified in believing that it is true, then Q2 should be equally true and justified. There's really no way around this as it is logically sound. So here, we can see that the transitive property of logic successfully preserves the truth and justification conditions by virtue of Q1's entailment of Q2, but Gettier's first case leaves us feeling uneasy. Even when we add a third proposition that has, as its subject, the same subject as in Q1, the justification and truth should not change.

But what I think makes this peculiar is the generalization of Q1 to Q2. Q2 and existential propositions, by nature, claims that there exists a certain set (namely, that there exists something that has bovinity, if bovinity is the essential property of bovines). If at least one member of this set exists, then Q2 is true. Since Q1 entails the existence of a member of the set defined by Q2, Q2 becomes true by virtue of its extension from Q1. In addition, the existence of any other member of the set defined in Q2 will also make Q2 true (e.g., "Bo is a cow" will also make Q2 true, even if Bessy undergoes a transpecies operation and turns herself into a goat).

It is here, I think, that the uneasiness in the first case of the Gettier problem can be explained. Smith knew that P2-Jones was a member of a set (i.e., men with 10 cents in their pocket) and that P1-Jones would get the job. So when the instantiation (Jones) is generalized (a man with 10 cents in his pocket), the generalization is justified and true only because the instantiation is justified and true. In other words, P1 and P2 together prescribe the the justification and truth of P3. I would, then, like to say that P3 is justified and true only insofar as P1 and/or P2 is justified and true. P3 is knowledge only when P1 and/or P2 are also knowledge, and then cease to be knowledge if P1/P2 cease to be knowledge (the idea of P1/P2 no longer being knowledge begs the question of what qualifies as justification, as mentioned in the first paragraphs in this post).

That is not to say that the likes of P3 could never by themselves satisfy the JTB conditions. If Smith knew that he had 10 cents in his pocket as Jones did, and knew that Smith and Jones were the only ones being considered for the job, P3 would be by itself justified and true. However, in Gettier's first case, Smith was only justified in believing that Jones would get the job and that Jones had 10 cents in his pocket. In Gettier's case, then, P3 is knowledge only if P1/P2 are knowledge. When P1/P2 fails (or if you want to say that it never was knowledge, then you can say that too), so does P3.

I think the constraints are similar for the second case. The only difference here is that instead of making an existential claim that includes a certain category of things as members of the set, we are adding an arbitrary propositions to the set. I think we can say that both of Gettier's cases involve making propositions from an instantiation to making a proposition from a set of possible instantiations.

Anyway, my conclusion is that P3 is knowledge if and only if P1 and P2 are knowledge. I say this because that P3 is an extension of P1 and P2, and little else alone. If you want to say that P1 and P2 are knowledge because they would have been true, then so is P3, but only up to the point when the hiring manager changed his mind (unless you want to say P1 is still knowledge even after that fact). If you want to say that P1 and P2 are not knowledge because they are predictive by nature and thus subject to falsity, then P3 is also not knowledge. You can discuss which of these schools of thought you think is best, but I prefer to stay away from these tough questions.

This solution is akin to Alvin Goodman's solution (or rather, his epistemological theory that tries to buff up the justification condition to avoid the Gettier problem) but the scope of his theory is much greater. That is, he tries to explain the connection between the world and the contents of our experience (I think), and then includes a little tidbit about how a something in the experience must cause a justified belief. It is to my understanding, anyway, that he runs into a bit of trouble when defining the necessary/sufficient causal relationship between experience and belief. I tried to avoid this burden by compartmentalizing the perculiarity to the logical transformations of knowledge, regardless of whatever JTB could ever be satisfied (of course, I take for granted that it can).

This is long, confusing, and unclear, and I apologize. I'll try to write more concisely and in a more timely manner in the future.