Wednesday, April 29, 2009

Knowledge and the Gettier Problem

It has long been accepted in epistemology that the conditions for something to be considered "knowledge" are that it must be a justified, true belief. We would not say that one knows that P (P being a proposition where, say, P is "the sky is blue") if that person does not hold the belief that P, and it should be fairly clear that beliefs are fundamentally necessary for any knowledge. That belief must also be true, for we wouldn't allow false beliefs to pass for knowledge lest we must allow the delusions of a madman to count as knowledge. Lastly, we must enforce that one must be justified in having a true belief, for we would not say that someone who dreamt the winning lottery numbers actually knew the winning lottery numbers.

Let me just say that I don't intend to dwell (just yet) on the metaphysical implications of belief, the nature and degree of justification, referential ambiguity, etc., as interesting or relevant they may be. I think several of these might be mentioned later, but for now and for the sake of explaining the Gettier problem, let's adopt the common-sense notion of knowledge.

The philosopher Edmund Gettier posed some serious questions against the justified, true belief conditions for knowledge (henceforth JTB). In his short paper "Is Justified True Belief Knowledge?" published almost half a century ago, Gettier exposed some flaws in the epistemological definition of knowledge that (as far as I know) have yet to be reconciled while remaining consistent with the common-sense notion of knowledge. There are two original cases that Gettier gives, and are as follows:
[original found here]

Case 1
Smith and Jones are both applying for a job. Smith was told by the hiring manager that Jones would get the job. Smith also knows that Jones has 10 cents in his pocket because Jones told Smith and Jones has no reason to lie (and yes, Jones has 10 cents in his pocket). Now, we can now say that Smith knows the following:

P1-Jones will get the job.
P2-Jones is a man with 10 cents in his pocket.
P3-A man with 10 cents in his pocket will get the job.

We can see here that given the P1 and P2, we can, by the transitive property, derive P3. We know that P1 and P2 satisfy JTB conditions, and likewise, the P3 satisfies the JTB conditions and thus, Smith knows that "a man with 10 cents in his pocket will get the job."

But it just so happens that the hiring manager had a last minute change of heart and decided to hire Smith instead. And as it turns out, Smith, not knowing so himself, also has 10 cents in his pocket. Would we say that Smith knew that P3? P3 turned out to be both justified and true (and of course, it's a belief), but I (and most other people, I bet) would hesitate to designate such to be knowledge.

Case 2
Smith knows that Jones owns a Ford: Jones works for Ford, is absolutely in love with Ford cars, and has vowed to never own a vehicle of another brand. So we have:

P1-Jones owns a Ford.

Let's now say that Smith has a friend named Brown whose location in unknown to Smith. Given P1, we can make:

P2-Jones owns a Ford or Brown is in Barcelona.

We are able to do this by creating a disjunctive proposition in which JTB conditions are preserved via P1. By creating [P1 v anything], and assuming that P1 is true and justified, [P1 v anything] is also true and justified (by virtue of the logical fact that the truth of at least one component in a disjunctive proposition makes the whole proposition true). We, then, are to accept that Smith knows that P2.

However, unknown to Smith, Jones had just sold his Ford to pay for his mortgage after being laid off from the Ford factory. It also happens to be the case that Brown, with whom Smith hasn't spoken to in years, is in Barcelona. P2 turns out to be true, but does Smith know that "Jones owns a Ford or Brown is in Barcelona"? Again, I'm hesitant to categorize this as knowledge.

So...
How do we explain away these problems? While there are many possible routes to take, many that were proposed by Gettier's contemporaries were unable to remedy the necessary and sufficient conditions of knowledge without destroying the common-sense notion of knowledge. Put your suggestions in the comment, but try to keep your theory consistent with the common-sense notion of knowledge. Also, while many related topics are certainly relevant to the discussion, I would like to focus on the logical intricacies of the problem.

7 comments:

  1. "A broken clock is still right twice a day."

    I think the problem in both Gettier cases lies in the justification for the beliefs. Although both beliefs turn out to be true, the method at which they arrived at is logically spurious...just like the man who dreams the winning lottery numbers.

    I will attack the second case first because the logic is weaker. The only rationale for believing Brown to be in Barcelona is that its not logically inconsistent with Jones owning a ford. If you explained why you thought Jones was in Barcelona to a man on the street, you would probably have less credibility that the man who dreamed the winning lottery numbers.

    As for the first case, the justification for believing P3 is based on P1 and P2, when one of them becomes untrue, the justification for the belief disappears (even if the belief is still objectively true). Both cases turn on the justifications for the beliefs.

    ReplyDelete
  2. The predictive character of knowledge that these epistemologies assume is a fundamental misunderstanding of what knowledge is. Here, I will 1) highlight relevant errors in scenario 1 and 2) hypothesize a different understanding of knowledge .

    Based on the information given to him, Smith is able to conclude with good certainty that he will not get the job. He knows that right now, at this moment, he does not have the job and so must act according to that belief -- he must go home, get back on the phones, check websites, activate contacts, etc. Smith will conduct the activities of his life according to what he not only believes will be true, but that is true every moment leading up to the one prior to the reversal of the decision in the same it will be true he has a job. In order to live his life productively, he must conflate his belief with knowledge and act upon its implications as if they were necessarily true.

    These examples are extremely useful in displaying the limited power of the notion of knowledge. Our categorization of certain beliefs as knowledge is ultimately a convention that simplifies our efforts in prioritizing our activities. Knowledge itself does not exist; at least not in the sense that it has the capacity to conclude what is and always will be true.

    How would we possibly plan out our day, month or life if we treated the possibility that the sun will explode tomorrow (or something similarly existence-shattering and unlikely yet still distinctly possible) with seriousness? If it was at any time acceptable to use that small possibility as a basis for belief, world goes to shit. But while other beliefs are more well justified, they are only well justified enough for us to assume their truth in order to live our lives. Nothing is well justified enough to classify as true in all cases. We don’t know for sure. Given our current technology can’t know for sure. We can, however, offer our best guesses for why such a thing will or will not happen (labeled, again for conventions sake, as theories.) Things are only “true” as far as they have not yet been untrue. All knowledge is theoretical.

    I think this is called solipsism, which is a sort of postmodernism, and whose epistemology concedes that knowledge has no positive or predictive character. What is commonly regarded as knowledge is true as far as it is not true – but it is stipulated as always having the ability to be not true. Our grounds for assuming their continued existence would be logically infallible given their premises. An essay I read for my philosophy class in freshman year of college argued that "Man will always be at the center of his picture of the universe." While my argument does not necessarily advance our understanding of the relationship between common sense conceptions of knowledge and the Gettlier problem, a question is only as affective as its answers are actionable. Any notion of knowledge must consider its presence in our lives, how it is important for us.

    Given my last comment, I am at least aware of the possibility that my argument has reached beyond the boundaries prescribed by minku.. but I don’t really know if they have. If they have, will you tell me and tell me how?

    Otherwise, I really look forward to your guys thoughts on this.

    ReplyDelete
  3. I wanted to comment on your criticism of the first case. I think what you're getting at is that Smith's knowledge is that it is predictive by nature and that the matter to which the knowledge pertains could change. I wrote a little bit about this in the continuation that I'm working on.

    Also, I wanted to keep this within the scope of our everyday experiences. The metaphysical questions of whether we really can know anything in the world, though interesting, doesn't have a definite answer. I think we all have to make the "leap of faith" in trusting that our conscious experience of the world is directly caused by an objective world. That is, we should take our experiences of the world for what it is.

    ReplyDelete
  4. My other confusion, equally unlikely to be informative as it ails to match the depth I earlier attributed to it, lies with my argument that the logic of these premises has advanced as far as it can. The previous contribution seems applicable to our everyday, common sense idea of knowledge. JTB takes for granted the “leap of faith” agreed to be necessary for conventionalizing knowledge, made especially obvious as it was stated in the original thought: "...it should be fairly clear that beliefs are fundamentally necessary for any knowledge."

    The posted response, though mangled by the inconsistency of its focus, means to point out that JTB must account for that leap of faith in its conditions; otherwise, knowledge is not being taken for what it is and mistakes about its reliability are made, as was the unfortunately fortune case for Smith.

    If we were to add to any JTB proposition "The truth of each given condition is subject to falsity at any time," Smith`s supposition would easily become voided and reconfigured in order to accommodate the change in reality. It seems only natural that this should be done.

    As far as the logic of the problem goes, the logic, serially, seems solid (keeping in mind, of course, my limited logical abilities:)) To me, the logic of its premises is flawed and needs laterally logical adjustment.

    However, extending our understanding of JTB to include the obvious fallibility of conventional (every day) knowledge seems like an easy answer. More than likely if this was the solution to our question, it’s unlikely the best logician among us would be wondering about its answer. Something more subtle is being asked that I can't see.

    So what is really the question here? Help!

    ReplyDelete
  5. Fuck!!!!! Please add this portion to the top of my most resent post before this one! i ucjke du copying it from word.

    Almost exactly what I`m trying to say (as well as in many fewer words.) Thank you for clearing that up for me. I very much was trying to keep this in the scope of what you suggested and I`ll try to be better about it with my next comment.

    But first I have to admit I`m still a bit confused about what the scope is -- which I think may possibly be more than a trivial confusion.

    Most likely, however, my confusion is just trivial: By within the scope of the problem, do we mean that we assume the validity of JTB conditions? Probably, right? Problem solved.

    ReplyDelete
  6. I think I'm a little confused as to what the "scope" is as well. The best I can explain it is that the JTB conditions would be necessary and sufficient for everyday knowledge, such as in the sense that I know that John is in Japan or I know that the swine flu is a virus. Basically, we have a common-sense notion of knowledge that allows us to say that someone knows something and someone doesn't know something. This is what the JTB conditions are supposed to explain (I think), but clearly is not free from errors (as seen in the Gettier problem where it meets all of the necessary and sufficient conditions for knowledge--JTB--but we wouldn't say that it is knowledge.

    ReplyDelete
  7. I just wanted to add another thing: the idea that something "could" change is certainly interesting and relevant to epistemology, but I don't know if that fits into the framework on which this problem is presented. I think that deals with the issue of certainty, but that is something that addresses a different epistemological question.

    The JTB conditions are only effective after we accept that knowledge is possible to the extent that we say that knowledge exists in our everyday use of the concept. For example, I would say that I know an apple will fall to the floor if I drop it. I would also say that I know that gravity is the reason for that phenomena.

    Now, the question of whether this COULD change (i.e., it turns out that gravity does not exist and it is simply quantum tricksters who are willfully pushing objects toward more massive objects) is beyond the scope here. We know that knowledge (if it can be called knowledge) can change, in that we were wrong about it. But of course, a thousand years ago, people "knew" that the world was at the center of the universe. Whether such should be considered knowledge does not really interest me here, but only in the sense that I "know" gravity exists even if it's possible that it doesn't.

    I think I have to say that adding a "subject to falsity" condition to the JTB conditions would be either redundant or destructive or both. It could be redundant if we already accept that certain things we consider knowledge could be wrong (i.e., in the case of new discoveries). It could also be destructive in that it would render the idea of knowledge inconsistent with our everyday reliance on it (i.e., I want this apple to be on the floor, but dropping it might not result in the apple falling...).

    Basically, I want to avoid the question of what kind of justification we need, what it is to be true, etc. Without dismissing its significance, I want to take for granted whatever degree of justification and truth we use for everyday knowledge.

    ReplyDelete