Tuesday, April 13, 2004

Skepticism and Possible Worlds

This post will explain Robert Nozick's Conditional Theory of Knowledge, how it solves the problem of skepticism, problems with the theory, and how Keith DeRose develops it so as to overcome these problems (and provide a better answer to the skeptic).

Nozick's theory is quite cool. A simple version of it is as follows...
S knows that P iff:
  • P is true

  • S believes that P

  • If P were false, then S would not believe that P

  • If P were true, then S would believe that P
The subjunctive conditionals might look a bit odd - especially that last one - but I think they make a lot more sense if interpreted in terms of close possible worlds.

To briefly explain 'possible worlds': We live in one possible world, let's call it "actuality". But you can imagine that things could have been different, in many (indeed, infinitely many) ways. When we conceive of an alternative possibility (say, that I'm sitting watching TV now instead of typing this), then that is an alternative "possible world". The greater the discrepancy from reality, the more "distant" that possible world is from actuality.

So, to explain Nozick's subjunctive conditionals:
a) in the closest possible worlds where P is false (unlike actuality), S no longer believes that P.
b) in all other close possible worlds where P is also true, S does believe P. (How close? Nozick suggests all those worlds that are closer than the first not-P world.)

Note that we are not concerned with extremely distant worlds - that is, it is possible to "know" something even if you haven't ruled out some (extremely unlikely) alternative possibilities.

Now, when this theory is applied to skeptical scenarios, we get the following results:
1) I know that I have two hands
but 2) I don't know that I'm not a (handless) brain-in-a-vat (BIV).

To explain why:
1) I have a true belief that I have two hands. In the closest possible worlds where I do not have two hands, it is because I lost them in some sort of accident, which I of course would be well aware of, and so I would then not believe that I have two hands. Furthermore, in all close worlds where I do have two hands, I also believe that I do. All the conditions are fulfilled, so I have knowledge of this fact.

2) I have a true belief that I am not a BIV. But in the closest possible world where this is false (i.e. where I am a BIV), I nevertheless would still believe that I was not one (since I would have had all the same conscious experiences as I have now). The third condition for knowledge is NOT met, so I do NOT know that I'm not a BIV.

Nozick embraces these results, but surely the contradictory nature of these abominable conjunctions counts against the theory. Fortunately, DeRose found a way to iron out the inconsistencies, by combining Nozick's theory with Contextualism.

Contextualism says that the epistemic standards required for knowledge will vary, and are context-dependent. The basic idea is that according to normal standards we know that we have hands (and thus DO know that we're not BIVs), but according to higher standards we don't (and don't know that we're not BIVs).

DeRose's key insight was to embrace Nozick's conditional theory and its 'possible worlds', but to drop the strict requirements, and instead allow the number of possible worlds under consideration to vary according to context. The strength of S's epistemic position (with regard to belief P) depends on how well S's belief in close possible worlds matches the truth in those respective worlds. The more possible worlds there are where S would have an accurate belief about P, the stronger S's epistemic position is (here and now) with regard to P.

He offers a visual metaphor here which I found illustrative: Imagine our world ("actuality") surrounded by all the close and distant possible worlds, modelled in a sort of 3-d space. Now imagine a sphere ballooning out from the centre (i.e. the actual world), but stopping the moment it comes to a world where S fails one of the two subjunctive conditionals previously mentioned (i.e. #a- S believes P when it is false, or #b- S doesn't believe it when it is true). Equivalently: S believes that P iff P is true in that possible world.

Now, the size of this sphere describes the strength of S's epistemic position. If small, then S can only claim to know P according to very low standards, whereas if the sphere is very large, then S's knowledge is correspondingly strong (after all, it means that S would be very unlikely to have formed a false belief here... things would have had to go very differently (since it is a very distant world) for S to have been mistaken). By restricting comparative knowledge claims to similar epistemic contexts (i.e. sphere-sizes), you avoid the contradictions entailed by Nozick's theory.

So, to apply this new & improved theory to the skeptical scenarios:
1) I have very strong knowledge that I have two hands (because you would have to go out to a VERY distant world before I had a mistaken belief about this!)

likewise, 2) I have very strong knowledge that I am not a BIV. How is this? Well, once again, you have to go out a very long way before you can find a possible world where I would have a mistaken belief about it.

So why do we find the skeptic's argument so convincing? Why do we feel that we don't know that we're not BIVs?

DeRose's answer is that mentioning skeptical scenarios raises the standards of knowledge so high that we cannot meet them. So (according to those extreme standards), the skeptic is right... our "sphere of knowledge" is not large enough to extend all the way out to those (extremely distant) possible worlds.

Just one thing remains to be explained: how does this 'raising of standards' occur?
DeRose posits the Rule of Sensitivity, which effectively says that when knowledge about P is mentioned, we tend to raise the standards of knowledge (if need be, and for an appropriate duration) so that S's belief in that particular P becomes sensitive. That is, the sphere of knowledge must extend all the way to the first possible world where P is false (like Nozick originally suggested).

That means that whenever anyone mentions BIVs, suddenly the standards for knowledge are raised to this absurdly large sphere, which must extend out all the way to that (extremely distant) possible world where S is a brain in a vat! It is no surprise that we do not have knowledge according to these excessive standards.

But, thankfully, our knowledge in more normal contexts is preserved. For most of our beliefs which we think we 'know', our sphere of knowledge extends out quite a fair distance, so we do have knowledge, according to contexts where the required standards are more moderate (i.e. smaller than the size of our sphere).

Thus the Skeptic is refuted, without any bizarre side-effects. If anyone knows of (or can think of) any objections to this solution, I would be very curious to hear them...?


  1. you don't happen to have a copy of nozick's original paper do you? that'd be useful reading...

  2. That was extremely useful in clarifying the possible world scenario. I wouldn't necessarily have concluded that it actually refutes the sceptic. It certainly makes the sceptic argument less relevant, and allows one seeking to identify knowledge to focus on the more relevant information rather than forever trying to defeat the sceptic. The problem that the sceptic's argument creates still looms. That is, one can, in the De Rose and Nozick's sense have knowledge, but this is determined externally, if the subjunctive conditionals are actually true. If we are in the actual world, as we suppose we are, then they are satisfied, yet our actual world may be the one where we are a BIV where they would not be satisfied.

    So if we are in the real world, then they are satisfied and we have a high level of knowledge of them. But we have no way of knowing that we actually are in the real world and therefore no way of knowing that we have that knowledge.

    Therefore we are still not really any further than we were before.

    Thank you very much though. I found this explanation very helpful.

  3. I'm studying degree level philosophy and was struggling with the possible-worlds theory. Finally I understand! Thank you.

  4. Problem's with Nozick's analysis:

    Martine argues that Nozick's view is unacceptable because it does not require a belief to be justified in order for someone to have knowledge:

    "A problem for it is that it seems that someone could have a belief that P which tracked the fact that P even though he was not justified in believing P" (Martin, P30)

    Counter-example of person S who makes a bet that will gain him $10 if either Gumshoe wins the first race, or Tagalong wins the second race or they both win their respective races. Furthermore, suppose that Tagalong is such a bad horse that there is no hope of winning the second race. Now, S infers that Gumshoe won the first race from the fact that he receives $10 from the cashier, but we would not want to say that S knows that Gumshoe won, even though this case satisfies all Nozick's conditions for knowledge.

    It is a condition of the success of Martin's and Garrett's counter-examples to Nozick that illustrate one must not only have a reliable method, but must also believe one's method to be reliable in order to have knowledge.

    The way in which Nozick replies to the sceptical challenge is problematic because it relies on the notion that counterfactuals are not transitive (transitive = requiring direct object, involving some relation between terms); which can be shown to be erroneous.

    To conclude, then I would argue that Nozick's answer to scepticism falls down on two accounts. Firstly, it can be shown that Nozick's account of knowledge is not sensitive to examples where true belief is arrived at by way of an unreliable method. Secondly, Nozick's answer to scepticism only works if counterfactuals are not transitive, and it can be shown that they do "like all conditionals, sustain transitivity in context" (Wright, P140)

    ****These infos are all from this website:

  5. Interesting.

    (1) I don't think the Gumshoe counterexample succeeds. The proposition in question is that Gumshoe won. If the agent forms this belief on the basis of a bad logical inference (which just happens to work out in the actual world), there are presumably close possible worlds where the agent forms the belief even when it isn't true. Irrational agents are not going to be reliable truth-trackers.

    (2) On the interpretation I gave in the post, the counterfactuals truly are not transitive. In any case: DeRose's contextualism, as discussed in the latter half of my post, develops Nozick's account in a way that doesn't depend on intransitivity.

  6. I think that in explaining how one knows that they have two hands you have assumed what you were trying to prove. To say that in the closest possible worlds where you do not have two hands you are aware of this - due to an accident or something of the sort - assumes that the closest possible worlds are not brain-in-vat-type scenarios, which they would be if in the actual world we are brains in vats. So if these closest possible worlds involved brain-in-vat-type scenarios then condition 3 would not be satisfied and you (by Nozick's standards) could not claim to have knowledge that you have two hands

  7. If you're going to say that you know you have hands if that belief is true and it tracks the truth then i guess that is fine by your definition of knowledge but i still think the sceptical objection has weight because it remains true that one cannot be sure that their belief is true. The stronger sceptical position - that knowledge is impossible - is what you have refuted by showing the possibility of knowledge under your definition, but it still stands that we cannot be sure of the factual truth of many of our beliefs. You might be right that beliefs that havn't been shown to be true can still count as knowledge but the sceptic can still maintain that we cant be sure that it is knowledge, which isn't much better than no knowledge at all.

  8. But it's trivial that we can't be absolutely certain of most things. If that's all the skeptic claims, then everyone agrees with him. (Of course we would disagree with the claim that sub-certain knowledge "isn't much better than no knowledge at all", but you haven't given any reason to accept that. Perhaps this is the real point of contention.)

    P.S. This would be a better place to continue the discussion.


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