Friday, 20 April 2012

Outline of Nozick's "Knowledge"


SYNOPSIS:

Robert Nozick argues that S knows that p if and only if:

(1) p is true.
(2) S believes that p.
(3) If p weren’t true, S wouldn’t believe that p.
(4) If p were true, S would believe that p and not-(S believes that not-p).

When (3) and (4) hold, S’s belief is said to “track the truth”.


OUTLINE:

Step 1: Nozick begins by impugning the standard causal account of knowledge.

Argument: The causal theory suffers from at least two weakness: (i) It fails to apply to cases of mathematical and ethical knowledge. (ii) It faces difficulties in specifying the appropriate type of causal connection.  For example, consider the case of an envatted brain that is caused (via direct electro-chemical stimulation) to have the belief that it is in a vat. Such a brain would not know it is in a vat even though the fact that it is envatted is causally connected to the belief that it is.

Upshot: We need to replace the causal requirement with a knew condition for knowledge.

Step 2: Nozick introduces a third requirement for knowledge which he thinks immunizes it from Gettier counterexamples.

Argument: Suppose S believes that (p):“someone in the office owns a Ford” based on his belief that Brown owns a Ford, when it is in fact someone else in the office, Jones, that owns a Ford, and not Brown.  S would fail to satisfy the subjunctive conditional: “If p weren’t true, S wouldn’t  believe that p”, since he would continue to believe (p) even if Jones did not own a Ford.

Upshot: We can avoid Gettier counter-examples if we adopt the following subjunctive conditional as a necessary condition for knowledge: “If p weren’t true, S wouldn’t believe that p”.
                           
Step 3: Nozick claims that the preceding subjunctive conditional illuminates difficulties relating to the “relevant alternatives” analysis of knowledge.

Argument: Compare an agent driving through a country side with only real barns and one driving through a countryside with mostly fake barns and one real barn. If both formed the true belief that he was looking at a barn, the relevant alternative analysis suggests that, given that the latter is unable to rule out the possibility that he is looking at a fake barn, only the former has knowledge. We can make sense of this by noting that if the second agent were looking at a fake barn, he would believe it was real.  He therefore fails to fulfil the preceding subjunctive conditional. 

Upshot: We can make sense of why an agent lacks knowledge when he is unable to rule out relevant alternatives if we adopt the following necessary condition for knowledge:  “If p weren’t true, S wouldn’t believe that p”.

Step 4: Nozick concedes that the preceding subjunctive conditional is not sufficient for knowledge.

Argument:  Since the envatted brain, in our previous example, is caused to believe it is in a vat by those who put it in a vat, it would not believe that it was in a vat if it were not envatted.  The envatted brain therefore fulfils the preceding subjunctive conditional.

Upshot: The subjunctive conditional, “If p weren’t true, S wouldn’t believe that p”, is not sufficient for knowledge because it does not guarantee that S’s belief is sensitive to the truth.

Step 5: Nozick introduces a second subjunctive conditional in order to make sense of why the envatted brain does not know it is in a vat.

Argument: If the envatted brain were not electrically stimulated to believe that it was in a vat by its envatters, it would not believe it was in a vat even if it remained true that it was in a vat.  Hence, the following counterfactual is not true of the envatted brain: “If p were true, S would believe that p”.

Upshot: We can accommodate the intuition that the envatted brain lacks knowledge if we adopt the following necessary condition for knowledge: “If p were true, S would believe that p”.

Step 6: Nozick argues that his second subjunctive conditional can handle Gilbert Harman’s dictator example.

Argument: A newspaper reports, truly, that a dictator has been killed, but later, falsely, denies the story. Everyone comes to believe the false report, except for S, who read the original story but failed to learn about the retraction.  Given the assumption that S would have believed the false report had he read it, Harman claims that S does not know that the dictator has been killed. Nozick’s second subjunctive conditional is able to preserve this intuition: Since S would have believed the false report, it is not the case that if it were true that the dictator was killed, S would believe that the dictator was killed.

Upshot:  Nozick’s second subjunctive conditional allows us to preserve the intuition that the subject in Harman’s dictator example lacks knowledge.

Step 7: Nozick observes that the sceptic may be seen as denying that we fulfil Nozick’s first subjunctive conditional.

Argument: If we were all envatted brains or deceived by an evil demon, we would continue to believe as we do.  Thus, the sceptic may argue that one of the following two claims is true of us: “If p were false, we wouldn’t believe that p” or “If p were false, we might believe that p”. Either would entail that we fail to satisfy the following subjunctive conditional: “If p were false, S wouldn’t believe that p.”

Upshot: According to the sceptic, we do not have knowledge because we fail to satisfy Nozick’s first subjunctive conditional.

Step 8: Nozick maintains that sceptical scenarios (henceforth, SK) are not in the not-p neighbourhood of the actual world, and therefore do not prevent us from satisfying his first subjunctive conditional.

Argument: Even if p were false, it would not be true that SK.  This is because there are no not-p worlds, in the neighbourhood of the actual world, where SK obtains. Consequently, the fact that S would continue to believe p if SK obtained, does not prevent S from fulfilling the subjunctive conditional, “If p were false, S wouldn’t believe that p”. 

Upshot: Sceptical scenarios do not prevent us from satisfying Nozick’s first subjunctive conditional.

Step 9: Nozick concedes that the sceptic is right when she insists that we do not know that not-SK.

Argument: Given that Nozick’s first subjunctive conditional is necessary for knowledge, S can know that he is not a brain in a vat only if the following were true: If S were a brain in a vat, he would not believe he was not a brain in a vat.  However, since S would still believe he was not a brain in a vat even if he were a brain in a vat, his belief does not satisfy Nozick’s first subjunctive conditional. 

Upshot: Given that we would believe that we were not brains in a vat even if we were, we do not know that we are not brains in a vat. 

Step 10: Nozick argues that acknowledging that the sceptic is right when she says that we do not know not-SK does note entail that we do not know things that entail the denial of SK. 

Argument: It does not follow that if S knows that p: “I am awake and sitting in a chair in Jerusalem” and knows that p logically implies q: “I am not a brain in a tank at Alpha Centuri”, that S knows q. This is because the fact that S’s belief that p co-varies with the truth of p, does not mean that, in cases in which S knows that p logical implies q, S’s belief that q also co-varies with the truth of q.  Hence, knowledge, which requires the co-variation of the fact that p and the belief that p, is not closed under known logical implication.

Upshot: The sceptic’s challenge that I do not know that I am awake and sitting in Jerusalem because I do not know that I am not a brain in a tank, which presupposes that knowledge is closed under known logical implication, misses its mark. 


CONCLUSION:

Nozick concludes that a belief counts as knowledge only if it tracks the truth.


DISCUSSION QUESTION:

1. Is Nozick’s truth-tracking account simply a version of the causal theory of knowledge? Why or why not?

2. What does it mean to say that knowledge is closed under known logical entailment?  Why does Nozick think that this view of knowledge is mistaken? Do you agree with Nozick? Why or why not?

3. Does Nozick hold that the sceptic is mistaken when she insists that we do not know that we are not brains in a tank at Alpha Centauri?  Why or why not? Do you agree? Why or why not?

4. Does Nozick hold that the sceptic is mistaken when she insists that, given that I do not know that I am not a brain in a tank, I do not know that I am currently sitting and reading a book? Why or why not? Do you think Nozick’s argument succeeds? Why or why not?

7 comments:

Benjamin Altshuler said...

Nozick faces the nameless skeptic, but seems to fare victoriously despite conceding some points to his opponent. Nozick grants that his theory of knowledge cannot deny the possibility of skeptical arguments (SK). However lack of evidence against something does not make it true. While we don't track the fact that SK doesn't hold, we do track some other facts, some of which challenge SK. As long as the skeptic also buys into these basic truths that we track and hold to be true, it is difficult to maintain support for a skeptical argument. Thus, Nozick ventures that the skeptic is mistaken.

This makes sense to me and goes to show how hard it is out there for a skeptic, but I wonder if we cannot take this one step further:
Even if we were brains in vats, we would not believe we were brains in vats, and further would not know that we were brains in vats. This is because, as the SK goes, the alleged brains in vats receive electrical stimulation to believe they are not brains in vats. If this electrical stimulation is powerful enough to construct a reality separate from in-vat existence, surely it is powerful enough to influence propositional logic. More clearly, if we were brains in vats, we would not receive the signals to wonder if we were brains in vats, skeptical of the reality we knew. The ability to be skeptical, I believe, disproves the potential skeptical argument.

(That is unless the powers controlling my brain vat want me to write this...)

Taylor ffitch said...

First of all, I have to say I'm a pretty big Nozick fan at this point, Jesse James example notwithstanding. I see that there's some tightening up to do on the closest possible world side of things, but this also seems like an area where we already have some intuitions to guide us toward the beginnings of a definition. For example, in the Jesse James example we talked about, my instinct is that changing the moment when the mask falls off is in some way not in the spirit of the question we are actually asking. I'm not sure that restricting things to the same mode of perception like we talked about in class completely solves the problem, but it is a start.

In response to question 3, we have to clarify that Nozick agrees with the skeptic that we cannot know we are not brains in vats. However, we can know that we are, in my case, sitting in a chair in the libe. The skeptic's case that we do not know this relies on the logical implication that because I do not know p (that I'm not a brain in a vat) that I don't know q, which is logically implied by p (that I'm in the libe). Nozick argues that this isn't so, because my belief that q must vary with q's truth, which it doesn't if I only use logic to conclude q. Therefore my uncertainty about whether I'm a brain in a vat doesn't transfer to uncertainty about whether I'm sitting in the libe. If I understood this all correctly, that is.
In response to Ben, I'm not sure that imagining a possible world in which we are brains in vats that additionally can't be skeptical gets us anywhere new, as there is an equally possible world in which we are brains in vats that are only being given incorrect sensory stimuli about where we are, in which case skepticism and being in a vat are not mutually exclusive.

Andrew Cely said...

I agree with both of the above posts in terms of question 3, in that through logic, we cannot know for certain that we are not "brains in vats" as suggested by the skeptics, but rather we must set a foundation for our knowledge in the known world, similar to our earlier unicorn examples.

For instance, when the two propositions "Charlie is a unicorn" and "unicorns do not exist" are put forth, both are considered true, but based on different understandings. The first is true in the fictional world created by the artist of Charlie, since unicorns cannot exist in our "real" world. Whereas the first has a foundation in a fictional world, the second has a foundation in out "real" world, and is thus true for those parameters. Thus, when determining knowledge, it is important to realize the parameters with which one works. In this case, we have knowledge of our world as we perceive it to be true. There are laws of nature, tendencies which have been repeated and proven to be true, and this is what we consider to be true in this case. As such, we have knowledge of this supposed "real" world. Simply because we might be brains in vats has no bearing on the fact that we know and understand how the world which we perceive works and operates on a daily basis. Just as we have knowledge of the fictional world of charlie the unicorn as a subset of our "real" world, we would also be able to have knowledge concerning our perceived "real" world as a subset of our possible brain in vats world.

Russell Buehler said...

I think it's clear that, as presented, Nozick seems to have the best case. That said, I'm not convinced that he's right or that other accounts can't be repaired well enough to eventually surpass it. Even ignoring the Jesse James example, I'm pretty unhappy with the lack of clarity thus far on `nearest possible worlds' and unconvinced that knowledge shouldn't be closed under entailment. The latter, especially, seems highly counterintuitive to me.

In response to the conversation on skepticism thus far, I'm going to have to disagree with Benjamin's suggestion that the envater's electrical stimulation is powerful enough to change propositional logic. If by `propositional logic' we mean the formal logical system, it is entirely definitional, and I struggle to see how it can be changed and yet remain propositional logic. Say, for example, that the envaters decide to make a minor change to the truth-functionality of 'v'--in this case, no longer is propositional logic under consideration, but rather an entirely different system that bares some resemblance to propositional logic. I take Benjamin's point to be, then, that the envaters have the ability not to change propositional logic, but rather to convince the envated brain that a different system tracks truth when it, in fact, does not (i.e. that another system occupies the space most believe to be occupied by propositional logic). To do so requires not just that the envaters produce a new reality, but that they actively control what the brain believes is possible based on meaning; in particular, they must make some things impossible or unconceivable which are possible/conceivable to preserve their system, and some things possible/conceivable which are impossible/unconceivable in order to rule out propositional logic proper. These actions are categorically stronger than simply affecting a brain's sense perceptions and less obviously possible. Indeed, I believe you need to make quite a few non-controversial assumptions about the mind to do so.

Moving to Benjamin's main argument, I agree completely with Taylor; the argument fails because--even if we grant the envater's the ability to control our notion of possibility / conceivability--there's absolutely no reason why they couldn't stimulate the belief that we might be a brain in a vat. Thus having this belief in no way undermines that possibility.

Finally, I think Andrew's argument is an interesting one (although I disagree with it as well). To make it work, though, we need to both explicate how the world against which something is being evaluated is selected and to accept that there are (apparently) infinitely many such possible worlds. Of course, there's also the problem that I certainly don't think I'm just talking past someone when I say they don't know the world exists (and they assert they do) and that competing accounts will have an Occam's razor argument against his proposal (in particular, I think a subsistent entities account could deal a great deal of damage).

Ethan Linehan said...

Hello Dr. Archer. I came across your blog doing some research for E.J. Coffman's epistemology class at UT and I recognized your name from having you as my formal logic teacher. I wanted to say that this is a great blog post, that your logic class was one of my favorite classes, and that I hope you're doing well in D.C.

AVERY ARCHER said...

Thanks for stopping by and for the kind words, Ethan. I have fond memories of the UT logic classes. Hope you're well.

Anonymous said...

Could someone clarify what exactly SK stands for?