Epistemology Handout 6: Tue, 9/20
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Nozick and the Sceptic
1. Notes on conditionals
• In reading Nozick, it is important to distinguish three types of conditionals:1
1. The material conditional: P ⊃ Q.
Intuitive interpretation: Either p is false or q is true.
Possible worlds interpretation: ‘P ⊃ Q’ is true in the actual world if and only if: either P is false in the actual world or Q is true in the actual world.
2. The subjunctive conditional: P ☐→ Q
Intuitive interpretation: If P were true, then Q would be true; if it were the case that P, then it would be the case that Q.
Possible worlds interpretation: ‘P ☐→ Q’ is true in the actual world if and only if: in all of the worldsmost similar to the actual world in which P is true, Q is true as well.
3. Strict conditionals (i.e. entailments): P ⇒ Q
Intuitive interpretations:
i. The truth of P necessitates the truth of Q.
ii. If P is true, Q must be true.
Possible worlds interpretation: ‘p ⇒ q’ is true if and only if: in all worlds in which P is true, Q is true as well. Or, suppose we give a possible worlds interpretation to ‘☐’: ‘☐Φ’ is true if and only if ‘Φ’ is true in all possible worlds. Then, we have the following possible worlds interpretation of entailments: ‘p ⇒ q’ is true if and only if ‘☐ (P ⊃ Q)’ is true.
• An example where a subjunctive conditional is true but the corresponding strict conditional is false: How many of you had serious aspirations to learn how to juggle, but soon realized that you lacked the requisite hand-eye coordination? If this doesn’t apply to you, pretend that it does. Now, the following subjunctive conditional plausibly holds true of you:
(i) If it were the case that I had better coordination, then I would have learned to juggle.
In all possible worlds most similar to the actual world in which you have better coordination, you learn how to juggle. However, the corresponding entailment does not hold true of you:
(ii) My having better coordination entails that I learn how to juggle.
There are possible worlds in which you have better coordination, but fail to learn how to juggle. Just consider a world in which you have better coordination, but get hit by a bus before you have a chance to cultivate you natural prowess for juggling. Notice that this second possible world is less similar to the actual world than the possible worlds considered in evaluating the truth of (i). For it differs from the actual world in respects (1) and (2), as opposed to (1) alone:
(1)You have better coordination.
(2) You get hit by a bus.
2. The canonical argument for philosophical scepticism (again)
• The canonical argument concerning knowledge:
Let P be any empirical proposition.
(1) For S to know that P, S must know that he is not in a sceptical scenario.
(2) S cannot know that he is not in a sceptical scenario.
(3) S cannot know that P.
• The Simple Closure Principle:
(SC) If S knows that P and if P entails Q, then S knows that Q.
Equivalently: For S to know that P, S must know -Q for all propositions Q that are incompatible with P.
Intuitive idea: For S to know that P, S must be able to rule out all alternatives to P.
• A subsidiary argument for premise (1) of the canonical argument concerning knowledge:
(1) (SC) If S knows that P and if P entails Q, then S must know that Q.
(2) P entails that S is not in a sceptical scenario.
(3) If S knows that P, then S must know that he is not in a sceptical scenario.
3. Nozick’s account of knowledge
• Nozick’s slogan: Knowledge is true belief that tracks the truth. Nozick’s basic idea is that knowledge is a matter of having a true belief that bears the right type of connection to the fact that makes it true. Specifically, it is a matter of having a true believe that is sensitive to the presence or absence of this fact.
• Nozick’s analysis of knowledge: S knows that P iff:
(1) P is true; and
(2) S believes that P; and
(3) –P ☐→ –S believes that P); and
(4) P ☐→ (S believes that P).
• It is important to note that conditions (3) and (4) invoke subjunctive conditionals, as opposed to strict conditionals. Condition (3) does not affirm that –P entails that S does not believe that P. That is, it does not entail that in all possible worlds in which P is false, S does not believe that P. Rather, condition (3) affirms that if it were not the case that P, S would not believe that P. In the nearest possible worlds in which P is false, S would not believe that P. Similarly, condition (4) affirms that in those worlds (circumstances) most similar to the actual world (situation) in which P is true, S would believe that P.
4. Nozick and closure
• The closure principle (SC) comes out false under Nozick’s account of knowledge. To see this, imagine that the Real World Hypothesis is true at some possible world. (For now, don’t worry about whether this is the actual world or not.) By hypothesis, these subjects are surrounded by objects, events, and people that for most part possess the properties they believe them to have. Now, take a subject S who, under normal lighting conditions, forms the true belief that there is a computer in front of him.
• S meets all four of Nozick’s conditions for knowledge. S possesses a true belief that there is a computer in front of him. Furthermore, if there were not a computer in front of him, S would not believe that there is a computer in front of him. Last, in the situations most similar to S’s actual situation where there is a computer in front of him, S would still believe that there is a computer in front of him.
• However, S does not know that he is not in a sceptical scenario—say, that he is not a brain in a vat being deceived by evil scientists. This is because S does not satisfy Nozick’s third condition on knowledge. If S were a brain in a vat being deceived by evil scientists, he would not believe that he is a brain in a vat being so deceived.
• Here we have a case where:
(i) S knows that P (that there is a computer in front of him); and
(ii) P entails Q (that S is not in a sceptical scenario; yet
(iii) S does not know that Q (that he is not in a sceptical scenario.
Thus, (SC) fails under Nozick’s account of knowledge. That is, it is a consequence of Nozick’s account of knowledge that knowledge is not closed under entailment.2
6. Nozick’s response to the sceptic
• Perhaps the most attractive feature of Nozick’s response to the sceptic is that it seems to be a sensible response. Nozick makes concessions to the skeptic that, on reflection, seem somewhat plausible, yet argues that these concessions do not jeopardized our run-of-the-mill empirical knowledge.
• Nozick’s major concession to the sceptic is that he grants the truth of premise (2) of the canonical argument. As seen in the previous section, it is a consequence of Nozick’s account of knowledge that we cannot know that we are not in a sceptical scenario. However, with some reflection, this may seem to be a reasonable concession. How could we know that we are not brains in vats given that, if we were, our experiential lives would be qualitatively indistinguishable? What could conceivably count as evidence that we are not victims of a sceptical scenario?
• However, under Nozick’s account of knowledge, both premise (1) and the conclusion of the canonical argument come at false. Again, as seen in §5, a subject can know that there is a computer in front of him even if he cannot know that he is not in a sceptical scenario. Thus, premise (1) of the canonical argument is false. Furthermore, the fact that a subject can know that there is a computer in front of him directly implies the falsity of the conclusion of the canonical argument, as this conclusion claims that it is impossible for a subject to know any empirical proposition.3
• Thus, Nozick’s account involves an important, but perhaps reasonable concession to the sceptic: We cannot know that we are not in a sceptical scenario. However, despite this concession, Nozick’s account has the consequence that we are capable of all sorts of generic empirical knowledge. The upshot, ultimately, is that sceptical scenarios are not a threat to our possession of basic empirical knowledge.
7. Counterexamples to Nozick
• There are several well-known counterexamples to Nozick’s account of knowledge.
1. Jesse James, the ineptly masked bank robber.4
2. Nozick’s account entails that a subject can know that the thing he picked is a white mouse without knowing that the thing that he picked is a mouse.5
• There are also some counterexamples to Nozick’s account of knowledge that are less widely known:
3. Nozick’s account entails that a subject S can know that P and Q despite the fact that S does not know that P and S does not know that Q. In other words, the following plausible distribution principle fails under Nozick’s account of knowledge:
(DP) If S knows that P and Q (i.e., S knows the conjunction of P and Q), then S knows that P and S knows that Q.6
4. Nozick’s account entails that a subject a subject can know that he knows there is a computer in front of him. However, it also entails that a subject cannot know that any of his empirical beliefs amount to knowledge.
• What the last three of these counterexamples bring to light is that Nozick’s rejection of closure is a double-edged sword. On the one hand, the fact that closure fails is precisely why premise (1) of the canonical argument for scepticism—the Cartesian condition on knowledge—comes out false. On the other hand, these counterexamples surface precisely because knowledge, on Nozick’s analysis, is not closed under entailment.7
8. Nozick and closure revisited
• The simple closure principle (SC) is not particularly plausible.8 However, the case above can easily be modified to show that the following refined, and vastly more plausible, closure principle also comes out false under Nozick’s analysis of knowledge:
(RC) If (i) S know that P and (ii) P entails Q and (iii) S knows that deduction preserves truth and (iv) S competently deduces Q from P thereby coming to believe that Q, then S knows that Q.
• Here, one needs to tread carefully. Nozick’s account does not entail that deductions of the sort described by never yield knowledge. His account simply has the consequence that they sometimes fail to yield knowledge.
• However, the fact that Nozick’s analysis has the consequence may be sufficient to discount it all together. How, one may ask, can a subject fail to know that Q if he meets all of the conditions specified by (RC)? Doesn’t the very fact that a subject can fail to know that Q under these conditions by itself show that Nozick’s account of knowledge is unacceptable.
9. Critical assessment of Nozick’s response to the sceptic
• Setting counterexamples and issues about closure to one side, perhaps the deepest worry about Nozick’s account of knowledge is that it turns out to be far more concessive to the sceptic than one would think at first blush. One way of getting at this issue is by asking the following question: Does Nozick show that it is merely possible for us to have knowledge, or does he show that we actually possess it.
• With a bit of reflection, it’s easy to see that even if we grant Nozick his account of knowledge, he has merely established the weaker of these results: Knowledge is possible. Despite some misleading rhetoric, Nozick has not given us even the slightest reason to think that we actually possess any empirical knowledge. So, setting counterexamples and worries about Nozick’s rejection of the refined closure principle (RC) to one side, the situation is essentially this: we may have empirical knowledge or we may lack it; however, Nozick has given us no reason to think that we possess it. To be sure, this is weaker than the sceptical conclusion of the canonical argument: It is impossible for us to possess empirical knowledge. However, it is hard to see that we are better off knowing that it is possible for us to have empirical knowledge, given that we don’t have the slightest reason to think that we actually have it.
• For those of you who are comfortable with the apparatus of possible worlds, here’s another way of voicing this criticism. All Nozick shows is that there are certain possible worlds (possible ways our universe may be) where we possess empirical knowledge and there are certain possible worlds where lack all empirical knowledge, but we haven’t been given the slightest reason to think that the actual world is one of the former, rather than the latter.
1Unfortunately, logic textbooks are not uniform in the notation they use for the material conditional. Some use the symbol ‘⊃’, others use the symbol ‘→’. In this handout, I employ ‘⊃’ for the material conditional because Nozick uses ‘→’ for the subjunctive conditional. As opposed to Nozick, I will use the standard symbol ‘☐→’ to express subjunctive conditionals. I use ‘⇒’ to express ‘entails’ and ‘☐’ to express ‘necessarily’.
2As Nozick notes, the reason knowledge is not closed under entailment is that Nozick’s third condition on knowledge is not closed under entailment.
3Premise (1) of the canonical argument is often known as the ‘Cartesian condition on knowledge’ as a result of Descartes’ insistence that he must know that he is not in a sceptical scenario in order to have even the most basic items of empirical knowledge. That Nozick’s account entails the falsity of the Cartesian condition on knowledge is one of its most important features.
4Derived from a counterexample developed in McGinn’s “The Concept of Knowledge.”
5Derived from a counterexample developed in an unpublished manuscript by Kripke.
6(DP) is known as a distribution principle because it affirms that knowledge distributes over conjunction. Those of you with familiarity with basic modal logic will notice similarities with the modal operator ‘☐’, which is used to express necessity. The similarities are not accidental. Epistemic logic is one of the more exotic, yet interesting, applications of the standard formal apparatus for modal logic.
7In each of these examples, we have a case where a subject knows that a and fails to know that b, despite the fact that a entails b. In (2), S knows that (Ma & Wa) despite failing to know that Ma. In (3), S knows that (P & Q) despite failing to know that P. In (4), S knows that S knows that P, yet S does not know that (∃ϕ)(S knows that ϕ).
8See Epistemology.Handout.1 and Stroud’s “The Problem of the External World."