Lasonen-Aarnio argues that a problem that might seem to affect only multi-premise closure (MPC), having to do with the accumulation of risk, is also a problem for single premise closure (SPC).

Here are the epistemic closure principles in question, as formulated by Lasonen-Aarnio:

(SPC) For all propositions P, Q, and all subjects s, if s knows P, and s comes to believe Q solely based on competent deduction from P, while retaining knowledge of P throughout, then s knows Q (157).

(MPC) For all propositions P₁, …, P_n, Q, and all subjects s, if s knows each of P₁, …, P_n, and s comes to believe Q solely based on competent deduction from P₁, …, P_n, while retaining knowledge of P₁, …, P_n throughout, then s knows Q (158).

Risk, or the “danger of error,” is a property of beliefs that is conceptually tied to epistemic luck. Lasonen-Aarnio suggests that we use ‘risk’ as a placeholder for something that knowledge can tolerate a little of, but that in excess quantities makes a true belief lucky in a way that disqualifies it from being knowledge (165). One sort of thing that fits the bill is the believed proposition’s objective chance of falsity. It must be conceded, on pain of skepticism, that one can know propositions with a slight objective chance of their being false. For example, barring an unacceptable skepticism about our knowledge of the future, I had better be capable of knowing that if I drop my pen on the table it will land on the table; but in an indeterministic world there is a very slight objective chance that if I drop my pen on the table, it will tunnel through (162). So knowledge can tolerate a small objective chance of falsity. On the other hand, if I believe that P but there is a high objective chance that P is false, then it is just luck if my belief is true, and so I do not know P (163). Although the objective chance of falsity is one source of risk, it should not simply be identified with risk, since as we shall see Lasonen-Aarnio argues that there is another source of risk.

The problem for MPC is that risk accumulates across multi-premise entailment—propositions that are only slightly risky to believe can jointly entail a proposition that is so risky to believe that it cannot be known. For example, let P₁, …, P_n be propositions that I know but whose objective probabilities fall slightly short of 1, and suppose I deduce the conjunction P₁&…&P_n and come to believe this conjunction on the basis of the deduction, retaining knowledge of P₁, …, P_n throughout. Given a large enough n, the objective probability of P₁&…&P_n will be low enough that it is just luck that my belief that P₁&…&P_n is true. So I do not know P₁&…&P_n, and MPC fails (162-163).

The preceding problem for MPC exploited the fact that the objective probability of the conclusion of a multi-premise entailment can be lower than the objective probability of any of the premises. It might seem, then, that SPC does not face an analogous problem, since if P entails Q, then Q’s objective probability is at least as high as P’s (158-159).

In order to introduce an analogous problem for SPC, Lasonen-Aarnio argues that competent deduction does not mean infallible deduction—often when one successfully performs a competent deduction, there was a small objective chance that the deduction would fail—perhaps as the result of a quantum event in one’s brain (165). This small objective chance of deductive failure, which Lasonen-Aarnio calls deductive risk, contributes to whether or not the deduced belief is lucky; that is, contributes to the risk of the deduced belief. So risk can accumulate even across single premise entailment; the fact that one’s competent deduction from P to Q was slightly risky can result in one’s belief that Q being slightly riskier than one’s belief that P. SPC will fail when s knows P but the risk of s’s belief that P falls just below the threshold above which beliefs are too risky to know, and s’s competent deduction of Q from P involves some deductive risk. The deductive risk will push the risk of s’s belief that Q above the threshold, so s will fail to know Q (164-165).

Lasonen-Aarnio also provides a more concrete counterexample to SPC that requires assuming a “most worlds safety” account of knowledge and a corresponding account of competent deduction (166-169). This counterexample, which strikes me as successful but is too complex to detail here, is of special importance given the popularity of safety accounts of knowledge.

Reviewed by Leo Iacono
Loyola University New Orleans

The Journal of Philosophy, volume CV, number 9 (September 2008), pages 518-539.

Main authors discussed: Stewart Cohen, James Van Cleve, Michael Bergmann (Bergmann discussed in the Appendix)

Jonathan Vogel revisits his bootstrapping argument against reliabilism and defends it from the charge that internalism has the same problem.

Let’s review the bootstrapping argument. Imagine Roxanne is wondering whether or not her gas gauge is reliable. Suppose it is reliable, but Roxanne isn’t aware of this. If reliabilism is true, it seems Roxanne can know that her gas gauge is reliable by using the following argument.

Roxanne’s Track Record Argument

1. The tank is full. (Formed by looking at the gas gauge)
2. The gas gauge reads “FULL” (Perception)
3. The gas gauge reads “FULL” and the tank is full. (Inference)
4. Therefore, the gas gauge worked correctly this time. (Inference)
   (Repeat n times)
5. The gas gauge worked n times. (Inference)
6. Therefore, the gas gauge is reliable. (Induction)

As long as the processes that generate beliefs in (1)-(6) are reliable, then Roxanne can know that the gas gauge is reliable. What’s bizarre is that Roxanne used the gas gauge to come to believe premise (1) in her argument. So, reliabilism seems to permit an impermissible form of reasoning. Call this form of reasoning “bootstrapping.”

It has been alleged that allowing for bootstrapping is not peculiar to reliabilism (Cohen 2002, Van Cleve 2002, and Bergmann 2004). Arguably, any epistemic principle that permits  that justification without requiring antecedent justification for thinking that one’s faculties are reliable will likely permit bootstrapping. Consider some Chisholmian version of internalist foundationalism that holds that the mere fact that something appears red to you can justify you in believing that the thing is red. Peter, like Roxanne, can bootstrap with the following argument.

Peter’s Track Record Argument

1. The ball is red. (Formed by looking at the ball)
2. I am having a visual perception that the ball is red. (Introspection)
3. I am having a visual perception that the ball is red and the ball is red. (Inference)
4. Therefore, vision worked correctly this time. (Inference)
   (Repeat n times)
5. Vision worked n times. (Inference)
6. Therefore, vision is reliable. (Induction)

Vogel maintains that there is a way out for internalism. The version of reliabilism that Vogel criticizes holds that you never need to know about reliability. This never needing to know about reliability is arguably the source of the bootstrapping problem. Vogel maintains that there are two alternatives for the internalist. First, the internalist can maintain that you always need to know about the reliability of the source in order for the source to yield justified beliefs. The worry about this option, as many have noted, is that it seems to lead to skepticism.

The second option would be that you only sometimes need to know about the reliability of the source in order for it to yield justified beliefs. A version of internalism that holds that you only need knowledge of reliability sometimes could avoid bootstrapping without entailing skepticism.

So when do you need to know about the reliability a source? Vogel’s answer is, roughly, when one attempts to bootstrap. He notes that the following is an independently plausible epistemic principle.

(NRC) A belief that an epistemic rule R is reliable cannot be justified by the application of R, i.e., neither the conclusion itself nor any belief which supports the conclusion may be justified in virtue of the application of R.

NRC is basically a prohibition on rule circular reasoning. I assume that Vogel thinks that any version of internalism that allows for NRC as an exception clause can avoid bootstrapping worries. But it’s a bit unclear how the application of NRC is supposed to work. At one point, Vogel claims that Roxanne does not know (1) in her track record argument (p. 526), and given his criterion above it must be because she’s engaged in a bootstrapping argument.

This claim about Roxanne seems to be at odds with what Vogel says in response to what he calls “the rollback problem.” Let’s use Peter to illustrate the roll back problem. The roll back problem is that it seems that if Peter is not justified in believing (6) in his track record argument, then he must not be justified in believing (1), (2), (3), (4), or (5) in his track record argument. However, (3) follows from (1) and (2). (4) follows from (3). (5) follows from any n times you repeat tokens of (1)-(3) to reach a token of (4). It seems like (1) and (2) are the only genuine options for the propositions in the track record argument that you are not justified in believing.

Vogel’s response to the rollback problem doesn’t concede (as I thought he might, given what he says on p. 526 about Roxanne) that persons in bootstrapping scenarios aren’t justified in believing their first premise. The track record arguments go astray elsewhere. Vogel gives us another example of a bootstrapping argument involving memory to illustrate his response to the rollback problem. His version of the argument includes variables. To simplify, I’ll fill in the variables.

Memory Track Record Argument:

(M2) I’m out of of milk. (supported by internal memorial evidence)
(M3) I seem to remember that I’m out of milk.
(M4) I seem to remember that I’m out of milk and I’m out of milk.
(M5) Memory is reliable.

Vogel considers two possible responses to the rollback problem. First, one might argue that in order to make the inference from (M4) to (M5) you need to be justified in believing not only that your memory got it right, but also that it is not mistaken. In other words, you need to be justified in believing (M4*).

(M4*) It’s not the case that I seem to remember that I’m out of milk and it’s not the case that I’m out of milk.

The problem with this response, as Vogel notes,  is that (M2) entails (M4*). Embracing this response seems to commit one to denying closure.

Vogel seems more sympathetic to the second response which seems to be as follows. The justification for (M5) conferred by (M4) is merely prima facie. It can be defeated. One of those conditions in which the justification that (M4) confers on (M5) is defeated is when rule circular arguments are being employed. Because the justification (M4) provides for (M5) is defeated, and (M4) does not entail (M5), your lack of justification for (M5) does not imply a lack of justification for (M4). And so you’re not forced to give up (M2).

I have a number of worries about the moves Vogel makes in this paper, but because of space, I’ll note two. Vogel notes that the first response to the rollback problem comes at a high price, denying closure. However, the second response has a cost too. The second response allows you to reach the conclusion that your faculties worked once. Suppose Peter is wondering whether he should trust his perception in a particular instance of having formed the belief that the ball is red. If internalist foundationalism is true, he has a pretty easy method. Just run the track record argument up to premise (4), and he has his answer.

The second worry is that it seems open to an externalist to employ Vogel’s strategy. As Vogel says, it’s independently plausible to suppose that circular reasoning is pernicious, and then he recommends that internalist foundationalists tack on an anti-bootstrapping proviso to their theory. If we assumed that there is nothing objectionable about this strategy, then it seems that reliabilists could take Vogel up on this recommendation too.

Other References:

Bergmann, M. (2004). Epistemic Circularity: Malignant and Benign. Philosophy and Phenomenological Research, 69(3), 709-727.

Cohen, S. (2002). Basic Knowledge and the Problem of Easy Knowledge. Philosophy and Phenomenological Research, 309-329.

Van Cleve, J. (2002). Is Knowledge Easy or Impossible? Externalism as the Only Answer to Skepticism. The Skeptics, Ashgate, Aldershot, 45–59.

Reviewed by Andrew Cullison
SUNY Fredonia

Main authors discussed: David Lewis and Jason Stanley

The fallibilist claims that it’s possible to know p even if your evidence for believing p does not entail p.  It seems that infallibilism entails scepticism because it seems that we don’t have infallible grounds for most of our beliefs about the external world.  Trent Dougherty and Patrick Rysiew defend fallibilism from David Lewis’ criticism and address Jason Stanley’s criticism of Rysiew’s earlier response to Lewis.

As Lewis (1996: 550) observed, overt statements of the fallibilist view seem contradictory.  Consider this concessive knowledge attribution (CKA):

(1)     I know that Harry is a zebra, but it might be that Harry is just a painted mule.

Lewis claims the second conjunct flatly denies what the first asserts.  Rysiew (2001) defended fallibilists from the charge that their view is contradictory, arguing that CKAs only seem contradictory.  In ordinary speech, he said, “It might be that ~p” pragmatically imparts that the speaker doesn’t know that p (2001: 493).

Stanley (2005) criticized Rysiew’s proposed defense because it didn’t offer any semantic account of epistemic possibility statements.  Rysiew agreed with Lewis that (1) captured the fallibilist’s view but claimed that (1) could express a truth.  The problem, according to Stanley,  was that given a standard treatment of epistemic modals Rysiew’s defense would fail.  Consider:

(EPk)     p is epistemically possible for S iff ~p isn’t obviously entailed by something S knows.

If (EPk) is correct, (1) entails:

(2)     I know that Harry is a zebra, but I do not know that Harry is not just a painted mule.

Since (2) must be false, it appears (1) must be false as well.

Dougherty and Rysiew (2009) offer a defense of fallibilism that builds on Rysiew’s (2001) earlier work and meets Stanley’s challenge to provide a semantic account of epistemic possibility statements on which (2) isn’t a consequence of (1).  Siding with Lewis against Stanley, they say that (1) does capture the fallibilist’s view.  Against Lewis, they insist that (1) can express a true proposition.  To explain how (1) could be true when it is agreed by all that (2) is false, they reject (EPk) and offer in its place this account of epistemic possibility:

(EPev)     p is epistemically possible for S iff ~p isn’t entailed by S’s evidence.

To explain why (1) seems defective, they give a pragmatic explanation.  If there are genuine reasons to doubt (i.e., reasons to doubt that do not arise simply from the recognition that there is some non-zero chance of having made a mistake), then it is acceptable to assert ‘It might be that ~p’, but inappropriate to ascribe knowledge to oneself given that there are genuine reasons to doubt.  According to Grice’s Maxim of Quality, you shouldn’t say what you believe you lack adequate evidence for.  To say that you know, you deny that you lack adequate evidence for your belief and this clashes with the claim that there are real reasons for doubt.  If, however, the reasons to doubt are simply that there is some non-zero chance of being mistaken it seems Grice’s Maxim of Relation recommends not introducing such chances into the conversation by asserting that it is epistemically possible that ~p  since these are not significant reasons for doubt (2009: 129).

Their pragmatic account may be sufficient to explain the oddity of CKAs, but note that to meet Stanley’s challenge they replaced (EPk) with (EPev).  They can’t do this without rejecting Williamson’s claim that evidence just is knowledge:

(E=K) S’s evidence consists of all and only the propositions known to S.

Their defense of fallibilism succeeds only if Williamson’s equation (E = K) is wrong.  They acknowledge this in a footnote saying, “that principle is sufficiently controversial that most would join us in assuming that the distinction between (EPk) and (EPev) is real” (2009: 127).

While (E=K) is controversial, I wish they had said more about the relation between (EPk) and (EPev) than just this.  There are two reasons that I think (E=K) needs to be revised.  According to (E = K) if you know p non-inferentially, you can then add additional propositions to your body of evidence via competent deduction.  That seems odd.  I think of inference as a way of applying old evidence to justify new beliefs and acquire new knowledge without having to acquire new evidence.  According to (E = K) if you know p and someone else fails to know p for purely Gettierish reasons, you have evidence they lack.  That seems odd, too.

If we revise (E=K) to accomodate these points, it seems we could still say that there is this connection between knowledge and evidence:

(IKSE)     If S knows p non-inferentially, p is part of S’s evidence.

If (IKSE) is true, immediate knowledge of p’s truth suffices for p’s inclusion in your evidence. While (E = K) might be controversial, (IKSE) seems far less controversial.  To deny it, you have to say that more is needed to get p into your evidence than just non-inferential knowledge.  (Remember that we want a non-sceptical view.  If we want a non-sceptical view, should we really insist that we need more than knowledge to get something into our evidence?  What would that be, superknowledge?)  If (IKSE) is true, a CKA of the form ‘I know p, but it might be that ~p’ would express a false proposition on Dougherty and Rysiew’s view if the speaker knew non-inferentially that p.

Let ‘p’ be the proposition that S has hands.  If S could assert truthfully that it is possible that she does not have hands (or that she’s a handless BIV), according to (EPev) S’s evidence does not include the proposition that she has hands.  (The only way that they could deny that S could assert this truthfully is if they say that whenever S knows she has hands she has evidence that entails that she has hands.)  It follows from the fact that her evidence does not include the proposition that she has hands and (IKSE) that she does not know that she has hands.  Perhaps they will just deny (IKSE), but (IKSE) is a consequence of:

(IJBSE)     If S is non-inferentially justified in believing p, p is part of S’s evidence.

If they deny (IKSE) they also have to deny that S can be non-inferentially justified in the belief that she has hands.  As a fallibilist, I’d prefer to retain (IJBSE) and (IKSE) if possible.

Reviewed by Clayton Littlejohn
Southern Methodist University