A forum for VE lucubration

Monday, April 30, 2007

Goldman and Olsson's 'Conditional Probability Solution' to the Swamping Problem

Goldman and Olsson (forthcoming) in “Reliabilism and the Value of Knowledge” offer several insightful responses to the ‘swamping problem.’ I think that the ‘conditional probability’ solution that they offer is the most interesting; evaluating this solution requires attention to some important, and sometimes unnoticed, aspects of the problem.

The swamping problem has been articulated a variety of ways, and unfortunately, different versions of the problem have been referred to under the same label.

Here’s a general and (hopefully) uncontroversial formulation of the problem, as presented by Goldman and Olsson:

Template Swamping Argument

(S1) Knowledge equals reliably produced true belief (simple reliabilism)
(S2) If a given belief is true, its value will not be raised by the fact that it was reliably produced.
(S3) Hence: knowledge is no more valuable than unreliably produced true belief. (reductio)

(S2) of the argument expresses what has been called the ‘swamping premise.’ Of course, (S3) is counterintuitive, and so the idea is to either reject the swamping premise, or to reject simple reliabilism (S1).

The swamping premise expresses a conditional claim. Those who want to save reliabilism are burdened, as it were, to show how a reliably produced true belief is more valuable than an unreliably produced true belief.

Kvanvig (2003) throws down the gauntlet at this point and suggests that we can, in principle, rule out a rejection of (S2).

His suggestion is that reliability is a valuable property for a belief to have insofar as it is valuable for a belief to be ‘objectively likely to be true.’ He argues that for a reliabilist to suppose that reliability is a valuable property for a belief to have for reasons other than its being likely to be true (i.e. say, because the “normative dimension that accompanies the right kind of objective likelihood of truth introduces a new valuational element distinct from the value of objective likelihood” (Kvanvig 2003b, p. 51) would seem magical, he says, “like pulling a rabbit from a hat” (51).

He argues further that being ‘objectively likely to be true’ isn’t a property that, when added to a true belief, increases its value, and thus, (S2) is true.

Goldman and Olsson take issue with Kvanvig’s reasoning here for a couple of reasons. First is what I’ll call the ‘entailment’ objection. Goldman and Olsson think that Kvanvig overlooks the fact that although being reliabily formed entails being likely to be true, being likely to be true doesn’t entail being reliably formed. They say:

John may have acquired his belief that he will contract lung cancer from reading tea leaves, an unrealiable process, and yet if John is a heavy smoker, his belief may well be likely to be true” (Goldman and Olsson, p. 8)

Goldman and Olsson overstate what they take to be the crime here. This example would damage Kvanvig’s view only if Kvanvig actually defended that the entailment goes both ways, that is, that (as Goldman and Olsson attribute to him) “Being produced by a process that normally produces true belief just means being likely to be true” (Goldman and Olsson 8). Kvanvig says nothing to pin him to such a biconditional. His view is, rather, that the extent to which being produced by a reliable process is a valuable property for a belief to have is exhausted by the extent to which being likely to be true is a valuable property for a belief to have. And so, an objection to Kvanvig’s claim here should take the form, rather, of pointing out some feature of being produced by a reliable belief forming process that is valuable for a belief to have in a way that is not reducible to the value that a belief would have qua being objectively likely to be true.
This is, indeed, the route they go in their ‘conditional probability’ repsonse. They argue that being produced by a reliable belief forming process can be valuable for a belief in a way that merely being objectively likely to be true isn’t valuable, and further, that its value is such that when combined with a true belief, yields a collectively more valuable whole. They write:

“Knowing that p is more valuable than truly believing that p. What is this extra valuable property that distinguishes knowledge from true belief? It is the property of making it likely that one’s future beliefs of a similar kind will also be true. More precisely, under reliabilism, the probability of having more true belief (of a similar kind) in the future is greater conditional on S’s knowing that p than conditional on S’s merely truly believing that p. (p. 16)

This claim, if correct, would amount to a counterexample to the swamping premise, which recall, says:

(S2) If a given belief is true, its value will not be raised by the fact that it was reliably produced.

Goldman and Olsson, thus, think that a true belief will be more valuable if produced by a reliable process because, as such, it contributes to the diachronic goal of having more true beliefs (of a similar kind) in the future. I want to turn to an example that helps illustrate their idea; it is the espresso example Zagzebski uses to support the swamping premise. Goldman and Olsson write:

If a good cup of espresso is produced by a reliable espresso machine, and this machine remains at one’s disposal, then the probability that one’s next cup of espresso will be good is greater than the probability that the next cup of espresso will be good given that the first good cup was just luckily produced by an unrealiable machine. If a reliable coffee machine produces good espresso for you today, and it remains at your disposal, it can normally produce a good espresso for you tomorrow. The reliable production of one good cup of espresso may or may not stand in the singular-causation relation to any subsequent good cup of espresso. But the reliable production of a good cup of espresso does raise or enhance the probability of a subsequent good cup of espresso. This probability enhancement is a valuable property to have (p. 16)

This attempted assault on the espresso analogy scores a victory at the expense of betraying a deeper, and perhaps untractable, defect in the ‘conditional probability’ response. The victory, in short, is that it gives an explanation for why two equally good cups of espresso might be such that one is more valuable than the other; this explanation rejects an assumption that Zagzebski seemed to make in the analogy, which is that ‘taste is all that matters’ for espresso (as she thought, ‘being true’ is what matters for a belief).
This sword cuts two ways, though. Consider that True Temp is a reliable belief former, and so the conditional probability of his future beliefs (of a similar kind) being true is greater given that they are formed from a reliable process (i.e. a reliable thermometer, perhaps purchased at the same store as you’d find a reliable espresso maker), than it would be had his beliefs been merely true, but unreliably produced. But, we should object, True Temp is not a knower, and so whatever makes his state valuable should not be as valuable as it would be if he were a knower. However, the conditional probability view has no way to explain this. In sum, the conditional probability response to the swamping argument works only if True Temp knows. But he doesn’t. So it doesn’t work. (Or so my objection goes…)

Here’s a second objection:

Suppose I have cancer and am in the hospital, and my 12 year old boy (I don’t really have one) is playing baseball in the little league world series. He has been practicing every day from sun up till sun down in hopes of making it to the world series and hitting a homerun. It is the ninth inning of the game, and my son (little Johnny) is up to bat. I am watching the television screen with intensity as he shouts (this one is for you, Dad!). The pitch is on the way, and then……

(Option A): The television suddenly blacks out. Knowing I might die any minute, I decide that Johnny has practiced hard and probably hit a home run, and so I believe that he did, although sadly, I realize I will never know. (And then I die, my last thoughts being ones of curiosity).

(Option B): The television does not black out, and I get to see Johnny hit the home run on TV. In fact, (for even more evidence) my hospital is close to the baseball field, and the ball comes through the window and lands on my bed. I know that Johnny hit the home run, and then I die (in peace).

On the conditional probability view, my true belief in Option B (in which I form my belief from reliable processes, i.e. watching a previously non-deceptive TV broadcast, which doesn’t display phantom images) is more valuable state than my true belief in Option A in so far as the true belief in B was produced by a reliable process, and as such, raises the probability that future beliefs (of a similar kind) will be true. However, as I know I am dying, I have no interest in future beliefs, as I am aware I am in my last throes. (And, in fact, I don’t form any more future beliefs of a similar kind). The conditional probability approach, then, seems committed to claiming that my true belief in B is no more valuable than my true belief in A. But surely that’s not true!

Okay, those are my worries. I’d love to hear any thoughts!

Tuesday, April 24, 2007

Challenging the Swamping Premise

The ‘swamping’ argument against reliabilism has been advanced on several occasions (i.e. Kvanvig 2003, Swinburne 1999, Zagzebski 2004, W. Jones 1997, and others), and is, at least prima facie, quite persuasive.

The crucial premise in the argument is, as Kristoffer Ahlstrom (whose formalization I am using) calls it, the swamping premise.

(1) V (SB R,T that p) = V (SBT that p).

The swamping premise has been defended a variety of ways. Zagzebski (2004), for example, defends (1) with her ‘espresso analogy.’ She argues that good espresso from an unreliable espresso machine is just as valuable as good espresso from a reliable espresso machine. Analogously, she thinks, for beliefs. Being produced from a reliable process doesn’t add value to a true belief. And, thus, (1).

Kvanvig (2003) defends the premise with his ‘two lists’ argument; if you want to know where you can get chocolate, and you are given a list telling you where chocolate is sold, and another list telling you where chocolate is ‘likely’ to be sold, then a conjunction of the two lists is no more valuable than the first list. The value of the second list is ‘swamped’ by the value of the first. So to, he thinks, for beliefs. If a reliably produced belief is valuable because it is ‘likely to be true’, then adding this property to a belief already stipulated as true does not increase its value.

The next premise is:

(2) V (SK that p) > V(SBT that P)

But because reliabilists just define knowledge as (SB R,T that p), we derive:

(3) V (SK that p) > V (SB R,T that p). Therefore:

(4) SK that p  df. SB R,T that p

(Note: the move from (3) to (4) relies on an implicit premise that: a difference in value between x and y entails that x  y. This assumption, as a side note, lurks in the background as Meno is reasoning to his conclusion that knowledge just is true belief).

If the ‘swamping premise’ (i.e. P1) can be adequately defended, it is not difficult to show how further premises will lead to a conclusion that process reliabilism is a false theory of knowledge.

There exist some recent attempts to vitiate the swamping argument. I am interested to know whether any succeeds.

First attempt: Kristoffer Ahlstrom and the diachronic goal.

Ahlstrom argues that the swamping premise is true only if our cognitive coal is conceived of synchronically; that is, only if the value relative to which other epistemic states are valuable by virtue of promoting that value, is having true beliefs now. He argues in favour of a reconstrual of our cognitive goal as diachronic—as having true beliefs not only now, but also later. Under such a framework, he thinks, a reliably formed belief is more valuable than a mere true belief. Here’s Ahlstrom:

To be (or have been) reliably formed is such a component since being (or having been) reliably formed implies something about the etiology of the belief in question—an etiology that, if repeatedly instantiated, will promote our diachronic goal to attain and maintain true beliefs through tracking the truth. To believe truly, however, is no such diachronic component since it carries no promise to the effect that the belief was formed in response to the way the world is rather than as a result of mere luck. This is why the presence of truth cannot make the epistemic value of believing reliably otiose”. (Ahlstrom, “An Argument Concerning Swamping”)

I agree with Ahlstrom that a ‘synchronic’ conception of our cognitive goal is unhelpfully narrow, however I am not convinced that stipulating a ‘diachronic’ goal gets us the result he wants. My worry is this: the property of a belief that best promotes a diachronic goal is ‘permanence’ of a belief (i.e. see Williamson’s cross-temporal explanation of the value of knowledge in his 2000b), however, permanence attaches to a belief not by virtue of its etiology, but by virtue of the extent to which we hold conviction with regard to the belief. Maybe I’m missing something here.

Second try: Goldman and Olsson No. 1

Goldman and Olsson in “Reliabilism and the Value of Knowledge” bring up an interesting case which, they admit, is not at the crux of their argument, but is nonetheless worth mentioning here. They suggest that in at least some deployments of the word ‘know’, we mean nothing other than ‘truly believes.’ Therefore, in at least some cases, it is no more valuable to know than to truly believe. The example they cite is one from Hawthorne (2004) who imagines that a classroom is asked ‘Who knows the capital of Austria?” The idea here is that: whomever says ‘Vienna’ is credited as knowing, and ipso facto, knowledge in such cases just is true belief.
Two problems here. Firstly, I think that it is more likely that in the classroom case, we just ‘misuse’ the word know (in the same way that we might use ‘deny’ sloppily rather than ‘refute’). But that aside, even if the case were legitimate, and we infer from that that some cases of knowing aren’t more valuable than their true-belief counterparts, it wouldn’t establish anything that we haven’t already learned from Sosa’s sand on the beach case. There are some propositions such that knowing them isn’t more valuable than truly believing them.

Second try: Goldman and Olsson No. 2

This case is the interesting case. It is an attack of Kvanvig’s two lists’ argument. Goldman and Olsson think that Kvanvig’s two lists argument relies on allegedly spurious thesis of ‘property parasitism’:

Property Parasitism: If the value of property P* is parasitic on the value of property P, then the value of P and P* together does not exceed the value of P. (Goldman and Olsson, p. 10)

Goldman and Olsson think property parasitism is false by way of counterexample: Suppose, they argue, that you have a ticket worth $1000 and another ticket that has a 10% chance of winning $1000. Clearly you would want both the $1000 and the ticket more than you would want merely the $1000. But, they think, if property parasitism is true, then the $1000 ‘swamps’ the value of the ticket, and thus, you should not prefer the conjunction of the two over the $1000.

This is quite clever. I’m afraid, though, that there is a subtle disanalogy between what Kvanvig is trying to do with the two lists argument (about wanting chocolate) and with the money case. In Kvanvig’s case, you goal is a true belief. You can’t get ‘truer than true’ and so once you have a true belief, then adding the property that it is ‘likely to be true’ doesn’t add to the value. On the Goldman/Olson case, though, it remains possible that your conjunction (i.e. of the $1000 and the ticket) could amount to something ‘more valuable than $1000), and for that reason, it seems to be relevantly disanalogous to what takes place when we adopt truth as a goal.

There are other ways to go about saving reliabilism form the swamp (i.e. Pritchard’s ‘final value’ discussion of reliable processes, as well as Greco’s ‘intrinsic value of success through ability’ defense of virtue reliabilism), but I’ll stop the discussion here and see if anyone thinks that any of the first three examples are legitimate reasons to deny the swamping premise.