MODAL ANALYSIS OF THE SKEPTICAL PARADOX AND THE GETTIER-PROBLEM

David Lewis has articulated a position that analyses epistemological problems in terms of the possibilities they establish. Accordingly he defined ‘knowledge’ as a match between possibilities: possibilities obtaining for the subject and the possibilities that the attributors are not allowed to ignore. Lewis’s approach amalgamates two different standpoints. On the one hand there is a subject and the possibilities obtaining for her (whether or not she knows that they do or do not obtain) and on the other there are the possibilities that the attributors, i.e. those who assess the subject’s epistemic state, are not allowed to ignore. To aid his definition Lewis argued for a set of rules that guide the attributors as to which possibilities they are allowed to ignore and which they are not. Lewis’s account has a remarkable consequence. The type of possibility articulated in a Gettier-example turns out to have the same feature as a possibility articulated in the skeptical hypothesis. Namely, these possibilities resemble the actual (or the possibility considered as actual) in terms of subject’s evidence. This suggests that these possibilities are tokens of the same type. 

Let us concentrate on three sets of possibilities that the attributors are never allowed to ignore. The three types of possibilities that need to be considered here are articulated in terms of Lewis’s rules as: any possibility that actually obtains for the subject (The Rule of Actuality); any possibility that the subject believes to obtain or ought to believe to obtain (The Rule of Belief); and any possibility that saliently resembles the actual world in terms of the subject’s evidence (The Rule of Resemblance). The Rule of Resemblance, unlike the previous two rules, picks out a pair of possibilities. A possibility is first made relevant by the Rule of Actuality say, and given that there is a possibility that resembles actuality in terms of subject’s evidence this latter possibility is also relevant. The Rule of Resemblance is meant to capture the explanation of why the subjects fail to know in Gettier-cases. For instance, the world that actually obtains for Henry is the world in which he is surrounded by façade barns while accidentally looking at a real one. The world that saliently resembles the actual world of Henry’s is the one in which he is looking at a façade barn. Therefore, by the input of the rules of Actuality and Resemblance, knowledge should not attributed to Henry because the resembling world (here: the world in which Henry looks at a façade) is never properly ignored by the attributors. By stating various versions of Gettier-cases Lewis makes a good case for joint operation of Rules of Actuality and Resemblance. 

However, when discussing the applications of the Rule of Resemblance Lewis noticed the following problem.

… Actuality is a possibility uneliminated by the subject’s evidence. Any other possibility W that is likewise uneliminated by the subject’s evidence thereby resembles actuality in one salient respect: namely, in respect of the subject’s evidence. That will be so even if W is in other respects very dissimilar to actuality—even if, for instance it is a possibility in which the subject is radically deceived by a demon. Plainly, we dare not apply the Rules of Actuality and Resemblance to conclude that any such W is a relevant alternative—that would be capitulation to skepticism. The Rule of Resemblance was never meant to apply to this resemblance! 

So, what Lewis is effectively denying is that the Rule of Resemblance ought not to apply to skeptical possibilities. After all, this ‘capitulation’ to skepticism means that the skeptical possibilities are never properly ignored and hence always relevant. The Rule of Actuality states that the actual world of the subject is always relevant, the skeptical possibility resembles the actual world perfectly as far as evidence goes, hence, the skeptical possibility is relevant. Clearly this is not what Lewis (or anyone) wants.

Lewis’s above exception provides us with a clue. The possibility by which knowledge is denied from the Gettier-subject yields a denial also in the skeptical case. In other words, the possibility in which the subject is radically deceived by an evil demon is a possibility that resembles the actual in terms of a subject’s evidence. The actual possibility cannot be properly ignored and neither can the resembling possibility. That is, the possibility in which the subject is looking at the façade barn resembles the actual world in terms of the subject’s evidence and since the actual world (many façades yet the subject looking at the real one) is not properly ignored, then neither is the one where the subject is looking at the façade. Same pattern occurs with the skeptical possibility: the possibility in which the subject has apparently perfect evidence for believing that she has hands yet she is deceived, resembles the possibility that actually obtains for her. The possibility that actually obtains is never properly ignored and neither is the possibility that evidentially resembles the actual. Hence, the subject fails to know. Thus, by Lewis’s rules the subject fails to know because the possibility by which the knowledge is denied in a Gettier-case and the possibility by which the knowledge is denied in the skeptical case both resemble the actual world in terms of the subject’s evidence.

Lewis’s exception provides us with a piece of evidence that these two apparently very different problems are related. The first is presented as a counterexample to a definition of knowledge and the other as an argument against a subject’s knowledge of a large number of empirical propositions. However, Lewis’s analysis of these problems in terms of possibilities reveals that there is more in common between them than it first appears. Namely, in both cases the subject fails to know because there is a possibility in which her evidence is the same as in the actual world. Let us turn to this data.

The possibility described in a Gettier-case (Henry and the façade barn) and the possibility described in the skeptical hypothesis (envatted brain) are not possibilities where merely not-p. The fact that this possibility resembles actuality in terms of the subject’s evidence makes the possibility automatically convincing. That is, the skeptical hypothesis is convincing because the subject holds phenomenologically same evidence if she were a victim of the scientist as she would hold in the actual world. Furthermore, unless Henry was unaware of any changes in his environment between the normal and façade land, we would not hold that his belief is justified. When we are convinced of the counterexample to the JTB definition or of the skeptical paradox, the possibility presented has to convince us that the subject blamelessly fails to know. As Lewis put it, it has to be a possibility that resembles the actual in terms of the subject’s evidence. When a possibility resembles the actual in terms of the subject’s evidence it makes the subject blameless regarding the failure to know because it is not the case that the subject has ignored a vital piece of evidence and consequently fails to know. And that is exactly what happens in both the Gettier-case and the skeptical paradox; the subject’s evidence fails to distinguish between the possibility presented and the actual. For instance in the Henry-case the resembling possibility is one where he is looking at a façade barn and in the skeptical paradox it is the possibility in which the subject is envatted. These possibilities, call them resembling possibilities, ought to be enough to persuade anyone of the falsity of a knowledge attribution, which is made to a subject that is taken to occupy an actual possibility.

A further investigation into similarities between these problems may be conducted by asking whether protecting a belief against the Gettier-situation protects the belief from the skeptical hypothesis, and vice versa. Surely, if the clause ends up precluding the skeptical hypothesis also, the possibilities used have something in common. Indeed, as noted earlier the Gettier-problem needs to be understood as answering the challenge by establishing a clause, which if met, precludes the Gettier-type situation. In other words, a condition for knowledge needs to be established which precludes the belief from being ‘Gettiered’. Effectively this appears to be what the defenders of various modal condition(s) have had in mind. For instance, it has been argued that the anti-luck condition makes truth condition redundant.  This is equivalent to saying that whenever the anti-luck condition is met, the truth-condition is met. Now, we can ask if this condition is met, then does this protect the belief from the skeptical hypothesis also?

Testing whether an answer to the skeptical problem would answer the Gettier-problem requires us to imagine that an evidential state supporting a belief p meets a condition that protects beliefs from the skeptical paradox. Let us call this condition ‘super-evidence’ and characterize it roughly as a condition, which provides the subject with the strongest possible evidence for the proposition believed.  Then, it seems plausible to say that if the belief is supported by super-evidence, this evidence excludes the skeptical hypothesis. In other words, the super-evidence must signal a difference between a belief that is held by a deceived victim and a normal subject. Granted by definition, the question then becomes, does super-evidence also rule out that beliefs are not held in an environment where the possibility of mistake is nearby? By definition, the ‘super-evidence’ condition should rule out all resembling possibilities and this includes those possibilities where barn façades surround the subject. Of course, the notion ‘super-evidence’ needs to be interpreted suitably widely, but the intuitive support for this is strong. Surely, if the belief meets the super evidence condition then the belief is hooked to the environment so strongly that it is not possible to be in phenomenologically same evidential state between two possibilities.

The second test for similarity is whether we can show any connection between the Gettier-problem and the arguments used to generate the skeptical paradox. In other words, we are looking for a connection between infallibilism and the Gettier-problem on the one hand, and closure and the Gettier-problem on the other.

Let us first get clear however on the nature of the exact explanation for the belief’s failure to count as knowledge in Gettier-style case. In these cases there has to be a sense in which the subject fails to know through no fault of her own. I.e. if she were to blame the justification/evidence condition wouldn’t be met. This means that for a possibility to generate a genuine Gettier-case it needs to be, according to the subject’s introspection, identical to a possibility that would qualify as ‘normal’. For instance, when Henry arrives at the façade barn land there are no markers of which he is aware to tell him what the environment is like. If there were, we wouldn’t attribute justification to him. This is where our intuition plays a role in Gettier-cases. These possibilities have to be such that the subject has apparent reasons to believe that her belief is connected to the truth-makers of the belief and that we accept that the proposition believed is backed by (inconclusive) evidence.  Now, if the subject cannot be blamed for the lack of knowledge, then what or who should? My suggestion, siding with Lewis, is that the environment is the culprit. The actual world obtaining for the subject is such that she cannot distinguish between that and a non-façade world.

In the skeptical argument the epistemic closure fails to do it’s job. Knowledge of an ‘easy-to-know’ empirical proposition doesn’t transmit to knowledge of the falsity of the skeptical hypothesis. The same argument can be run against Henry;

1. Henry knows (by JTB) that X is a barn 

2. Henry knows that ‘X is a barn’ entails that ‘Henry is not in a façade environment’

3. If Henry knows that ‘X is a barn’ and Henry knows that ‘‘X is a barn’ entails that ‘he is not in a façade environment’’ then Henry knows that ‘Henry is not in a façade environment’.

 Therefore,

4. Henry knows that he is not in a façade environment

Anyone familiar with Henry’s situation will agree that (4) is false. Hence (1) is rejected just as the skeptic rejects (1’) ‘S knows p’. The difference between the skeptical paradox and the above argument is that with the skeptical paradox we don’t want to reject (1’). Indeed, to reject (1’) would be to go along with the skeptic. In the above argument one opts to keeping the closure but blames the definition instead. It seems that one could plug any definition in (1), as long as it is less than ‘super-evidence’ and we should get (4), and again, reject (1). In other words, if the subject has less than super-evidence for her belief there will be space for a Gettier-type case. So, when the closure argument (1 - 4) is used to generate the rejection of the tripartite (JTB) definition it appears perfectly acceptable. Contrast this with familiar closure arguments used to generate rejection of empirical knowledge in the skeptical paradox where the rejection of ‘S knows p’ is not acceptable. So, the difference between the two arguments boils down to a difference between our reactions to the argument. We are more attracted to S knowing an empirical proposition than we are to a definition of knowledge.

The closure principle plays exactly the same kind of role above as it does in the argument plausibly used by the skeptic. Indeed, given any less-than-super-evidence support in (1) closure will make sure that (4) doesn’t follow because the transmittance will fail in (3).  Just as we reject transmittance of knowledge in the skeptical argument concerning knowledge of the environment we are in, the reason for the plausibility of the skeptic’s case is that we cannot distinguish between what we take to be actual and the alternative possibility. This is strong evidence for the thought that if one thinks that closure plays a role in the skeptical paradox, one might as well accept that it plays a role in arguments against the definition of knowledge generated by Gettier-cases. 

Infallibilism can be similarly used to support Gettier-counterexamples. The infallibilist intuition (as applied here ) would then be something like: for Henry to know that X is a barn, he should exclude all possibilities in which it is not. The façade barn environment is a possibility which, by its very construction Henry cannot distinguish from the possibility in which barns are ‘easy-to-know’. An evidence condition or the like can quote the reason for this failure to distinguish. Hence, Henry’s belief fails the infallibilist intuition and fails to be knowledge.

One might resist this reasoning by saying that surely the failure is in distinguishing  between a façade barn and a real barn, not in distinguishing between the environments. I will reply to a similar worry below and say only this. In Goldman’s description of the Henry-case he wrote that “, unknown to Henry, the district he has just entered…,” . The important piece of information here is that Henry doesn’t know that he has arrived in a different environment (otherwise his barn belief wouldn’t be Gettiered). So, Henry cannot distinguish between the environment he started from, the environment in which he is looking at the real barn among the façades, and the environment in which he is looking at a façade barn. The infallibilist requirement is vague enough to allow the subject to be mistaken about the environment just as well as to be mistaken about a proposition. Hence, Henry’s belief fails to be knowledge by failing to meet the infallibilist requirement.

One of the most striking implications of arguments presnted is that the subject in the Gettier-possibility (Henry in the Façade barn-land pointing to a real barn) and that subject in the actual world fail to know for the same reason. Namely, because they cannot distinguish the possibility they occupy from the (resembling) possibility in which their belief is false. This explains the intuitive plausibility of the Gettier-situation and the skeptical hypothesis. In other words, neither the Gettier-possibility nor the skeptical possibility would count as a genuinely knowledge defeating possibility if the possibility occupied by the subject were such that it could be distinguished from the one considered as actual.

However, there appears to be an intuitive difference in the actual possibility of the Gettier-case and the skeptical paradox. In the Gettier-possibility (Henry pointing to the real barn in a façade environment) the subject fails to know because of the environment he is in, and this environment is actual. So, it seems that the subject’s knowledge here fails in the actual world. With the skeptical paradox the story appears different. There is no immediate negative response to the question of whether the subject fails to know that she has hands. Rather, this response is achieved via the fact that the subject fails to know the falsity of the skeptical hypothesis. Because the subject fails to know the falsity of the skeptical hypothesis, she fails to know that she has two hands. The failure to know does not appear to be as intuitive as it seems to be with the Gettier-example. This response, if tenable, would point to a flaw in my reasoning because it suggests that even though the subject fails to distinguish between the truth and falsity of the proposition believed, she fails to do so, first in the actual possibility (Gettier) and second, in a counterfactual possibility (skeptical hypothesis).

My reply is that the intuition here is misleading. By concentrating on the notion of ‘distinguishability’ we can show this. To capture the problem with the skeptical hypothesis we need to argue that the subject cannot distinguish between the possibility he is occupying (actual) and the possibility asserted by the skeptical hypothesis (Evil Demon, etc.). This type of failure doesn’t seem apparent in the Gettier-problem. There, the subject’s actual world is already such that she cannot distinguish between the truth and falsity of the proposition believed, as opposed to the actual world which we safely assume to be such that the truth of ‘I have hands’ is distinguishable from its falsity. So, the intuition is that Henry’s actuality is knowledge ‘unfriendly’ with respect to barns and façades, unlike the case of the skeptical paradox in which the actual world is knowledge friendly with respect to practically all empirical propositions.  

The source for this intuition is that we have it merely because we assume that the actual world is friendly in terms of our knowledge of many empirical propositions, not because we have proved that it is. Compare this to the assumption that ‘Henry’s perception is reliable with respect to barns and facades’ fails when it is entertained by Henry, the assumption that ‘S is reliable with respect to which world she is in’ fails. The thought can be captured in terms of distinguishability by saying the following: in the Gettier-problem the subject’s world is indistinguishable from the actual world and similarly in the skeptical-hypothesis the subject’s world (actuality) is indistinguishable from that described by the skeptical hypothesis. This entails that the ‘distinguishability’ has to be understood in two ways. One, the truth of the proposition believed is indistinguishable from its falsity (‘I have hands’, ‘X is a barn’). Two, the possibility occupied by the subject is indistinguishable from the possibility described in the Gettier-case/skeptical hypothesis. In the Gettier-case this indistinguishability clause entails that the possibility occupied by Henry is indistinguishable from itself. Hence, by taking into account these two sides of ‘indistinguishability’ the misguided intuition driving the objection can be explained away because it extends to cover the plausibility of the Gettier-counterexample with the same notion that it uses to cover the skeptical argument.

The claim that I have been arguing for is the following. Both the Gettier-counterexample and the skeptical paradox spring from the same source. This source is the inability to distinguish between the world considered as actual and a cleverly formed possible world. A cleverly formed possibility is a possibility where the proposition is indistinguishable from its negation. Therefore, the difference between these problems is, in the sense specified, on the surface level. The difference between the Gettier-counterexample and the skeptical paradox boils down to differences in the use of the same possibility.  Thus, to follow Crispin Wright’s recent thread: “The key skeptical thought is, …, that some of the ways in which circumstances might be cognitively disadvantageous are potentially undetectable.”  This is precisely that also drives the Gettier-problem.

Bibliography

Gettier, Edmund,  ‘Is Justified True Belief Knowledge?’, Analysis, (1963) pp. 121 –123.

Goldman, Alvin ‘Discrimination and Perceptual Knowledge’, The Journal of Philosophy, Vol. LXXIII, no. 20 (1976), pp. 771-791.

Heller, Mark, ‘The Proper Role for Contextualism in an Anti-Luck Epistemology’, Philosophical Perspectives 13, (1999), pp. 115-129

Lewis, David, ‘Elusive Knowledge’, Australasian Journal of Philosophy , (1996), pp. 549 – 567 (p. 549-50)

Sturgeon, Scott, ‘The Gettier-Problem’, Analysis 53.3. 1993, pp. 156-164.

Wright, Crispin,‘(Anti-)Sceptics Simple and Subtle: G.E. Moore and John McDowell’, Philosophy and Phenomenological Research Vol. LXV, No. 2, 2002