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Gettier problem

DOI
10.4324/9780415249126-P022-1
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DOI: 10.4324/9780415249126-P022-1
Version: v1,  Published online: 1998
Retrieved October 18, 2019, from https://www.rep.routledge.com/articles/thematic/gettier-problems/v-1

2. Defeasibility analyses

Defeasibility analyses of knowing attempt to exploit the insight that specific propositions are true (for example, ‘Nogot owns no Ford’), whose hypothetical inclusion in the set of propositions that one believes would have a negative impact either upon the justified status of the belief or upon the justified status of the proposition that p (see Knowledge, defeasibility theory of). For instance, Peter Klein (1971) advanced the requirement: ‘No proposition is true such that if one were to believe it, then the justification condition would not hold’. We might call such a truth a ‘defeater’ of p. The requirement shows that one fails to know that p in the following case:

  • Tom Grabit’s Twin: One is well-acquainted with Tom Grabit, and clearly sees him steal a book from the library. But in consequently coming to believe that p, ‘Tom stole the book’, one does not realize that t, ‘Tom has an identical twin and that the twin was in the library around the time of the theft’.

Similarly, if in the two variants of the Nogot case mentioned above one were also to have the true belief that not-f, then one would not be justified in believing that p.

But here we encounter the difficulty of avoiding Gettier-type cases without creating further problems, one such problem being the generation of non-Gettier-type counterexamples. Klein’s defeasibility analysis faces this difficulty concerning a variant of the Tom Grabit case as it was originally described by Keith Lehrer and Thomas Paxson (1969) – one indeed knows that p but does not realize that t: ‘Tom’s mother has testified to police that f: “Tom has an identical twin and was miles away from the library at the time of the theft”’, and that t′: ‘The twin is not real and Mrs Grabit is lying’. If one were merely to come to believe the misleading evidence that t without also coming to believe the truth that t′, one would not be justified in believing that p.

In response, Klein (1981) deepened the defeasibility approach by requiring, roughly, that the combination of a defeater (such as t) with S’s evidence should not remove S’s justification for believing p, essentially through justifying S in believing a false proposition (such as f). But the resulting analysis of knowing is too weak to deal with a variant of the Nogot case in which (1) after coming to believe that n: ‘Nogot owns a Ford’, S sees, as luck would have it, a true sentence expressing a disjunction, d, which, unsuspected by S, is such that any defeater of n entails one or another disjunct of d that S is not presently justified in believing; (2) on the basis of believing that n, S comes to believe that p: ‘n or d‘; (3) it is true that n because Nogot is lucky enough to win a Ford in a raffle while in the company of S. Defeaters of n fail to be defeaters of p, since they support its second disjunct. Yet there need be no other truths that defeat p. So Klein does not show why S fails to know that p.

Perhaps this case of Lucky S and Lucky Nogot could be handled by a sufficiently clarified defeasibility condition inspired by John Barker’s (1976) concern with the fact that there may be other truths, which, when combined with a defeater of p and with S’s evidence for p, restore S’s original justification for believing p. (Yet Klein’s 1981 work pointed out that restoring evidence may be too easy to come by, for example, exact specifications of nearby lookalikes whose nearness should deny knowledge – such as a real twin in a variant of the Grabit case; see also the case of the Back-Up Volcano in Shope (1981).)

In a sophisticated defeasibility account, Barker’s perspective is extended by John Pollock (but in a fashion that may fail to handle the case of Lucky S and Lucky Nogot). Pollock (1986) focuses on the justification for the statement that p which is provided by an argument whose premises are drawn from the reasons forming one’s basis for believing that p. He defines the defeat of such an argument by a set, S, of propositions as a situation where: (1) one has the reasons in question and it is logically possible for one to become justified in believing that p on the basis of those reasons; and (2) one believes the members of set S, where S is consistent with the proposition that p and is such that it is not logically possible for one to become justified in believing that p on the basis of the combination of one’s present reasons and the members of S. As a condition of one’s knowing that p, Pollock proposes that the rational presumption in favour of believing that p created by reasons drawn from one’s present reasons for believing that p is undefeated by the set of all truths. Pollock appears to be requiring that the following conditional proposition, R, must be true: ‘If one were to retain one’s present reasons for believing that p and were to believe the members of the set of all truths, then one would be justified in believing that p on that basis’. Thus, one lacks knowledge in the original Nogot case because of the inclusion of the proposition that Nogot owns no Ford in the set of all truths. In contrast, one succeeds in knowing in the case of the lying Mrs Grabit thanks to the inclusion in the set of all truths of the proposition that t′ (Plantinga 1993a gives fuller exposition).

Some examples of introspective knowledge are a challenge for defeasibility theories and Pollock (1992) seeks to handle them by treating conditionals as true when they have logically or metaphysically impossible antecedents. For instance, when one knows that p: ‘I believe that f‘, one’s reasons for believing may include the presence of the introspected state, one’s believing that f. Suppose that one does not realize that it is false that f. At least for some instantiations for ‘f‘, the antecedent of Pollock’s conditional involves the impossible situation of retaining one’s reason, that is continuing to believe that f, while also believing that not-f – since the proposition that not-f belongs to the set of all truths. (In contrast, Klein needs here to maintain the less-than-obvious claim that S’s believing the conjunction ‘Not-f and S believes that f’ justifies S’s believing that S believes that f.)

But Pollock’s treatment of conditionals as being true when they have impossible antecedents opens his analysis to non-Gettier-type counterexamples concerning one’s coming to believe that one is in a particular mental state through inference from false beliefs rather than through introspection. On the basis of a justified but imperfect psychological theory, I may justifiably believe the following two propositions that I do not realize are false – f 1: ‘Everyone has memories of early childhood’, and f 2: ‘Everyone who has memories of early childhood believes everyone to have memories of early childhood’. On this basis I come justifiably to believe the true proposition that b: ‘I believe that f 1‘. Pollock’s account incorrectly entails my knowing that b, since it will be impossible for me to retain my reasons for believing that b while adding the true beliefs that not-f 1 and that not-f 2.

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Citing this article:
Shope, Robert K.. Defeasibility analyses. Gettier problem, 1998, doi:10.4324/9780415249126-P022-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/thematic/gettier-problems/v-1/sections/defeasibility-analyses.
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