Other Theories of Knowledge
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In Section 4.4,1 argued that any plausible theory of knowledge must include conditions that guarantee truth. Truth should not be tacked on as a further condition. This must be so in order to avoid the Gettier problem. I also argued that no internalist condition on knowledge could provide the necessary guarantee of truth. The only way that the truth of a belief can be assured is by a connection between fact and belief. In Chapters 4 and 5, I defended the claim that it is a causal link (more precisely, a k-causal connection) that is needed to make that connection. In this chapter, I examine alternative theories of knowledge that suggest a different sort of connection between fact and belief. In each case, I discuss whether or not the proposed connection is a necessary condition for knowledge and compare it with the k-causal condition.1 I then discuss, putting objections to the particular theory to one side, whether or not the proposed connection allows knowledge of platonic objects.
KeywordsActual World Mathematical Knowledge Causal Power Mathematical Proof Brain State
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- 1.This discussion draws on material in Cheyne (1997a).Google Scholar
- 2.Nozick discusses all examples in terms of a possible-worlds analysis. It does not appear that his account would fare any better under alternative analyses.Google Scholar
- 3.The conditions need to be amended so as to fix the method of belief acquisition across the relevant counterfactual situations (Nozick 1981, p. 179), but my criticisms do not depend on this point.Google Scholar
- 4.If F is an essential property of a, then it will not be possible for a to be not-F, but it will still be possible for a not to exist.Google Scholar
- 5.He could just as easily have claimed that (T1) is vacuously met in such cases, as this would seem to fit with a possible-worlds analysis. If p is necessarily true, then p is true in all possible worlds. So it is not the case that S believes that p in the closest worlds in which p is not true, because there are no such worlds.Google Scholar
- 6.Fumerton (1987, p. 179) points out that (T2) is insufficient because someone determined to believe all mathematical propositions presented to him would satisfy (T2) for those which are true.Google Scholar
- 7.Armstrong restricts p to states of affairs in which some individual a has some property F (p. 170), but this will not affect my comments or criticisms.Google Scholar
- 8.Goldman offers his example as a counterexample to the sufficiency of Armstrong’s account, but that is not relevant here.Google Scholar
- 9.He states that ‘if B raises the probability of A, then the ratio of close worlds in which A obtains is higher in the set of worlds in which B obtains than in the entire set of worlds’ (p.26)Google Scholar
- 10.David-Hillel Ruben (1990) argues that non-causal, but metaphysically real, relations (in particular identity and part-whole relations) may be cited in an explanation (pp.209–33). But, in the context of knowledge conditions for beliefs, causal theorists will accept that causal connections may be extended by such relations. See also my Section 6.4.Google Scholar
- 11.Adapted from Pappas & Swain (1978, pp. 27–28). See also Lehrer & Paxson (1969).Google Scholar