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Deductive closure principle

DOI
10.4324/9780415249126-P011-1
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DOI: 10.4324/9780415249126-P011-1
Version: v1,  Published online: 1998
Retrieved April 18, 2024, from https://www.rep.routledge.com/articles/thematic/deductive-closure-principle/v-1

3. Closure and reliabilist theories of knowledge

Let us consider the reliabilist approach to the analysis of the concept of knowledge, according to which knowing that P is a matter of having a reliably produced true belief that P. On many such accounts, the justification condition for knowledge is either analysed as, or replaced by, a reliability condition (see Reliabilism). Whether Closure fails on such an analysis depends on how reliability is conceived. On one conception (Goldman 1976), in order for S’s belief that P to count as reliably produced, S must be able to discriminate the actual situation in which P is true from those relevant possible situations in which P is false. This is close to the relevant alternatives theory, and Closure will accordingly fail. If a possible situation in which P is false and S is envatted is not a relevant one, then S can know that P without being able to discriminate the actual situation from the one in which S is envatted. Now consider S’s claim to know the logically implied proposition that S is not envatted. A possible situation in which S is envatted is plausibly regarded in this case as a relevant alternative possibility. Since, as we assumed, S is unable to discriminate the actual situation from a vat situation, it follows that S does not know that S is not in a vat. Thus Closure fails, since S can know that P without knowing that S is not envatted.

Reliability is sometimes conceived as having an explicitly counterfactual dimension. For example, Robert Nozick’s (1981) ‘tracking’ analysis of knowledge contains this counterfactual condition: if P were false, then S would not mistakenly believe that P. Suppose that S claims to know that S is sitting, on an occasion when S is sitting in a perfectly normal environment. If S were not sitting, then, presumably, S would be standing, or lying down, or the like. In such a counterfactual circumstance, S would not mistakenly believe that S is sitting. So S’s claim to know that S is sitting satisfies Nozick’s counterfactual condition (as well as the other conditions for knowing, we may suppose). Now consider S’s claim to know the logically implied proposition that S is not in a vat. If S were in a vat, then, presumably, S would mistakenly believe that S is not in a vat. So S does not satisfy the counterfactual condition for knowing that S is not in a vat. Thus on the present analysis, S knows that S is sitting but fails to know that S is not a brain in a vat.

According to an alternative counterfactual conception of reliability, whether a belief that P is reliably produced does not necessarily depend on what one would believe in counterfactual circumstances in which P is false. Instead, we focus on the process which issues in the belief. A belief-forming process will count as reliable just in case the process actually yields a sufficiently high ratio of true beliefs and also would yield the required ratio in counterfactual circumstances similar to one’s actual circumstances (which might not include circumstances in which P is false). Closure will hold on this version of reliabilism. Suppose that one forms the correct belief that one has hands via an ordinary perceptual process. Then one forms the further belief that one is not disembodied in a vat, via the belief-forming process of deductive inference. This inferential belief issues from a process that is obviously reliable in the sense under consideration. Thus if the original belief issues from a process which is reliable in that sense and therefore amounts to knowledge, then so will the inferential belief.

In the end, we see that even though the denial of the closure principles we have discussed would aid in the refutation of scepticism, whether these principles hold is a controversial matter which depends on the nature of knowledge and justification.

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Citing this article:
Brueckner, Anthony. Closure and reliabilist theories of knowledge. Deductive closure principle, 1998, doi:10.4324/9780415249126-P011-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/thematic/deductive-closure-principle/v-1/sections/closure-and-reliabilist-theories-of-knowledge.
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