Deductive closure principle

2. Justification and relevant alternatives

Fred Dretske (1970) describes a case which appears to be a counterexample to both closure for justification and Closure itself (assuming that justification is a necessary condition for knowledge). Here we see again that the assessment of Closure depends on one’s views about the analysis of the concept of knowledge. At the local zoo, one sees some striped animals in an enclosure marked ‘Zebras’. One’s evidence justifies a belief that these animals are zebras. However, one’s evidence does not count towards their not being cleverly disguised mules (since one would have exactly similar evidence were it a hoax). Therefore, one’s evidence does not justify one in believing the proposition that these animals are not cleverly disguised mules, even though one recognizes (we will suppose) that that proposition is logically implied by the zebra proposition for which one has justification.

A sceptically minded philosopher might well object that it is far from clear that one’s evidence does justify a belief that the animals are zebras. To the extent that one’s evidence does not count against the cleverly disguised mule hypothesis, the sceptic would say, it does not count in favour of the zebra hypothesis.

Dretske sketches a general theory of knowledge which bolsters his appeal to brute intuition about the proper analysis of the zebra case (intuition which might beg the question against scepticism). He holds that when S knows that P in some particular context, there is a range of relevant alternatives (counter-possibilities) to P which is a subset of the set of all alternatives to P. To know that P, it is only required that S be able to rule out the relevant alternatives to P. On this theory, Closure fails, because there will be situations in which S knows that P, knows that R is an alternative to P (knows that not-R is logically implied by P), and yet is unable to rule out R (fails to know that not-R). These are situations in which R is an irrelevant alternative to P.

The main motivation behind the relevant-alternatives theory is to provide a way of blocking the Cartesian sceptical argument. Therefore, we need an account of relevance according to which the sceptic’s bizarre alternatives to ordinary propositions about the external world turn out to be irrelevant. This will make it possible for one to know that one has hands while lacking knowledge that one is not a disembodied brain in a vat. There is little agreement among relevant-alternative theorists on the analysis of the concept of relevance. One view is that an alternative R is relevant with respect to a particular claim to know that P if and only if the objective probability of R meets some specified level. If there are hoaxing zoos in one’s vicinity, then this could render the cleverly disguised mule possibility a relevant alternative in the zebra case. Another view is that alternative relevance is determined by various features of the conversational context in which a knowledge attribution is made (a context which might not include the putative knower). The mentioning of alternatives might be such a contextual feature, so that the brain in a vat alternative can become relevant in a philosophical discussion of knowledge.

It has been argued (Klein 1981) that closure for justification holds even though (as Dretske claims) one’s evidence E may justify a belief that P without justifying a belief of a deduced proposition, such as that one is not in a vat. On this view, even though E does not justify one’s belief that one is not in a vat, one still has an adequate reason for believing that proposition. This is because P itself becomes available as evidence for the deduced proposition, given that E justifies one’s belief that P.