Whereas Keith Lehrer (1974) has argued in favor of a holistic positive coherence theory of justification, John Pollock and Joseph Cruz (1999) have criticized Lehrer's theory by suggesting that the basing relation fails to distinguish between having reason for believing something and believing something for a reason. This post's aim is threefold. First, I will offer an outline of Lehrer's theory as Pollock and Cruz see it. Then, I will explore the criticism Pollock and Cruz level against Lehrer's theory. Finally, I will attempt to provide a possible rejoinder to the criticism on behalf of Lehrer.
Lehrer's Holistic Positive Coherence Theory of Justification
Lehrer's holistic positive coherence theory states that a belief p for an agent S is justified if and only if S believes
that p is more probable than any other belief that competes with p. The beliefs that compete with p include not only those beliefs that are incompatible with p but also those beliefs that are logically consistent with p. Lehrer bases this consideration on the lottery paradox. Suppose that S holds a ticket in a lottery. S believes that some ticket in the range 1-1,000 will be drawn, but believes that her ticket will not be drawn. S can consistently hold for any - and therefore every - particular ticket in the range 1-1,000 will not be drawn. It follows that S knows that no ticket in the range 1-1,000 will be drawn. This contradicts S's original belief that ``some ticket will be drawn.'' Lehrer presumes that one cannot be justified in holding inconsistent sets of beliefs. So, Lehrer must formulate a definition of "competition" that will yield for S that she is not justified in believing that any ticket will not be drawn in the lottery paradox.
Lehrer's definition of "competition" is that "any belief p competes with another belief q if and only if S believes q to be negatively relevant to p" (Lehrer 1974, p. 76). That q is negatively relevant to p means that the probability of p assuming that q is true is less than the probability of p without that assumption. This definition of competition will, in turn, resolve the lottery paradox. For any given ticket not being drawn will raise the probability of any other ticket being drawn.
Pollock and Cruz's Criticism of Lehrer's Theory
Pollock and Cruz argue that Lehrer's theory suffers from a problem of the basing relation. The basing relation distinguishes between having good reason for believing something and believing something for a good reason, which is somewhat equivalent to the distinction between a justifiable belief and a justified belief. According to Pollock and Cruz, "any correct epistemological theory must allow this distinction (Pollock and Cruz 1999, p. 79) They believe that Lehrer's positive holistic coherence theory fails to be compatible with this distinction.
Pollock and Cruz argue that the basing relation is at least partly causal. In order for someone to be justified in holding a belief on a certain basis, the belief should arise out of that basis in
some appropriate way. Pollock and Cruz do not believe that this is possible for those who hold a holistic positive coherence theory. They believe that the notion of justified belief will not make sense within such a theory unless the coherence relation accounts for "the belief's cohering with one's overall doxastic system can cause one (in an appropriate way) to hold the
belief" (Pollock and Cruz 1999, p. 79). It follows that the coherence relation must be "appropriately causally efficacious" in the formation of belief.
There are only two possibilities of belief formation for the person who advocates a holistic positive coherence theory. On the one hand, the causal chain might be "doxastic." S may at first come to believe that p coheres with her other beliefs and then S comes to believe p on that basis. Pollock and Cruz reject this characterization of belief formation since we do not
ordinarily have any such beliefs about coherence, and such an account leads to an infinite regress. On the other hand, it could be possible that the causal connection in the basing relation causes a belief in p without the believer having any beliefs about whether p coheres with his other beliefs. Pollock and Cruz reject this since it seems implausible that the
coherence relation is such that p's cohering with S's other beliefs can cause belief in a nondoxastic way.
Pollock and Cruz conclude that "it seems that coherence relations will always involve elaborate logical relationships between beliefs, and the holding of such relationships can only be causally efficacious by virtue of one's coming to believe that the relationships hold" (Pollock and Cruz 1999, p. 80). It is unlikely that any holistic coherence relation can be
appropriately causally efficacious in belief formation to allow the distinction between justified and merely justifiable beliefs. This seems to provide a "strong reason" and "at least suggests the rejection of" all positive coherence theories, especially Lehrer's holistic positive coherence theory of justification.
Rejoinder on behalf of Lehrer
The criticism that Pollock and Cruz raise against Lehrer calls for the basing relation to be "appropriately causally efficacious." They define the basing relation in this way: "A belief p
is a reason to believe q if and only if it is logically possible for S to become justified in believing q by believing it on the basis of p. (Pollock and Cruz 1999, p. 35). Built into this
definition of a basing relation is the notion of cause and effect. In this case, S's believing q is caused by the base belief: p. Such a causal notion of the basing relation presumes a sort of linear theory that Lehrer may not be willing to accept. In coherence theories, beliefs are not justified by other beliefs, but they are justified by playing an important role within the total system of beliefs. This is especially true of holistic coherence theories like Lehrer's.
Holistic positive coherence theories assert that a justified belief is determined by its relationship to all other beliefs in a way that cannot be decomposed into linear reasons. We
could analogize holistic coherentism with a three-dimensional web, such as a spider's web, in which each belief is a connecting node, held together by other beliefs. Each belief receives justification from many other kinds of propositions. This requires that our belief system function as a whole and provides the best explanation of the relevant beliefs, holistically.
Pollock and Cruz criticise Lehrer's theory because it fails to distinguish between having reason for believing something and believing something for a reason. If the basing relation is at least partly causal as Pollock and Cruz seem to suggest, then Lehrer must relinquish his holistic theory. It seems that Pollock and Cruz have confused the causal role of beliefs with their justificatory role. When they claim that the basing relation is at least partly causal, they seem to equate a belief's causal role with a belief's justificatory role. For Lehrer, one
cannot equate the causal role with the justificatory role of a belief. A belief p may justify another belief q for S, even though we cannot say that p caused S to believe q. It may be the case that p caused S to believe q, but it need not be so for S to be justified in believing q. Pollock and Cruz have collapsed an important distinction that make it appear Lehrer's theory fails to distinguish between a justifiable belief and a justified belief, but this is not the case if we distinguish between a belief's causal and justificatory role.