Branden Fitelson (forthcoming) provides counterexamples to Richard Feldman’s principle that Evidence of Evidence is Evidence (EEE). Here’s the principle in its initial (naïve) form:
(EEE1) If E (non-conclusively) supports the claim that (some subject) S possesses evidence which supports p, then E supports p. (Fitelson forthcoming: 1).
Fitelson’s counterexamples to (EEE) work by presupposing the “positive relevance” (i.e., increase-in-probability) notion of evidential support. In footnote 6 he indicates a more substantive principle of evidential support might be wielded in defending (EEE). In this post I want to explore this possibility, specifically in relation to the notion of propositional justification. Consider the following principle of propositional justification:
S is justified in believing that p iff S’s total evidence sufficiently supports p (Neta 2007: 197).
Though there are many issues that could be raised with this formulation of propositional justification, let’s see if a less demanding iteration of the principle could be used to resist Fitelson’s counterexamples to (EEE). Neta’s principle suggests the following notion of evidential support:
(1) E (evidentially) supports p iff S’s total evidence includes E and S’s total evidence (necessarily) supports p.
The counterexample to (EEE1) involves drawing a card c at random from a deck. All the evidence we are given regarding c is as follows:
(E1) c is a black card.
(E2) c is the ace of spades.
(p) c is an ace.
Imagine a guy named John knows what card c is, and the evidence above constitutes all the facts about the case. This means the following is the case:
(2) E1 supports the claim that John possesses evidence (E2) which supports p.
Positive relevance creates a problem for (EEE1) because (E1) doesn’t raise the probability of (p). (E1) alone is probabilistically irrelevant to (p); so, even though (E1) supports (E2), the second conjunct in (EEE1) is false (i.e., E1 doesn’t support p).
How does the counterexample fare under principle (1) instead of positive relevance? John’s total evidence includes (E1), and John’s total evidence (E1 and E2) necessarily supports (p). (E1) alone doesn’t necessarily support (p), but it also doesn’t support (not-p), and when coupled with (E2) it does necessarily support (p). In fact, (E2) entails (p). John’s total evidence might not sufficiently support (p), but his total evidence does necessarily do so. The next iteration of (EEE) runs as follows:
(EEE2) If E1 supports the claim that S possesses evidence E2 which supports p, then the conjunction of E1 and E2 supports p (Fitelson forthcoming: 2).
This seems like the defense I just gave for (EEE1), assuming (1). Didn’t I just claim the conjunction of (E1) and (E2) supports (p)? If so, then, assuming evidential support principle (1), it looks like the next counterexample will sink (EEE2). However, I think (EEE2) and (1) escape unscathed. Fitelson’s counterexample to (EEE2) is about a guy named Joe:
(E1) Joe has a full head of white hair.
(E2) Joe is over 35 years of age.
(p) Joe is bald.