Evidence

In what follows I will point to a problem in Jonathan Schaffer’s conception of evidence given his contrastive epistemology. I will outline Schaffer’s substantive epistemic conditions, followed by an argument which points to certain implications of Schaffer’s theses amounting to an account of evidence which is factive. This factivity of evidence is problematic, however, as the conditions on evidence are weaker than those on knowledge.

Schaffer provides several substantive theses for his contrastive execution of the contextualist proposal that knowledge is the elimination of relevant alternatives. Specifically, Schaffer proposes three necessary and sufficient conditions for knowledge:

(K) Kspq iff:

1. p,
2. S has proof that p rather than q,
3. S is certain that p rather than q on the basis of (2).¹

The first condition states that knowledge is factive, or logically stronger than truth. In this case, then, the entailment Kspq→p holds. The second condition is Schaffer’s interpretation of a justification condition, one which he calls restricted infallibilism about evidence. Proof, so defined by Schaffer, is conclusive evidence, evidence defined in terms of Lewisian elimination:

(Elim) possibility p is eliminated for S (at t) iff p is inconsistent  with S’s total experience e (at t). S has conclusive evidence that p rather than q, on this interpretation, iff q is eliminated for S.²

This infallibilism is restricted, however, in terms of the context partition ∏, where the space of eliminable possibilities are just those ‘live options’ relevant to the conversation. The final condition is that of belief with the addition of a basing clause, what Schaffer terms restricted indubitabilism about belief. One’s belief must be indubitable in that one must be certain, or lack any doubt, of p’s truth. Further, it must be properly based, which is a causation-rationality hybrid:

(Base) S’s proof must be a rationalizing, non-deviant cause of S’s certainty.³

This condition is restricted in the same fashion as (K.2), where the space of possibilities open to doubt are just those members of the context partition ∏, the possible answers to the question under discussion.

Given that Schaffer relies on a position-to-know closure schema⁴, it would behoove him to sharpen his definition of evidence. Evidence is defined as the ternary relation Espq, which consists in both the elimination of the alternatives q to p and some positive support for p. I assume, from his brief discussion, that evidence also imports all those contrastive qualities previously discussed of knowledge concerning the contrast variable q, and that elimination is defined as previously noted in (K.2) and (Elim). These provisions prompt an additional question, however, as to Schaffer’s commitment to the factivity of evidence. Due to the wording of (K.2) and (Elim), proof of p rather than q consists in S having conclusive evidence, a restricted infalliblism about evidence. This definition needs clarification, as conclusivity could break in one of two directions:

1. Evidence could be conclusive in the objective sense, which would clearly amount to the truth of p, or
2. Evidence could be considered conclusive in the subjective sense, which might be considered as some high level of credence obtained by S.

We must remember here that Schaffer considers evidence as the elimination of salient relevant alternatives to p, and what must be conclusive is not so much the truth of p directly, but the elimination of the context parameter q. Further, there must be some unspecified level of positive support for p. Evidence would then seem to provide support for p indirectly, through the infallible elimination of salient alternatives q.

The use of the term infallible here would seem to point to (1) rather than (2), for if one were to be wrong about one’s elimination of q in the objective sense, one could not consider one’s evidence infallible. If the term used were perhaps a restricted dogmatism about evidence, then perhaps (2) might be tenable. Differently put, (2) would seem to be a misled view of evidence for reasons regarding the level of credence necessary to be committed to the proof of one’s evidence. If the level of credence necessary for proof is to be considered the subjective probability of 1, then one would be committed to a level sufficient to that for which one might rationally bet one’s life on one’s evidence. It is quite difficult to find many contingent propositions that a rational human being would bet one’s life on. As such, to be committed to the proof of the evidence of contingent propositions to the point that it is conclusive would be taking a quite dogmatic stance on one’s evidence.

Given this, it would seem that (1) would be the more appropriate stance considering Schaffer’s comments on evidence. To be clear, however, it is not that the evidence for p is infallible; rather, it is the evidence against q, as the evidence for p may be minimal at best. As such, (1) may be restated as the necessary condition:

1. S has evidence for p if S has established the falsity q.

This condition would commit Schaffer to the inference rule Epq→~q.

This entailment is unsettling. For, if we are to assume, given Schaffer’s contrastive modification of evidence, that p and q are pairwise exclusive for the evidence relation as they are for the knowledge relation⁵, the further entailment must hold: Epq→((p & ~q) v (~p & q)). Putting these together, by conditional proof, provides: Epq→p⁶. And thus evidence is factive. This is a troubling result, as Schaffer does not stipulate the necessity for much, if any, positive support for p. As such, the truth of some proposition p may be obtained simply by the elimination of all salient relevant alternatives to p. The question must be posed to Schaffer, then, regarding the status of contexts in which all but one alternative is eliminable but actuality is not salient. In cases such as these it would seem that one’s evidence would entail the truth of p, even if p is false.

For example, suppose that in a fit of passion, a man, Jim, stabs another, Bob, in an obviously critical fashion, in the midst of a crowded room. The room is populated by both witnesses to the scene as well as police officers. The officers, true to their role, capture Jim and begin interviewing witnesses as to the question of the perpetrator of Jim’s murder. Evidence amounts quickly intimating Jim to the point of the elimination of all salient alternatives to the participants of this particular context. Unbeknownst to anyone in this circumstance, however, Bob has some undiagnosed heart problems; specifically, his health is such that a blood clot stopped his heart just milliseconds before the knife hit, rendering the knife wound epiphenomenal to Bob’s death. As such, direct perceptual evidence of Jim’s attack provides the elimination of those possible alternatives that some other perpetrator might have stabbed Bob, and Bob’s lack of vital signs provide direct evidence of his death. Coupling these pieces of evidence allows for the elimination of all those alternatives to Bob’s murderer other than Jim, with the possibility of Bob dieing of natural causes outside the epistemic range of those involved. This situation, then, provides all that is needed to imply the truth of the proposition p: {Jim is Bob’s murderer}, even though the truth of p diverges from actuality.

Initially, a stipulation along the lines of Lewis’s rule of actuality might seem fitting, where actuality is always relevant, but this rule fails to draw out how exactly actuality would be taken into account in a case such as that of Jim and Bob. In such cases, it would seem the agents within the context would be afflicted by some form of presupposition failure, giving the actuality rule an ad hoc flavor. Further, the way in which the question might be presented within the context could eliminate actuality as a viable member of the answer partition—this could be provided for in the previous example by noting that the police interrogating witnesses provide a lineup and state the question explicitly. When the question is posed in this way, the rule of actuality would contradict a previous stipulation of Schaffer’s, that when the question under discussion has some explicit possible answers, the answers countenanced must be set to the explicit values.⁷