Hardwig (Reference Hardwig1985, Reference Hardwig1991) maintains that our epistemic reliance on experts is typically blind, in the sense that when we acquire reasons to believe a proposition P because an expert asserts P, we typically don't know, and often couldn't possibly know, the evidence that the expert has for P. Consider for instance an expert EXP and a proposition P about facts within her expertise domain. (EXP could be an astrophysicist and P a hypothesis about black holes.) Take the proposition:

Also consider a layman, or an expert in an area different from EXP's, LAY. According to Hardwig, in ordinary contexts, E is for LAY evidence for the proposition:

And this is so even if the evidence that LAY would think EXP has for P were unknown or – because of LAY's lack of appropriate training and skills – inaccessible and even ungraspable to LAY. (Cf. Hardwig Reference Hardwig1985: 339 and 1991: 699). Hardwig claims that LAY's learning E can give LAY reasons for believing P and, provided P is actually true, LAY's learning E can also make LAY know that P.Footnote ¹ I find these propositions prima facie plausible, so I will grant them.

Hardwig claims, however, that E itself ‘does not constitute evidence for the truth of P. For [LAY's] reasons for believing that P are not evidence for the truth of P’ (1985: 337), where evidence for P is ‘anything that counts towards establishing the truth of P’ (336). Succinctly, according to Hardwig:

Hardwig is certainly right in claiming that our reliance on experts is typically blind in the sense explained at the beginning of this paper. I doubt, however, we should assent to Hardwig's more radical thesis (NE), according to which an expert's testimony that P doesn't generally count as evidence for P for a non-expert hearer. In this paper, I first show that (NE) engenders tensions within Hardwig's overall view of epistemic reliance on experts and makes it imply unpalatable consequences. Then, I make a case against (NE) that exploits an important result of Bayesian epistemology. I concede that Hardwig could still hold to a precisification of (NE) in the face of my Bayesian criticism. I argue, however, that this precisification, while reducing the philosophical relevance of (NE), wouldn't resolve tensions internal to Hardwig's views.

Before proceeding, let me suitably restrain the application domain of (NE). Reflexive predictions are those that directly cause or contribute to cause the truth (or falsehood) of what they predict (cf. Romanos Reference Romanos1973). Reflexive predictions are quite common in social sciences. Here is an example: consider the proposition that (P’) the stock market is about to enter a bearish period (i.e. a period of falling prices). Imagine that expert EXP’, a leading financial economist, publicly asserts P’. Also suppose that LAY learns that:

Ordinarily, E’ counts for LAY as evidence for the proposition that:

It is a well-known fact that if suitable boundary conditions are satisfied (perhaps the existence of enduring economic instability), a public statement like the one made by EXP’ can on its own cause stock prices to fall. It is thus hard to deny that E’ is for LAY also evidence for P’ when LAY knows that the boundary conditions are satisfied. For learning E’, in this case, is for LAY something that counts towards establishing the truth of P’. It would be uncharitable, however, to take examples like this to constitute falsifications of (NE). For Hardwig didn't certainly intend to apply (NE) to cases in which there is a special evidential link between E and P known by LAY.

Note that reflexive predictions are absent in natural and (pure) mathematical sciences, for the predictions of experts in these sciences generally don't cause or contribute to cause the truth or falsehood of their contents. Considering this, to avoid unnecessary complications, let me simply stipulate that P in (NE) is a placeholder for propositions of natural or mathematical sciences only.

Even so restrained (NE) still looks problematic. An immediate problem is that in epistemology and everyday life, testimony – whether a layman's testimony or an expert's testimony – is normally taken to be a source of evidence.Footnote ² Thus (NE) is prima facie at odds with both mainstream epistemology and common sense.Footnote ³ There are subtler problems. As Almassi (Reference Almassi2007: 62–5) has argued, (NE) seems to make Hardwig's overall view of epistemic dependence on experts internally incoherent.Footnote ⁴ In brief, Hardwig himself emphasizes that scientists are very often epistemically dependent on other scientists just as laymen are. In science, because of lack of time or competence, any given expert EXP will in very many cases rely on the testimony of some other expert EXP* to acquire reasons to believe some proposition P. EXP*'s testimony that P will in turn rationally enable EXP to testify that P to some other subject LAY (cf. Hardwig Reference Hardwig1985: 345–8.) Thus, if (NE) is correct, in very many cases in which EXP testifies that P to LAY, EXP won't have evidence for P. For EXP's reasons to believe P are only testimonial. This is in tension with Hardwig's claim that when LAY learns E – i.e. receives EXP's testimony that P – LAY normally acquires evidence that (K) EXP has evidence for P. If (NE) is true, this claim by Hardwig is presumably false.

Hardwig might try to settle this conflict by partly revising his view – precisely, by claiming that when LAY learns E, LAY thereby acquires evidence for K only if LAY knows that EXP's testimony that P is based on EXP's autonomous research. However, this wouldn't solve all problems. Consider in fact that in many of the cases in which LAY relied on EXP's testimony that P, as a result of LAY's unfamiliarity with EXP's field or lack of relevant information, LAY could not discern whether or not EXP's testimony is based on EXP's autonomous research. And in many others of these cases, LAY could easily conclude that EXP's testimony is not based on EXP's autonomous research.Footnote ⁵ Hence, it seems plausible that in very many of the cases in which LAY relied on EXP's testimony that P, LAY would not have evidence for K. Note that these cases are presumably situations in which LAY would rationally rely on EXP's testimony. In spite of this, Hardwig contends that what makes LAY's reliance on EXP's testimony that P rational is in general the fact that LAY has good reasons to believe that EXP's opinion about P is more trustworthy than her own (cf. 341) because LAY has evidence for K (that is to say, because LAY ‘has good reasons to believe that [EXP] has conducted the inquiry necessary to have evidence for believing that P’; 337, my emphasis). Thus Hardwig's view would still be incoherent, for his general explanation of the rationality of our reliance on experts would be incoherent. It is clear that if Hardwig simply dropped (NE), these problems would all vanish.

Rejecting (NE) would block another unpalatable consequence of Hardwig's view of epistemic dependence (one that Almassi Reference Almassi2007 doesn't discuss). Hardwig himself acknowledges that claiming that EXP knows that P Footnote ⁶ on the basis of a reason for believing P that constitutes no evidence for P is ‘paradoxical and counterintuitive’ (Reference Hardwig1985: 345). Assenting to this claim, according to Hardwig, ‘would require dramatic changes in our analysis of what knowledge must be’ (348–9). Nevertheless, Hardwig (Reference Hardwig1985: 348 and Reference Hardwig1991: 699) insists that we should very probably assent to it once we realize that reliance on expert fellows with regard to matters of knowledge is a pervasive phenomenon within the scientific community. Precisely, Hardwig emphasizes that any given scientist EXP will typically be able to produce fresh knowledge only by relying on some antecedent knowledge that P acquired through the testimony that P from some other scientist EXP*. Given (NE), this seems to imply that scientists typically know many propositions without evidence for them (cf. Hardwig Reference Hardwig1985: 345–8). Hardwig concedes that an alternative conclusion that we might prefer to draw is that when a proposition is known, it is known by, not individuals singularly considered, but a community of individuals as a whole. This would allow us to stick to the intuition that the knower that P – i.e. a scientific community as a whole – does possess evidence for P (cf. Hardwig Reference Hardwig1985: 349). Nevertheless, this alternative conclusion would also require revising the ordinary notion of knowledge, which attributes knowledge primarily to individuals rather than communities. If Hardwig dropped (NE), his views of epistemic dependence would require no change in our standard assumptions about knowledge.

Hardwig (Reference Hardwig1985: 336–7) offers a few arguments in favour of (NE) – arguments aiming to show that E doesn't actually count towards establishing the truth of P.Footnote ⁷ Hardwig contends, for instance, that E doesn't make the case for P stronger (cf. 337), and that ‘truth claims cannot be established by an appeal to authority, nor by investigating what other people believe about them’ (337). Almassi (Reference Almassi2007: 59–62) has given good reasons to think that Hardwig's arguments in favour of (NE) are inconclusive. Rather than dissecting Hardwig's arguments once again, I prefer to make a more direct case against (NE), one to the effect that (NE) turns out to be normally false when quite natural formalizations of epistemic notions that Hardwig would seem to presuppose are put into operation. My argument deploys Shogenji-Roche theorem of transitivity of incremental confirmation (see Shogenji Reference Shogenji2003 and Roche Reference Roche2014).

As we have seen, Hardwig explicitly characterizes the notion of evidence for P used in (NE) as ‘anything that counts towards establishing the truth of P’. Let's call evidence ₁ any proposition that, if learned by a subject, would count for that subject towards establishing the truth of another proposition. The informal notion of evidence₁ naturally translates into the Bayesian notion of incremental confirmation. Let's assume, accordingly, that for a subject SUB, X is evidence₁ for Y just in case the degree of SUB's rational credence in Y (interpreted as subjective probability) would increase if SUB learned X. Succinctly:

Arguably, Hardwig (Reference Hardwig1985) also makes use of a different notion of evidence. Hardwig typically deploys the expression ‘good reasons to believe P’ to refer to EXP's evidence for P. It appears rather plausible, therefore, that when Hardwig claims that (K) EXP has evidence for P, he intends to say that EXP has evidence sufficiently strong to sustain her (plain or outright) belief in P. Let's call evidence ₂ any proposition that, if learned by a subject, would rationally sustain the subject's belief in another proposition. The informal notion of evidence₂ naturally translates into the Bayesian notion of absolute confirmation. Let's assume, accordingly, that for a subject SUB, X is evidence₂ for Y just in case the degree of SUB's rational credence in Y would exceed an appropriate threshold value t (intuitively, the one certifying plain belief), if SUB learned X. Succinctly:

Consider now the following conjunction:

(i) says that provided that SUB knows that Y is true, SUB's degree of credence in Z would not drop if SUB learned that X is also true. (ii) says that provided that SUB knows that Y is false, SUB's degree of credence in Z would not drop if SUB learned that X is true. Roche (Reference Roche2012) generalizes an important proof by Shogenji (Reference Shogenji2003) and shows the following theorem of transitivity of incremental confirmation:

Incremental confirmation is known not to be transitive, in the sense that the conjunction of (1) and (2) alone (i.e. without any additional assumption such as (C)) is known not to entail (3). (TR) describes a special case in which incremental support is transitive: if (C) is added to (1) and (2), then (3) follows.

Roche (Reference Roche2014) gives an example in which a subject SUB's evidence₁X for the proposition that (Y) another subject has evidence₂ for Z is, for SUB, also evidence₁ for Z because (1), (2) and (C) in (TR) are satisfied. In Roche's example X doesn't describe an expert's testimony that Z, and not even a testimony.Footnote ⁹ However, Roche's example is suggestive of a counterexample to (NE) that I now detail.Footnote ¹⁰

I will use (EV1), (EV2) and (TR) to show against (NE) that E (the proposition that EXP has asserted P in the role as an expert) is for LAY evidence₁ for P in quite ordinary cases. Let's assume that LAY's background information is the everyday one. Let's also assume that LAY has thought of P for the first time (perhaps because someone has talked to her about P) but that LAY doesn't know whether any expert in the relevant research field has found evidence₂ for P. Now take Pr to represent LAY's degree of credence, and let's replace X with E, Y with K, and Z with P in (TR). It is easy to verify that on the above assumptions, (1), (2) and (C) prove all intuitively true after the replacements.

To begin with, since LAY doesn't know whether any of the relevant experts has found evidence₂ for K, LAY shouldn't believe K (the proposition that EXP has evidence₂ for P). Given (EV2), it should consequently be the case that Pr(K) ≤ t. It is intuitive, however, that if LAY learned E, her credence in K should lift to the effect that Pr(K|E) > t. For if (E) EXP asserts P in the role as an expert, EXP should presumably believe P. Consequently, it should be the case that (K) EXP has evidence₂ for P. As Pr(K|E) > Pr(K), (1) is true. Note that this conclusion is coherent with Hardwig's claim that, normally, E is for LAY evidence₁ for K.

Consider now that since LAY doesn't know whether any relevant expert has found evidence₂ for P, LAY shouldn't believe P. Given (EV2), it should thus be the case that Pr(P) ≤ t. It is very intuitive, however, that if LAY learned K, LAY should come to believe P to the effect that Pr(P|K) > t. Since Pr(P|K) > Pr(P), (2) is also true.Footnote ¹¹

Consider now (i) Pr(P|E & K) ≥ Pr(P|K). This inequality intuitively says that E (the proposition that EXP has asserted P) is not a defeater of LAY's degree of credence in P based on K. For, according to (i), if LAY learned E after learning K, her credence in P should not decrease.Footnote ¹² If P were a proposition of social sciences, EXP's assertion that P might have a bearing on P's likelihood, thus E might turn out to be a defeater of LAY's degree of credence in P based on K. We have excluded, however, that P is a proposition of social sciences. When P is a proposition of natural or mathematical science – like in the present case – it is intuitive that E is not a defeater of LAY's degree of credence in P based on K. E could become such a defeater if LAY were provided with apposite background information, but this background information would be different from the everyday one, which we have assumed to be that of LAY.Footnote ¹³ Thus, (i) is also true.

Consider finally (ii) Pr(P|E & ~K) ≥ Pr(P|~K). It looks very plausible that if LAY learned that K is false, the degree of LAY's credence in P shouldn't decrease even if LAY also learned E. Again, if P were a proposition of social sciences, EXP's assertion that P might have a bearing on P's likelihood; thus LAY's learning E might lessen LAY's credence in P based on ~K. But we have excluded that P is a proposition of social sciences. Therefore, (ii) is true. As both (i) and (ii) are true, (C) is true.

Since (1), (2) and (C) are true, it follows through (TR) that (3) Pr(P|E) > Pr(P). This implies, via (EV1), that E is for LAY evidence₁ for P.Footnote ¹⁴

To summarize, suppose that: the notions of evidence₁ and evidence₂ are explicated in terms of respectively (EV1) and (EV2), P is a proposition of natural or mathematical sciences, and LAY initially relies on ordinary background information without knowing whether any expert has found evidence₂ for P. When these conditions are satisfied, E is for LAY evidence₁ for P. This result disproves (NE). For it shows that there are quite ordinary cases in which EXP's testimony that P is for LAY evidence for P in the sense of counting towards establishing the truth of P.

Before concluding, let me consider a possible response to my Bayesian objection. This response naturally stems from the suggestion by Hardwig – mentioned above – to ascribe knowledge to a scientific community as a whole, rather than individuals, as an option to block counterintuitive consequences of (NE).Footnote ¹⁵ In short, Hardwig could first emphasize that the expression:

1. (I1) Anything [X] that counts towards establishing the truth of P,

2. used by him to characterize the notion of evidence, has (at least) two legitimate precisifications. Namely:

3. (I2) Anything X that counts towards establishing the truth of P for a given individual;

4. (I3) Anything X that counts towards establishing the truth of P for a given community as a whole.

Let's say that when (I1) is precisified into (I2), X qualifies as individual-focused evidence for P. This seems to me to be the general notion of evidence most commonly presupposed in philosophical and non-philosophical discussions involving epistemic assessments. Let's also say that when (I1) is precisified into (I3), X qualifies as community-focused evidence for P. This general notion of evidence doesn't appear to be as widely used as the former.Footnote ¹⁶ In this case X is conceived of as a piece of information given to an epistemic community taken as a whole. Consequently, the testimonial exchanges within the epistemic community are thought of as trading in, not evidence, but only reasons to believe propositions. These exchanges are thought of as capable of spreading over the individuals of the community only – so to speak – the rational force of the evidence given to the community as a whole. It would seem to follow from this characterization that a proposition X satisfies (I3) only if X is not the testimony that P.

After telling apart these two general notions of evidence, Hardwig would emphasize that my Bayesian formalization interprets (I1) specifically as (I2). Thus the general notion of evidence actually regimented by (EV1) and (EV2) and presupposed in my Bayesian objection is just one of individual-focused evidence. Hardwig would also claim that, in contrast to this, he interprets (I1) specifically as (I3) when he discusses epistemic dependence on experts. Hence, in that context, he presupposes the notion of community-focused evidence. Hardwig would conclude from this that the precisification of (NE) that he actually endorses – stating that for LAY,Footnote ¹⁷EXP's testimony that P is not community-focused evidence for P – is actually true. Hardwig would also emphasize that my Bayesian objection cannot affect this conclusion. For my objection actually targets a distinct precisification of (NE) – the one that states that for LAY, EXP's testimony that P is not individual-focused evidence for P.

Let's assess this possible response. If Hardwig distinguished between the two alternative precisifications, (I2) and (I3), of (I1) and endorsed just (I3) while discussing epistemic dependence on experts, the precisification of (NE) that he would accept would actually be true. Furthermore, it seems correct to say that my Bayesian objection should properly be interpreted as presupposing the alternative precisification (I2) of (I1). Thus my objection would actually be irrelevant to whether or not Hardwig's accepted precisification of (NE) is true.

Although this outcome might appear very important, note – to begin with – that it wouldn't help Hardwig resolve the tensions afflicting his overall view of epistemic reliance on experts. Consider in fact that in very many cases in which EXP testified that P to LAY, EXP wouldn't have community-focused evidence for P. For EXP's reasons to believe P would be just testimonial. This would clash with Hardwig's (precisified) claim that when LAY receives EXP's testimony that P, LAY typically acquires community-focused evidence for believing that EXP has community-focused evidence for P. Hardwig could try to settle this conflict by claiming that when LAY receives EXP's testimony that P, LAY thereby acquires community-focused evidence for believing that EXP has community-focused evidence for P only if LAY knows that EXP's testimony is based on EXP's autonomous research. However, there would presumably be very many cases in which LAY would rationally rely on EXP's testimony that P without having that knowledge. This would conflict with Hardwig's (precisified) explanation of the rationality of relying on the testimony of experts. As this explanation says that what makes LAY's reliance on EXP's testimony that P rational is, in general, the fact that LAY has community-focused evidence for believing that EXP has community-focused evidence for P. These wouldn't probably be lethal difficulties for Hardwig's view. However, Hardwig should work a bit to render it internally coherent.Footnote ¹⁸

A more serious drawback of this possible response by Hardwig is that it would turn (NE) into a much less interesting thesis. Suppose first that the general notion of evidence to which (NE) is meant to apply were characterized in terms of (I1) without any further precisification, in agreement with my interpretation of it in the first part of the paper. This characterization would be so generic that it would probably include any notion of evidence in use in philosophical and non-philosophical contexts. So interpreted, (NE) would have quite significant consequences. For instance, (NE) would presumably entail that ordinary and apparently innocent statements such as ‘the testimony by expert EXP supplies strong evidence for P’ – made in, say, courts of law – are in fact literally false. By the same token, (NE) would entail that whenever epistemologists assert that some expert's testimony that P is evidence for P, they assert the false. So interpreted, (NE) would be a very surprising and indeed revolutionary thesis. If true, (NE) would bear great philosophical importance.

Now suppose that (NE) were precisified through (I2), to apply only and specifically to community-focused evidence in accordance with Hardwig's possible response to my Bayesian objection. In this case the truth of (NE) would have no consequence for any claim to testimonial evidence that presupposed a distinct notion of evidence. For instance, if this precisification of (NE) were true, expert's testimony would still count as evidence in the Bayesian sense regimented by (EV1), which has quite a wide application range in formal epistemology. Another way to describe this drawback is the following: as emphasized before, expert's testimony is customarily claimed to be evidence in mainstream epistemology and everyday life. The truth of (NE) would disprove these claims only if the subjects making them intended by ‘evidence’ specifically community-focused evidence. But this is presumably false in the largest majority of the cases. In conclusion, if (NE) were interpreted as applying to just community-focused evidence, (NE) would be bereaved of most of its philosophical relevance. Pursuing this defence strategy would probably result in nothing but a Pyrrhic victory.Footnote ¹⁹