2. HOMOGENEOUS COMPETENCE

The homogeneous competence condition says that each individual's choice C _i is correct with the same probability greater than $\displaystyle{1 / 2}$. However, it is a widely shared opinion that the assumption that a group's members are homogeneous in competence is unrealistic even when we look at standard applications of the CJT. Clearly, the same holds for the application of the CJT I am exploring here, for it seems implausible that individuals really exhibit the same degree of competence, expressed by a probabilistic value, about the epistemic status of Gettiered subjects.

This problem might be solved by adopting a different version of the CJT that allows for heterogeneity. In their seminal Reference Grofman, Owen and Feld1983 paper, Grofman, Owen and Feld show that the CJT is applicable to any competence distribution no matter how skewed by taking into account the group's average competence only.Footnote ⁴ This amounts to making room for a heterogeneous competence condition. Dietrich (Reference Dietrich2008) aptly formulates such a condition as follows. Let ${\bar p^x}$ indicate the group's average competence:

• $\quad\quad\quad\quad\quad\quad\quad\quad\quad {\bar p^x}: = li{m_{n \to \infty}} (\,p_1^x + \ldots + p_n^x )n$ (existsFootnote ⁵ and) $ \gt \displaystyle{1 \over 2}$.

This competence condition captures the intuitive contention that members of large groups display different degrees of competence regarding the targeted issue, and it does not alter the asymptotic part of the theorem.

As for the non-asymptotic part, it is commonly held that it does not generally hold when we make room for heterogeneity across individuals. However, under certain assumptions, even the non-asymptotic part of the theorem can be restored. For instance, Ben-Yashar and Paroush (Reference Ben-Yashar and Paroush2000) show that if we assume both that the independence condition is met and that each group member's competence exceeds $\displaystyle{1 / 2}$, but we do not know what the specific distribution of competence within the group is, the probability that the group's choice is correct is greater than the probability of a correct choice made by a member of the group chosen at random.Footnote ⁶

This brief overview shows that it is possible to make room for a more realistic understanding of how competence is distributed across members of the group: in order to prove the asymptotic conclusion and, under certain conditions, the non-asymptotic conclusion of the CJT, members need not be equally competent.

However plausible the homogeneous competence condition may be, though, it must be stressed that when we focus on intuitions about philosophicalia such as the concept of knowledge, the satisfaction of the competence condition cannot be taken for granted, for it is far from clear who can be credited with such an initial competence about Gettier cases in the first place. This worry leads us to discuss the problem of whose intuitions deserve to be taken into account.

A closer look at the literature on philosophical expertise and intuitions reveals that two cases need to be canvassed: on the one hand, the competence condition is satisfied by laymen only; on the other hand, only a group formed by experts, i.e. professional philosophers, can be credited with the required degree of competence.

3. INDEPENDENCE

Let us turn now to the independence condition. To begin with, let us say that the notion of independence used in the standard formulation of the CJT is that choices are independent conditional on the state of the world X: we cannot learn anything new about the state if we have already conditionalised on it.Footnote ¹⁵ This state-conditional notion of independence is needed to state the asymptotic part of the theorem. However, many authors in the contemporary literature on the CJT have observed that this conception of independence is unrealistic, in that it does not take into account possible ways in which individuals' choices cannot be independent. Let us consider some examples.

Boland (Reference Boland1989), and Boland et al. (Reference Boland, Proschan and Tong1989) notice that individuals can influence each other, thereby making their choices causally (and probabilistically) interdependent. However, as pointed out by Ladha (Reference Ladha1992), causal and probabilistic independence can fall apart, since individuals can be interdependent because there is another common cause different from the state of the world. In fact, Ladha (Reference Ladha1992) offers a new version of the CJT which preserves heterogeneous competence and replaces the state-conditional independence condition by the condition that choices are correlated in the sense that individuals are influenced by various schools of thought or opinion leaders.Footnote ¹⁶

Following the lead of Ladha, several authors have recently explored the possibility of replacing state-conditional independence by alternative independence conditions which are meant to keep track of a multiplicity of factors that can affect the individuals' choices. Let me mention two attempts in this direction which can prove useful to the present investigation.

Dietrich and List (Reference Dietrich and List2004) consider the case in which a jury has a shared body of evidence and maintain that when this situation holds, we should make room for an evidence-conditional independence condition to the effect that the shared body of evidence is the intermediate common cause of individuals' choices.

Dietrich and Spiekermann (Reference Dietrich and Spiekermann2013a, Reference Dietrich and Spiekermann2013b) go one step further by claiming that conditionalisation has to include several common causes which can well go beyond shared evidence. The idea, in a nutshell, is that in order to account for all common causes affecting individuals' choices, we had better adopt a problem-conditional notion of independence in which we conditionalise on the entire decision problem, conceived here as “the task of finding a certain correct alternative x (0 or 1) under certain circumstances c”.Footnote ¹⁷ The notion of a circumstance is meant to include both evidential and non-evidential (public or private) factors which affect individuals' choices.

Before going on to establish what notion of independence is best suited for the CJT-based socio-epistemological argument, it must be noticed that revisions of the original independence condition give rise to different versions of the CJT. In general, the original non-asymptotic part of the theorem still holds whereas the original asymptotic part does not. More specifically: in Ladha's CJT, except in rare cases, i.e. when the size of the group is particularly large and opinions are not too highly correlated, the probability that the majority is right does not converge to 1 as the group size increases. When we conditionalise on the shared body of evidence the way Dietrich and List (Reference Dietrich and List2004) do, we prove a weaker result than the asymptotic conclusion of the original CJT. That weaker result says that the overall jury reliability at best approaches the probability that the evidence is truth-conducive. This, in turn, can be interpreted as the probability that, from a God's-eye viewpoint, the evidence points to the truth. Its value is typically below 1, reflecting the possibility of misleading evidence. Dietrich and Spiekermann (Reference Dietrich and Spiekermann2013a) prove the classical non-asymptotic conclusion and a new asymptotic conclusion which excludes the idea that large groups are infallible, namely that the probability of getting it right tends to 1 as the size of the group increases.

The overview of several treatments of the independence condition pursued so far will enable us to answer the following question: which notion of independence should we endorse in order to develop a realistic socio-epistemological argument in favor of the reliability of the Gettier intuition?

It should be kept in mind that we are considering two cases: on the one hand, the case in which the competence condition is satisfied by a group formed by laymen and the target of epistemological inquiry is the Western concept of knowledge; on the other hand, the case in which the competence condition is satisfied by a group of experts and the target of epistemological inquiry is knowledge itself, and not anyone's concept of knowledge. Let us analyse these two cases in turn.

In order to provide a realistic notion of independence in the first case, it seems plausible to conditionalise on (at least) the following two factors. First: if the upshot of Gettier cases is taken to be possibly a cultural prejudice, then Western laymen's reactions to them are all affected by the fact of being caused by the same culture, as it were. Second: one may claim that since the individuals involved in Weinberg, Nichols and Stich's experiment are all faced with the same Gettier case, they share the same body of evidence. These considerations suggest that the more realistic approach to the independence condition in this scenario is the problem-conditional notion of independence proposed by Dietrich and Spiekermann, for this notion enables us to take into account various common causes, i.e. being part of the same culture and being exposed to the same evidence, that affect individuals' intuitive judgements about Gettier cases.Footnote ¹⁸

The problem-conditional notion of independence affords the means to offer a realistic representation of laymen's independence during the evaluation of Gettier cases; for this reason, we should touch on the features of the version of the CJT stated with such an independence condition which are mostly relevant to the present discussion. To begin with, Dietrich and Spiekermann's CJT involves a revision of the competence condition: competence is conditional on the problem. Secondly, their problem-conditional competence condition takes into account homogeneous groups. Thirdly, the original asymptotic conclusion is weakened. Let us take these three issues in reverse order.

On reflection, the third consequence is not so worrisome for the socio-epistemological argument. Bear in mind that the argument aims to establish the following thesis: the fact that a large group of individuals have the Gettier intuition enhances the evidential status of the intuition to such an extent that it provides us with a defeasible justification for the content of the Gettier intuition. To my mind, infallibility is not required to obtain such a defeasible justification. Therefore, I take this feature of Dietrich and Spiekermann's CJT to be perfectly acceptable in the context of the socio-epistemological argument.

Having clarified this, let us turn to the problem-conditional competence condition. Dietrich and Spiekermann observe that the new problem-conditional competence condition is needed since it is possible to show that, when a problem-conditional notion of independence is coupled with a classical notion of competence, large groups are worse than small groups or single individuals.Footnote ¹⁹ The notion of problem-conditional competence rests on the tenet that the probability that an individual opts for the right choice depends on how difficult the problem is. The probability exceeds $\displaystyle{1 / 2}$ when the problem is easy, it is smaller than $\displaystyle{1 / 2}$ when the problem is difficult, and it is equal to $\displaystyle{1 / 2}$ on boundary problems. In a nutshell, the probability that an individual chooses the right answer depends on the easiness or on the complexity of the problem at issue. Thus, in order for the probability that each individual will have the right opinion to exceed $\displaystyle{1 / 2}$, we should countenance the idea that it is easy to establish that the character of Gettier cases does not know the targeted proposition.

Various factors may have a bearing on whether the task of deciding if Gettiered subjects really know or only believe the targeted propositions is easy or difficult. To mention but one, the easiness of the problem may vary depending on the Gettier case one is facing. For instance, one might think that it is fairly easy to establish that in the Ginet–Goldman's fake barn scenario the subject does not know that the object she is looking at is a barn while, at the same time, finding the Chisholm's sheep scenario more difficult to assess because the intuition that the subject does not know that there is a sheep in the field is less solid, or vice versa. However shaky intuitions may be, though, I will concede that deciding whether a Gettiered subject really knows or only believes the targeted proposition is not a difficult task; in other words, I grant that individuals' competence exceeds $\displaystyle{1 / 2}$.

In light of these considerations, we can go back over the two aspects of Weinberg, Nichols and Stich's experiment I put aside in section 2.1: namely, whether one of the ethnic groups involved in the Weinberg, Nichols and Stich's trials is more competent than the others, and whether one of these groups faces a (more) difficult decision environment.

As far as I can see, when we consider groups formed by non-philosophically trained individuals only, it is difficult to ascertain whether one group displays more competence on the task than another, since it is far from clear whether there are specific and culturally determined factors which make the intuitions of a given ethnic group more competent than those of another. Moreover, much of the existing research in experimental philosophy has been operating under the tacit assumption that laymen's intuitions are all equally legitimate. So, we can safely regard different ethnic groups as being alike with respect to their average competence.

As for the decision environment, it seems unlikely that, in this particular case, distinct ethnic groups face radically different decision environments. For one thing, they deal with the same task, viz. answering the question whether a Gettiered subject really knows or only believes the targeted proposition. It also seems that individuals are all exposed to the same evidence on the problem: they are presented with the same Gettier case, and there is no group that displays more familiarity with Gettier cases, for experimental subjects are undergraduates without any training in philosophy. Furthermore, we can exclude the possibility that one of the ethnic groups faces a difficult decision environment because of misleading opinion leadership: as a matter of fact, there are no recognised leaders in these groups, nor is it plausible to hold that for example the Western group is biased because influenced by the opinion of a well-known analytic epistemologist who thinks that Gettiered subjects do not have knowledge, since Western participants are laymen without any familiarity with contemporary epistemology.

Having clarified this, let us turn now to the fact that the problem-specific competence condition is defined for homogeneous groups. Let us state this condition more precisely. First, notice that for each individual i, Dietrich and Spiekermann consider an event R _i, which is the event that an individual i chooses correctly. This is but a notational convenience, for choices and correct choosing events are interdefinable given x.Footnote ²⁰ Dietrich and Spiekermann define an individual i's (problem-specific) competence as $p_i^\pi = Pr({R_i}\vert \pi )$, the probability that i chooses correctly conditional on the problem π: the value varies depending on how easy the problem is.

Surely, homogeneity is a limitation of Dietrich and Spiekermann's CJT: as pointed out in section 2, the homogeneity condition is highly unrealistic in our case, and it is often rejected in standard applications of the CJT. Yet, homogeneity should not be regarded as a necessary condition for this version of CJT, and I believe that it is possible to widen the span of Dietrich and Spiekermann's CJT to encompass heterogeneous groups.

The mathematical development of such a more general version of CJT will have to be deferred to further works. However, let me briefly outline a general strategy. The key move will be to replace problem-conditional competence by average problem-conditional competence.Footnote ²¹ More precisely, let ${\bar p^\pi} $ indicate the average problem-specific competence:

$${\bar p^\pi} = li{m_{n \to \infty}} (\,p_1^\pi +... + p_n^\pi )n \gt \displaystyle{1 \over 2}.$$

That is, the average problem-specific competence condition is the limit of the finite-group average problem-specific competence. This formulation of the average problem-specific competence condition is the natural extension of Dietrich's 2008 average competence: it is an extension since it conditionalises on the entire decision problem, whereas Dietrich's 2008 competence condition conditionalises on the state only.

I submit that it is reasonable to expect that after dropping the homogeneity group competence condition, the probability that the majority is right in choosing a certain option given that the chosen option is correct would continue not to converge to 1 as in the previous asymptotic conclusion of Dietrich and Spiekermann's CJT (bear in mind, however, that this weaker conclusion does not undermine the socio-epistemological argument for the reason offered above). As for the non-asymptotic conclusion, it would cease to hold if we simply dropped the homogeneity condition, just as in the classical CJT. Yet, more sophisticated ways of modeling heterogeneity might recover the non-asymptotic conclusion, just as described in the case of the classical CJT in section 2.Footnote ²²

This completes my analysis of the CJT-based socio-epistemological argument for the reliability of the Gettier intuition in the case where laymen satisfy the competence condition and the target of epistemological inquiry is the Western concept of knowledge. Let us turn now to specify the conditions that must be met in order for the CJT-based socio-epistemological argument to hold in the second case, where the target is the extra-mental phenomenon of knowledge and the group is composed of professional philosophers only.

The original state-conditional independence condition does not seem to square with the current philosophical practice. One can point to the fact that being an analytic philosopher, one might share possible biases or methods of inquiry proper of analytic philosophy. In this sense, all analytic philosophers cannot be said to be independent of each other. Moreover, a philosopher can certainly benefit from the interaction with other philosophers working on the same topic, since the exchange of ideas and feedback have a positive impact on the development of one's own ideas. There is much more to be said about philosophical practice, but these remarks suffice to support the claim that it is unrealistic that professional philosophers satisfy the original state-conditional independence condition: hence, if we want to avail ourselves of the CJT in the case where the competent group is composed of philosophers, we had better adopt a problem-conditional independence condition, for such a condition requires us to conditionalise on common causes which may be arguably taken to affect philosophers' intuitive judgements, such as having the same methods, being influenced by the same school of thought (i.e. analytic philosophy), and so on and so forth. This entails that even when we appeal to the CJT-based socio-epistemological argument in this second case, we should develop a more general CJT which includes both the realistic problem-conditional independence condition proposed in Dietrich and Spiekermann (Reference Dietrich and Spiekermann2013a) and the average problem-conditional competence condition suggested above.

4. CONCLUSION

In this paper, I aimed at shedding new light on Goldman's suggestion that the CJT could play a role in the context of a socio-epistemological argument for the reliability of intuitions, such as the Gettier intuition. I pointed out that Goldman's original proposal is implausible, in that it relies on a version of the CJT which holds under unrealistic conditions. Nonetheless, this does not make the socio-epistemological argument ipso facto doomed. I explored other formulations of the conditions of the CJT by drawing on the ongoing debates on philosophical methodology. In particular, I proposed to modify the conditions by taking into account two different views on the target of philosophical areas of inquiry such as epistemology, and on philosophical expertise. So, where does the foregoing discussion leave us?

I claimed that the most appropriate version of the CJT for the socio-epistemological argument should have a problem-conditional independence condition and a heterogeneous problem-conditional competence condition, and I ventured a tentative hypothesis on how this CJT can be developed. But it remains an open question how to fill out the mathematical details of this new CJT. Be that as it may, if my analysis has provided any insight into the CJT-based socio-epistemological argument for the reliability of the Gettier intuition and has placed it on the table as a real option, I will rest content for now and leave the mathematical development of a more general CJT as a topic for future research.Footnote ²³