Knowledge Indicative and Knowledge Conductive Consensus

in Journal of the Philosophy of History

Abstract

A traditional proposition in the philosophy and the sociology of science wants that consensus between specialists of a scientific discipline is a reliable indicator of their access to genuine knowledge. In an interesting reassessment of this principle, Aviezer Tucker has analyzed the implications and the significance of this thesis in relation to historical research, and has established that parts of the historiographical community that display high degrees of consensus among their practitioners can be described in terms of the same relationship existing in empirical sciences between the exemplification of significant level of agreement and shared knowledge. After a concise summary of Tucker’s general view of the relationship between consensus and knowledge and an analysis of its discussion by Boaz Miller, this paper proposes a critical discussion of the limits and the virtues of this approach and concludes that it is possible to assume that a theory of the sort outlined by Tucker and Miller may describe in an exhaustive way the dynamics of the consensual communities only after some important caveats and integrations. In the closing section, a brief review of Tucker’s picture of historiographical consensus will be proposed.

Abstract

Abstract

A traditional proposition in the philosophy and the sociology of science wants that consensus between specialists of a scientific discipline is a reliable indicator of their access to genuine knowledge. In an interesting reassessment of this principle, Aviezer Tucker has analyzed the implications and the significance of this thesis in relation to historical research, and has established that parts of the historiographical community that display high degrees of consensus among their practitioners can be described in terms of the same relationship existing in empirical sciences between the exemplification of significant level of agreement and shared knowledge. After a concise summary of Tucker’s general view of the relationship between consensus and knowledge and an analysis of its discussion by Boaz Miller, this paper proposes a critical discussion of the limits and the virtues of this approach and concludes that it is possible to assume that a theory of the sort outlined by Tucker and Miller may describe in an exhaustive way the dynamics of the consensual communities only after some important caveats and integrations. In the closing section, a brief review of Tucker’s picture of historiographical consensus will be proposed.

1. Knowledge Indicative Consensus

It is not necessary to possess a thorough expertise in historiography to note that historians committed to different values, educated in different contexts and participating to different collective identities share analogous beliefs about the nature of history and the epistemic reliability of particular recounts of historical events. The historiographical community, in this sense, appears to be organized in a way that closely parallels the distribution of substantive and methodological agreement among practitioners of empirical disciplines, in which scientists’ work builds on a range of assumptions, theories and models that are accepted as valuable by the vast majority of the scientific community, and that may be revised, to adopt Kuhn’s terminology,1 only in result of deep paradigmatic transformations. Tucker’s theory2 amplifies and strengthens this analogy to argue in favor of the idea according to which historiographical consensus is normally a reliable indicator of historiographical knowledge or, in other words, according to which distributed patterns of propositional agreement among the historiographical community are best explained, in most cases, under the suggestion that the propositions surrounded by massive acceptance convey knowledge. Although aware of the fact that consensus could be conceived as a collateral effect of the epistemological desiderata that allow historians to produce acceptable theories and not as an intrinsic value of the scientific agenda, Tucker suggests that this hypothesis manifests a remarkable combination of wide explanatory power and openness to be supported without any specific commitment to a particular position in the theory of knowledge, and argues that, both in historical research and in science in general, a situation of substantive consensus c is likely to be knowledge-based when it exemplifies the following properties: it is uncoerced (U(c)); it is uniquely heterogeneous (H(c)), it is sufficiently large (L(c)). Furthermore, Tucker holds that if a given community of historians whose positions are not inscribed in a framework of substantive consensus nevertheless ground their research on a consistent and widely accepted set of cognitive values (that is to say on shared formal standards such as accuracy, productivity, simplicity, analyticity, and so on),3 the epistemic dynamics occurring between members of such population will be statistically likely to be knowledge conductive.

Let us call respectively KIH (“knowledge indicative hypothesis”) and KCH (“knowledge conductive hypothesis”) these two theses and let us say, as a first approximation to the subject, that on a plausible and intuitive view a group P can be described as believing that φ iff most of its members believe that φ, and it is common knowledge in P that most of its members believe that φ.4 To engage in a discussion of Tucker’s proposition, consider the following conditional: if a concrete situation of historiographical consensus c among members of a population P on the modes of representation of an object O exemplifies a certain class of properties K (in this case, K = {H(c), U(c), L(c)}),5 then c supports KIH, i.e. P can be thought of as likely to have O-related knowledge. Agreed on the fact that this conditional is a prima facie acceptable representation of Tucker’s view, and that the detection of some key properties of P formally constitutes the only consistent strategy to load the conditional with an effective antecedent, what about the validity of the conditional itself? First of all, Tucker agrees on the intuitive postulation that consensus is not a sufficient nor a necessary condition to argue that members of P participating in c are ipso facto sharing knowledge about O.6 After all, some cases of consensual arrangement among P-like communities may be explained at best by assuming that the agreement has been reached in virtue of pervasive biases7 or non-cognitive interests. Unsurprisingly enough, it is very difficult to find a philosopher who asserts a bare or naive consensus theory of truth, that is to say a treatment of the notion of “truth” normatively based, without further qualifications, on cases of agreement in non-ideal communities.8 Nevertheless, Tucker explicitly assumes that if it can be proven that shared knowledge is the best explanation for a situation of consensus c on O describable in terms of the conditions U(c), H(c) and L(c), then c marks a region of the social space populated by agents whose beliefs insisting on O are likely to form a true theory of O.

A first argument in favor of this view could be given by the apparent compatibility between the assumption that a population need not aim at consensus for the achievement of a rational mediation between beliefs9 and the idea that consensus can constitute a positive evidential factor in demarcating groups of cognizers that share actual knowledge.10 Some have argued that a thesis like KIH should be evaluated by studying the recurring properties of the types of collective practices that in different occasions have determined consensuses that can overtly be characterized as indicators of knowledge.11 Such approach would nevertheless be useless in evaluating the intuition elaborated by Tucker’s theory, because it could be spent only as a tool to deduce from cases of consensus that clearly exemplify K the rules of professional conduct that inform them, and perhaps generalize such rules in the elaboration of a norm requiring that any situation of consensus should be represented as a reliable indicator of knowledge iff it can be considered the outcome of processes falling under the class of operations allowed by such rules. However, given that we are investigating the epistemic implications of situations of consensus as such and not as outcomes of consensus generating processes, the study of types of epistemic processes that are likely to generate a situation of agreement12 or that are likely to prevent it from developing13 seems to fall outside the scope of our assessment of Tucker’s position. Rather, assume that c is constitutively open to be considered as an indicator of different facts related to the community P of agents that inform it. What Tucker aims to maintain at the most general level is that if P exemplifies a relevant class K of attributes, then the agreement c displays sufficient characteristics as to rule out the hypotheses that are directly inconsistent with the idea that it supports KIH and should be interpreted as reflecting common knowledge on O.

As a first terminological refinement, it is important to stress that the assumption of a positive compatibility between P and KIH cannot be held, as Tucker appears instead to be inclined to think,14 as informing an “explanation” of c’s genesis, and that this requirement is not inconsistent with the natural impression that K can refer to the set of operations in virtue of which a situation of agreement like c is instituted by P in the first place. For if the spectrum of properties emphasized by Tucker insisted on the practices from which c should result in order to support KIH, our investigation of the relationship between distributed agreement and knowledge would fall into the type of analysis that Tucker is trying to dismiss, namely into a consideration of P’s consensus generating processes. This means that before an assessment of the actual possibility to provide a general account of K, the theory has to clarify in which sense its characterization of consensus should be conceived as independent from the processes that sustain its production in a population. It seems fair to say that Tucker is not aware of this complication, and that further remarks need to be provided if we want to rescue his sketch. One obvious suggestion could be holding that his theory is useful to address situations in which consensus among a group of agents has already been established and in which, accordingly, the practices of the members of the community in question have reached some basic propositional equilibrium. In this view, the epistemic behaviors taking place in a community would reflect a situation of consensus only if they were open to be illuminated by the postulation that they rely on the shared, perhaps implicit assumption that the common beliefs that ground them are true. Suppose that at t0 a group P of agents is debating on which proposition, among a range of possible options, should be regarded as the proper solution to a problem J about an object O. Suppose that at t1 the members of P have reached a situation of consensus by means of processes contributing to a collective result displaying the properties defined by K, and have consequently agreed that φ is the proposition in question. Suppose also that from t1 to t2 the members of P focus their attention on problems different from but related to J, and that the series of epistemic activities performed by members of P after the agreement reached in t1 observably rely on the assumption that φ is a non-improvable solution for J. Finally, suppose that at t2 further epistemic control pushes members of P to revise their adhesion to φ and move towards a solution to J based on the settlement of a different theory of O. The question is: which of these specific clusters of collective procedures is addressed by the observations provided by Tucker? It certainly cannot be the group of agreement dynamics occurring from t0 to t1, since Tucker explicitly argues that the processes by means of which a consensual equilibrium is reached are not relevant to test KIH; nor it can be what happens after t2, since in this time slot there neither is a situation of consensus. As a consequence, the only alternative left is assuming that Tucker’s theory aims at stating that if the consensual dynamics existing in tokens of the type situation described by the interval between t1 to t2 exemplify the properties listed in K, then such consensual dynamics are consistent with KIH, and can be reliably assumed as indicators of a concrete sharing of knowledge among members of P.

Provided these stipulations, if it is true that Tucker’s approach to the study of KIH seems to offer a promising strategy to theorize about the epistemic implications of consensual dynamics, it is equally true that the way in which he carries this out, by talking of “consensus” in general terms and ignoring the division we have sketched, is likely to be vulnerable to complaints of underspecification. It seems in fact that the only consistent way to rescue Tucker’s view of KIH would be requiring that the properties defined by K are exemplified not by the epistemic dynamics that, in P, inform the elaboration the positions insisting on the subject addressed by the convergence of beliefs that determines c, but by the epistemic dynamics that follow and, in a sense, surround the consensual convergence on the subjects that KIH intends to assume as appropriately known by members of P. The clarification I am introducing may seem subtle, but is perhaps not unworthy of consideration, because although the core remark underlying it is noticeably ineloquent with respect to the general hypothesis that Tucker’s perspective can be taken as a by and large correct way to approach the problems we have so far been issuing, it actually establishes significant restrictions as to the range of objects that we can expect to be described by a theory constructed under conditions comparable to those defended by Tucker. In this interpretation of KIH (let’s call it KIH*) the reference to K can outline something salient about the probabilistic relationship in P between a consensus c on the theory of an object O and the possibility that c indicates the sharing of a concrete knowledge of O among members of P not on condition that c develops from collective dynamics describable via K, but on condition that the epistemic procedures implemented by P after the acceptance of the association of φ to O (a) can be characterized in terms of K, (b) rely in a relevant sense on the truth of φ, and (c) do not show to be oriented toward a revision of φ. In this perspective, KIH* assumes a significant probabilistic value not in result of some properties of the state of convergence between beliefs that determines the characterizability of the social situation existing in P as c, but in result of the counterfactual proviso that if in P the association of φ to O endures in time despite the progressive implementation of epistemic practices that (a) presuppose in a significant sense a settled theory of O (and, as a consequence, can disconfirm φ) and that (b) show to support a characterization in terms of K, then the probability of KIH’s being a thesis that effectively describes P’s consensus on O becomes comparatively significant and assumes a position of statistical advantage in comparison with hypotheses assuming that the credential convergence that determines c, for example, is the result of a series of biases ordered by extra-epistemic attractors that, if deactivated, would increase the probability over time of a revision of the beliefs on O shared by members of P.15 Moreover, it is plausible that a comparable counterfactual accommodation of KIH based on the reference to sequences of potential revisions of φ offers a clearer, although not exhaustive, indication of what kind of statistical data the theorist should consider in assessing KIH’s plausibility, namely the number of potential revisions over time. Tucker’s formulation, in fact, restricts itself to pointing out that, once competing hypotheses have been excluded, KIH is a probabilistically plausible interpretation of the situation of agreement existing among members of the population P, but is not capable of furnishing an indication of the type of data that should be taken into consideration in the elaboration of an explicit measurement of the probability that single cases of epistemic consensus support KIH.

Miller’s contribution guarantees to offer significant improvements to Tucker’s sketch, but shares with Tucker the same methodological approach to KIH. In fact, although for Miller a situation of consensus c supports KIH iff the collective dynamics occurring in the population P that determines c can be described via the reference a class of properties K* (different from K) and therefore his paper argues in a different way in favor of the high-order thesis according to which there exists a set of para-equilibrium conditions in virtue of which any situation of distributed agreement in a population can be interpreted at best by assuming that its members share knowledge,16 Miller’s model does not offer any upgraded account of the post-equilibrium dynamics in virtue of which it may be plausible to assume that the modes of distribution of collective agreement in a given population are compatible with a confirmation of KIH. The central idea, therefore, is the same as Tucker’s, although differently developed: if a situation of consensus c shows to be based on a set of relevant conditions, then KIH holds for c. One notable difference, nevertheless, should be clearly emphasized. According to Tucker, the set of properties that justify KIH for single cases of collective agreement does not include the convergence on cognitive values; furthermore, a theory of consensus is entitled to refer to cognitive values just to clarify that their distributed adoption in a population P of agents connected by extensive agreement on substantive topics increases the possibility that the consensual dynamics occurring in P are knowledge conductive. According to Miller’s “social calibration condition,” by contrast, such poles of procedural meta-agreement can ground the possibility to discover a confirmation of KIH in cases of substantive consensus.

2. Knowledge Conductive Consensus

For the sake of our purposes, we don’t need to enter in an articulate and detailed assessment of the advantages and the disadvantages of Tucker’s original proposal and of its readjustment in Miller, but we need at least to underline in detail some of the theoretical nodes involved in the complex relationship between consensual dynamics and knowledge conductiveness. Interestingly enough, Miller does not show any substantial interest in the development of the (abundantly stressed by Tucker) theme of conductiveness, although it is clear that between the observations on the sharing of cognitive values offered by Tucker e and the theory of K* structured by Miller there is not any prima facie incompatibility. In this sense, a theorist interested in a synthesis between the analyses presented by these two scholars could consistently integrate Miller characterization of K* with a commitment to the idea that the convergence on a set of shared cognitive values between members of P supports KCH. The proposition according to which the convergence on a set of shared cognitive values would support KCH in a set S of individual and concrete cases of consensus is in fact insensitive to the requirement that terms of S also support KIH. As a consequence, KCH does not require, to be held as true for all S-like instances, that KIH delivers a reliable characterization of all the concrete situations of consensus enclosed in S. On the other hand, KIH and KCH are also (a) truth-functionally non-correlated, or such that the assumption of the plausibility of one of the two hypotheses is not conditional on the possibility to maintain that the other is excluded by the para-equilibrium properties overtly exemplified by P, and (b) interested in explaining two substantially different phenomena. In this sense, KCH should hold as a statistically reliable theory of consensual dynamics both for concrete cases in which there exists an actual distributed convergence on the adoption of particular beliefs, and for concrete cases in which, lacking a substantive credential homogeneity, members of P are pooled by a commitment to the same epistemic tasks and to a common set of cognitive values. A supporter of KCH should therefore be willing to maintain that the sharing of cognitive values can be knowledge conductive both in a situation of consensus and in a situation of credential dispersion, and perhaps to reinforce her statement by observing that if we look at how things work in concrete cases, the revision of sets of commonly accepted cognitive values is usually preferred in virtue of the comparative (and of course prospective) explanatory advantages that new values allow to achieve.17

One natural suggestion to look at the problem from a different perspective could be reducing the complex web of properties that define the sharing of cognitive values to a neutral notion of “respect” for the epistemic contributions of members of one’s community and analyzing whether or not a network P of actors connected by systematic relations of mutual respect can be thought of as augmenting the possibilities that P produces knowledge.18 This assumption does not correspond exactly to Tucker’s theory (in which there is no reference to relations of respect), but it is perhaps a dependable instrument to assess its validity. In fact, although Tucker does not assume that the consequent of the counterfactual expressing KCH is verified only when the sharing of cognitive values in a population assumes the specific mode of realization of a subjective impression of respect, it is difficult to conceive what the sharing of cognitive values could consist in if not in light of the possibility to think that X agrees to the same cognitive values as Y’s iff X, subjected to an adequate stimulus, elicits a behavior legitimately categorizable in terms of “respect” towards Y’s opinions. This being said, given that it is possible to assume that the adhesion to common cognitive values in a scientific community does not have to be paired to explicit respect but it is possible to assume that any explicit impression of respect is conditional on the sharing of cognitive values, it should be also possible to determine whether a theory of the sort of KCH could hold in cases in which the moderation of substantive dissensus19 in a homogeneous community gives rise to a web a systematic relations of mutual respect. At a minimum level, an analysis oriented in this direction should test the possibility to maintain that if among a couple of epistemic agents X and Y there exists a relationship of mutual respect and substantive disagreement, the epistemic ecosystem realized by X and Y is more likely to produce knowledge and turn into a fully consensual group that an epistemic ecosystem composed by actors among which there exists a relationship made of mutual disrespect and substantive disagreement.

The most important problem of Tucker’s theory, under this point of view, seems to be posed by the fact that it seems impossible to elicit an authentic relation of respect if not under conditions of minimal substantive agreement or, in other words, by evidence suggesting that behind any disposition to express sincere respect for the adhesion to an opinion one disagrees with is hidden a kind of latent propositional agreement.20 If this were true, the prima facie reliability of Tucker’s sketch of KCH would not result from the fact that it is capable of furnishing an approximately adequate picture of the relationship between the sharing of cognitive value and the achievement of a situation of consensus based on the convergence on actual knowledge (and therefore from the fact that it is possible to say that Tucker’s observations allow to argue in favor of the thesis that the convergence of cognitive values statistically leads to a consensus describable in terms of KIH), but from the fact that an inclination toward substantive consensus seems to be already embedded in any convergence on common cognitive values, and that it is just possible, but not at all necessary, that such consensus supports KIH. Indeed, although dissensus and respect are de facto consistent, the relationship between consensus and higher-order information on others’ beliefs21 is more complex than it might be suggested at first by a commonsensical interpretation of the fact that agents can disagree and still mutually value their opinions. Obviously, the degree of consensus in a given community P depends on the distribution of first-order beliefs among members of P: the greater the number of first-order beliefs shared among its population is, the higher the degree of consensus among exponents of P will be. However, the degree of consensus in P cannot depend only on the distribution of first-order beliefs among members of P. For example, consider a scenario in which a population of scientists P is split between two sub-communities P1 and P2; P1 holds that φ whereas P2 holds that not-φ. If both P1 and P2 highly distrust the other party’s opinion, the result is quite obvious: members of P1 will stick to their preference for φ while members of P2 will continue to hold that not-φ. Conversely, if P1 and P2 respect to some extent the other party’s opinion (for example because they realize that their contrasting defenses of φ and not-φ are grounded on comparable methodological commitments and evidential standards), the two parties may reach a situation of consensus by agreeing on equal, positive but lower probabilities for φ and not-φ. Thus, first-order consensus between members of P can partly be a function on the consensus on the second-order beliefs held by P. As a consequence, we can say (a) that to a higher degree of mutual respect corresponds, with an acceptable deal of approximation, a higher degree of potential consensus, and (b) that as long as the sharing of cognitive values is describable with the same instruments that we need to introduce in order to capture the distribution of respect in a scientific community, then it can be only be expected in general terms that the sharing of cognitive values in P is likely to generate a situation of consensus (not a situation of consensus based on knowledge), and that the dynamics underlying the achievement of such agreement support KCH only in cases where the consensus reached in virtue of the sharing of cognitive values supports KIH. In this sense, a more specific consideration of the subjects addressed by Tucker’s theory of KCH may show that it is impossible to verify KCH in cases in which the agreement produced by mutual respect does not support KIH and, consequently, that KCH cannot be a general theory of consensual dynamics.

It is somewhat interesting that Tucker considers irrelevant a discussion of Lehrer and Wagner’s outline of the conditions under which substantive consensus may be reached, whereas, upon closer examination, their approach draws extensive inspiration from the same basic distinction between orders of beliefs that, if my observations are correct, exclude the possibility that KCH may be taken as a general theory of the agreement on cognitive values. In Lehrer and Wagner’s model (LWM),22 first-order and higher order beliefs are represented in a non-homogenous way: first-order beliefs are subjective probabilities, whereas higher order beliefs are represented as weights that each agent grants to other agents’ subjective probabilities. At each stage agents update their beliefs to weighted averages of the beliefs distributed in their community, and convergence to consensus is likely to occur if all weights are positive. Now, the idea of conciliating this picture of pre-consensual dynamics with a standard Bayesian analysis about the mechanisms involved in the modification of a web of beliefs by an agent belonging to P in result of her consideration of other agents’ beliefs may sound problematic.23 In a recent paper, for example, Richard Bradley has defended the claim that in a Bayesian perspective it cannot be the case that the posterior probabilities assigned to φ by an agent X belonging to P, given the judgments on φ of the population (P – X), depend on these judgments and the epistemic weight that the group (P – X) attaches to them but not on the weight assigned by X to her own evaluation of φ, and has argued that LWM fails to explain why in a setting in which P is exhausted by three agents X, Y and Z, X’s response to the beliefs of agents Y and Z should depend on the probabilistic independence between Y and Z’s opinions, so that if Z’s judgment on φ is perfectly correlated with Y’s judgment on φ (in other words, if Z is a “follower” of Y), X should only respond to Y’s judgment.24 Nevertheless, it is also possible that Bradley’s criticisms are too hasty. First, Bradley is able to conclude that LWM is too coarse-grained because he presupposes that epistemic weights express only the value granted to subjective estimates. But this is hardly the case. In a dynamic scenario in which (i) X started with granting a given weight ω to Y’s belief, (ii) Z was added to P, (iii) X realized that Z is a mere follower of Y, and (iv) X took Z’s opinion to be plausible, X would not be automatically required to give a positive weight to Z while still attributing ω to Y. The fact that in such situation the normatively rational thing to do for X would be to split ω between Y and Z or to assign a zero weight to Z still fits within LWM. Second, it is not sure whether or not the Bayesian account of epistemic independence endorsed by Bradley can itself be considered to be appropriately fine-grained. For instance, the fact that Z is a mere follower of Y is not sufficient to guarantee that Z’s opinion should not matter to X. After all, even if Z agreed to defend φ on the basis of exactly the same arguments provided by Y for φ, Z might still have other good reasons to follow Y with respect to φ, perhaps because Z has noticed that Y’s past predictions regarding issues substantively related to φ proved to be reliable and sufficiently accurate as to expect that X’s access to comparable third-order information should result in the assignation to Z of a positive weight.

It is important to stress that the emphasis on the conditions under which a situation of consensus c supports KIH in the sense suggested by Tucker and Miller (that is to say in the light of the conditional “if c displays a certain set K / K* of properties, then c supports KIH”) is naturally compatible with the assumption that there may be situations in which c supports KIH without displaying the characteristics defined by K / K*. For example, suppose that at a time t agents of a population P in a situation of dissensus have formed an opinion about φ’s truth. Suppose furthermore (a) that such agents’ states of opinion about φ are given by their subjective estimate of φ’s probability and (b) that they disagree as to what the probability for φ is. Most likely, the strategy adopted by P to issue a collective probability for φ will depend on the goals pursued by P. If agents join P for epistemic reasons, and therefore in order to maximize the likelihood of reaching truth, the best organization for P to that end might differ from an organization appropriate to the goal of merely reaching a value acceptable by all the agents involved in P. If none of P’s members possesses second-order information on the reputation of other members of P, P is likely to converge to a simple compromise hypothesis determined by the average of all the subjective probabilities associated to theories by its members. In such case, a considerable number of agents involved in P will feel that the agreement reached by the group does not constitute an epistemic improvement if compared to their own initial estimate. By contrast, if the agents participating to P can regulate their evaluation of the credibility of other members’ opinions on the basis of some information regarding the probability that they may be right, the output produced by the network will probably be perceived as more satisfactory than the outcome generated by the averaging mechanism involved in the previous case. Imagine to have a population debating on the truth of a proposition φ; suppose that the agents of this population have all an exact knowledge of the φ-related expertise of all the other members of the same population; suppose also that such knowledge was known to a social scientist trying to predict the behavior of the network during the production of a common position on φ. In this case, the theorist could impose a normative constraint on the behavior of agents in the network by devising some function having local estimations of φ and local assignment of weights as inputs and an integrated estimation of φ that maximizes the chances of being correct as output. The problem is that members of concrete populations in general have no knowledge about the probability that the agents in the group is right in proposing φ. At best, each agent has her own beliefs on others’ degree of expertise on φ-related issues, and there is no reason to expect that second-order beliefs held by two agents X and Y on the expertise of a third agent Z will be consistent. Naturally, given that agents disagree about their respective expertise, any choice of any weighting scheme applied to the agents’ evaluations will appear to be inadequate to some members of P, and (again) the output of the aggregation mechanism implemented by X, Y and Z will be perceived by at least one of them as a compromise.

It could be pointed out that LWM appears to offer a significant improvement on the problems we have so far discussed, since it seems to show that comparable situations can trigger social mechanisms generating both decision-theoretic and epistemic fitness. Indeed, LWM indicates that if all the agents in a group assign a weight (a) to each other’s evaluation of φ, (b) to others’ judgments about φ-expertise, and (c) to others’ expertise in recognizing others’ φ-expertise, then, under apparently weak conditions of respect (in the above sense), the individual computations of agents’ final evaluations of φ given the weights they assign to each other’s degree of expertise converge to one fully consensual probabilistic estimate of φ’s likelihood. The advantages offered by LWM are therefore twofold: on the one hand, it interprets the aggregation procedures occurring in P as oriented to something more than a mere compromise; on the other, it promises to offer a good description of procedures of rational aggregation, given that each agent use information concerning other agents’ expertise as higher order evidence in favor of or against φ and that the output value chosen by the group can be thought of as integrating more data than those on the basis of which single cognizers in the network provide their initial estimate of φ’s probability. Furthermore, it shows that in a group composed by agents interested in structuring a collective theory on a subject systematic dissensus cannot be prescribed on a general normative basis, since for any arrangement of population and distribution of opinion, rational consensus is the only condition by means of which the network can hope that each of its members improves her degree of belief in her thesis. This being said, it is important to stress that if it is not absolutely clear in what sense LWM could want to argue that comparable aggregation processes maximize the “epistemic quality” of the outcome given the information available to agents in the network, it is at least sufficiently clear that LWM cannot be taken as a naïve theory suggesting that dissensus cannot be normatively prescribed because the implementation of a procedure of rational agreement in a population systematically implies the maximization of the truthlikeness of the opinions held by its singular members. Intuitive restraints regarding the impossibility to completely overlap consensual theories with theories conveying actual knowledge hold here as usual.

3. The Historiographical Case

It is clear that the observations we have so far presented with respect to the consensual dynamics occurring in populations of actors interested in the coordinated performance of epistemic tasks are intended to hold also in the case of historiography. As a consequence, the validity of KIH* for a consensual community of historians should be conditional (a) on the characterizability of the practices occurring in such community in terms of a set of salient properties (be its extension closer to the list of attributes furnished by K or K*) and (b) on the fulfillment of the requirement that the epistemic dynamics surrounding the adhesion to the proposition φ that determine the agreement prove to be sensible (i) to a dispositional analysis in terms of behavior that rely on the truth of φ and (ii) to counterfactual considerations based on an inference to the best explanation suggesting that the preservation of the adhesion to φ after a growing number of potential revisions improve the possibility that the consensus on φ is grounded on φ’s truth. Bearing these caveats in mind, let us consider a highly standardized but indicative example borrowed from the territory of intellectual historiography. Let us assume, broadly, that a group of agents P displaying all the adequate properties as to serve as a sample for KIH* converges at a time t on the assignation of an interpretation I to a past written document D, and that such assignation of meaning is not revised by P despite the fact that the group, as time passes, goes through periods of convergence towards consensus and phases of strong dissensus on subjects related to the association of I to D. Even intuitively, the characteristics of the collective dynamics occurring in P that define the degree of plausibility of a description of P under KIH* cannot be exhausted by the properties exemplified by P at t, but need to be (a) detectable in the set of properties exemplified by P at t and after the occurrence of the convergence on I and (b) associated to the progressive lack of a revision of the collective assumption according to which the assignation of I to D constitutes a reliable theory of D. For example, if the association of I to D is maintained by P for a symptomatic period of time (tωtα) despite the fact that from tα to tω members of P manifest significantly high degrees of dissensus in relation to subjects related to D, the hypothesis that the convergence on I may be illuminated by KIH* becomes statistically attractive, although in principle fallible and open to be abandoned in the light of explicit evidence against it.

As far as the question of cognitive values is concerned, on the other hand, we have said that Tucker’s proposal is centered on the assumption that the convergence on a common spectrum of cognitive values in a population P whose composition exemplifies some set K of relevant characteristics is likely to indicate that the epistemic dynamics occurring in P support KCH. Now, we can certainly agree with Tucker on the need that the sharing of cognitive values, in order to be interesting, has to emerge in P when P exemplifies an appropriate set of properties, and that it is only in light of the fact that P realizes K / K* that the emphasis on the sharing of cognitive values can make a difference in the evaluation of the correctness of a theory interested in a comparable sense in the collective dynamics involved in P. On the other hand, it is possible to say that in order to discuss the relationship between convergence on a common set of cognitive values and KCH it is not necessary to elicit the properties that the population in question should exemplify in order to support KIH. We can therefore exclude from the parameters that our assessment should take into consideration the variable determined by the need that P satisfies the requirements contained in K / K* and, in order to develop a manipulation useful to give us some direct information on the relationship between convergence on common cognitive values and KCH, let us assume that the value of such variable is predetermined in such a way that P actually exemplifies K or K*. Having identified the conjunction of the conditions [exemplification of the properties K / K*] and [sharing of cognitive values] as the necessary basis to consider KCH a statistically plausible description of the dynamics occurring in P and having fixed the value of the variable [exemplification of the properties K / K*], let us examine in specific the covariance between the statistical plausibility of KCH and the parameter [sharing of cognitive values]. Tucker’s observations on this point are relatively intuitive, but not completely ineloquent. First of all, Tucker is concerned with showing that despite the fact that K’s extension is in principle open to discussion, groups of organized actors that develop a position of dissensus toward the rest of the historiographical community usually present properties that are clearly inconsistent with the control functions that K is intended to perform. In this sense, if it is true that the reduction of K’s extension to {U(c), H(c), L(c)} can in principle be open to debate, it is nonetheless relatively easy to determine which families of properties cannot be exemplified by P if we want to take P as a sample that supports KIH. For example, P cannot be constituted by agents with a strong homogeneity of extra-epistemic interests whose achievement may be preferred to the respect of objectivity.25 In order for the management of historiographical research by a community of actors to be methodologically respectable, it is therefore critically important, for Tucker, that the agreement of the cognitive values that regulate the practice of historical disciplines is preferred to the tendency to ground research on non-cognitive or therapeutic values.

The impression that one has in reviewing Tucker’s observations on this subject is that the reluctance to drop the theorem according to which the possibility of talking about a historiographical “community” is conditional on the possibility to refer to an agreement on cognitive values pushes him to generalize their basis of encapsulation and their content almost to the point of making them absolutely non-specific. Let’s go back to the above example and suppose that two members A and B of the community P develop a dissensus on the association of I to D; A presents arguments in favor of the thesis that I is a good theory of D, whereas B argues for the hypothesis that D can be properly illuminated only via the assignation to D of an interpretation I*. Suppose also, to follow Tucker’s terminology, that the assignation of I to D constitutes an occasion of application and validation of A’s non-cognitive values and an occasion of disconfirmation of B’s non-cognitive values. Tucker admits that the content of different historiographical interpretations is influenced by the non-cognitive values of their proponents, and that members of a historiographical community gathered around a systematic consensus on cognitive values may nonetheless present different solutions to the same problems, but assumes that such divergences, to be included in a pattern of dynamics based on an authentic consensus on cognitive values, need to rest upon a fundamental agreement on which procedural choices and methodological commitments may shape their treatment. Consequently, interpretive conflict in a historiographical community P among whose members there exists a situation of methodological consensus is possible only as long as the parties involved in the conflict build their theory of D in accordance (a) with a core set of substantive statements about D shared by all P’s members and (b) with P’s common cognitive values. Upon closer examination, if it is true that Tucker’s sketch cannot be simply prescriptive but must also contain a descriptive component (that is to say furnish an adequate representation of the mechanisms of marginal dissensus that are concretely present in the historiographical community), Tucker’s account is prone to the risk of depriving the sphere of historiographical cognitive values of any exclusivity, and making it parasitic on the methodological commitments of empirical sciences in general. After all, it appears difficult to think of a description of the cognitive values that ground the existence of particular historiographical communities under which their investment in concrete research could de facto rest immune from the contamination of substantive values without reducing the former ones to something very similar to the set of fundamental commitments that constitute scientific method (for example, empirical grounding, an interest in justification and consistency, and perhaps falsifiability). The alternative, therefore, seems to be much more rigid than the nuances of Tucker’s approach to the problem may induce to consider. Either interpretive dissensus in P can be expected to be consistent with the preservation and the employment of the cognitive values of P, or radical dissensus is incompatible with the agreement on cognitive values. Although it is evident that Tucker would prefer the first hypothesis, it is not equally clear how this could be reconciled with the need to maintain that the reproduction of the methodological parameters of experimental sciences in other fields is the best strategy to obtain reliable knowledge, at least if such hypothesis were not supported with arguments borrowed from formal theories of knowledge, and therefore from an area of philosophical inquiry that Tucker has assumed to be irrelevant for the analysis of these problems. My impression, overall, is that Tucker’s analysis would have been much more instructive, or at least polemically engaging, if it tried to assess the unique characteristics and implications of the structural commitments that regulate historical research. Maybe, after all, a reduction of the basic methodological commitments of historiography to the key procedural properties of other scientific disciplines is the most correct strategy to generate a consistent theory of the factors that determine the unity of the historiographical community. But wouldn’t it be problematic, in such case, to argue for the application of a theory like KCH to historiography without extensively assessing its validity in other domains of science?

1) T. Kuhn, The Structure of Scientific Revolutions, 3rd ed. (Chicago, IL: University of Chicago Press, 1996).

2) A. Tucker, “The Epistemic Significance of Consensus”, Inquiry, 46 (2003), 501‐521; id., “Consensus and Historiographic Knowledge”, in Our Knowledge of the Past (Cambridge: Cambridge University Press, 2004), 23–45.

3) I am not completely confident about the fact that “cognitive values” is a felicitous expression to describe the class of items sketched in brackets. In any case, in the course of this paper I will conform to this terminological preference, which is the one adopted by Tucker, in the hope that this choice will make more transparent and understandable my discussion of his position.

4) See M. Gilbert, “Modeling Collective Belief ”, Synthese, 73 (1987), 185–204. This requirement may also be read in accordance with Gilbert’s non‐summative account of group belief, according to which members of a population P collectively believe that φ iff they are jointly committed to believing that φ as a body (see her “Belief and Acceptance as Features of Groups”, Protosociology, 16 (2002), 35–69). In this view, in order for P to collectively believe that φ it is not required that members of P individually believe that φ, but only that they (a) have agreed to let φ stand as the position of the group, (b) endorse φ when participating in group activities, and (c) publicly defend φ when acting as group representatives. See also M. Gilbert “Remarks on Collective Belief ”, in F.F. Schmitt (ed.), Socializing Epistemology: The Social Dimensions of Knowledge (Lanham, MD: Rowman & Littlefield, 1994), 235–256.

5) Drawing inspiration from K.B. Wray, “Collective Belief and Acceptance,” Synthese, 129 (2001), 319–333, and form M. Gilbert “Belief and acceptance as features of groups”, I prefer this neutral and coarse-grained formulation to the more intuitive but arguably inappropriate “members of P share beliefs on O,” because “collective beliefs” are species of acceptance rather than proper belief. There are several and important differences between belief and acceptance, and we cannot recall them all here. Let us nonetheless emphasize the difference that most closely interests our analysis: while it is possible to accept a proposition without genuinely believing it, it is impossible to believe in a proposition without accepting it. For example, an agent X involved in the adhesion to a theory T about an object O formulated by its community P may accept T without genuinely believing T, for example because although X agrees to the stipulation that T represents the public position on O of the group, at the same time X assigns higher subjective probability to another theory T* of O (for example the theory T* of O that, in the preliminary phases of the elaboration of the consensus she tried to present to the group as the most reliable and convincing, and whose collective probability was mediated by the judgments of all members of P). A list of the most significant discussions of the theme of acceptance compared to the key characteristics of believing should include: A. Goldman, “Acceptance and Uncertainty”, in Epistemology and Cognition (Cambridge, MA: Harvard University Press, 1986), 324–343; G. Harman, Change in View (Cambridge: Cambridge University Press, 1986); L.J. Cohen, “Belief and Acceptance”, Mind, 98 (1989), 367–389; L.J. Cohen, An Essay on Belief and Acceptance (Oxford: Oxford University Press, 1992); K. Lehrer, Metamind (Oxford: Clarendon Press, 1990); M. Bratman, Faces of Intention (Cambridge: Cambridge University Press 1999); K. Frankish, Mind and Supermind (Cambridge: Cambridge University Press, 2004).

6) See B. Miller, “When is Consensus Knowledge Based?”, forthcoming on Synthese: “to assess whether a situation of knowledge obtains, we need to eliminate veritic luck, epistemic misfortune and non‐cognitive reasons as possible good explanations of the consensus”.

7) See A. Goldman, Knowledge in a Social World (Oxford: Oxford University Press, 1999), 357. More extensively, J. Beatty, “Masking Disagreement Among Experts”, Episteme: A Journal of Social Epistemology, 3 (2006), 52–67.

8) See R.L. Kirkham, Theories of Truth: A Critical Introduction (Cambridge, MA: MIT Press, 1992). See also D. Christensen, “Disagreement as Evidence: The Epistemology of Controversy”, Compass, 4 (2009), 756–767.

9) See P.A. Roth, Meaning and Method in the Social Sciences (Ithaca, NY: Cornell University Press, 1987), 127–128; Goldman, Knowledge in a Social World, 70–1.

10) See N. Rescher, Pluralism: Against the Demand for Consensus (Oxford: Clarendon Press, 1993), 55–57.

11) R.J. Evans, In Defense of History (New York, NY: Norton, 1999).

12) K. Lehrer, C. Wagner, Rational Consensus in Science and Society: A Philosophical and Mathematical Study (Dordrecht: Reidel, 1981).

13) I. Levi, “Consensus as Shared Agreement and Outcome of Inquiry”, Synthese, 62 (1985), 3–11; P. Caws, “Committees and Consensus: How Many Heads are Better than One”, Journal of Medicine and Philosophy, 16 (1991), 375–391.

14) Our Knowledge of the Past, 27.

15) A further clarification is perhaps needed at this point. My argument is not that a theory of the sort of Tucker’s (and, as we shall see, of Miller’s) is insufficient toto coelo to determine if concrete cases of consensus are likely to be knowledge based. Suppose we are called to test KIH on a situation of consensus in a community P at a time t; suppose also that we are demanded to evaluate the statistical probability of the hypothesis that the credential agreement that constitutes it is grounded on genuine knowledge and that, to this end, we do not have access to any information regarding the history of the epistemic practices occurred in P before t and to occur in P after t; in intuitive terms, suppose therefore that the task we are required to perform is to evaluate the compatibility between P and KIH at t on the basis of some sort of photography of P at t providing us only static P-related data. In this case, resorting to an analytical approach like that sketched and encouraged by Tucker is probably the best way to go. My point, on the other hand, is that if we want to increase the plausibility of our ascription of knowledge to a network of consensually ordered agents while we do have some dynamic information regarding it, then we should pay attention to its evolution over time and determine whether or not its history satisfies some relevant requirements.

16) See Miller, “When is Consensus Knowledge Based?”: “My argument is twofold: (a) a consensus is likely to be knowledge based when knowledge is the best explanation thereof; (b) knowledge is the best explanation of a consensus when three conditions obtain together: (1) The Social Calibration Condition – all parties to the consensus are committed to using the same evidential standards, formalism and ontological schemes; (2) The Apparent Consilience of Evidence Condition – the consensus is based on varied lines of evidence that all seem to agree with each other; (3) The Social Diversity Condition – the consensus is socially diverse.”

17) Compare with Tucker, Our Knowledge of the Past, 37.

18) In its most reductive sense, “respect” could be defined as the disposition to attribute to other agents’ opinions a value different from 0 in result of the acknowledgment of their epistemological credibility. Suppose that an agent X believes that an event e has a probability PX(e) = 0.8, whereas e’s likelihood according to an agent Y is PY(e) = 0.60. Let us assume that X believes that Y’s opinion has the chance of being correct with a probability PX(PY(e)) = 0.90 and that X’s degree of confidence in her own opinion (PX(PX(e))) is 0.50. In this situation, a relation of “respect” between X and Y exists because, given X’s disposition to shape her opinion on a subject according to others’ opinion on the same subject, the final value of ΣX(e) = ½ × (PX(PY(e)) × PY(e) + PX(PX(e)) × PX(e))) = ½ × (0.90 × 0.60 + 0.50 × 0.80) = 0.47 is influenced by PY(e) and not only by PX(PX(e)) × PX(e)) (which can happen iff PX(PY(e)) ≠ 0).

19) The term ‘dissensus’ is here preferred to the more common ‘dissent’ to emphasize the public and collective nature of the phenomenon in question versus the private and subjective connotation standardly associated in English to the latter term.

20) See D. Coady, “When Experts Disagree”, Episteme, 3 (2006), 68–79; R. Bradley, “Taking Advantage of Difference in Opinion”, Episteme, 3 (2006), 141–155.

21) The label “higher-order information” is simultaneously used (a) to contrast “first-order beliefs” as the beliefs held by an agent X about the external world and (b) to refer to the set of beliefs held by X about the beliefs of other agents. The “higher-order beliefs” that are relevant for our analysis, naturally, are those representing the probability that other agents’ first-order beliefs may contain adequate descriptions of the world. This probability is constitutively sensitive to the sharing of the same formal dispositions that Tucker lists under the category of “cognitive values”. See B. Skyrms, “Higher Order Degrees of Belief ”, in D.H. Mellor (ed.), Prospects for Pragmatism (Cambridge: Cambridge University Press, 1980), 109–138.

22) Lehrer & Wagner, Rational Consensus in Science and Society. See also M.H. De Groot, “Reaching a Consensus”, Journal of American Statistical Association, 69 (1974), 118–121.

23) The idea that LWM specifies the only rational way of aggregating probability judgments, in particular, has been attacked by many scholars in the field. Those interested should see at least B. Loewer, R. Laddager, “Destroying the Consensus”, Synthese, 62 (1985), 3–11, and R.E. Goodin, “Consensus Interruptus”, The Journal of Ethics, 5 (2001), 121–131.

24) See Bradley, “Taking Advantage of Difference in Opinion”, 148–152.

25) See the reference to movements of historical revisionism interested in denying the Holocaust in Tucker, Our Knowledge of the Past, 33, 39–45.

  • 2)

    A. Tucker, “The Epistemic Significance of Consensus”, Inquiry, 46 (2003), 501‐521; id., “Consensus and Historiographic Knowledge”, in Our Knowledge of the Past (Cambridge: Cambridge University Press, 2004), 23–45.

  • 4)

    See M. Gilbert, “Modeling Collective Belief ”, Synthese, 73 (1987), 185–204. This requirement may also be read in accordance with Gilbert’s non‐summative account of group belief, according to which members of a population P collectively believe that φ iff they are jointly committed to believing that φ as a body (see her “Belief and Acceptance as Features of Groups”, Protosociology, 16 (2002), 35–69). In this view, in order for P to collectively believe that φ it is not required that members of P individually believe that φ, but only that they (a) have agreed to let φ stand as the position of the group, (b) endorse φ when participating in group activities, and (c) publicly defend φ when acting as group representatives. See also M. Gilbert “Remarks on Collective Belief ”, in F.F. Schmitt (ed.), Socializing Epistemology: The Social Dimensions of Knowledge (Lanham, MD: Rowman & Littlefield, 1994), 235–256.

  • 5)

    Drawing inspiration from K.B. Wray, “Collective Belief and Acceptance,” Synthese, 129 (2001), 319–333, and form M. Gilbert “Belief and acceptance as features of groups”, I prefer this neutral and coarse-grained formulation to the more intuitive but arguably inappropriate “members of P share beliefs on O,” because “collective beliefs” are species of acceptance rather than proper belief. There are several and important differences between belief and acceptance, and we cannot recall them all here. Let us nonetheless emphasize the difference that most closely interests our analysis: while it is possible to accept a proposition without genuinely believing it, it is impossible to believe in a proposition without accepting it. For example, an agent X involved in the adhesion to a theory T about an object O formulated by its community P may accept T without genuinely believing T, for example because although X agrees to the stipulation that T represents the public position on O of the group, at the same time X assigns higher subjective probability to another theory T* of O (for example the theory T* of O that, in the preliminary phases of the elaboration of the consensus she tried to present to the group as the most reliable and convincing, and whose collective probability was mediated by the judgments of all members of P). A list of the most significant discussions of the theme of acceptance compared to the key characteristics of believing should include: A. Goldman, “Acceptance and Uncertainty”, in Epistemology and Cognition (Cambridge, MA: Harvard University Press, 1986), 324–343; G. Harman, Change in View (Cambridge: Cambridge University Press, 1986); L.J. Cohen, “Belief and Acceptance”, Mind, 98 (1989), 367–389; L.J. Cohen, An Essay on Belief and Acceptance (Oxford: Oxford University Press, 1992); K. Lehrer, Metamind (Oxford: Clarendon Press, 1990); M. Bratman, Faces of Intention (Cambridge: Cambridge University Press 1999); K. Frankish, Mind and Supermind (Cambridge: Cambridge University Press, 2004).

  • 7)

    See A. Goldman, Knowledge in a Social World (Oxford: Oxford University Press, 1999), 357. More extensively, J. Beatty, “Masking Disagreement Among Experts”, Episteme: A Journal of Social Epistemology, 3 (2006), 52–67.

  • 8)

    See R.L. Kirkham, Theories of Truth: A Critical Introduction (Cambridge, MA: MIT Press, 1992). See also D. Christensen, “Disagreement as Evidence: The Epistemology of Controversy”, Compass, 4 (2009), 756–767.

  • 9)

    See P.A. Roth, Meaning and Method in the Social Sciences (Ithaca, NY: Cornell University Press, 1987), 127–128; Goldman, Knowledge in a Social World, 70–1.

  • 10)

    See N. Rescher, Pluralism: Against the Demand for Consensus (Oxford: Clarendon Press, 1993), 55–57.

  • 11)

    R.J. Evans, In Defense of History (New York, NY: Norton, 1999).

  • 12)

    K. Lehrer, C. Wagner, Rational Consensus in Science and Society: A Philosophical and Mathematical Study (Dordrecht: Reidel, 1981).

  • 13)

    I. Levi, “Consensus as Shared Agreement and Outcome of Inquiry”, Synthese, 62 (1985), 3–11; P. Caws, “Committees and Consensus: How Many Heads are Better than One”, Journal of Medicine and Philosophy, 16 (1991), 375–391.

  • 17)

    Compare with Tucker, Our Knowledge of the Past, 37.

  • 20)

    See D. Coady, “When Experts Disagree”, Episteme, 3 (2006), 68–79; R. Bradley, “Taking Advantage of Difference in Opinion”, Episteme, 3 (2006), 141–155.

  • 24)

    See Bradley, “Taking Advantage of Difference in Opinion”, 148–152.

Sections

References

2)

A. Tucker, “The Epistemic Significance of Consensus”, Inquiry, 46 (2003), 501‐521; id., “Consensus and Historiographic Knowledge”, in Our Knowledge of the Past (Cambridge: Cambridge University Press, 2004), 23–45.

4)

See M. Gilbert, “Modeling Collective Belief ”, Synthese, 73 (1987), 185–204. This requirement may also be read in accordance with Gilbert’s non‐summative account of group belief, according to which members of a population P collectively believe that φ iff they are jointly committed to believing that φ as a body (see her “Belief and Acceptance as Features of Groups”, Protosociology, 16 (2002), 35–69). In this view, in order for P to collectively believe that φ it is not required that members of P individually believe that φ, but only that they (a) have agreed to let φ stand as the position of the group, (b) endorse φ when participating in group activities, and (c) publicly defend φ when acting as group representatives. See also M. Gilbert “Remarks on Collective Belief ”, in F.F. Schmitt (ed.), Socializing Epistemology: The Social Dimensions of Knowledge (Lanham, MD: Rowman & Littlefield, 1994), 235–256.

5)

Drawing inspiration from K.B. Wray, “Collective Belief and Acceptance,” Synthese, 129 (2001), 319–333, and form M. Gilbert “Belief and acceptance as features of groups”, I prefer this neutral and coarse-grained formulation to the more intuitive but arguably inappropriate “members of P share beliefs on O,” because “collective beliefs” are species of acceptance rather than proper belief. There are several and important differences between belief and acceptance, and we cannot recall them all here. Let us nonetheless emphasize the difference that most closely interests our analysis: while it is possible to accept a proposition without genuinely believing it, it is impossible to believe in a proposition without accepting it. For example, an agent X involved in the adhesion to a theory T about an object O formulated by its community P may accept T without genuinely believing T, for example because although X agrees to the stipulation that T represents the public position on O of the group, at the same time X assigns higher subjective probability to another theory T* of O (for example the theory T* of O that, in the preliminary phases of the elaboration of the consensus she tried to present to the group as the most reliable and convincing, and whose collective probability was mediated by the judgments of all members of P). A list of the most significant discussions of the theme of acceptance compared to the key characteristics of believing should include: A. Goldman, “Acceptance and Uncertainty”, in Epistemology and Cognition (Cambridge, MA: Harvard University Press, 1986), 324–343; G. Harman, Change in View (Cambridge: Cambridge University Press, 1986); L.J. Cohen, “Belief and Acceptance”, Mind, 98 (1989), 367–389; L.J. Cohen, An Essay on Belief and Acceptance (Oxford: Oxford University Press, 1992); K. Lehrer, Metamind (Oxford: Clarendon Press, 1990); M. Bratman, Faces of Intention (Cambridge: Cambridge University Press 1999); K. Frankish, Mind and Supermind (Cambridge: Cambridge University Press, 2004).

7)

See A. Goldman, Knowledge in a Social World (Oxford: Oxford University Press, 1999), 357. More extensively, J. Beatty, “Masking Disagreement Among Experts”, Episteme: A Journal of Social Epistemology, 3 (2006), 52–67.

8)

See R.L. Kirkham, Theories of Truth: A Critical Introduction (Cambridge, MA: MIT Press, 1992). See also D. Christensen, “Disagreement as Evidence: The Epistemology of Controversy”, Compass, 4 (2009), 756–767.

9)

See P.A. Roth, Meaning and Method in the Social Sciences (Ithaca, NY: Cornell University Press, 1987), 127–128; Goldman, Knowledge in a Social World, 70–1.

10)

See N. Rescher, Pluralism: Against the Demand for Consensus (Oxford: Clarendon Press, 1993), 55–57.

11)

R.J. Evans, In Defense of History (New York, NY: Norton, 1999).

12)

K. Lehrer, C. Wagner, Rational Consensus in Science and Society: A Philosophical and Mathematical Study (Dordrecht: Reidel, 1981).

13)

I. Levi, “Consensus as Shared Agreement and Outcome of Inquiry”, Synthese, 62 (1985), 3–11; P. Caws, “Committees and Consensus: How Many Heads are Better than One”, Journal of Medicine and Philosophy, 16 (1991), 375–391.

17)

Compare with Tucker, Our Knowledge of the Past, 37.

20)

See D. Coady, “When Experts Disagree”, Episteme, 3 (2006), 68–79; R. Bradley, “Taking Advantage of Difference in Opinion”, Episteme, 3 (2006), 141–155.

24)

See Bradley, “Taking Advantage of Difference in Opinion”, 148–152.

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