1. Introduction: Strategic science skepticism and the argument from disagreement
Suppose you are not a scientific expert, but you know that scientists do research to test a particular scientific claim. Suppose further that you, then, come to know that there is disagreement about that claim in science. How should you react? You should be less confident about the claim than you were before. At least, this advice—to lose confidence in the claim—is the core idea of an argument that strategic science skeptics use to undermine scientific claims: the argument from disagreement. In this paper, my aim is to analyze and to debunk this argument of strategic science skeptics that has been neglected as a subject for thorough philosophical analysis.
Before delving into an analysis of the argument, it is helpful to situate the argument in the context of a larger phenomenon: strategic science skepticism and the claims and arguments of strategic science skeptics. Described as a general phenomenon, strategic science skeptics contest and criticize scientific claims solely to promote economic interests and political agendas.Footnote 1 Skepticism of this sort targets research in climate science, environmental science and health science—that is, strands of research relevant for the industry and for policy-makers.Footnote 2 Consider a well-known example for illustration.Footnote 3 According to climate scientists, there is very good evidence that human CO2 emissions are a major cause of global warming. Yet, strategic science skeptics openly disagree with climate scientists. And strategic science skeptics present arguments for why they disagree, but they disagree for strategic reasons—to achieve certain economic and political goals of their own and/or their sponsors (for instance, the goal of the fossil fuel industry to sell oil and to prevent political regulation of their business). The intended effect of the strategic science skeptics’ claims is to create public distrust in climate science.
Strategic science skeptics use a whole range of arguments to contest scientific claims. One pervasive class of skeptical arguments is directly concerned with the empirical evidence for scientific claims. Relying on such arguments targeting empirical evidence, strategic science skeptics raise objections to scientific research by criticizing that the empirical evidence—produced by scientists’ research—does not support the scientists’ hypotheses. Science skeptics also actively engage in doing research to produce their own (alleged) counterevidence to publicly funded research. Skeptical arguments directed at empirical evidence are implemented in various ways: for instance, by cherry-picking the empirical evidence, by choosing biased research methods to obtain empirical evidence, and by refining concepts used to describe and interpret empirical evidence. Philosophical reflections on strategic science skepticism have been preoccupied with skeptical arguments targeting empirical evidence.Footnote 4
The skeptical argument taking center stage in this paper is strikingly different. The argument from disagreement is not directly concerned with empirical evidence. Instead, the argument operates in the domain of the social epistemology of science: it is concerned with a specific form of testimonial evidence. The argument rests on assumptions about how justification depends on the awareness of disagreement and, respectively, agreement among the testimonies (or reports) of scientists. While the skeptics’ own arguments targeting empirical evidence are often the means to generate disagreements, the skeptical argument in the focus of this paper is concerned with drawing a conclusion from a disagreement after it has been generated. The key idea underlying this argument from disagreement is that someone who is not a scientific expert, a lay person, should lose confidence in the truth of a scientific claim once that person has come to know that there is a disagreement about the claim. I will take a normative stance: I will analyze and debunk this argument. That is, I will show why it is flawed.Footnote 5
More precisely, the plan of the paper is as follows. In section 2, I will propose a reconstruction of the argument from disagreement as a deductively valid inference from two premises to a conclusion. In section 3, I will develop what I call the Justificatory Account of Multiple Testimony that will serve as the basis for debunking the argument. This account provides a normative characterization of how learning about agreements and disagreements is connected to confirming and disconfirming scientific claims. I will draw on Bayesian confirmation theory as a framework for articulating a precise version of this account. For this purpose, I treat Bayesian confirmation theory (i) as a tool for debunking the skeptics’ argument (that is, I will apply, but not attempt to defend or improve, Bayesianism), (ii) as a normative theory of how confirmation should work (aligning with the general normative stance of this paper), and (iii) as one possible normative frameworkFootnote 6 for articulating the Justificatory Account of Multiple Testimony and for debunking the skeptics’ argument. In sections 4 and 5, I will use the Bayesian version of the Justificatory Account of Multiple Testimony to argue that both premises of the skeptics’ argument from disagreement are false. Hence, the skeptics’ argument is flawed because it is not sound. Section 6 presents the conclusions of my arguments.
2. Analyzing the argument from disagreement
In its perhaps most iconic form, the argument from disagreement is stated in a confidential, internal document of the tobacco industry, the infamous “Smoking and Health Proposal” (Brown and Williamson 1969). Indeed, historians of science regard this document as the paradigmatic case of strategic science skepticism and as the model that guided strategic science skeptics in extending skepticism from biomedical research on the health effects of smoking cigarettes to other sciences (including environmental and climate sciences).Footnote 7 Moreover, the key phrase of the document—“doubt is our product”—has inspired the analytic terminology of doubt mongering, of producing doubt, and of ignorance that historians of science and subsequently philosophers have begun to use (see footnotes 1–4 for references).
In the document, a public relations strategy is proposed allowing the tobacco industry to respond to biomedical research on the adverse health effects of smoking—research that is the basis of regulation of and lawsuits against the tobacco industry. The strategy is abstractly characterized as follows: “Our consumer I have defined as the mass public, our product as doubt, and our message as truth well stated, and our competition as the body of anti-cigarette fact that exists in the public mind” (Brown and Williamson 1969, 3–4).Footnote 8 The document offers advice on how to handle a situation in which the “mind of the general public” (Brown and Williamson 1969, 4) is in the grip of “anti-cigarette facts” and “misinformation” (ibid.) stemming from biomedical research and supporting, for instance, the claim that smoking causes lung cancer. To change the “mind of the general public” (ibid.), it is suggested to create “doubt” about the relevant scientific information:
Doubt is our product since it is the best means of competing with the ‘body of fact’ that exists in the mind of the general public. It is also the means of establishing controversy. Within the business we recognize that a controversy exists. However, with the general public the consensus is that cigarettes are in some way harmful to the health. If we are successful in establishing a controversy at the public level, then there is an opportunity to put across the real facts about smoking and health. (Brown and Williamson 1969, 4)
The advice is to establish a “controversy” via raising “doubt” about those scientific claims that are troublesome for the economic interests of the tobacco industry. Questioning and criticizing scientific claims is instrumental to creating the impression in the “mind of the general public” that there is a disagreement or controversy about the scientific claims. In a first approximation, this strategic advice attempts to exploit a connection between (i) the public becoming aware of there being a “controversy” or a disagreement—instead of an agreement—about a scientific claim within science, and (ii) as a response to this awareness, an increased doubtfulness or, equivalently, a decreased confidence regarding that scientific claim in the “mind of the general public.”
The second prominent instance of the argument from disagreement is exemplified by the advice of Frank Luntz, a political consultant of the Republican Party in the United States.Footnote 9 Luntz writes the following about research in climate science to promote the Republican political agenda (that includes protecting the business interests of the fossil fuel industry and preventing its regulation): “The scientific debate remains open. Voters believe that there is no consensus about global warming within the scientific community. Should the public come to believe that the scientific issues are settled, their views on global warming will change accordingly” (quoted after Michaels Reference Michaels2008a, 198; original emphases).
Luntz discusses a situation that differs from the problem that the “Smoking and Health Proposal” addresses. As described above, the tobacco industry faced a public opinion according to which there is agreement within biomedical sciences regarding the effect of smoking—and the skeptics’ aim was to raise doubt about the existence of such a consensus within science. By contrast, Luntz’s strategic advice intends to perpetuate an already existing public impression of disagreement within climate science and to prevent a public perception of scientific agreement from emerging.
To prevent that the public “comes to believe that the scientific issues are settled,” Luntz suggests creating the impression that the research results of climate science are not settled yet and that, instead, there is a still “open” scientific debate including disagreements and “a lack of scientific certainty” within the climate scientific community (Michaels Reference Michaels2008a, xi, 198; Reference Michaels2008b, 91–93). Luntz draws on the same connection between public awareness of disagreement and decreased confidence of the public that is already implicit in Brown and Williamson (1969). Interestingly, Luntz frames this connection in terms of belief. On the one hand, if the public perceives scientists to agree on a scientific claim, then the public will strongly believe it (i.e. be confident about the truth of the claim). On the other hand, if the public thinks that there is scientific disagreement about a claim, then “their views on global warming will change accordingly”—that is, the public will disbelieve the claim at issue or believe it less strongly.
The skeptics do not present their argument from disagreement in a standard premise–conclusion form. I propose the following reconstruction:
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1. Disagreement Premise: A member of the public learns that there is disagreement about a scientific hypothesis H.Footnote 10
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2. The Doubt Rule: If a member of the public learns that there is disagreement about a scientific hypothesis H, then this person should be less confident about the truth of H (that is, less confident than before having learned about the disagreement).
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3. Conclusion: Thus, the member of the public should be less confident about the truth of H.
Let me add two clarificatory remarks about this reconstruction before moving on to describing the challenge the argument poses.
The first remark concerns the expression “member of the public” in my reconstruction. I use an individualistic approach by referring to individuals who are members of the public instead of to a collective subject as suggested by the skeptics’ expressions such as “the mind of the general public.” I choose this approach, because, for present purposes, it is not necessary to commit to any substantive talk about collective agents and their mental states.
The second remark concerns room for interpretation in reconstructing the second premise. The Doubt Rule allows for different possible versions:Footnote 11
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(i) Disbelief version: If a member of the public learns that there is disagreement about a scientific hypothesis H, then this person should disbelieve H (i.e. believe that ¬H is true).
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(ii) Suspension-of-judgment version: If a member of the public learns that there is disagreement about a scientific hypothesis H, then this person should suspend judgment about the truth (and falsity) of H.
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(iii) Low-confidence version: If a member of the public learns that there is disagreement about a scientific hypothesis H, then this person should have low confidence in the truth of H.
The version of the Doubt Rule I choose in the reconstruction above is what one might call the lowering-confidence version. It demands that a member of the public should—having learned about a disagreement regarding hypothesis H—become less confident about the truth of H. I take the lowering-confidence version to be the weakest version of the Doubt Rule. In other words, I assume that it is an easier task for strategic science skeptics to defend the lowering-confidence version than to defend the three other possible versions of the Doubt Rule. I will work with this version of the Doubt Rule, because it constitutes the most charitable way of reconstructing the skeptics’ argument from disagreement. If one rebuts the weakest version of the Doubt Rule, as I intend to do, then its stronger versions become untenable in one sweep.
The challenging character of the skeptics’ argument from disagreement arises from the central role of agreement (or consensus)Footnote 12 as a marker for credible and justified scientific claims. Indeed, many historians and philosophers of science accept such a central and productive epistemic role of agreement in science and take it as the subject of their analyses.Footnote 13 To dramatize the challenge, strategic science skeptics who draw on the argument from disagreement can happily accept the view that agreement is central to good science and to the credibility of scientific claims. Then, the skeptics diagnose that there is disagreement—hence, no agreement—about a specific scientific claim (such as the claim that smoking causes lung cancer). From the skeptics’ point of view, this is all that is needed to apply the argument from disagreement to a scientific claim they would like to undermine.
I will explore a way of debunking the argument from disagreement. Indeed, Oreskes and Conway present a glimpse of such an argumentative strategy: “If the scientific community has been asked to judge a matter (as the National Academy of Sciences routinely is)—or if they have self-organized to do so (as in the Ozone Trends Panel or the IPCC), then it makes sense to take the results of their investigations very seriously. […] It does not make sense to dismiss them just because some person, somewhere, doesn’t agree” (Oreskes and Conway Reference Oreskes and Conway2010, 272–73; emphasis added). I read this passage as follows: Oreskes and Conway would like to maintain that agreement plays a crucial and productive epistemic role in science. At the same time, they would like to reject the skeptics’ argument from disagreement. The problem with Oreskes and Conway’s approach is not that it is implausible. Instead, the real problem consists in the lack of a detailed argument supporting it. For this reason, my main goal is to provide such a detailed argument. I base this argument on the Justificatory Account of Multiple Testimony.
3. The (Bayesian) Justificatory Account of Multiple Testimony
In the previous section I have assumed, alongside historians and philosophers of science as well as—perhaps surprisingly—with strategic science skeptics, that agreement plays a central epistemic role in science. But what could this epistemic role be? I will propose an account according to which the epistemic role of agreement consists in justifying or confirming scientific claims.Footnote 14 Since I consider agreement and disagreement as a special sort of testimonial evidence (as I will explain below), I will attempt to capture this justificatory role in terms of the Justificatory Account of Multiple Testimony. I will present the general version of the Justificatory Account of Multiple Testimony (subsection 3.1). To make the notion of justification or confirmation figuring in this account more precise, I will develop a version of the account that is articulated with the help of Bayesian confirmation theory (subsection 3.2).
3.1. The Justificatory Account of Multiple Testimony—general version
To develop the Justificatory Account of Multiple Testimony, I will first lay a terminological foundation: I will propose a definition for the key concepts of agreement and disagreement as forms of testimonial evidence consisting of the testimonies or witness reports of scientists. In a second step, I will make an assumption about which different kinds of reports are relevant in scientific contexts. In a final third step, I will articulate the Justificatory Account of Multiple Testimony itself.
First step: Testimonial definitions of agreement and disagreement. I will draw on the concept of testimony taking center stage in social epistemology.Footnote 15 In social epistemology, testimonies are also referred to as the reports of witnesses. I will use the notions of testimonies and of witness reports interchangeably and I will assume that in scientific contexts scientists can and occasionally do act as witnesses by reporting or testifying to the truth or falsity of propositions.
I propose to define the notions of scientific agreement and disagreement as consisting of the testimonies or reports of multiple witnesses, where the reports regard the truth of some proposition.Footnote 16
Testimonial Definition of Scientific Agreement: There is a scientific agreement about a proposition R if and only if multiple witnesses (typically scientists) all report that proposition R is true.
Testimonial Definition of Scientific Disagreement: There is a scientific disagreement about a proposition R if and only if multiple witnesses differ in their reports as to whether proposition R is true—some say it is, others say it is not (that is, others say that ¬R is true).
In what follows, I will adopt these definitions of scientific agreement and disagreement.Footnote 17 If defined in this way, both agreement and disagreement can play the role of testimonial evidence consisting of the testimonies or reports of multiple witnesses, or so I will argue below.
Second step: Characterizing reports in science. Are there reports in science? If so, what is the content of scientific reports? The Justificatory Account of Multiple Testimony I am about to develop is flexible in allowing for different kinds of reported propositions. In science, reports come in different (often published) forms,Footnote 18 including the following:
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1. The report of a scientist may consist in summarizing the results of the scientist’s research: that is, the empirical evidence she obtained by using a specific method and how this empirical evidence should be interpreted with respect to confirming or disconfirming a hypothesis of interest. Consider a toy example of what such a report might look like: “In my laboratory, I heated water, used a mercury thermometer, and measured that the water boiled at about 100 degrees Celsius. This is empirical evidence confirming the hypothesis that water boils at 100 degrees Celsius.” The non-toyish form of such a report is a research paper.
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2. Reports sometimes express the expert assessment of a scientist regarding the justificatory status of a hypothesis based on the state of the art in the research of a scientific field. A typical locus for this kind of report is a meta-study or an assessment report. Again, imagine a simple example for illustration: “Given the research in my field of expertise, I can say that the hypothesis that smoking causes lung cancer is empirically well-confirmed.”
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3. Reports can be expert judgments on a specific subject matter for which there is, at the time, no available empirical evidence, but the judgment is informed by research on directly related matters. For instance, an expert might testify in the following manner: “Although there is no empirical evidence at present as to how the new virus V is transmitted, it is likely that V is transmitted via respiration given that there is a vast amount of research on the transmission of similar viruses and this research provides strong empirical evidence for this mode of transmission.”
I do not claim that this list is an exhaustive and systematic typology of scientific reports. I merely assume that, if it makes sense to talk about the reports of scientists at all, the list presents plausible examples of such reports.Footnote 19
Third step: Articulating the Justificatory Account of Multiple Testimony. Having provided testimonial definitions of agreement and disagreement, and having clarified the character of scientific reports, I now proceed to articulating the Justificatory Account of Multiple Testimony. I begin with a general version of the account.
Justificatory Account of Multiple Testimony (general version): The reports of multiple witnesses justify some hypothesis H if and only if the total testimonial evidence (that is, the entirety of reports) provides a reason for an epistemic agent to belief that H is (more likely to be) true.
Henceforth, I will adopt the following convention regarding notation: R denotes a positive report justifying or confirming H, while ¬R refers to a negative report that disconfirms H (and, hence, confirms ¬H).Footnote 20
Consider a toy example to illustrate the general version of the account (inspired by the first kind of scientific report listed in the second step above). Suppose that the hypothesis H in question is that water boils at 100 degrees Celsius. Imagine further that ten scientists do their experiments individually to test this hypothesis and they all report the following proposition R afterwards: “In my experiment, I measured that water boiled at 100 degrees Celsius.” Finally, assume that—surely, counter to fact—the ten reports are all the reports there are regarding this hypothesis. These ten reports constitute the total testimonial evidence (the entirety of reports). This is a situation of agreement. According to the Justificatory Account of Multiple Testimony, these ten reports justify the hypothesis that water boils at 100 degrees Celsius if and only if the ten reports provide a reason for an epistemic agent to believe that this hypothesis is (more likely to be) true.
Note that, in this toy example, I assume that there is agreement in the sense defined above: all ten scientists report the same proposition. However, I will argue in section 5 that agreement is not necessary for justifying a hypothesis via testimonial evidence. Even if witnesses disagree, the total testimonial evidence might still justify the hypothesis in question. Hence, to make conceptual room for something less than agreement (relative to a group of witnesses), I refer to “the reports of multiple witnesses” when articulating the Justificatory Account of Multiple Testimony in its general version.
3.2. The Justificatory Account of Multiple Testimony—Bayesian version
The general version of the Justificatory Account of Multiple Testimony raises a question: What does the vague demand that reports provide a reason to believe a hypothesis amount to? Bayesian confirmation theory provides one possible and fruitful way to make the rough idea of providing a reason to believe a hypothesis more precise.Footnote 21
Justificatory Account of Multiple Testimony (Bayesian version): The reports of multiple witnesses confirm hypothesis H if and only if the following condition holds: when an epistemic agent learns about the total testimonial evidence (the entirety of reports), then the agent should have greater confidence in the truth of H.
Bayesians interpret the vague notion of an epistemic agent having greater confidence in the truth of a hypothesis in terms of subjective probabilities: the agent assigns a posterior probability to H being true, P*(H), that is greater than the prior probability the agent assigned to H, P(H). In the context of multiple reports, the prior probability is the probability the agent assigned to H before receiving the reports, whereas the posterior probability is the probability the agent assigns to H after having received the reports.
If we use W i (R) to express that one of n witnesses, witness i, reports that proposition R is true, and K to express background knowledge, then Bayesians articulate the Justificatory Account of Multiple Testimony via this inequality (for i = 1, …, n):
${{\bf{P}}^*}\left( H \right) = {\bf{P}}{\rm{[}}H{\rm{|}}{W_1}\left( R \right),{\rm{\;}} \ldots, {W_n}\left( R \right),{\rm{\;}}K] \gt {\bf{P}}(H{\rm{|}}K{\rm{)}}.$
This Bayesian articulation rests on three basic assumptions. First, I adopt Earman’s proposal to state the Bayesian version explicitly as being conditional on the background knowledge K of an epistemic agent (Earman Reference Earman1992, 33–34; Reference Earman2000, 26–27 and 55). I take such background knowledge to include previously acquired empirical knowledge (that is, previously obtained research results, including empirical evidence) as well as methodological and conceptual knowledge, shared and accepted in a field of scientific inquiry.Footnote 22
Second, I assume that, if an epistemic agent learns the total testimonial evidence—that is, the reports W 1(R), …, W n (R)—then it does not make a difference to the posterior probability whether the agent learns the entire testimonial evidence all at once or in chunks over time.
Third, I assume for simplicity’s sake that an epistemic agent obtains the posterior probability of H via the updating rule of strict conditionalization, according to which (testimonial) evidence is believed with certainty.Footnote 23 In other words, appealing to Bayes’ theorem, the posterior probability P*(H) is determined as follows:Footnote 24
${{\bf{P}}^*}\left( H \right) = {\bf{P}}[H|{W_1}\left( R \right),\; \ldots, \;{W_n}\left( R \right),\;K ]= {1 \over {1 + \;\left( {{{{\bf{P}}(\neg H|K)} \over {{\bf{P}}(H|K)}}} \right) \times \left( {{{{\bf{P}}[{W_1}\left( R \right)|\neg H,\,K]} \over {{\bf{P}}\left[ {{W_1}\left( R \right){\rm{|}}H,\,K} \right]}} \times \cdots \times {{{\bf{P}}[{W_n}\left( R \right)|\neg H,\,K]} \over {{\bf{P}}\left[ {{W_n}\left( R \right){\rm{|}}H,\,K} \right]}}} \right)}}.$
To see how the Bayesian version works, it is helpful to assume that two conditions hold: the Minimal Reliability Condition and the Conditional Independence Condition. The second condition is strictly speaking not a necessary one, if one would like to adopt the Justificatory Account of Multiple Testimony. I appeal to it mainly to keep the exposition of the Bayesian version simple. Indeed, there are various proposals of how to phrase and to weaken the (simplifying or idealized) notion of conditional independence to render it plausible in scientific contexts (involving collaboration and exchange between scientists).Footnote 25 It is not my goal to assess the merit of such proposals. Here, my focus will be on the minimal reliability of witnesses.
According to the Minimal Reliability Condition, it is more probable that a witness W i reports R if the conjunction of H and, as already indicated above, background knowledge K is true rather than if ¬H and K is true. This condition expresses the intuition that, for a reliable witness, the content of a report (R or ¬R) depends sensitively on the truth of H and K. Mathematically, we can express the Minimal Reliability Condition Footnote 26 regarding W i ’s reporting of R as follows in terms of likelihoods:
$\displaystyle{\bf{P}}\left[ {{W_i}\left( R \right){\rm{|}}H,{\rm{\;}}K} \right] \gt {\bf{P}}\left[ {{W_{\rm{i}}}\left( R \right){\rm{|}}\neg H,\,K} \right].$
The assumption that a witness is minimally reliable can also usefully and equivalently be expressed as a likelihood ratio that is greater than 1:
${{{\bf{P}}[{W_i}\left( R \right)|H,\,K]} \over {{\bf{P}}\left[ {{W_i}\left( R \right){\rm{|}}\neg H,\,K} \right]}} \gt 1.$
Moreover, it holds that a witness W i is minimally reliable with respect to reporting R if and only if W i is also minimally reliable in reporting ¬R:
${{{\bf{P}}[{{\rm{W}}_{\rm{i}}}\left( {\rm{R}} \right)|{\rm{H}},{\rm{K}}]} \over {{\bf{P}}\left[ {{{\rm{W}}_{\rm{i}}}\left( {\rm{R}} \right){\rm{|}}\neg {\rm{H}},{\rm{K}}} \right]}} \gt 1 \Leftrightarrow {{{\bf{P}}[{{\rm{W}}_{\rm{i}}}\left( {\neg {\rm{R}}} \right)|\neg {\rm{H}},{\rm{K}}]} \over {{\bf{P}}\left[ {{{\rm{W}}_{\rm{i}}}\left( {\neg {\rm{R}}} \right){\rm{|H}},{\rm{K}}} \right]}} \gt 1$
The Conditional Independence Condition requires that the reports of multiple witnesses asserting that R (and, respectively, that ¬R) is true be probabilistically independent, conditional on whether H and K is true (or whether ¬H and K) is true. The intuition expressed by this condition is that the report of one witness is not affected by what other witnesses report. The Conditional Independence Condition with respect to reporting R is stated as follows in formal terms (for i = 1, …, n):
${\bf{P}}\left[ {{W_i}\left( R \right){\rm{|}}{W_1}\left( R \right),{\rm{\;}} \ldots, {\rm{\;}}{W_{i - 1}}\left( R \right),{\rm{\;}}{W_{i + 1}}\left( R \right), \ldots, {W_n}\left( R \right),{\rm{\;}}H,{\rm{\;}}K} \right] = {\bf{P}}\left[ {{W_{\rm{i}}}\left( R \right){\rm{|}}H,{\rm{\;}}K} \right],$
and respectively for ¬R:
${\bf{P}}\left[ {{W_i}\left( {\neg R} \right){\rm{|\;}}{W_1}\left( {\neg R} \right),{\rm{\;}} \ldots, {\rm{\;}}{W_{i - 1}}\left( {\neg R} \right),{\rm{\;}}{W_{i + 1}}\left( {\neg R} \right), \ldots, {W_n}\left( {\neg R} \right),{\rm{\;}}\neg H,{\rm{\;}}K} \right]$
$= {\bf{P}}\left[ {{W_i}\left( {\neg R} \right){\rm{|}}\neg H,{\rm{\;}}K} \right].$
There is also a second and equivalent way to express conditional independence (for i = 1, …, n):
${\bf{P}}\left[ {{W_1}\left( R \right), \ldots, {W_n}\left( R \right){\rm{|}}H,\,K} \right] = {\bf{P}}\left[ {{W_1}\left( R \right)|H,\,K] \times \cdots \times {\bf{P}}[{W_n}\left( R \right){\rm{|}}H,\,K} \right]$
and
${\bf{P}}\left[ {{W_1}\left( {\neg R} \right), \ldots, {W_n}\left( {\neg R} \right){\rm{|}}\neg H,\,K} \right] = {\bf{P}}\left[ {{W_1}\left( {\neg R} \right)|\neg H,\,K] \times \cdots \times {\bf{P}}[{W_n}\left( {\neg R} \right){\rm{|}}\neg H,\,K} \right].$
In what follows, I will appeal to the second way of stating independence.Footnote 27
To summarize, if the Minimal Reliability Condition and the Conditional Independence Condition are satisfied, then the Bayesian Justificatory Account of Multiple Testimony holds.
To simplify matters for the remainder of the paper, I will talk straightforwardly about likelihood ratios and not about posterior probabilities. In doing so, I will appeal to what I will call the Confirmation Likelihood Principle, according to which multiple reports confirm H if and only if the likelihood ratio (regarding all relevant reports) is greater than 1. Formally, we can express this principle as follows (for i = 1, …, n):
${\bf{P}}[H|{W_1}\left( R \right),{\rm{\;}} \ldots, {\rm{\;}}{W_n}\left( R \right),{\rm{\;}}K] \gt {\bf{P}}(H{\rm{|}}K{\rm{)}} \Leftrightarrow {{{\bf{P}}\left[ {{W_1}\left( R \right),{\rm{\;}} \ldots, {\rm{\;}}{W_n}\left( R \right){\rm{|}}H,\,K} \right]} \over {{\bf{P}}\left[ {{W_1}\left( R \right),{\rm{\;}} \ldots, {\rm{\;}}{W_n}\left( R \right){\rm{|}}\neg H,\,K} \right]}} = :x \gt 1.$
The Confirmation Likelihood Principle is the formal core of the Bayesian version of the Justificatory Account of Multiple Testimony.Footnote 28
With this principle in place, let me turn to an illustration of how the Bayesian version of the Justificatory Account of Multiple Testimony works. Suppose that two witnesses, W 1 and W 2, both report R, expressed as “W 1(R)” and “W 2(R)”. These reports constitute the total testimonial evidence in the imagined situation. In other words, we imagine a scenario of agreement regarding R (in the sense of agreement defined in subsection 3.1). Given that the two witnesses are minimally reliable and report independently, their individual likelihood ratios can be multiplied (see the second way of expressing conditional independence) and the product of their individual likelihood ratios is greater than 1. This can be stated—regarding the minimally reliable and conditionally independent reporting of R—by the following inequality, in which each fraction expresses the likelihood ratio for a single witness (for i = 1, 2):
${{{\bf{P}}[{W_1}\left( R \right)|H,\,K]} \over {{\bf{P}}\left[ {{W_1}\left( R \right){\rm{|}}\neg H,\,K} \right]}} \times {{{\bf{P}}[{W_2}\left( R \right)|H,\,K]} \over {{\bf{P}}\left[ {{W_2}\left( R \right){\rm{|}}\neg H,\,K} \right]{\rm{\;}}}} \gt {{{\bf{P}}[{W_i}\left( R \right)|H,\,K]} \over {{\bf{P}}\left[ {{W_i}\left( R \right){\rm{|}}\neg H,\,K} \right]{\rm{\;}}}} \gt 1.$
Now, if the inequality above holds, then, according to the Confirmation Likelihood Principle, the reports of the witnesses W
1 and W
2 (the total testimonial evidence) confirm H—that is, the posterior probability is greater than the prior probability
${\bf{P}}(H|K)$
.Footnote
29
It is worth stressing the increased confirmatory power of multiple reports in comparison to a single report. Although each single report considered in isolation constitutes confirming evidence for H, in this illustration the product of the two individual likelihood ratios is greater than the individual likelihood ratio of each witness considered in isolation. For this reason, the reports of the two witnesses—the total testimonial evidence in this situation—provide stronger confirming evidence for the truth of H than the report of either W
1 or W
2 in isolation. That is, the posterior probability
${\bf{P}}[H|{W_1}\left( R \right),{W_2}\left( R \right),K]$
is not only greater than the prior probability
${\bf{P}}(H|K)$
but also greater than the posterior probability resulting from conditionalizing on only one of the two witness reports in isolation—that is,
${\bf{P}}(H|{W_i}\left( R \right),K)$
. (The distinction between the total testimonial evidence and a single report considered in isolation will resurface in subsection 5.1.)
In what follows (especially in section 5), I will use the notion of Collective Reliability as a term of art to refer to the product of the likelihood ratios of a specified group of witnesses. (In the illustration above, the specified group consists of the witnesses W 1 and W 2.) The notion of Collective Reliability draws on reliability as defined in terms of likelihood ratios (already introduced for individual witnesses in the Minimal Reliability Condition above).
4. The counterargument from unreliable witnesses (against the Disagreement Premise)
To debunk the skeptics’ argument, I begin with a counterargument to the Disagreement Premise. In a first step, I will propose that Bayesians should revise this premise. Then, I will argue that the revised premise does not hold, at least typically, if the reports of skeptics are part of a disagreement.
First, observe that the Disagreement Premise in its original form (section 2) does not require that witnesses (who disagree) be minimally reliable ones. However, on the Bayesian version of the Justificatory Account of Multiple Testimony, witnesses must be minimally reliable, if their reports that R (or that ¬R) are supposed to confirm (or to disconfirm) H. For this reason, a proponent of the Bayesian version should reject the Disagreement Premise as not being sufficiently well formulated and insist on revising it as follows:
Revised Disagreement Premise: A member of the public learns that minimally reliable (and independently reporting) witnesses disagree in their reports (some report R, while others report ¬R) regarding a scientific hypothesis H.
It is useful to explain briefly why Bayesians should indeed reject and revise the original form of the premise. For this purpose, it is important to realize that witnesses might fail to be reliable in two different ways.Footnote 30
First, a witness might be non-reliable in the sense that it is probabilistically irrelevant for the report R of a witness whether H is true (given K). Mathematically, non-reliability can be expressed as follows:
${{{\bf{P}}[{W_i}\left( R \right)|H,\,K]} \over {{\bf{P}}\left[ {{W_i}\left( R \right){\rm{|}}\neg H,\,K} \right]}} = 1.$
Another way in which a witness might fail to be minimally reliable is even more drastic, as an unreliable witness might be anti-reliable in the following sense of the term:
${{{\bf{P}}[{W_i}\left( R \right)|H,\,K]} \over {{\bf{P}}\left[ {{W_i}\left( R \right){\rm{|}}\neg H,\,K} \right]}}{\rm{ \lt}}1.$
In other words, it is more probable that the witness provides a positive confirming report R if H is false than if H is true (given K). A concrete illustration might consist in a witness reporting R to intentionally mislead someone to believe that H is true.
I take it as a premise that the Confirmation Likelihood Principle can be adapted (by drawing on Bayes’ theorem)Footnote 31 to describe the logical relationship between the likelihood ratio of a witness, on the one hand, and confirmationally neutral and disconfirming reports, on the other hand. For present purposes, this adaptation takes the form of two principles:
-
(i) If the likelihood ratio of a witness W i with respect to reporting R is equal to 1, then the report of the witness is confirmationally neutral with respect to H (relative to K)—that is,
${\bf{P}}{\rm{[}}H{\rm{|}}{W_i}\left( R \right),{\rm{\;}}K] = {\bf{P}}(H{\rm{|}}K{\rm{)}}$
. -
(ii) If the likelihood ratio of a witness W i with respect to reporting R is smaller than 1, then the report of the witness disconfirms H (relative to K)—that is,
${\bf{P}}{\rm{[}}H{\rm{|}}{W_i}\left( R \right),{\rm{\;}}K] \lt {\bf{P}}(H{\rm{|}}K{\rm{)}}$
.
Now, according to principle (i), if a non-reliable witness reports R, then the report is confirmationally neutral with respect to H. Stating that a report is confirmationally neutral does not imply that an epistemic agent ignores the report or “silences” the witness. To the contrary, an epistemic agent learns this report but then realizes that the resulting posterior probability equals the prior probability assigned to the hypothesis. If one imagines multiple non-reliable witnesses, the situation remains unchanged: even the reports of multiple non-reliable witnesses do not increase the posterior probability, as the Collective Reliability is equal to 1.
According to principle (ii), the report of an anti-reliable witness (that R) should be taken to disconfirm H. If multiple anti-reliable witnesses report that R, then the disconfirming impact on H increases, as the Collective Reliability of anti-reliable witnesses gets smaller as the number of such witnesses grows.
Moving on to the second step, suppose an epistemic agent learns that there is a disagreement about a hypothesis (partly or entirely) because strategic science skeptics themselves provide disconfirming reports. Does the epistemic agent learn in this situation that there is the kind of disagreement required by the Revised Disagreement Premise? In other words, is the premise true of such situations? The answer turns on the question of whether the agent should think that the skeptics report in a minimally reliable way.
To address this question, I will build on various criteria (or indicators) for ascribing unreliability proposed in the research literature on strategic science skepticism.Footnote 32 I realize that these criteria might be controversial, and my goal here is not to defend or evaluate these criteria. I only intend to explore the consequences of accepting some of these criteria in a Bayesian framework.Footnote 33 I believe a plausible case can be made that skeptics, at least typically, fail to qualify as minimally reliable witnesses if one accepts these criteria.Footnote 34
To start with a prominent proposal for such a criterion, Oreskes and Conway diagnose that strategic science skeptics typically lack scientific expertiseFootnote 35 in the field of research they target (2010, 8, 270–73).Footnote 36 If one takes the lack of expertise as a criterion for not being a reliable witness, then skeptics should, at least typically, be deemed unreliable (at least, regarding a specific field).Footnote 37 As a consequence, a skeptic’s report fails to constitute disconfirming evidence and one should not be less confident about a hypothesis “just because some person, somewhere, doesn’t agree” (Oreskes and Conway Reference Oreskes and Conway2010, 272). The Bayesian version of the Justificatory Account of Multiple Testimony can express this consequence in a precise way, if one accepts Oreskes and Conway’s criterion for assigning unreliability. Indeed, the Bayesian version provides a nuanced distinction of two failures of minimal reliability and the corresponding rational changes of belief.
If one considers the research literature more broadly, one can rely on further criteria for diagnosing that skeptics are unreliable witnesses (criteria potentially complementing the lack of expertise criterion). For instance, the reports of skeptics frequently contain systematic errors. From a philosophical perspective, these errors are analyzed in different ways; for instance, errors are described as skeptics assessing empirical evidence and how it supports a hypothesis in outright distorting (Douglas Reference Douglas2009; Carrier Reference Carrier, Christian, Hommen, Retzlaff and Schurz2018; Reutlinger Reference Reutlinger2020) or misleading ways (Steel Reference Steel2018), as violating methodological standards (Wilholt Reference Wilholt2009; Biddle and Leuschner Reference Biddle and Leuschner2015), and as avoiding quality-control mechanisms (such as peer review) accepted in the relevant scientific community (Oreskes and Conway Reference Oreskes and Conway2010). For current purposes, I take the presence of systematic error to indicate a lack of reliability.
If one accepts these criteria, then one has good reasons for deeming skeptics unreliable witnesses—that is, non-reliable or anti-reliable witnesses.Footnote 38 However, as argued above, the Revised Disagreement Premise requires that witnesses be reliable. Hence, an epistemic agent does not learn the sort of disagreement expressed by the Revised Disagreement Premise (that is, a disagreement among reliable witnesses) if the agent learns about the existence of a disagreement (partly or entirely) constituted by the reports of unreliable skeptics. In other words, the Revised Disagreement Premise is not true of such situations. This result constitutes a serious limitation to the ability of strategic science skeptics to use the argument from disagreement to undermine specific scientific hypotheses (I will return to this issue of limitation in subsection 5.4).Footnote 39
5. The counterargument from total testimonial evidence (against the Doubt Rule)
Another way to debunk the skeptics’ argument from disagreement consists in rejecting the Doubt Rule. The skeptics seem to suppose that the Doubt Rule is a general rule holding in all (or an indefinitely wide range of) situations. I will use the Bayesian Justificatory Account of Multiple Testimony to develop the counterargument from total testimonial evidence to reject the Doubt Rule as a general rule, since it fails to hold in certain situations. I will do so by arguing that there are situations in which an agent learns about the disagreeing reports of witnesses (in relation to a hypothesis H) and the agent is not forced to lower her confidence in H but to be more confident about the truth of H.
The key idea of the counterargument is as follows. The Justificatory Account of Multiple Testimony—especially in its Bayesian version—does not require agreement to confirm a hypothesis via testimonial evidence. What really matters for confirming a hypothesis is whether the total testimonial evidence—that is, the entirety of reports given by independently and reliably reporting witnesses—confirms the hypothesis. To illustrate what the total testimonial evidence might amount to, it is useful to distinguish two situations. In the first situation, we assume that all the reporting witnesses are equally minimally reliable (subsection 5.1), while in the second situation all witnesses are minimally reliable but not equally so (subsection 5.2). I will argue that the two situations constitute failures of the Doubt Rule as a general rule (subsection 5.3) and discuss the merit of a possible, charitable revision of the Doubt Rule (subsection 5.4).
5.1. First situation: Equally reliable witnesses
Suppose that the reporting witnesses are all equally minimally reliable—that is, they all have the exact same likelihood ratio—and they report independently of one another. To illustrate, imagine a concrete realization of this kind of situation with a group of three witnesses, W 1, W 2, and W 3. Two of them, W 1 and W 2, report that R is true. The third witness, W 3, reports that ¬R is true. This is a situation of disagreement, according to the testimonial definition of disagreement (subsection 3.1). Given that all witnesses are equally minimally reliable and report independently, W 1 and W 2 exceed W 3 in terms of Collective Reliability. This is the case if the following inequalities hold:
${{{\bf{P}}[{W_1}\left( R \right)|H,\,K]} \over {{\bf{P}}\left[ {{W_1}\left( R \right){\rm{|}}\neg H,\,K} \right]}} \times {{{\bf{P}}[{W_2}\left( R \right)|H,\,K]} \over {{\bf{P}}\left[ {{W_2}\left( R \right){\rm{|}}\neg H,\,K} \right]{\rm{\;}}}} \gt {{{\bf{P}}[{W_3}\left( R \right)|H,\,K]} \over {{\bf{P}}\left[ {{W_3}\left( R \right){\rm{|}}\neg H,\,K} \right]{\rm{\;}}}} \gt 1,$
${{{\bf{P}}[{W_1}\left( {\neg R} \right)|\neg H,\,K]} \over {{\bf{P}}\left[ {{W_1}\left( {\neg R} \right){\rm{|}}H,\,K} \right]}} \times {{{\bf{P}}[{W_2}\left( {\neg R} \right)|\neg H,\,K]} \over {{\bf{P}}\left[ {{W_2}\left( {\neg R} \right){\rm{|}}H,\,K} \right]{\rm{\;}}}} \gt {{{\bf{P}}[{W_3}\left( {\neg R} \right)|\neg H,\,K]} \over {{\bf{P}}\left[ {{W_3}\left( {\neg R} \right){\rm{|}}H,\,K} \right]{\rm{\;}}}} \gt 1.$
In a situation involving equally minimally reliable witnesses, the total testimonial evidence confirms H, given the Confirmation Likelihood Principle, if a majority of the witnesses reports that R is true. In the imagined situation, W
1 and W
2 are the majority, W
3 is the minority, and the total testimonial evidence consists of the three reports W
1(R), W
2(R), and W
3(¬R). If so, the relevant posterior probability
${{\bf{P}}^*}\left(H\right) = {\bf{P}}{\rm{[}}H{\rm{|}}{W_1}\left(R\right), {W_2}\left(R\right), {W_3}\left(\neg R\right),{\rm{\;}}K]$
is greater than the prior probability
${\bf{P}}{\rm{(}}H{\rm\space{|}}\space K)$
.
Recall the distinction between the total testimonial evidence and one single report (out of multiple reports) considered in isolation (subsection 3.2). It is true that the report W 3(¬R), taken in isolation, disconfirms H. However, the reports of W 1 and W 2 (that R) confirm H more strongly than the report of W 3 (that ¬R) disconfirms H. Hence, the total testimonial evidence (all three reports) confirms H in this situation of disagreement.
Abstracting from this specific illustration with three witnesses, Bayesians can rely on the following more general verdict: a majority of equally reliable (and independent) witnesses reporting R provides confirming testimonial evidence for H, because the majority’s Collective Reliability (that is, the product of the likelihood ratios of the members of the majority) is greater than the minority’s Collective Reliability (that is, the product of the likelihood ratios of the members of the minority who reliably and independently report ¬R).Footnote 40
5.2. Second situation: Witnesses differing in reliability
The Bayesian approach is, however, not necessarily a matter of a majority of reliably and independently reporting witnesses. Indeed, it is a virtue of the Bayesian version of the Justificatory Account of Multiple Testimony to illuminate the limits of such political metaphors in epistemology (here, talk of majority and minority). This becomes clear if one supposes that the reporting witnesses are all minimally reliable, but some witnesses are more reliable than others.Footnote 41 Furthermore, suppose that there is a disagreement regarding proposition R within such a group of n unequal witnesses: one subgroup of witnesses reports R, while another subgroup reports ¬R. According to the Confirmation Likelihood Principle, what matters for confirming H via the reports of multiple witnesses in this kind of situation is that the Collective Reliability of the subgroup of witnesses W 1, …, W m reporting R is greater than the Collective Reliability of the subgroup of witnesses W m+1, …, W n reporting ¬R. Mathematically, this claim can be expressed as follows:
${{{\bf{P}}\left[ {{W_1}\left( R \right){\rm{|}}H,\,K} \right]} \over {{\bf{P}}\left[ {{W_1}\left( R \right){\rm{|}}\neg H,\,K} \right]}} \times \cdots \times {{{\bf{P}}\left[ {{W_m}\left( R \right){\rm{|}}H,\,K} \right]} \over {{\bf{P}}\left[ {{W_m}\left( R \right){\rm{|}}\neg H,\,K} \right]{\rm{\;}}}} \gt$
${{{\bf{P}}[{W_{m + 1}}\left( R \right)|H,\,K]} \over {{\bf{P}}\left[ {{W_{m + 1}}\left( R \right){\rm{|}}\neg H,\,K} \right]{\rm{\;}}}} \times \cdots \times {{{\bf{P}}\left[ {{W_n}\left( R \right){\rm{|}}H,\,K} \right]} \over {{\bf{P}}\left[ {{W_n}\left( R \right){\rm{|}}\neg H,\,K} \right]{\rm{\;}}}} \gt 1.$
In this kind of situation, confirming reports can be realized in at least three different ways: (i) the subgroup of witnesses reporting R is the majority (this is similar to the first situation, except that now the witnesses may differ in their individual reliability within the subgroup); (ii) the subgroup of witnesses reporting R and the subgroup of witnesses reporting ¬R are of equal size, but the former is collectively more reliable than the latter; or (iii) the subgroup of witnesses reporting R is a minority of highly reliable witnesses whose Collective Reliability exceeds that of a majority of less (but still minimally) reliable witnesses reporting ¬R.
5.3. The lesson from both situations
The Doubt Rule does not hold in both situations described in subsections 5.1 and 5.2. In both situations, an epistemic agent need not be less confident about H after learning about a disagreement.
In the first situation, the minority’s reports (that ¬R) do not force an epistemic agent to lower her confidence in H. To the contrary, if one considers the total testimonial evidence—including the majority’s reports (that R)—and the majority’s greater Collective Reliability, one should assign a higher posterior probability to H.
In the second situation, the mere existence of disagreeing reports (whether they are the reports of a minority or not) does not force an epistemic agent to be less confident about H. To the contrary, the agent should be more confident about H, considering the total testimonial evidence, if the witnesses reporting R exceed the witnesses reporting ¬R in their Collective Reliability.
In sum, what really matters for confirming a scientific claim via multiple testimonies is not necessarily agreement and not even what the majority of witnesses reports. Confirmation depends on whether the subgroup of witnesses reporting R has a greater Collective Reliability than the subgroup reporting ¬R. And this is possible even if witnesses disagree. Hence, the Bayesian version of the Justificatory Account of Multiple Testimony provides an argument for rejecting the Doubt Rule as a general rule and, thereby, one additional way to debunk the argument from disagreement.
5.4. Revising the Doubt Rule and the Argument from Disagreement?
I just provided an argument for rejecting the Doubt Rule as a general rule. In response, one might charitably ask whether the skeptics could respond to this counterargument by appealing to an appropriately revised, non-general version of the Doubt Rule that holds only under specific conditions. Based on the Bayesian Justificatory Account of Multiple Testimony and the lessons of subsection 5.3, one could revise this premise as follows:
Revised Doubt Rule: If a member of the public learns that minimally reliable (and independently reporting) witnesses disagree in their reports regarding a scientific hyothesis H and the subgroup of witnesses who reliably (and independently) report ¬R has greater Collective Reliability than the subgroup of witnesses reliably (and independently) reporting R, then this person should be less confident about the truth of H.
Suppose one accepts the Revised Doubt Rule. If one also accepts the Revised Disagreement Premise, one obtains the Revised Argument from Disagreement. If so, how should one assess this revised argument?
Being able to state the Revised Argument from Disagreement exemplifies the fruitfulness of the Bayesian version of the Justificatory Account of Multiple Testimony, as this account is able to articulate what the skeptics would have to show to render their argument sound, or at least to render its premises generally more plausible.
Furthermore, proponents of the Bayesian version could accept that the revised premises are generally more plausible than the original ones. At the same time, they could argue that the skeptics have the burden of argument to show that the revised premises are in fact true in crucial kinds of situations: namely, when the skeptics use the argument to criticize specific scientific hypotheses (such as “smoking causes lung cancer”). It remains to be seen whether the skeptics are able to accomplish this task. In this regard, I am, for once, skeptical myself. I am confident that it will be considerably more difficult for strategic science skeptics to exploit the revised version of the argument from disagreement than its original version.
6. Conclusion
I have provided a rational reconstruction of the strategic science skeptics’ argument from disagreement. To debunk the argument, I have presented the Justificatory Account of Multiple Testimony—particularly in its Bayesian version—as a normative epistemological treatment of the relationship between testimonial evidence and confirmation (and disconfirmation). I have relied on this account to argue against both premises of the argument from disagreement. Finally, I have indicated what it would take to revise the argument and expressed doubts that the revised argument puts the skeptics in a better position to use it.
Acknowledgments
First and foremost, I would like to express my special thanks to Leon Assaad, Stephan Hartmann, and Maria Kronfeldner for their repeated and productive feedback on earlier drafts of the manuscript; philosophical discussions with them encouraged and enabled me to develop my claims and arguments. I also thank two anonymous reviewers for this journal, kind audiences (in Kraków, Munich, and Vienna), and students at Ludwig-Maximilians-Universität München for productive comments that helped to improve the manuscript.
Funding Statement
None to declare.
Declarations
None to declare.
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