Simulation models and probabilities: a Bayesian defense of the value-free ideal

1. Introduction

The extensive use of computer simulations in all domains of contemporary science has raised many epistemological and philosophical questions. Some of them have turned around the issue of whether computer simulations pose essentially new philosophical and methodological problems when compared to the traditional products of theoretical sciences such as hypotheses, theories, and models.^1–4 Many other advances in the epistemology of scientific simulations have been made in the last years, in which a diversity of topics in the philosophy of science have been explored.^5–10 One of the much-debated issues was whether social values play an unavoidable role in the building, assessment, and use of computer simulations, which, consequently, provide a case against the traditional value-free ideal of science, according to which science should be neutral concerning moral or political issues.

Because some computer simulation models, such as climate models, have deep implications regarding policymaking, the question concerning the proper place of social values in science has been recently addressed and discussed by many philosophers.^11–14 Traditionally, all discussions of the ideal of a value-free science have been conducted within the domain of scientific hypotheses and theories, more precisely, they have turned around the problem of the acceptance of scientific hypotheses.^15,16 To the best of my knowledge, Eric Winsberg^6,17,18 was the first philosopher of science who addressed the issue of the value-ladenness of the assessment of computer simulations, and since then the topic has been extensively debated, in particular regarding climate models.^19–23

In this article, I will argue that the value-free ideal is tenable regarding the assessment of computer simulation models. I will intend to show that social values play a negligible role when computer simulation models are employed to assign probabilities to the different hypotheses that scientists entertain and, more specifically, that the epistemic uncertainty and opacity of complex simulation models of climate do not force us to presuppose value judgments.

The structure of the article is the following. In section 2, I state the value-free ideal of science and its main assumptions. In section 3, I discuss a standard criticism of that ideal, the so-called “argument from the inductive risk,” and its extension to methodological decisions concerning the recollection and analysis of the evidence. In section 4, I provide a Bayesian response to the inductive risk argument. In section 5, I analyze the question of the epistemic uncertainty and opacity of computer simulations. In section 6, I examine the question of whether the assessment of simulation models of climate presupposes value judgments. In section 7, I argue that the use of complex simulation models to assign probabilities to different hypotheses does not prevent the application of standard Bayesian methods. In section 8, I summarize the main conclusions of the article.

2. The value-free ideal and its critics

Since Max Weber proposed the ideal of a value-free social science at the very beginning of the 20th century,^24,25 this ideal was the target of much criticism by philosophers, scientists, and policymakers. According to it, all scientific products, such as hypotheses, theories, or models, should be free of social values. In Weber’s terms, they have to be free of judgments concerning moral, political, or social issues. Weber aimed at protecting the newly born science of sociology from political bias. He was concerned with the objectivity of the social sciences, which he regarded as threatened by the distortions produced by the intrusion of value judgments in the body of scientific knowledge. The ideal was regarded as universal, that is, as a set of epistemic norms that holds for the whole of science.

The value-free ideal rests on a distinction between two different kinds of values: social and epistemic values. The class of social values includes all aesthetic, moral, and political values, that is, all those that can be called practical values. The class of epistemic values includes all theoretical values, such as internal consistency, empirical adequacy, simplicity, explanatory, and predictive power, compatibility with background knowledge, and others. These are, roughly speaking, the theoretical or epistemic virtues we usually attribute to scientific products such as hypotheses, theories, or models. Some authors have distinguished between epistemic and cognitive values,^16,23,26 but for the sake of my argument, I will not need that distinction. I will assume that the class of epistemic values includes all non-social values. The standard position concerning the value-free ideal is that the epistemic assessment of all scientific products rests exclusively on epistemic values. Accordingly, value judgments concerning epistemic matters are admissible as part of the body of science if they are explicitly stated. A natural scientist that puts forward a new hypothesis or model can safely refer to it as more simple or explanatory than a rival hypothesis or model. This kind of epistemic judgment does not threaten the objectivity of science; on the contrary, they are part and parcel of the scientific business itself. Social values, by contrast, should not play any role in the epistemic assessment of scientific products, although they do play a role in the decision of applying those products.

A traditional criticism of the value-free ideal has consisted in arguing that it is not possible to distinguish epistemic values from social values, or more generally, that there is not a distinction between fact and values.^19,27,28,29 Although the issue is still under debate, I will not address this criticism here. I will assume that even if there is not a sharp demarcation between epistemic and social values, the main examples of each kind of value are clear enough to be used as the basis for the value-free ideal.

As Lacey ¹⁵ has pointed out, the value-free ideal has several dimensions. The first dimension is neutrality. A scientific theory or model is neutral when it does not include any value judgment involving social values. If so, it does not logically entail any value judgment concerning such kinds of values either. I will assume here that computer simulations are neutral in the former sense, that is, that they do not contain value judgments as components because they are not the kind of scientific product capable of including value judgments. The neutrality concept assumes that theories are sets of sentences or propositions and that value judgments themselves are expressed in sentences, which may appear as components of a given theory. A theory is not value-neutral if it includes explicitly at least one value judgment. Computer simulations are neutral in this respect because they are not set of sentences.

The second dimension is autonomy. Whatever the way in which the concept of autonomy is understood, I think it has been established beyond any reasonable doubt that scientific practices and processes are not autonomous from extra-scientific matters, such as political, social, and economic concerns, or, in short, that science is not independent of other social systems.^15,16 I will thus assume without further argument that the design, construction, and use of computer simulations is not an autonomous enterprise and, as a consequence, it is not free of social values.

The third dimension of the value-free ideal concerns the impartiality of science. It is said that science is impartial because the acceptance or rejection of scientific theories or models should not be made based on social values. The thesis of the impartiality of science does not assume that the discovery, pursuit, and application of scientific products are value-free activities. On the contrary, it admitted that they are performed based on social values. The simple fact of opening (or closing) a research project presupposes a moral or political assessment of its probable consequences on society, that is, of the probable effects of its application to a certain domain of phenomena. The thesis of the impartiality of science is restricted, to use the traditional terminology of the philosophers of science, to the context of justification of scientific theories or models.

The ideal of impartiality has been the main target of most recent criticisms of the concept of value-free science. Before examining the arguments of the critics, it is convenient to clarify the ideal itself. In the first place, the ideal of impartial science is not a descriptive, but a normative thesis. Like any other ideal, it describes a desirable, but not necessarily actual, state of affairs. It does not claim that science is always impartial, but rather that it should be. Impartiality is, for the defender of the value-free ideal, constitutive of good science, more precisely, of any good practice regarding the appraisal of scientific products such as hypotheses, theories, or models. The endorser of the value-free thesis is not committed to the claim that science is impartial. However, she is committed to the following two claims: i) that impartiality is possible, and ii) that impartiality is desirable.

All critics of the ideal of impartial science have argued against one or both of the former claims, even without making a clear distinction between them. However, the arguments against the first claim are of a different kind than the arguments against the second one. Something analogous applies to the criticism of any normative ideal. We can reject a regulative ideal because we think that it is not possible to adopt it or because we think that is not desirable to adopt it. In the first case, we can argue that the ideal is impossible because it is logically inconsistent, or because it is self-defeating, or because it demands something that, although logically and physically possible, we cannot fulfill in practice. In the second case, we can reject the ideal because it conflicts with other ideals or norms that we regard as more significant or important in some respects, or because the adoption of the ideal would produce undesirable consequences. Each of these reasons demands a specific argument, as is evident.

Here I will concern exclusively with the criticism according to which impartiality is not possible. There has been a specific class of arguments against the possibility of impartial science, which has been labeled methodological by Hempel. ³⁰ According to such arguments, the epistemic assessment of theories, models, and other scientific products rests on methodological decisions, which in turn presuppose value judgments based on social values. As a consequence, the acceptance or rejection of theories and models cannot be value-free, even in principle.

3. The argument from inductive risk revisited

The main methodological argument against the value-free ideal of science is presently known as the argument from inductive risk. It was originally formulated by Rudner ³¹ in the following terms. Rudner’s first premise is that, as a matter of fact, scientists accept and reject hypotheses. What is at stake here is rational acceptance, that is, one that is grounded on sound reasons. Rudner only takes into account evidence (in its narrow sense of observational or experimental data) as a sound reason to accept or reject theories. He also considers solely the case of the acceptance of a given hypothesis in light of the available evidence. His second premise is that no finite amount of evidence verifies a scientific hypothesis or at least a scientific theory; at most, evidence can confirm a theory to some degree. Given that we cannot be certain that a theory or hypothesis is true, acceptance is a risky business. We can never exclude the possibility of accepting a false theory, no matter how much confirmatory evidence we have at our disposal. In the best cases, we can assign to theories a degree of confirmation, expressed as a conditional probability on the available evidence. But what is the degree of confirmation that guarantees a rational acceptance of that theory? Or, in simpler terms, how much evidence is sufficient for accepting a theory? The acceptance of a theory may have undesirable consequences if the theory in question turns out to be false. We can make a serious mistake in accepting such a theory. Similar considerations apply to the case of rejection.

If this is so, before accepting a given theory or hypothesis scientists must decide when the evidence is “sufficiently strong.” Rudner’s ³¹ fundamental tenet is that this is “a function of the importance, in a typical ethical sense, of making a mistake in accepting or rejecting the hypothesis” (p. 2). That is, we will require more (and more stringent) evidence to accept a hypothesis that, in case of being false, would produce harmful consequences. For that reason, all scientists qua scientists must make value judgments of the ethical type, and as a consequence, social values are necessarily involved in the appraisal of scientific theories and hypotheses.

We can restate Rudner’s conclusion in the following terms. The decision of accepting or rejecting theories is not a purely epistemic affair and, for that reason, is not ruled solely by the norms of theoretical reason. It is also a practical affair and, as such, it has to be submitted to the norms of practical reason. The acceptance or rejection of scientific products has generally practical effects outside of science and the scientific communities and that is why it should be assessed based on social values. Of course, the question of the practical consequences of scientific hypotheses and theories is a matter of degree: it seems evident that a medical hypothesis concerning the efficiency of a drug has a higher potential impact on society than a cosmological hypothesis concerning the amount of dark matter in the universe. But in any case, the endorser of the argument argues, this fact does not exempt the acceptance of cosmological hypotheses from a practical assessment. The conclusion to the effect that a given theory has no significant social consequences is also the outcome of such kind of assessment.

Jeffrey ³² provided the standard Bayesian reply to the argument from inductive risk. He simply denied Rudner’s first premise, according to which scientists do accept and reject hypotheses and theories. Against Rudner’s claim, Jeffrey ³² remarked that “it is not more the business of the scientist to accept hypotheses about degrees of confidence than it is to accept hypotheses of any other sort” (p. 246). From a Bayesian point of view, the proper role of a scientist is just to assign probabilities to the different hypotheses with respect to all available evidence. As is known, Bayesian statistical methods, in opposition to classical statistical inference, do not provide rules of acceptance for probable hypotheses. According to Bayesians, the assignment of probabilities does not presuppose social values or value judgments because it is purely epistemic, that is, it is performed solely on the basis of the available evidence and the background knowledge of previously known information.

The Rudner–Jeffrey controversy was commented on by Levi^33,34 and it then waned for a long time, until it was revisited by Douglas. ³⁵ In the last two decades, the argument from the inductive risk was endorsed by Winsberg ⁶ and Douglas ¹⁶ and then discussed by many philosophers of science. The Bayesian reply to this argument was carefully scrutinized ³⁶ and something as a standard counterargument emerged from the extensive literature on this topic. ¹³

Rudner’s argument was extended by Douglas^16,35 to methodological decisions concerning the recollection and the analysis of the evidence, which she regarded as dependent upon social values. When experiments are performed and quantities are measured, many different methodological decisions are required, decisions that range from the experimental design to the statistical analysis of the data. Douglas has then argued that some of those decisions depend on an evaluation of the inductive risks involved in each specific case. Scientists have to make decisions about how to collect the data that arise from experimental tests; they have to decide even what counts as a genuine datum. For instance, let us imagine that a medical experiment on laboratory rats is designed to detect the presence of degenerating cells as a consequence of the administration of a given drug. Degeneration of cells is a matter of degree so that scientists must decide what counts as a degenerating cell and how to detect it. Suppose there are two tests at their disposal, of which one is more specific than the other whereas the other is more sensitive. If the first test is applied to the rats, it will produce a significant number of false-positive results, but a reduced number of false-negative ones. If the second test is applied, it will produce a few false-positive results, but many false-negative ones. Douglas ¹⁶ then claims that the choice of one test over the other involves an assessment of “the costs of false positives versus false negatives” and that “weighing those costs legitimately involves social, ethical, and cognitive values” (p. 104). Here, Rudner’s argument from inductive risk applies again: scientists should evaluate the social consequences of committing one or the other type of error before selecting a determinate test. Mutatis mutandis, the argument also holds for other kinds of methodological decisions, such as those that consist in selecting the statistical procedures for analyzing the data or the setting of statistical confidence levels.

In the above example, if the consequences of increasing the number of false-positive results are regarded as socially pernicious, responsible scientists should adopt more sensitive tests and more stringent methods for the analysis of the data, for instance, setting the confidence levels at higher values. In real science, many other practical considerations also play a role. For example, applying one of the tests may be much more expensive than applying the other. If the funding sources of the research are scarce, or the resources of the society are very limited, as is usual in many contexts, methodological decisions become strongly conditioned by economic reasons, not just by the ethical evaluation of the inductive risks. This predicament is very well-known to all computer scientists and engineers who design simulation models. A model that provides very accurate predictions may be extremely expensive in terms of computing time to the point of being economically unviable, whereas a slightly less accurate model may be quite viable from that point of view, despite being a bit riskier concerning its social consequences. In those cases, a sort of tradeoff between the different costs and benefits seems unavoidable. And more often than what we would expect or wish, economic interests prevail over ethical considerations. In any event, the decision rests on (sometimes conflicting) social values.

Douglas’ argument goes beyond Rudner’s claim that the strength and the amount of the evidence regarded as sufficient to accept a given hypothesis are dependent on value judgments. What she argues is that before the assessment of a hypothesis in light of the available evidence scientists have to make decisions concerning what they accept as evidence. This argument cannot be defused by Jeffrey’s claim that scientists do not accept hypotheses but merely assign probabilities to them. Certainly, those probabilities are conditional to the accepted evidence and surely will be different if some pieces of evidence were to be rejected for methodological reasons. Moreover, the argument in principle applies to theoretical hypotheses as well because methodological decisions concerning the recollection and analysis of the evidence are unavoidable in all empirical sciences. As a consequence, the defenders of the value-free ideal cannot reply to Douglas’ argument following Jeffrey’s strategy of denying the acceptance of hypotheses. However, a response is possible within the Bayesian framework, as I will show in the next section.

4. A Bayesian response to the inductive risk argument

Methodological decisions, such as those we have discussed above, are made within the framework of classical statistical inference, where most decisions are binary ones, that is, a matter of all or nothing (like choosing a more sensitive or a more specific test). Classical statistics assume that scientists have to accept or reject hypotheses in light of the evidence and that in performing this task they may commit the standard types (I or II) of errors. Jeffrey’s reply to the inductive risk argument denies precisely this point on the basis of his Bayesian commitments. I do not intend to examine here the controversy between those different approaches to the statistical methods. I will simply provide a possible reply to Rudner’s and Douglas’ arguments within the framework of Bayesianism, leaving the question of how they could be replied by endorsers of classical statistical methods open for further study.

Bayesians could reply that all methodological decisions, at least in principle, can be considered as part of the background knowledge on which conditional probabilities are estimated. Let us restrict ourselves to the case in which the Bayes theorem is used to calculate the posterior probability of a given hypothesis H in light of some piece of recently collected evidence E. As is known, we must start with some prior probabilities for H and E, which have to be estimated in light of the available background of established or accepted knowledge B. Employing the simplest formulation of the theorem, we have that Pr (H | E & B) = Pr (H | B) Pr (E | H & B)/ Pr (E | B), given that Pr (E | B) ≠ 0. In practice, Pr (E | B) is replaced with its equivalent formula of total probability: Pr (H | B) Pr (E | H & B) +Pr (¬H | B) Pr (E | ¬H & B). As a consequence, the use of Bayes theorem to calculate the posterior probability of H given E and B requires as input the prior probabilities Pr (H | B) and Pr (¬H | B) (which are not independent, so that one of them is enough to fix the value of the other) and the likelihoods Pr (E | H & B) and Pr (E | ¬H & B) (which are independent and do not need to add up to one).

In its workable form, the use of the Bayes theorem requires fixing the two likelihoods of the evidence E conditioned to the total background B, which includes not only the previously known evidence but also the general knowledge embedded in accepted theories and hypotheses of many different kinds (among them, for instance, those that were employed in the construction of the measuring instruments). If social values have any influence on the assignment of probabilities, they can affect just the priors, being the calculation of the posterior probabilities a matter of pure arithmetics. The Bayesian may then reply that in estimating Pr (E | H & B), we can include in B our knowledge of the methodological decisions made when E was collected, among them, that we have used a test with a given sensitivity and specificity. We would likely have assigned a different value to Pr (E | H & B) if we would have used another test. Assuming H and B, the prior probability of the evidence E may be affected by the decision of collecting that evidence employing one or another kind of test. For instance, if E is the number of infected persons belonging to a given population, the probabilities assigned to E given that the evidence was collected using a test T₁ (more specific) or a test T₂ (more sensitive) should be different. We will expect that Pr (E | H & B & T₁) < Pr (E | H & B & T₂), precisely because we know that T₁ produces a higher number of false positives than T₂. In this way, all the information concerning methodological decisions can be factored into the degrees of beliefs assigned to the evidence with which the prior probability of a given hypothesis is updated. The Bayesian can then circumvent the argument from inductive risk by factoring out the values that could have influenced the methodological decisions made before collecting the evidence.

Sometimes the prior probabilities are elicited from the agreement of the experts in the field. The fact that on many occasions there are strong disagreements between the experts does not pose a problem for the Bayesians because they regard all probabilities as personal or subjective, that is, as reflecting the degrees of beliefs of each individual agent. When scientists act as pure scientists, and not as policy advisors, they just calculate the probabilities of the different hypotheses, theories, or models they entertain on purely epistemic grounds. Those probabilities can be communicated to policymakers, who make their decisions based on the utilities they assign to the different probable outcomes of applying each hypothesis. This is the traditional division of labor according to Bayesian decision theory, a division between theoretical and practical matters that preserves the value-neutrality of pure science.

Winsberg^37,38 has called this argument “the Bayesian response to the argument from inductive risk” or the BRAIR (pp. 136, 393). There are different possible replies to the BRAIR.^39,40 One of them consists in arguing that the very choice of Bayesian statistical methods over the methods of classical statistical inference is made on the basis of social values. For instance, it could be argued that this choice reflects individualistic values concerning human beings, who are conceived of as being isolated ideal rational agents that endeavor to maximize their expected utilities based on their personal probabilities. This has been a standard criticism addressed to classical theories of rational decision. Bayesian methods, the argument goes, are likely to be adopted by members of free-market societies embedded in liberal democratic values but they are much less appealing to partisans of communitarian or collectivist conceptions of the social order. This argument may have a rationale behind it, but it is too general to be examined here. I will then assume that the decision of employing Bayesian methods can be justified using purely epistemic arguments that do not appeal to social values.

Winsberg has argued that the BRAIR cannot be applied to climate simulation models. His argument can also be extended to the use of complex models generally. I will address here the argument in all its generality and I will turn to climate models in the next section. It relies on the indisputable fact that every model is idealized to some degree and is built by abstracting some variables and parameters we regard as relevant, and by introducing some distortions we regard as false assumptions. Moreover, computer simulations necessarily have to add new distortions, such as the discretization of continuous equations, which are indispensable to make the model computationally tractable. From these premises, Winsberg ³⁷ proceeds to argue that scientists always compute their probabilities conditioned to a subset B’ of the total background knowledge B, a subset that “replaces some of the claims in B with a computationally tractable scientific model or set of models” (p. 146). Of course, B’ includes many distortions introduced by the models, distortions that will be regarded as false assumptions in light of the full background B. He writes that “in practice, scientists’ best attempts at estimating Pr (H | E & B) sometimes involve estimating Pr (H | E & B’) instead” (p. 146). Winsberg ³⁷ then concludes that “the distortions relative to B that scientists are willing to tolerate when developing (a model) M will depend in part on the purposes and priorities of their investigations, as well as the purposes and priorities that shaped any earlier layers of the model’s development” (p. 146). He adds that the predicament would not be essentially different, if we were to use imprecise probabilities, such as number intervals, instead of the sharp values calculated by the Bayesian methods. Parker and Winsberg ³⁹ have further elaborated on the argument along the same lines.

Winsberg’s argument aims at showing that social values do play a role in the assignment of probabilities to hypotheses. As we have seen, the priors are the only probabilities that can be influenced by social values. For the sake of simplicity, I will take now the case of the estimation of Pr (E | B) and Pr (H | B), where B is the full background knowledge available at a given moment. Within orthodox personalist Bayesianism, B stands for the beliefs accepted by each individual agent. For that reason, it hardly can be regarded as including all the scientific knowledge of the moment. If the agent is a scientist, B will include just the small subset of the established scientific propositions that the agent knows at that moment. Even so, the estimation of the priors of each agent is always made on the basis of the small subset of B that he or she regards as relevant for E and H. For example, if the scientist is a climate modeler and she has some knowledge of, say, quantum mechanics, that part of her background will play no role in estimating the priors of E and H (suppose H deals with the temperature rising in the next decade and E is a set of data concerning past temperature measurements). Prior probabilities are always estimated relatively to a subset of the agent’s beliefs, which, in turn, is a small subset of the available scientific knowledge. If the agent is working with a set of climate models {M}, this set will belong to his or her background B, and the prior probabilities assigned to E and H might be influenced by that precise background. And those probabilities could possibly be different if the agent were to accept a different set of models. However, nothing follows from this possibility about the actual probabilities that different agents may assign to the priors.

According to the standard personalist Bayesianism, no background knowledge can fix the degrees of belief of any agent. Two agents may share the same background but assign different probability values to the same hypothesis, and, conversely, they may have very different backgrounds and, nonetheless, assign the same probability to that hypothesis. There is no question concerning which assignment of the priors is right. To the extent that both assignments are coherent (i.e. that they satisfy the axioms of the probability calculus) they are equally acceptable. For the orthodox Bayesian, the prior probabilities assigned to any scientific hypothesis or any piece of evidence are not subject to further requirements than probabilistic coherence. They are just the personal degrees of belief belonging to individual agents. If social values have any influence on the assignment of prior probabilities, they cannot fix or determine any value for all the agents. Within the orthodox Bayesian framework, it is not true to say that Pr (H | B’) is or should be different from Pr (H | B) for a given agent. The agent is free to assign any value to H conditional to B or B’. Two agents may assign the same or different prior probabilities to H or E in light of B or of B’ regardless of the social values they endorse. There is not such a thing as the objective value of the priors. They are all subjective probabilities alike. If two agents assign the same priors to H and E, they necessarily will agree on the posterior probability of H given E, regardless of their backgrounds. Conversely, if they assign different values to the priors, they will obtain different posteriors for H given E. There is no such thing as the objective or the true value of Pr (H | E & B) to which Pr (H | E & B’) may or may not approximate. In practice, modelers estimate their priors relatively to a simplified background B’, determined by the many idealizations embedded into the model or set of models they use. However, this simplified background cannot fix the value of any of the priors.

Let us assume, for the sake of the argument, that the influence of social values on the assignment of the priors is so strong as to force two agents to assign different numbers to Pr (H | B’) and to Pr (H | B), and that the difference in the two assignations is due solely to the influence of the different social values they endorse. Parker and Winsberg ³⁹ have generalized the argument by arguing that, due to the influence of social values in the building of different simulation models, we will have to face a situation in which different prior probabilities are assigned to the same hypotheses H conditioned to different backgrounds B₁≠…≠B_k≠B (where B is the full background knowledge). If so, given the new piece of evidence E (one that is not in any of the B_i), the posterior probabilities for H should be different, that is, Pr (H | E & B) ≠Pr (H | E & B₁) ≠…≠Pr (H | E & B_k), except by mere coincidence. The same argument holds for the prior probabilities assigned to the evidence E conditioned to those backgrounds.

The Bayesian reply to this argument must be that, under plausible conditions, all those posteriors must converge to the extent that the evidence accumulates. This response is the same as their reply to the diversity of individual prior probabilities: the dependence of the posteriors on the different priors washes out when the resulting posterior probabilities are updated by Bayesian conditionalization. That is, the Bayesian may resource to the well-known theorems concerning the convergence of the posteriors. The differences between the priors Pr (H | B’) and Pr (H | B) tend to vanish when we learn from the experience because if they are updated in light of new pieces of evidence, the calculated posteriors sooner or later will converge to close values (in the limit, the difference between the posteriors tends to 0). The standard objection to this procedure is that probabilistic coherence in the assignment of the priors is not sufficient to guarantee the convergence of the posterior probabilities of different agents after a finite and reasonably low number of changes in their degrees of belief by Bayesian conditionalization. On one hand, if some agent assigns probability 0 to a given hypothesis, no convergence of his posteriors (which are always 0) with those of other agents is possible. On the other hand, if different agents assign very low (say, 0.00000001) or very high (say, 0.99999999) values to the prior probability of the same hypothesis, the convergence of their respective posteriors to reasonably close values will demand a practically impossible, although finite, numbers of updatings by conditionalization. Nonetheless, convergence is feasible in the framework of a tempered non-objective Bayesianism in which, in addition to coherence, some epistemic conditions are imposed on the assignment of the priors. ⁴¹ In the first place, all priors assigned to empirical hypotheses must be higher than 0 and lower than 1. In the second place, if those hypotheses are uncertain, the values assigned to their priors must not be very near to 0 or 1. These are reasonable requisites that reflect a non-dogmatic commitment to those beliefs for which there is scarce or not yet decisive evidence. It seems that uncertain hypotheses concerning the future value of empirical variables, such as those that enter into predictive simulation models, satisfy these conditions, so that we can expect a convergence of the posteriors. The aforementioned conditions imposed on the prior probabilities are necessary but not sufficient to guarantee the convergence of the posteriors in a reasonably short number of conditionalizations on new evidence. The speed of the convergence will depend on the particular values assigned in each case to the priors. In any event, those conditions are sufficient to guarantee convergence, and in many standard situations (when the values assigned to the priors are relatively far from the extremes, say when they fall within the interval [0.1-0.9]) the posterior probabilities will converge quite quickly. This is a purely mathematical procedure, on which social values cannot exert any influence.

To summarize the argument: if the posterior probabilities converge after a relatively short number of Bayesian conditionalizations, their dependence on the different priors is washed out. And when it happens, all value judgments that could have influenced the assignment of the priors are also washed out. This shows that the influence of social values on the determination of the posterior probabilities of scientific hypotheses is negligible, provided that some general reasonable conditions constrain the estimation of the priors. At most, social values might have a significant influence in the early stages of the appraisal of a theory or model, when a scarce amount of evidence is available. Nonetheless, when the evidence accumulates, the influence of social values on the probabilities assigned to the different hypotheses vanishes. Douglas ¹⁶ herself has acknowledged that “if we find new evidence, which reduces the uncertainties, the importance of the relevant value(s) diminishes,” and consequently, that “more evidential reasons in support of a choice undercut the potency of the value consideration, as uncertainty is reduced” (p. 97). This fits better with the value-free ideal of science than with the proposal of a value-laden science. It also fits well with the Bayesian statistical procedures, as we have pointed out.

5. Uncertainty and values in computer simulations

Most arguments against the value-free character of computer simulations rely on two general properties, which supposedly belong to all kinds of simulations. The first one is epistemic uncertainty and the second one is epistemic opacity. The main argument is that because computer simulations are epistemically uncertain and opaque, their assessment cannot be value-free.

Computer simulations are epistemically uncertain for a variety of reasons. In the first place, they usually rely on a model of the phenomena to be simulated. And we know that all scientific models are idealized in many respects; they work by abstracting, simplifying, approximating, and distorting the phenomena in different ways. The vast philosophical literature on modeling has clarified enough this point.^7,42,43 In the second place, although simulations are validated by comparing their predictions with the available data in the field, the data themselves are often both incomplete and uncertain. Except for some very special cases, we cannot have at our disposal all possible data concerning any phenomenon in nature. For that reason, validation is an inductive process, which is unavoidably fraught with all the uncertainties that beset inductive inferences. On the other hand, most data are inaccurate or imprecise because of the very nature of the experimental methods by which they are collected. Moreover, simulations usually run beyond the domain of the available data and permit us to make projections into the domain of the unexplored phenomena. Certainly, a given simulation may be validated by means of other simulations, which in turn have been accepted as reliable. However, this method will not dissipate the uncertainty in any one of the involved simulations. Of course, uncertainty is a matter of degree, and for that reason, some simulations may be regarded as more reliable than others to the extent that they deliver a higher rate of empirically adequate predictions.

Parametrization is a typical example of a technique that introduces uncertainty in simulations. To run a simulation we need to fix the values of all the empirical parameters of the mathematical model on which the simulation was built. Frequently, the real values of those parameters are unknown and we have at our disposal sparse data concerning their measurement. Sometimes, the uncertainty may be such that just the order of magnitude can be estimated. Here, certain drastic idealizations are required, for instance, setting the parameters to extreme values (typically 0, 1, or infinite), even when the experts are well aware that those are not and cannot be the real values. In principle, all parameters can be benchmarked or calibrated by different methods, but those procedures at best may reduce the uncertainty to some definite interval of values. In any event, experts have to agree at least on a set that contains the best values, that is, those that are regarded as the most adequate for the purposes of a given simulation. Here, it is argued, social values must play a role, because computer simulations, like any scientific model, are built for definite purposes and those purposes are shaped by interests, which, in turn, rest on social values. More specifically, the tolerable margins of error are dependent on the interests, so that they have to be settled on the basis of certain value judgments.

Computer simulations are also epistemically opaque, at least for fallible and cognitively limited human beings, as we are. Simulations are very complex entities, which involve many functions, parameters, variables, and other components. As a consequence, computational processes are epistemically opaque because no human agent (or group of agents) could possibly know the evolution over time of all the functions, variables, and other elements involved in the process of computing a given model, as Humphreys^2,5 has argued. Opacity, like uncertainty, is a matter of degree and on some occasions, it can be controlled or reduced. However, there is no doubt that some very complex computer simulations are epistemically opaque to a high degree. There are several sources of epistemic opacity in computer simulations, but in all cases, they imply some loss of knowledge. ⁸ More precisely, opacity implies that there are limits to the justification of the results of simulations. Because it is not possible to survey all the details concerning the evolution over time of the many variables and functions in a computational process, scientists cannot control the multiple steps that bring a given result about. For instance, if a computer simulation contains two errors that compensate each other to produce a true prediction, the epistemic opacity of such simulation may prevent the correction of those errors. The epistemic assessment of computer simulations is global and cannot descend to explore all the details of the different modules and submodules of which a given simulation is compounded.

The argument against the value-neutrality of computer simulations, then, goes like this: given the epistemic uncertainty and opacity of all epistemic simulations, it is not possible to know all the decisions that were taken across the process of building, tuning, and assessing a given simulation. No computer expert is in a position of disentangling all the details of a complex simulation. For that reason, the BRAIR argument cannot be applied: methodological decisions cannot be factored out and explicitly listed as part of the background knowledge on which Bayesian probabilities are assigned or calculated. Climate simulation models, according to critics of the BRAIR, provide a standard example of this predicament.

6. Climate simulation models

Climate simulation models are undoubtedly highly complex entities, which pose many significant epistemological questions.^44,45 No computer scientist could know all the details of the construction and working of a given model. The architecture of the models, in turn, is modular and experts can, at most, know a few of the many modules that take part in the functioning of a model. There cannot be a doubt that climate models are both epistemically uncertain and opaque. However, it is not obvious what this fact implies concerning the use of social values when climate simulation models are employed to calculate the probability of different hypotheses concerning the future state of the Earth’s climate. The standard argument in favor of the value-ladenness of the assessment of climate models relies essentially on their uncertainty. Eric Winsberg has worked out in detail this argument and that is why I will discuss exclusively his formulation.^6,37,38,39 I do not intend to investigate here a specific computer simulation, which is beyond the scope of this article, but just to examine the general argument to the effect that probabilities cannot be calculated in a value-neutral way.

Scientific models are accepted, as Winsberg ³⁷ points out because they are considered “adequate for the purpose” for which they were built (p. 139). For the sake of the argument, I will restrict the purpose to that of making predictions concerning the present state and the future behavior of the model target. Winsberg’s ³⁷ argument does not directly deal with inductive risk, but with prediction preferences; in his own words: “the preferences we have for making one kind of prediction compared to another” (p. 138). From now on, I will regard climate models as purely predictive devices. The so-called dynamical climate models do not aim exclusively at predicting the future values of some determinate variables, but also at representing some of the causal mechanisms responsible for the observed changes in the phenomena. For that reason, I will neglect all models of that kind in my discussion.

Winsberg’s ³⁷ first argument states that when we build a scientific model, “we usually do it with a set of purposes in mind, to some of which we attach a higher degree of importance” (p. 139, italics by the author). And, as Rudner has argued, the degree of importance we attach to a purpose is a function of social valuations. As a consequence, Winsberg ³⁷ concludes that the purposes and priorities of model builders will influence all the decisions taken during the process of the construction and the assessment of a model. Those decisions will concern, for instance, “not just which entities and processes are represented in a model but also how they are represented, including which simplifications, idealizations, and other distortions are more or less tolerable” (p. 139). In the case of the climate models, this is manifest when the values of their parameters “are chosen by optimizing the model’s performance” (p. 139).

Winsberg ³⁷ claims that social values are presupposed in model appraisal, which, in this respect, is not essentially different from model building. He remarks that in practice “model construction and model evaluation are not neatly separable” because “much informal evaluation occurs during the process of model construction” and, in the reverse direction, “what is learned via formal evaluation activities typically feds back into the model construction process” (p. 140). Winsberg then argues that climate simulation models, as well as other complex scientific models, embodied the values presupposed in many different decisions taken in the course of their construction. Complex models are not built from scratch but rather developed in a layered way. Climate models, in particular, are usually made by modifying pre-existing models, which, in turn, are descendants of older weather models. For that reason, the various decisions concerning purposes and priorities of earlier times made during the construction of previous models cannot be entirely undone and persist in later models. According to Winsberg, ³⁷ it is almost impossible for climate model builders “to completely and adequately keep track of the exact impact of these past modeling choices on their present models” (p. 140). And this is true for three different reasons.

In the first place, because climate models are enormously complex: they are built from many different modules and submodules and involve as much as a hundred parameter options. The interaction between the different modules is itself very complex and the process of coupling some submodules, which include their own parametrizations, is often a very difficult problem. Winsberg ³⁷ coined the expression “fuzzy modularity” to capture the phenomenon according to which one complex model cannot be decomposed into separately manageable pieces. On the contrary, he asserts, “the overall dynamics of one global climate model is the complex result of the interaction of the modules –not the interaction of the results of the modules” (p. 142).

In the second place, climate models exemplify what Winsberg calls a “distributed epistemic agency” because they are the product of the collaborative work of hundreds of scientists and engineers from very different domains of expertise, from pure mathematics to applied ecology. The epistemic agency is distributed both in space and time. Complex global climate models, for example, are the outcome of a piecemeal construction that usually requires many years of patient assemblage and mutual adjustment of their component modules. As a consequence, no single scientist or engineer could know the construction process of the model or the minute details of its architecture.

In the third place, complex models reflect the history of the many methodological choices made along the process of their construction. For that reason, according to Winsberg, ³⁷ “climate models acquire an intrinsically historical character and show path-dependency” (p. 143). Past methodological decisions are “generatively entrenched” in the sense that older decisions play a role in generating the options for solving problems available at later times. The relations of dependence between different decisions are often almost impossible to be disentangled. That is why Winsberg says that complex models are analytically impenetrable. We cannot track the sources of the successes and failures of these kinds of models up to single separable modules or submodules. This results in a sort of epistemic inscrutability of all complex simulation models, which only can be globally assessed in light of the empirical adequacy of their predictions.

The three facts about climate simulation models that Winsberg has pointed out show beyond any reasonable doubt that such models are both epistemically uncertain and opaque. However, it does not follow from these facts that they are not, or that they cannot be, assessed employing criteria that do not presuppose social values.

A possible response to the argument from the epistemic uncertainty of simulations by the defender of the free-value ideal consists in arguing that this very uncertainty should be made explicit when the conclusions obtained from simulation models are formulated. This is the strategy of hedging hypotheses by qualifying them with conditions regarding the error probabilities, the error thresholds, and, more generally, the limitations of the models employed in making probabilistic predictions. ¹⁹ Those hedged hypotheses should be communicated to policy advisors or policymakers, who must make their decisions in light of all the conditions that qualify the plain hypotheses. In this way, the influence of social values on the formulation of hypotheses can be, at least in principle, factored out.

Parker and Winsberg ³⁹ replied that the hedging strategy is not feasible. Because climate simulation models are epistemically opaque, no scientist could be in a position to make explicit all the uncertainties that beset the models in use. The situation is worse when multiple models are employed simultaneously, as is the case with climate models. For instance, if we were to choose to assign probability intervals to hypotheses, instead of single values, we would have at our disposal many different ways to do it. The decision made by a given scientist will be always a decision under uncertainty and it will be shaped by the experience with the particular set of models {M} with which that scientist was working in the past. And those models are themselves the outcome of past decisions that presupposed social values. As a consequence, those value judgments cannot be removed or factored out.

Some philosophers of science^16,23 have claimed that although social values do not have any direct evidential import they do play an indirect or second-order role in the epistemic assessment of computer simulations (or hypotheses generally). They perform that function by specifying the threshold or minimal probabilities for the acceptance or rejection of hypotheses. Here Rudner’s argument applies again if those thresholds are regarded as dependent on the assessment of the risk of making a mistake. But this assumes that the outcome of the epistemic assessment of computer simulations is their acceptance or rejection. In my view, this is a decision that concerns the evaluation of the usefulness of simulations for some practical purposes or, more broadly, to the context of the application of simulations. The proper task of computer scientists is completed when probabilities are assigned to the different hypothetical predictions and the uncertainties of the models on which they rely are made explicit, to the best of the knowledge at our disposal in each moment. The assessment of the usefulness of a given model for intended applications is not the aim of the scientist qua scientist, but rather qua policy advisor. And I do not deny that the scientist that entertains policy advising makes value judgments. ⁴⁶ What I claim is that those tasks can be distinguished and keep separate.

7. Handling complexity with Bayesian methods

The basic Bayesian tenet in favor of the value-free ideal is that computer scientists qua scientists do not accept or reject hypotheses but just probabilize them in light of the available evidence. The different probabilities should then be communicated to policymakers, who make the decisions of accepting or not such hypotheses. Those probabilities are the posteriors calculated by Bayesian methods. This assumes that priors can be assigned to the different hypotheses and the ensuing calculations can be performed to obtain the corresponding posteriors. In turn, all this presupposed that the agents that use Bayesian methods do possess the epistemic capacities to establish the priors and perform the required calculations. However, given the complexity and the holistic character of climate simulation models, this assumption could be questioned. It could be the case that hypotheses that entail definite predictions (usually probabilistic predictions) concerning climate change were so complicated that no individual agent might be in the position of assigning definite prior probabilities to them.

Let us consider the case of the prior probability of the evidence: Pr (E | H & B) (I am indebted to an anonymous reviewer for this example). To assign a value to it, an agent has to determine whether H logically implies E or not, because, if that hypothesis implies the evidence, Pr (E | H) = 1, whatever the background. When H is a very complex hypothesis, no agent could be able to know it, because she does not have sufficient capacities to prove that H implies E. Moreover, because of the complexity of that hypothesis, she might be completely uncertain concerning which evidences it implies. In actual situations, no climate scientist may be capable of answering the question. To determine how probable is E in light of H, climate scientists necessarily have to appeal to a model M or set of models {M}. Usually, climate models are extremely complex, so that a simulation must be run to apply them in order to know what they imply concerning the evidence. And the use of simulations necessarily rests on many idealizations, so that the background B has to be replaced with a more restricted and simplified background B’, as Winsberg and Parker^37,38,39 have argued.

This predicament is not entirely new or unsolvable. Bayesian methods permit the assignment of probabilities to whole theories, not just single hypotheses. Theories generally do not imply any evidence by themselves. It is necessary to employ a large set of auxiliary hypotheses and background knowledge to derive testable predictions from a determinate theory T. That system of hypotheses can be very complex so that given evidence E we may not be sure whether T & B imply E or not. In any event, if we are to apply Bayesian methods to calculate Pr (T | E & B), definite values or intervals must be assigned to the priors Pr (T | B) and Pr (E | T & B). This situation is not essentially different from the case of assigning probabilities to hypotheses based on complex simulation models. At most, it is a matter of degrees of complexity. The Bayesian recipe for handling these situations of uncertainty consists in estimating subjectively the prior probabilities in light of all the available evidence and awaiting the recollection of new evidence to update those probabilities. If we do not know whether T & B imply E, we should assign a value lower than 1 to Pr (E | T & B), but perhaps fairly near to 1, if we think that E is very probable in light of T and B. Different priors can be assigned by different experts. Bayesianism does not require intersubjective agreement on the priors, beyond the constraints of the probability calculus. If we then discover that T & B do imply E, the priors assigned to Pr (E | T & B) must be corrected because it is a theorem of the probability calculus that if T⊨E, then, Pr (E | T & B) = 1, whatever be the background B. If this is not the case, we should proceed to calculate the posterior probabilities of Pr (T | E & B) on the basis of the different priors assigned by the different agents. The Bayesian calculation will produce as many posteriors as different assignments to the priors were at stake. Beyond that point, if no agreement on the priors was possible, the Bayesian has to expect that repeated updatings of those posteriors on new pieces of evidence result in a convergence of the different posteriors.

Many practical complications may arise when experts are prompted to communicate their probabilities to policymakers, especially when the hypotheses at stake deal with socially significant issues, as is the case with predictions of the future values of climate variables. The available evidence might be sparse and hardly conclusive, the models in use so complex as to render the assignment of the priors very uncertain, and the disagreement between the experts so acute as to prevent any reasonable agreement on the posteriors to be communicated. Imprecise probabilities may provide some relief to the situation because in some cases the most reasonable decision is to assign a probability interval to the different hypotheses. Sometimes, a defined and sufficiently narrow interval will be enough to ground policymakers’ decisions. Again, this is often the case with hypotheses concerning global climate change; the well-known IPCC interval scale for probability -which runs from the “nearly certain” (0.99-1) to the “exceptionally unlikely” (0.01-0)- is based on this procedure. A hypothesis concerning the future state of a climate variable is regarded as “likely” if its probability lies within the interval (0.66-0.9). This is not a very precise probability, but for the moment it is the best experts can do with many uncertain complex hypotheses. If no agreement between the experts can be reached on probability intervals either, no definite probabilities can be communicated to the policymakers or the public. In such cases, policymakers must make their decisions on uncertainty concerning the expert’s judgments.

The use of imprecise probabilities has two advantages from the Bayesian standpoint. First, as Winsberg ³⁷ acknowledges, “it has the potential to diminish the influence that social values, via models or sets of models, exert on the conclusions reached” (p. 148). More precisely, if scientists use different models as background knowledge, even assuming that models embed values that influence the assigning of the priors, they can agree on setting the priors to a determinate interval that would be neutral concerning the different values at stake. Second, the prior probabilities assigned to a hypothesis will not converge to a precise unique value (much the less to certainty or probability 1) after a viable number of updatings, but rather to a narrower interval, so that if scientists have succeeded at reaching an agreement on the coarse probabilities assigned to the priors, they necessarily will agree on the less coarse calculated posteriors. And the possible influence of social values on the assignment of the priors will quickly diminish when the posteriors converge to the point of lying within narrower intervals.

Certainly, the calculated probabilities for the different hypotheses concerning climate change, being uncertain to some degree and at the same time socially relevant for practical decisions, can be communicated to the policymakers or the public in different ways and by several strategies that surely depend on social values (for instance, how much panic or alarm would be convenient to produce?). But this does not imply that the probabilities themselves are value-laden. The task of communicating scientific knowledge to non-scientists does not belong to the scientist qua scientist but qua policy advisor.

8. Concluding remarks: the tenability of the value-free ideal

There have been many misunderstandings concerning the ideal of value-free science, both by critics and defenders of that ideal. Many endorsers have argued that the ideal is possible and some critics have replied that it is not desirable. I have argued that the value-free ideal is possible, not that it is desirable. That normative claim certainly would require a different line of argumentation. Moreover, the value-free ideal does not imply that computer simulations, or any other scientific product, should not be submitted to non-epistemic assessments that rested on social values before applying or using them. An appraisal of the usefulness of simulations is required if they are to be applied in concrete situations.

I have acknowledged that the epistemic assessment of complex simulation models, such as climate models, is always uncertain to some degree due to their epistemic opacity. Although that uncertainty can be reduced when we have at our disposal more relevant data, or, more generally, when we collect more varied and reliable evidence with which simulation models can be validated, it surely cannot be eliminated. I have contended that this predicament does not imply the value-ladenness of the assignment of probabilities to different hypotheses on the basis of those simulation models. Granted, models are always built with a certain purpose in mind and for that reason, the decision of constructing a determinate model of some phenomena, and not a different one, rests on social values concerning their possible uses or applications to solve significant problems. However, the assignment of probabilities to hypotheses should be independent of all concerns regarding policy advising and policymaking. The specific job of an expert scientist is limited to probabilize the different hypotheses she entertains, say, different predictions concerning the future values of climate variables, such as the rise of the average global temperature on Earth’s surface. The only possible influence that social values may have on the assignment of probabilities, I have argued, lies in the estimation of the prior probabilities and likelihoods that are employed as inputs when Bayesian methods are used to calculate the posterior probabilities of the different hypotheses. Even when highly idealized models are employed and large portions of our accepted background knowledge are neglected, the influence of social values can be diminished to the point of becoming practically irrelevant to the assignment of probabilities (either single-valued or intervals) to hypotheses. Bayesian probabilities are not objective, but scientists can agree on intervals assigned to priors and likelihoods or expect a convergence of their different single-valued priors after a few cycles of Bayesian conditionalization on new pieces of evidence. For that reason, social values may play at most a significant role in the first stages of research, when the evidence for or against the different hypotheses at stake is rather sparse and fragmentary. To the extent that the evidence accumulates, the dependence on priors of the calculated posterior probabilities is washed out and, as a consequence, the influence of social values becomes negligible.

Finally, I contended that the complexity, epistemic opacity, and uncertainty of complex simulation models do not prevent the use of Bayesian methods for calculating the probability of hypotheses concerning climate change. The use of computer simulations in the assignment of probabilities does not introduce a difference in nature but just in degree: some simulations models are certainly more complex than other scientific models, but they are all epistemically opaque to some degree and the way they relate to the available evidence is generally not clear and straightforward. Uncertainty is a common feature of all predictions derived by using idealized models, but there is nothing radically different when such predictions result from complex computer simulations.