Determination of reliability and question-begging

In his story about the hypothetical worm-like first organism about to form the first belief, Plantinga assumes that the probability of that belief to be true is 0.5. This assumption leads him to commit two serious mistakes, or so I will argue. The first is about his simple method for estimating the reliability of a belief-formation mechanism; the second concerns circularity.

Plantinga's first mistake is to think that we can estimate the belief-formation mechanism's reliability of that organism by merely calculating the probability of the conjunction of the beliefs produced by it. This move doesn't capture the usual way to think about reliability as a tendency of a mechanism to produce more true than false beliefs.Footnote ⁷ So, a more adequate way to estimate the reliability of a mechanism is to check the proportion between true and false beliefs produced by it in the long run (for a given set of target propositions, and a set of initial conditions describing the features of environment and the proper functioning of the relevant cognitive process). Let us take a watchman as an example. Suppose that his task is to detect local criminals. He has to be attentive in order to recognize those who are on the list of the most wanted criminals by local police. Such a watchman is said to be a reliable one if his detection rates are higher than his failure rates. A maximal reliable watchman would be one who detects all and only those who are wanted. Of course, however, we expect some failures. If a criminal passes in front of his cabin and he doesn't form the corresponding belief or believes that there is no criminal around there, then we have a false negative. He falsely believes that such a person is not a wanted criminal. By the other hand, if the watchman arrests an innocent person, then we have a false positive. He believes that that person is a wanted criminal when, in fact, she isn't. So, a reliable watchman is one who besides the positive results, also provide us with very few false positives/negatives. Generalizing from this case we can state the following reliability criterion:

Now let us think about the watchman's reliability following Plantinga. Suppose you hire John, a novice watchman who hasn't much experience. One day John arrests a man and tells you that he is a criminal. You doubt John due his poor track record. In the absence of such track record, you simply assume that the probability of John's belief that the man is a criminal is 0.5. Then you realize that all the future reports of criminals provided by John will be just like that; given his poor track record, the probability of his beliefs about who is a criminal is just 0.5. So, you figure out how very low is the probability of a long conjunction of John's reports of criminals: 0.5 × 0.5 × 0.5 . . . Thus, you conclude that just because a long conjunction of John's beliefs about criminals is very improbable, he is not a reliable watchman. Poor John is fired!

It is easy to see that this kind of reasoning can be used to debunk the reliability of so many sources of information. Suppose that a historian finds out a lot of reports about an obscure mathematician who supposedly proved ten important theorems. Once the historian knows nothing about the reliability of the supposed mathematician, he stipulates that the probability of the correctness of the mathematician's proof of Theorem 1 is 0.5. And the same is true for Theorem 2, . . ., Theorem 10. So, P(T₁ & . . . & T₁₀) = 0.5¹⁰ = 0.0009765625. So, according to Plantinga's suggestion, our obscure mathematician is an unreliable one. And all of this was proved from the armchair! Something has gone very wrong.

Now let us consider Plantinga's second mistake. Suppose that it is reasonable to ascribe a probability 0.5 to the content of the first belief formed by the first belief-formation mechanism in our story. Since we expect that a cognitive mechanism is responsive to the features of the environment, we could ask how probable the content of the belief is given that the mechanism produced that belief. But these are different things: the latter is the posterior probability of p – namely,. P(p | Bp) – and the former is its prior probability – namely, P(p). It is not clear whether Plantinga is aware of this. But making it explicit helps us to see the implications for reliability. What I'll try to show below is that, regardless of Plantinga's supposed mistake in determining the reliability of the primordial organisms, his particular strategy couldn't be successful anyway, for he had to assume from the outset that the cognitive mechanism in question is unreliable.

Let us begin by reading Plantinga's assignment of 0.5 to the primordial belief as follows: equating the prior probability of p to its posterior probability. That is,

Taking into account Bayes's theorem, we have:

Note that P(Bp | p) can be read as the probability of positive results; remember that a reliable mechanism is one that produce positives. Moreover, a reliable mechanism shouldn't produce a considerable rate of false positives. According to the Total Evidence Rule,

This means that the prior probability of the organism having formed a belief that p depends on both the probability of positives and the probability of false positives (i.e. P(Bp | ~p)); in other words, reliability matters. Now it is easy to see that in order to preserve Plantinga's equality, P(Bp | p)/P(Bp) has to be 1. And we can get it, for instance, by stipulating the following: P(Bp | p) = (Bp | ~p).Footnote ⁹ This equality, however, gives us an unwelcome trade-off. For instance, suppose that P(Bp | p) = (Bp | ~p) = 0.95. In this case, despite the high probability of positives, we have the same probability of false positives. More generally, the rate of positives will be directly proportional to the rate of false positives; but what we really should expect is more positives and fewer false positives.Footnote ¹⁰ Thus, condition (ii) of RC is not satisfied; consequently, M is an unreliable mechanism.

Now if something like this is the case, then Plantinga needs to assume not only the equality between the prior and posterior probabilities of p, but also that the mechanism is unreliable. So, he is begging the question against the naturalist. He is assuming that the mechanism is unreliable to prove that it is unreliable.

The second reading of Plantinga's argument is that he is just assuming that P(p) = 0.5, assuming at first sight nothing about reliability. For instance, suppose that the organism had formed a belief or a proto-belief with the content p = ⟨Here is a predator⟩. Following Plantinga, we can say that the base-rate of predators is 0.5; that is, that in the particular environment of our hypothetical organisms, for each ten strange organisms, five organisms aren't predators. But we cannot simply conclude that each belief about predators formed by our hypothetical organism has a probability of 0.5. In doing so we would be treating belief-formation like a throw of a fair coin. But the correct way to account for belief is to take it as if it were like a biased coin. Since a belief (at least a perceptual one) is an output from the environment, its occurrence has some impact over P(p). So, what really should be relevant for Plantinga's purposes is P(p | Bp). That is, given that the organism detected something, and given that this detection – i.e. its belief that p – is to be a proper response to the environment, Plantinga cannot simply assume that the occurrence of the belief is irrelevant. So, just assume the prior of p is not enough. As pointed out above, to get a sense of the occurrence of Bp's impact we have to know the rates of positives and false positives, and, consequently, to know something about the reliability of the mechanism. Plantinga has no choice other than to assume the unreliability of the mechanism. If so, he begs the question once again.

In sum: either Plantinga holds that P(p | Bp) = P(p) = 0.5 or he holds only that P(p) = 0.5. In the first case he has to assume that the mechanism is unreliable, for there is no favourable trade-off between positives and false positives that allows the satisfaction of conditions (i) and (ii) of RC. In the second case, he has no option but to assume that the mechanism is unreliable, for the prior probability of a proposition is not enough to determine (un)reliability. Either way, he begs the question.

It might be objected that it is not fair to accuse Plantinga of question-begging because it does not make sense to assume the existence of a belief-forming mechanism previous to the existence of the first belief. So, assignments of reliability in primeval belief scenarios are improper.Footnote ¹¹ In fact, from an aetiological point of view, it is reasonable to assume that for a certain pre-existent biological structure to become a belief-formation mechanism it is necessary that a first belief should be produced by it; the determination of its particular cognitive function will depend on its evolutionary history. Nonetheless, there is a sense according to which it is sensible to assign reliability to that structure. The following analogy illustrates the point. Consider, for instance, a man who never in his life had practised archery. At first sight, we could not say whether such a man is a reliable archer or not. (For our purposes here, a reliable archer is one who hits the target – given proper circumstances – much more than he misses it.) After all, he had never shot a single arrow in his life. But suppose that that man has a severe visual disorder and his arms tremble due to a neurological condition. Now it is not inappropriate to say that such a man is an unreliable archer; he has a tendency or a disposition to miss the target much more than hit it. In counterfactual terms: in those possible worlds closest to the actual (worlds where the man has the same physical conditions and the environmental conditions are approximately the same) where he shoots an arrow, it is not the case that he hits the target. The same is true of belief-formation: the cognitive structures available to an organism prior to the formation of the primeval belief – even assuming that they still do not constitute a belief-formation mechanism – have a disposition to form false beliefs. To put this in counterfactual terms: in those possible worlds closest to the actual world where an organism with such and such cognitive structures living in an environment with such and such conditions forms the first belief, that belief is false. So, if the analogy holds, I see no obstacle to maintaining that Plantinga's argument is question-begging.

On balance, Plantinga's story about the first organism to form a belief cannot be successful on account of two crucial failures: calculating the probability of a long conjunction cannot determine the reliability of a mechanism; and the attempt to establish the unreliability of a mechanism based only in the Indifference Principle is question-begging.

Convincing evolutionists?

A second flaw in Plantinga's argument for DD is tied to his missing of a crucial aspect of evolutionary reasoning, namely, variation. When he imagines his worm-like population with each organism forming only 50 per cent of true beliefs, he's actually ruling out variation in that population: all individuals have approximately the same reliability in his representational capacities. But as all biologists remind us: no variation, no selection!

If some feature F evolved by natural selection in a certain population, then at least the following three conditions were fulfilled: (i) there were variations among the individuals in a population, for example, some organisms had F, some had it in a certain degree, and another organism had non-F; (ii) F enhanced the organisms fitness, and (iii) F is heritable. Although Plantinga's case fulfils conditions (ii) and (iii), it doesn't satisfy (i). Now, if Plantinga intends that naturalists recognize the putative improbability of our cognition's reliability given evolutionary naturalism, he has to make his case according to the correct pattern of evolutionary reasoning.

What if we reframe Plantinga's case taking into account condition (i)? It is quite simple, actually. We just need to add to the story organisms with belief-formation mechanisms having different degrees of reliability. To simplify, let us assume that the mechanism in question is a perceptual one,Footnote ¹² receiving external inputs from the environment and returning as output a representation – a belief – of some features of the environment. Call it M. M occurs in our population having some variation in reliability. Simplifying once more, we have three tokens of M: M⁺, M^+/−, and M⁻. M⁺ tends to produce more than 90% of true beliefs, M^+/− tends to produce 50% of true beliefs, and M⁻ tends to produce less than 50% of true beliefs:

But now we are not entitled to draw Plantinga's original conclusion. The following inference doesn't sound so wise:

1. (1) There are M⁺, M^+/− and M⁻.

2. (2) There is no necessary connection between truth and fitness.

3. (3) It is possible that an organism be the fittest in the population using false beliefs;

4. (4) Therefore, (it is probable) that the M^+/− or M⁻ was selected.

If we extend this reasoning to other biological characteristics, the result would be ubiquitous. For instance:

1. (1) In a population there are organisms capable of colour vision and organisms with no colour vision.

2. (2) There is no necessary connection between colour vision and fitness.

3. (3) It is possible that an organism be the fittest in the population while being colour blind.

4. (4) Therefore, (it is probable) that the kind of vision selected was a non-trichromatic one.

(If one accepts Plantinga's suggestion that evolution was guided, one can easily conclude that the likely hypothesis is that God used natural processes to give us colour vision!)

The flaw in the above argument is clear: just as we cannot assume by default that colour-blindness is the fittest feature in that population, we cannot do the same about M⁻ and M^+/− fitness. An example helps us to illustrate the point. A soccer team is searching for a goalkeeper. There are three candidates, the first being 90% reliable, the second 50%, and the third minor than 50%. Which goalkeeper would be hired? I suppose that simply assuming the possibility of a victorious team with an unreliable goalkeeper wouldn't convince the CEO's team to make the deal. A prudent CEO would try to calculate the cost/benefit relation of each candidate. For instance, if the team has an excellent defence, maybe a very good goalkeeper is not necessary; or maybe an attack with a high average score removes the need of an excellent goalkeeper; and so on. Considering several constraints and trade-offs, perhaps the middling goalkeeper is the best option. But the CEO needs to be sure of them in order to make his choice. The same is (almost) true for our belief-formation mechanisms. Depending on several constraints and trade-offs – such as environmental conditions, energy efficiency, etc. – an unreliable belief-formation mechanism could possibly be a good evolutionary investment. But to conclude this, Plantinga, just as the CEO above, needs to be sure that this possibility would be the most probable given an evolutionary model for natural selection.

Can we find this in Plantinga's argument? What kind of model, in the first place, would be adequate for his argument? I think that the most adequate one is an optimality model.Footnote ¹³ Optimality models are recurrent in evolutionary explanations of some trait in a given population (Beatty (Reference Beatty1980); Orzack and Sober (Reference Orzack and Sober2001); Rice (Reference Rice2015)). It is said that a feature F is an adaptation, according to an optimality explanation, because F, among those competing F*s, constitutes (or causes) the optimal strategy. These models take into account only natural selection as the relevant evolutionary force acting on a population.Footnote ¹⁴ I think that Plantinga's view is in accordance with this, for he talks about ‘fitness’, ‘adaptive behaviour’, and so on. Moreover, appealing to this kind of evolutionary tool could avoid objections like ‘his case lacks a minimal historical reconstruction of the causal chain involved in the evolution of relevant traits’, since optimality models were designed exactly to explain adaptations in an idealized way (Rice (Reference Rice2015)). Unfortunately, Plantinga doesn't provide us with sufficient information to build such a model. So, he doesn't provide even the least clue how to make the following prediction: the unreliable M will be fixed in the population by natural selection.

To see that is so, let us consider the minimal requirements to build an optimality model (Houston and McNamara (Reference Houston, McNamara and Pagel2002), 835–839): (1) a set of strategies, and (2) a currency to evaluate the strategies. Roughly, the strategies can be taken as the organism's behaviours (including its consequences) that enable him to deal with some situations. These strategies are constrained by several factors, for example, mechanical, energetic, environmental, etc. For instance, in a population where zebras spend time feeding and, in consequence, put themselves in danger from predators, running faster is a feasible strategy; shooting the predators using a machine gun, despite being a very good strategy, is not a real possibility to zebras. The ideal currency to evaluate a strategy is fitness. So, a ‘good’ strategy in this context is that which maximizes fitness; thus, an optimal strategy is one that (given the constraints) confers the maximal fitness value. Since fitness is a function of a particular behaviour or some combination of behaviours (or more generally design variables), when some other variable (e.g. energy efficiency) varies proportionately with fitness, it may be substituted for fitness (Beatty (Reference Beatty1980)). Using specific mathematical methods – which aren't necessary here – evolutionary biologists can determine which strategy is optimal and, thereby, explain why such and such behaviour (or another phenotypical characteristic) was fixed in a population.

Now we can ask the following questions: (i) what is the set of strategies in Plantinga's argument? And (ii) what is its currency? The set of strategies has to be formed with the combinations of behaviours and the cognitive mechanisms' outputs – namely, beliefs – (at least partially) causally responsible for such behaviours. For instance, the pair ⟨true belief, running⟩ represents a flight behaviour being produced by a true belief, such as a lion is coming; the pair ⟨false belief, shooting out the tongue⟩ represents a false belief, such as here is a fly, producing a feed behaviour, and so on and so forth. According to the simplification above we can obtain the following schemas: ⟨M⁻, behaviour⟩, ⟨M^+/−, behaviour⟩, and ⟨M⁺, behaviour⟩. In order to evaluate these strategies – that is, to determine which of them have the greater fitness values – it is necessary to stipulate the set of constraints to which the organisms are subjected. For instance, is there some trade-off between forming accurate representations of the environment and energy efficiency? Is a true belief more costly to an organism than a false one? Are inaccurate representations (or approximately false beliefs) are as good as accurate ones (or approximately true beliefs) to navigate through the environment? And so on and so forth. Since fitness is a function of the design variables (in this case, a pair ⟨belief, behaviour⟩) it is not possible to determine what pair ⟨M, behaviour⟩ maximizes fitness without first determining the payoffs of each strategy. So, Plantinga should have provided us something like the following:

But all he offers us is a thought experiment to the effect that it is possible that an organism could survive and reproduce using false or inaccurate beliefs as much as if it had used true or accurate beliefs. This possibility, however, has to be a ‘biological possibility’ – namely, a possible scenario given certain constraints and restrictions – not a mere logical possibility. But even this wouldn't be enough; this biological possibility has to be optimal. But Plantinga didn't provide us with such result. He didn't even try to show that the strategies' fitness values were such that x > z or y > z in order to argue that it would be most probable that the optimal strategy were found in the union of M⁻ and M^+/− sets. Or he could have insisted that the strategies are empirically equivalent – that is, that all of them have approximately the same empirical consequences – and because of this we should expect to find the strategy that was fixed in the population in the union of M⁻ and M^+/− rather than in the M⁺ set. But to do this it is necessary to estimate the several trade-offs and payoffs related to each strategy. So, the burden of proof is on Plantinga (at least this time!).

Perhaps we could read the case presented in the previous section not as an argument for DD, but as a case stating some constraints to the spreading of reliable belief-formation mechanisms in the population. But even so, it is noteworthy to recall that that the argument begs the question.

To recap: I said that a good argument to convince a naturalist to abandon the reliability thesis is one that would convince a professional biologist. And mere logical possibilities don't touch the biologists' heart; the minimum they expect is an optimality model. Plantinga should be able to make the precise prediction, using an optimality model, which an unreliable belief-formation mechanism (either M⁻ or M^+/−) would spread in the population in the long run. But he hasn't. So, we shouldn't expect that his argument is successful against naturalism.

GE and belief-revision

If DD is true, then the naturalist (i) at best cannot explain the reliability of our cognition, or, (ii) at worst, he is doomed to self-defeatedness (and irrationality). In order to avoid this embarrassment, Plantinga suggests substituting supernaturalism for naturalism. More specifically, he suggests the guided evolution hypothesis according to which God uses the evolutionary processes to create. In this sense, evolution and existence of God are consistent with each other. More precisely, he claims that the imago Dei hypothesis – namely, that God created us in his own image and resemblance – predicts that our cognitive mechanisms are the way they actually are (Plantinga (Reference Plantinga1993), (Reference Plantinga and Beilby2002), (Reference Plantinga2011)). So, what Plantinga really wants is to show that supernaturalism is ultimately rationally superior to naturalism. In this section I will argue that his strategy cannot be successful. In a nutshell, I think that Plantinga's replacement of naturalism for supernaturalism, despite his agreement with the LakatosianFootnote ¹⁵ view of science, is not effective against the naturalist.

Let us begin by supposing, for the sake of the argument, that Plantinga could provide a model to support DD. What exactly should be the biologist's reaction? If we consider the actual practice of biology, a sensible suggestion would be that they could interpret such result as a kind of evolutionary puzzle – that is, it is a fact that a certain group of organisms has a given trait, researchers assume that this trait is an adaptation, but standard assumptions about natural selection apparently make it improbable that such a trait has evolved. Biologists often face this kind of embarrassment: the monarch butterfly's bright colours and Thompson's gazelle stotting, for instance, appear to make them vulnerable to predators (Alcock (Reference Alcock2009)). Or consider biological altruism. Initially it was thought as challenging natural selection, since it was expected that an individual organism would never engage itself in behaviours that decrease its own fitness but increase a co-specific's fitness (Okasha (Reference Okasha2013)). The best prospect to solve this puzzle was not to reject naturalism, but to introduce a new hypothesis into evolutionary theory, namely, kin selection hypothesis. In general, biologists don't reject naturalism when faced with puzzles of that kind; instead, they continue their inquiry by trying to solve them within a naturalist framework (or at least in a non-guided evolutionary theory). I presume that the same is true for evolutionary puzzles about mind and cognition. There is no reason to think that the brain is an exception to evolutionary investigation.

Plantinga's suggestion is very bold: he intends that a naturalist feels convinced that natural selection alone, without any help of a supernatural guidance, couldn't produce organisms able to track truth. But this is unlikely to happen if all that Plantinga has to offer is a prediction based on a supposed good optimality model; or, in other words, if all he has to offer is an evolutionary puzzle about the reliability of cognitive mechanisms. It is reasonable to expect that evolutionary biologists (at least as members of a research programme) will try to exhaust all standard theoretical resources available, to put forward alternative evolutionary hypotheses, to develop new methods of modelling, and so on. For instance, they could explore the hypothesis that the reliability is a spandrel or a by-product of natural selection, or maybe that it is an exaptation; or occasionally find out some molecular evidence for a drift hypothesis. But this exhaustion doesn't guarantee that the scientific community will take seriously the hypothesis of guided evolution to the point that it incorporates it in scientific practice. The history of science has supposedly demonstrated that this kind of programme didn't turn out profitable (Mayr (Reference Mayr2020)).

In fact, Plantinga wouldn't feel intimidated by such reading of the history of science, for he thinks, contrary to it, that science and religion are in a deep concord. After all, he intends to convince naturalists that a sensible scientific understanding of the world makes sense only within a supernaturalist framework. Otherwise, our understanding of the natural world is fragmented – due to the apparently unsolvable puzzles – or, even worse, threatened by self-defeatedness – for we cannot rationally maintain both that we have knowledge or rational belief (and, consequently, that science is rational) and that natural selection gave us an unreliable cognition.

Now we can ask whether Plantinga's suggestion of replacing naturalism with supernaturalism is in accordance with the good policy of belief revision in science. As suggested above, it is plausible to think so. Let's begin by noting a well know general schema for belief revision, the Duhem-Quine Thesis, according to which no belief is immune to revision; consequently, no theory is immune to revision too. It is logically very simple:

This captures the intuitive idea that an inquirer, when faced with apparently disconfirming evidence against his hypothesis, needn't reject it immediately, for it is possible that an error is to be found in the set of auxiliary assumptions.

But DQ by itself doesn't dictate a specific policy. It doesn't tell us when to reject the hypothesis or when to reject some auxiliary hypothesis. Nor does it tell us whether we are to replace central or marginal beliefs in our system. Plantinga doesn't give us any indication. Maybe he is assuming a permissible criterion of belief revision, something like: if you have an observation contrary to his theory, and that theory is prima facie plausible, then replace any part of it. Or maybe he is assuming a moderate criterion like replace any part of the theory provided this replacement doesn't disfigure it so much. Or maybe a conservative criterion as the following: replace the minimum in order to maintain the theory very close to the original.

So, in order to provide a proper belief-revision guidance we can introduce Imre Lakatos's (Reference Lakatos, Lakatos and Musgrave1970) notion of a scientific research programme (SRP). A SRP contains three main sets of assumptions: (i) hard-core (HC), (ii) protective-belt (PB), and (iii) methodological (M) ones. The HC-assumptions are the heart of the programme;Footnote ¹⁷ they are protected from refutation by PB-assumptions, which are in general empirical propositions inferred from HC-assumptions conjoined with other theoretical and empirical propositions. Most of the empirical content of a theory (or SRP) is in the PB-set. M-assumptions provide the guidelines to design experiments, to replacement of auxiliary hypothesis, to the use of instruments, and so on. Newtonian mechanics, as well as Darwinian biology, are notorious examples of a SRP.

Following the DQ schema now we can obtain the following Lakatosian procedure of belief-revision:

The ‘properly’ clause is to be read as a non-ad hocness clause: the new assumption cannot be introduced merely to save the theory from refutation; it has to be capable of independent testing against the court of experience.

Now we are ready to interpret Plantinga's argument. First, we have to identify the structure of the programme that supposedly implies DD. Following Mitchel and Valone (Reference Mitchel and Valone1990), an optimization programme (ORP) contains at least four HC-assumptions: two general assumptions shared by almost all evolutionary research programmes, and two specific ‘primary’ assumptions concerning the optimality of the strategies. The PB-set in general is formed by the constraints on strategies and other empirical propositions. Although they are not explicit about M-assumptions, it is safe to say that they include propositions about how to calculate a specific fitness function, or how to create an evolutionary landscape, and so on. Second, we have to decide on what set of assumptions naturalism is to be introduced. Of course, not on the HC-set, for Plantinga (Reference Plantinga2011) reasonably notes that naturalism (and supernaturalism) is a ‘metaphysical add-on’ to evolutionary theory. The most plausible candidate is the M-set, since what blocks an auxiliary hypothesis like guided evolution is a naturalist methodological rule of thumb of the kind Don't posit supernatural entities or processes in order to explain natural phenomena. Of course that rule can be motivated by the acceptance of metaphysical naturalism, but not necessarily so. One reason to the adoption of methodological naturalism could be that supernatural explanations, despite the existence of supernatural entities, tend to be ad hoc, thereby leading the SRP to stagnation. Plantinga's argument, therefore, can be read as a suggestion to save ORP from refutation by rejecting a PB-assumption, namely the non-guided evolution hypothesis (NEH), and by adopting a specific guided evolution hypothesis, namely the imago Dei hypothesis (IDH):

1. (1) P(R | ORP & NEH) is low.

2. (2) R is the case.

3. (3) According to LDQ, we can replace some PB_ORP or some M_ORP assumption.

4. (4) If we replace MN for MS, then we can introduce the IDH.

5. (5) P(R | ORP & IDH) > P(R | ORP & NEH).

6. (6) Therefore, it is rationally preferable adopt ORP & IDH.Footnote ¹⁹

This suggestion is not misplaced from a historical perspective. For instance, Alfred Russel Wallace, co-discoverer of natural selection, explicitly rejected the idea that the human mind would be a product of natural selection (Gross (Reference Gross2010)). Although he didn't explicitly propose something like the guide evolution hypothesis, having said just that ‘a superior intelligence has guided the development of man in a definite direction, and for a special purpose, just as man guides the development of many animal and vegetable forms’ (Wallace (1780), cited in Gross (Reference Gross2010)), he never abandoned his belief in evolution. He converted to spiritualism, and believed that science and religion were ‘mutually supportive elements in a grander scheme of things’ (ibid.). So, it is very likely that he would accept GE if it were proposed to him.

Is this argument acceptable? I think not. And the reason is that IDH is difficult to test, that is, it is difficult to independently confirm or disconfirm it. There are a lot of logically possible auxiliary assumptions to be conjoined with HC-assumption in order to avoid refutations (Sober (Reference Sober2000)), and unless we can distinguish between acceptable and non-acceptable new BP-assumptions, we cannot say whether our attempts to avoid refutation are legitimate or simply an ad hoc manoeuvre. For example, Le Verrier's introduction of a new planet, Neptune, to explain a prediction failure based on Newtonian mechanics and the astronomical data available at that time, wasn't just a mere logical possibility, but a proposition that could be empirically tested. Had no astronomer observed (or at least detected) Neptune after several attempts to do it, probably another hypothesis would have been put forward, and maybe the insistence on the Neptune hypothesis would be considered as an ad hoc manoeuvre. By contrast, IDH appears to be less prone to empirical testing than the Neptune hypothesis. What kind of fact would be expected to observe (besides R) if IDH were true? Can we predict the existence of a particular trait in human beings? For example, assuming IDH and the traditional theistic conception of God, it would be expected that God had designed brains less prone to error and biases; but what we observe is a human brain able to create and believe even in the most absurd conspiracies, and this is the case even to highly educated people (Kahneman (Reference Kahneman2011); Haidt (Reference Haidt2013)). As it happens, most theists don't consider abandoning IDH in the face of apparent refutations like that. This is, therefore, an indication that IDH cannot avoid the status of ad-hocness.

It is in the PB-set that much of the development of science takes place. As noted by Kuhn (Reference Kuhn1962), a successful SRP is one whose practitioners can solve properly the puzzles that threaten it. However, it is not reasonable that a subset of PB-assumptions accumulates a great number of anomalies of its own to the point that it obfuscates the whole SRP. And it is exactly this that occurs with IDH; its introduction in ORP is very like the introduction of an epicycle into the planet's orbit, each new anomaly leading to the introduction of a new epicycle within of another epicycle, and so on and so forth.

Plantinga claims that theists are entitled to do science while keeping their theological beliefs in the background (Reference Plantinga1996, Reference Plantinga2011). He plausibly points out that a belief defeated by some evidence e and background knowledge k might not be defeated given the same e and a different background k′. So, faced with the observation that human cognition is too biased, theists could say that this evidence doesn't make it improbable that God guided the evolution of human cognition because in the theist's background is the proposition that God created cognitively limited beings (and, for example, cognitive limitation is important to soul-making). But if so, it would be more plausible to say that Plantinga is suggesting not the introduction of GE in the protective belt, but to create a new research programme, say, the Guided Evolution Research Programme (GERP). The HC-assumptions of GERP are those of ORP plus those of GE. The difference between GERP and ORP is that in the former, but not in the later, theistic assumptions are protected of the refutation by the auxiliary assumptions. So, in this case theists wouldn't be accused of ad-hocness.

I think we can grant this point. In principle nothing prevents the creation of a new research programme, and nothing prevents its acceptance by some scientists. At this level we can easily endorse Feyerabend's anarchist maxim that ‘everything goes’ (Feyeraband (Reference Feyerabend1993), 14). In the Lakatosian philosophy of science (as is common in the historical philosophy of science), the development of science is understood as the competition of SRPs. What determines the success of a research programme is its capacity to explain (including solving puzzles) and predict natural phenomena. If, in the long run, a SRP accumulates anomalies, turns to be unable to predict new observations, and more and more ad hoc assumptions are needed to save the phenomena, then this particular SRP is degenerating. And the fate of a degenerating SRP is to become just another chapter in the history of science.

Unfortunately we cannot assess the success of the putative GERP, even its immediate success. First, because GERP is just an indication to a future programme; as far as I know, there are still no scientists building optimality models based on theistic assumptions. Second, no specific hypothesis about the evolution of the reliability (as it is understood by philosophers) of human cognition was scientifically tested. Until now there has been much philosophical speculation, but few scientists appear to be sensitive to this question. Consequently, there are no theoretical alternatives within ORP to deal with the anomaly brought by DD.

In sum, nothing preventing the creation of GERP, theists are quite entitled to make science within a supernatural framework. By the other hand, GERP is still a ‘fictional’ SRP and ORP doesn't appear to be a degenerating programme. Therefore, the rejection of methodological naturalism, regardless of its appeal to theists, is innocuous regarding naturalists.

I'm inclined to agree with Kuhn that some radical change in view is more like a conversion than like a rational choice. In a possible scenario where a naturalist SRP is degenerating and even so scientists insist on pursuing their work, this doesn't prevent them recognizing the success of a rival SRP. This would constitute a sufficient basis for irrationality claims. But as mentioned above, this is not the actual scenario. Plantinga's argument, therefore, doesn't allow us to claim that in regard to the reliability of our cognition it is more rational to be theist than naturalist.