Between the possible and the actual

Consider the concept of tooth fairy, understood as a non-natural, magical being (a fairy) that takes children's baby teeth in exchange for a small payment. It is clearly a possible concept: it is possible that there is an entity e such that e falls under [tooth fairy]. But [tooth fairy] is not an actual concept: as far as we know, there is no entity that falls under it.Footnote ¹⁰ This does not seem much different from the concept of dinosaur; [dinosaur] is also a possible but non-actual concept: as far as we know, there is no entity that falls under [dinosaur]. But clearly [tooth fairy] and [dinosaur] are not on the same epistemological level. We might express this by saying that while the latter concept is plausible, the former is not.

One might reply that the scientific analysis of fossil records entitles us to accept rationally the proposition that between 200 and 65 million years ago there were entities that fell under [dinosaur]. On the assumption of presentism, we might extend the use of the term ‘actual’ (according to which a concept c is actual iff there is or there was an entity e such that e falls under c), so that [dinosaur] is an actual concept (or, at the very least, it is plausible that [dinosaur] is an actual concept). But how about the concept of black hole, a region of space-time where gravity is so strong that nothing – no particles or even electromagnetic radiation such as light – can escape from it? Many, including the most scientifically literate, claim to know that black holes exist. But belief in black holes was not always so. Before the demonstration in the 1960s that black holes were a prediction of general relativity, which was succeeded in 1967 by the discovery of neutron stars by Jocelyn Bell Burnell and the identification of Cygnus X-1 as the first known black hole in 1971, black holes were a mere mathematical curiosity. So, perhaps it is safe to say that before 1971, and definitely before 1960, [black hole] was not an actual concept: as far as we knew, there was no entity that fell under it. But even then, [black hole] was not on the same level as [tooth fairy]: we might say that although not actual, the pre-1960 concept of black hole was a plausible concept.

Here is perhaps a better example: the concept of a universe parallel to ours, understood within multiverse theories such as inflationary theory, as a disconnected space-time region that expands together, and which has its own laws of physics, its own collection of particles, its own arrangement of forces and its own values of fundamental constants. Unlike [black hole], [parallel universe] is not an actual concept: as far as we know, no entity falls under it. More than that: many critics claim that because their basic premise cannot be tested, multiverse theories are non-scientific. Translated into conceptual terms, this means that there can never be evidence to support the claim that there is an entity that falls under [parallel universe]; we do not know, and we will never know (because we cannot know) whether [parallel universe] is an actual concept. Still, [parallel universe] does not seem to be on the same epistemological level as [tooth fairy]. Besides being possible, [parallel universe] also seems to be a plausible concept.

Even concepts such as the concept of luminiferous aether – understood as a medium that permeates all space and though which light propagates – and the concept of caloric – a self-repellent fluid that flows from hotter bodies to colder bodies –  which are accepted nowadays as non-actual, perhaps as much as [tooth fairy], do not seem to be on the same epistemological level as [tooth fairy]. In some sense, it seems that [luminiferous aether] and [caloric] also are plausible concepts (or at the very least were, at some point of history).

All these concepts are such that

1. (2) There is an entity e that falls under concept c.

is philosophically/scientifically important. The discoveries of dinosaurs and black holes are important events in human intellectual history. It was important also to conclude that there is no such a thing as luminiferous aether and caloric. And it is intellectually important to know whether there are universes parallel to ours. It might be even intellectually important to know if tooth fairies exist. It might seem unimportant because we supposedly know that they do not exist. But if we were to discover that they do exist, that would be a very remarkable discovery!Footnote ¹¹

My main point here is this: these four concepts – the pre-1960 concept of black hole, [parallel universe], [luminiferous aether] and [caloric] – are not on the same epistemological level as [tooth fairy], although, like [tooth fairy], they are also possible and non-actual. This does not mean that they (the four concepts) are equally plausible. But the fact that there is an epistemic difference between them and [tooth fairy] points to the need for an epistemological label to qualify concepts and situate them between the merely possible and the actual. Therefore, I claim that while [tooth fairy] is not a plausible concept, the four mentioned concepts are (or were, in the case of [luminiferous aether] and [caloric]) plausible concepts.

But perhaps one does not share my intuition and disagrees that there is an epistemic difference between [tooth fairy] and [parallel universe], or between [tooth fairy] and [caloric]. But [tooth fairy] is just an example. Other concepts such as [gnome], [golden mountain], [bogeyman], [sandman] and [Pegasus] would do the job as well. I could even have used other examples instead of the pre-1960 concept of black hole, [parallel universe], [luminiferous aether] and [caloric]. What matters for my argument is that there is a clear epistemological difference between certain possible but non-actual concepts that might be expressed with the help of the adjective ‘plausible’. Therefore, conceptual plausibility might be reasonably said to be something situated between the merely possible and the actual.

In order not to rely on intuition alone, I provide a justification for the claim that while the pre-1960 concept of black hole, [parallel universe], [luminiferous aether], and [caloric] are (or were at some point) plausible concepts, [tooth fairy] is not. It is based on what might lie at the heart of many uses of the phrase ‘plausible concept’.

Often when people say that concept c is plausible, they seem to mean that c is explanatorily fruitful. For example, psychologist Bart Hoebel has argued that [food addiction] is a plausible concept because it helps to explain why sugar releases opioids and dopamine, brain pathways evolved to respond to natural rewards that are also activated by addictive drugs and which might be expected to have addictive potential (Avena et al. (Reference Avena, Rada and Hoebel2008), 20). Economist Eric Campton argues that [false consciousness] is a plausible concept because it helps to explain why some people can be systematically misled about the way others treat them and to form and cling sincerely to theories of social reality that distort reality, causing them to support policies that are harmful to them and to those they care about (Boudreaux and Crampton (Reference Boudreaux and Crampton2003), 28).

Given this understanding of conceptual plausibility, it seems fair to say that while [tooth fairy] is not plausible – it is not helpful in the explanation of any relevant phenomenon, in the broad sense of the term –  all our four concepts are explanatorily fruitful. The pre-1960 concept of black hole is part of the first exact solution to the Einstein field equations of general relativity proposed by Karl Schwarzschild in 1915. [parallel universe] and the more general concept of which it is part, [multiverse], help to explain several aspects of the structure and origin of the universe. [luminiferous aether] helped to explain why the apparently wave-based light propagates through empty space. And, for centuries, [caloric] helped to explain the phenomenon of heat.

In the section titled ‘A criterion for conceptual plausibility’ I will say more about conceptual plausibility as explanatory fruitfulness.

The philosophical import of conceptual plausibility

The three uncontroversial conceptual categories – conceptual possibility, conceptual actuality, and conceptual necessity – can all play some role in the rational acceptance of propositions, although not in a balanced way. Consider the following proposition:

1. (4) God exists.

Two of the main fronts of the debate over the rationality of (4) – the construction and analysis of arguments for and against the existence of God and the analysis of the concept of GodFootnote ¹² – can be described in terms of the concept of God. An indispensable part of the conclusion of any theistic argument, for example, is the proposition that there is an entity e such that e falls under [God]: a theistic argument aims at the conclusion that [God] is actual, or that it is probable that [God] is actual, or that it is more probable than not that [God] is actual, and so on. Some of these arguments are premised on the assumption that it is necessary that there is an entity e such that e falls under [God], that is to say, that [God] is a necessary concept (equivalently, that God is a necessary being). In its turn, the analysis of the concept of God concerns, among other things, the coherence or consistency of [God].

From a theistic perspective, arguments for the existence of God have been seen as providing a positive-propositional warrant for the rational acceptance of (4). Whether in isolation or cumulatively, theistic arguments have traditionally been seen as a source of warrant for rationally accepting the belief in God. In its turn, the analysis of (the coherence of) the concept of God might be seen as providing a minimal, negative-conceptual warrant for rationally accepting (4). Once again adopting the perspective of the theist and placing the burden of the proof on her, to believe rationally in (4) one must first show that [God] is not an incoherent concept: one must show that it is possible that there is an entity e such that e falls under [God].Footnote ¹³

It might be argued, however, that there is something between these two extremes: a positive-conceptual warrant for the rational acceptance of (4). Many people would reject, for mere conceptual reasons, the belief in the existence of a tribal and exclusivist God who demands exclusive worship for itself, even if this corresponds to a coherent concept. On the other hand, viewing God as a forgiving and compassionate father who loves equally all human beings, for example, seems to play the opposite role in many people's acceptance of theistic belief. The plausibility (or not) of a concept of God seems to play a role in the rational acceptance of God's existence.Footnote ¹⁴

Here an addendum is needed. Virtually every monotheistic religious tradition – and sometimes every school or order inside various traditions – has its own view of God. Similarly, philosophers have proposed and defended several different views of God. There is considerable variety even within what philosophers have labelled classical (and neo-classical) theism, pantheism, panentheism, process theism, and open theism. Despite using the expression ‘the concept of God’, I am following what seems to be the standard in contemporary philosophy of religion and assuming that for each of these views there is a corresponding concept of God. There is a plurality of concepts of God. Therefore, the correct way to state (4) would be as follows:

1. (5) There is an entity e which falls under g.

where g is a specific concept of God.Footnote ¹⁵

These are competing concepts of God. In fact, much of the motivation of proponents of a specific concept of God is to establish one's concept as the most defensible concept of God. Naturally, this is often accompanied by criticisms of rival concepts of God. In this connection, Huw P. Owen (Owen (Reference Owen1971), 3) has written as follows:

It is thus desirable that there are minimally objective ways to evaluate claims such as (6) or (7) below:

1. (6) Concept of God g is preferable to concept of God d.

2. (7) Concept of God g is preferable to all other concepts of God.

Although this might be done by appealing to the positive-propositional route mentioned earlier (showing, for example, that the existence of an entity that falls under g is more likely than the existence of an entity that falls under d), philosophers have seldom taken this route. Sometimes times a negative-conceptual route is used. Claims like (6) are justified by trying to show that d is inconsistent. It is not difficult, however, to see that this might be troublesome. For every charge that a (usually not-well-defined concept) c is inconsistent, one can always change the set of attributes assigned to c, or change the meaning of some of those attributes, so to escape the charge of inconsistency.

At other times (perhaps more often than not) (6) and (7) are justified by referring to some methodological-metaphysical view that supposedly supports g. Classical theists, for example, often defer to some version of perfect being theology to justify their concept of God (or a specific view of some divine attribute) over others. Process theists, on the other hand, refer to process philosophy to justify and support their concept of God. It is easy to see how problematic this can be. Unless one already makes the same the metaphysical assumptions as, say, perfect being theology and process theology, one will not find this type of justification very persuasive.

Thus, it would be useful to have other criteria to decide about claims like (6) or (7). If we accept the plausibility, positive-conceptual route as a candidate, the debate will not centre on finding consistency faults in competing concepts of God, nor in making specific metaphysical assumptions, but in showing that one's concept of God has some conceptual positive feature that justifies preferring it to other concepts of God. Alternatively, one can adopt a comparative approach and show that g is more plausible than d.

I am not claiming that this conceptual-positive route is better than other routes and therefore should be the sole arbiter of claims like (6) and (7). All I claim is that we can benefit from additional criteria for preferring one concept of God to another.

To sum up, conceptual plausibility seems important for philosophy of religion for two reasons. First, it could contribute to the general debate over the rationality of theistic belief. According to an evidentialist approach, for example, besides being consistent, a concept of God must also be plausible. Furthermore, in the absence of a successful argument for the conclusion that a specific concept of God g is actual, or that it is more probable than not that g is actual, an argument for the conclusion that g is plausible could play a positive role (although not decisive of course) in the rational acceptance of (5).Footnote ¹⁶ That would be a kind of external use of conceptual plausibility in the debate about God. Second, conceptual plausibility could contribute to the debate about whether a concept of God g is preferable to another concept of God d. This could be done either by showing that g is plausible, and d is not plausible, or by showing that g is more plausible than d. That would be a kind of internal use.

From propositional plausibility to conceptual plausibility

Let P be a proposition. We have agreed that if P is (actually) true then P is plausible; and that if P is plausible then P is possible. We have also agreed that conceptual actuality and conceptual possibility are to be defined in terms of their propositional counterparts. Let c be a concept. c is actual iff there is an entity e such that e falls under c; c is possible (coherent or consistent) iff it is possible that there is an entity e such that e falls under c. Therefore, if we are to take seriously the claim that conceptual plausibility lies between conceptual possibility and conceptual actuality, the following seems to be true:

1. (8) If c is actual, then c is plausible.

(Recall that I am assuming that any truth claim is to be understood within an epistemic context. (8), for example, can be restated as follows: if (it is known that) c is actual, then (it is known) that c is plausible.) This might be called a sufficient criterion for conceptual plausibility. We also have a necessary criterion:

1. (9) If c is plausible, then c is possible.

(8) and (9), however, cannot be turned into a necessary and sufficient criterion. First, because non-actual concepts might also be plausible. Second because we want a criterion that goes beyond mere possibility. After all, this was one of the motivations for introducing the idea of conceptual plausibility: to make epistemological distinctions within the category of possible non-actual concepts.

Following the above-mentioned connection between the non-epistemic propositional categories and their corresponding conceptual categories, one might propose the reduction of conceptual plausibility to propositional plausibility. In other words, one might propose that

1. (10) c is plausible iff the proposition that there is an entity e such that e falls under c is plausible.

Or, equivalently, that

1. (3) c is plausible iff the proposition that c is actual is plausible.

(10) entails both (8) and (9).Footnote ¹⁷

In the introduction, I said that for the cases I am dealing with, (3) might look like a promising definition of conceptual plausibility. One might say that the reason why [tooth fairy] is not plausible is that it is not plausible that there are tooth fairies; and the reason why [dinosaur] and [black hole] are plausible is that it is plausible that there were dinosaurs, and it is plausible that there are black holes, respectively. But does (10) work satisfactorily for all relevant cases?

(10) states that propositional plausibility is necessary and sufficient for conceptual plausibility. The sufficient side of (10)

1. (11) If the proposition that c is actual is plausible, then c is plausible.

does not seem problematic. Considering that the truth of the proposition that c is actual is sufficient for us to conclude that c is plausible (8), it seems fair to maintain that having evidence for such proposition is also enough for us to conclude that c is plausible.

Can the same be said about the necessary part of (10)?

1. (12) If c is plausible, then the proposition that c is actual is plausible.

Is propositional plausibility necessary for conceptual plausibility? One way to answer this negatively is to find counterexamples to (12). Or instead, ask the following question: is there any plausible concept c such that (it is reasonable to say that) the proposition that c is actual is not inductively supported by any evidence?

The answer seems to be yes. As I said, there is no evidential support for the claim that there are universes parallel to ours, understood within multiverse theories such as inflationary theory. Further, many critics claim that because the basic premise of these theories cannot be tested, there can never be evidence to support the claim that there is an entity that falls under [parallel universe]. So, it seems safe to say that the proposition that [parallel universe] is actual is not plausible. However, it makes sense to say that [parallel universe] is a plausible concept. It makes sense from an intuitive perspective, I claim, but also from a perspective where we take explanatory fruitfulness as the key element of conceptual plausibility. The same thing can be said about the pre-1960 concept of black hole, understood within the corresponding historical period. Although back then there was no evidential support for the existence of black holes (as I said, until the 1960s black holes were seen as a mere mathematical curiosity), it makes sense to say that back then [black hole] was a plausible concept.

We could ask an even stronger question: is there any plausible concept c such that (it is reasonable to say that) the proposition that not-c is actual is inductively supported by the evidence? Again, the answer is yes, if we accept that [luminiferous aether] and [caloric] are plausible concepts.

It seems then safe to say that conceptual plausibility cannot be reduced to propositional plausibility.Footnote ¹⁸ We need some independent criterion that allows us to classify possible but non-actual concepts as plausible.

A criterion for conceptual plausibility

I believe that the missing sufficient criterion lies in the notion of explanatory fruitfulness. As I have argued in the section titled ‘Between the possible and the actual’, many uses of the phrase ‘plausible concept’ seem to take plausibility as the same as fruitfulness. In its turn, conceptual fruitfulness is usually taken from within an explanatory perspective. This is no accident. There is an (at least implicit) explanatory component in most accounts of fruitfulness. When defining what fruitful theories are, for example, Thomas Kuhn says that they are theories that ‘disclose new phenomena or previously unnoted relationships among those already known’ (Kuhn (Reference Kuhn1977), 322). Carnap defines a fruitful concept as one that is ‘useful for the formulation of many universal statements (empirical laws in the case of a nonlogical concept, logical theorems in the case of a logical concept)’ (Carnap (Reference Carnap1962), 7).Footnote ¹⁹ I therefore propose the following definition of (conceptual) explanatory fruitfulness:

1. (13) c is explanatorily fruitful (or simply fruitful) iff there is a relevant phenomenon p that needs explanation, and there is a tentative credible explanation for p that has c as an indispensable conceptual part.

A crucial element of (13) is the phrase ‘tentative credible explanation’. While I am not assuming any philosophical theory of explanation, I take the term ‘explanation’ to be general enough to be compatible with most theories of explanation. If I were to provide a general account of what I mean by ‘explanation’ here, I would say the following. Suppose that E is such that E explains p; or more precisely, that E is the explanans of an explanation that has p as its explicatum. From an epistemic point of view, I take ‘E explains p’ to mean the following: when we take E into account, p is not as surprising as it seemed to be (independent of or prior to E). From a logical point of view, it means that E serves as evidence for p, or equivalently that p inductively follows from E.Footnote ²⁰ As this presupposes that E and p can logically relate to each other, I am assuming that E and p are descriptions or representations of something (which seems to be the standard meaning attributed to the terms ‘explanans’ and ‘explicatum’).Footnote ²¹

Second, by tentative explanation I simply mean that the explanation at hand is an attempt to explain p. It might not be the best explanation. It might even not be an accepted explanation. It might be a superseded explanation, for example, like the explanations associated with [luminiferous aether] and [caloric] (according to (13) and (14) then, these two concepts are plausible). But it must be credible. I take this term in the literal sense of ‘able to be believed’. A credible explanation is an explanation one would be able to believe. But of course, one might ask: credible to whom? Here I am supposing the existence of a shared background knowledge against which the credibility of propositions and explanations must be measured. Roughly speaking, anything consistent with this background is credible, and anything inconsistent with it is not credible.

Third, as the example of the concept of black hole indicates, I take the term ‘phenomenon’ very broadly, so broadly as to include scientific theories or any body of theoretical knowledge. Fourth, by saying that c is an indispensable conceptual part of the explanation I mean that c is part of its explanans E, and if we succeed in taking c away from E then ‘E explains p’ is no longer true. Finally, I am assuming that the fact that c is an indispensable conceptual part of E, and that E explains p, guarantees that c is possible.

Elaborating on what I said at the end of the section titled ‘Between the possible and the actual’, [tooth fairy] is not fruitful because it is not part of any explanation of any relevant phenomenon. In its turn, the pre-1960 concept of black hole is an indispensable conceptual part of the first exact solution to the Einstein field equations of general relativity proposed by Karl Schwarzschild in 1915. [parallel universe] is an indispensable part of the concept of multiverse; in its turn, [multiverse] is an indispensable part of inflationary theories, which explain several aspects of the structure and origin of the universe, such as, for instance, why the average density of the universe is so close to the critical density. Finally, while [luminiferous aether] was an indispensable part of several theories proposed between the seventeenth and nineteenth centuries that, among other things, tried to explain why (the apparently wave-based) light propagates through empty space, [caloric] was the key concept of a theory popular in the seventeenth and eighteenth centuries called caloric theory that aimed to explain the phenomenon of heat.

One might object that [tooth fairy] is explanatorily fruitful because it is an indispensable conceptual part of an explanation often given by adults to children as to why the teeth they put under their pillow the night before disappear and money is found in their place. But that is not a credible explanation. And the reason for this is obvious: the one who provides the explanation does not typically believe it, for one knows beforehand that the story is false. More generally, the story is not consistent with the shared background knowledge of the one who provides the explanation. (Another example of non-credible explanation, now associated with [sandman], is that the grit or rheum in one's eyes upon waking is the result of the Sandman's work the previous night.) Moreover, it might be said that the phenomenon at hand is neither relevant nor needs explanation (after all, every adult knows why the tooth disappears).

From (13) we get our missing sufficient criterion for conceptual plausibility:

1. (14) If c is explanatorily fruitful, then c is plausible.

One might object to (14) by saying that only by resorting to (11) can it be seen as a criterion for conceptual plausibility. The definiens of (13) seems to be a kind of inference to the best explanation: if E presupposes that there is an entity that falls under c, the fact that E explains p can be seen as supporting the proposition that c is actual is plausible. From (11), we then conclude that c is plausible. The flaw in this argument is obvious. Saying that there is a tentative credible explanation for p, (13) does not assume that it is the best explanation. As the cases of [luminiferous aether] and [caloric] show, it does not even assume that it is a good or accepted explanation. Furthermore, it is not necessary that E presupposes that there is an entity which falls under c: one might adopt an instrumental, non-realistic perspective regarding c, for example.

It is important to remember that (14) is a sufficient but non-necessary criterion. It might be that a concept c is plausible but not fruitful; one might for instance know that there is an entity which falls under c, which by (8) allows one to conclude that c is plausible. Nevertheless, from (13), along with (8) and (11), we can build a sufficient and necessary criterion for conceptual plausibility:

1. (15) c is plausible iff one of the following conditions is met: (i) c is actual; (ii) the proposition that c is actual is plausible; (iii) c is explanatorily fruitful.

One might object that there are actual concepts that are not fruitful. Take the concept of grue, for example, defined as follows: an object falls under [grue] iff the object is either green and has been observed before now, or blue and has not been observed before now. Clearly [grue] is an actual concept: there are grue objects. But it is hard to see how [grue] can be explanatorily fruitful. Therefore, [grue] does not seem to be a plausible concept. The reply to this is straightforward. According to (15), fruitfulness is just one of the conditions that might be meet for a concept to be plausible: if c is fruitful, then c is plausible. But if c is actual, then c is also plausible. As stated in (8), conceptual actuality is a sufficient criterion for conceptual plausibility. Therefore, to the extent that [grue] is actual, [grue] is a plausible concept, even though it does not seem to be fruitful.

Towards a comparative approach to conceptual plausibility

This is, of course, a qualitative approach. All it aims at is the question of whether concept c is plausible or not. As such, it is silent on the question of whether c is more plausible than c′, where c and c′ are different concepts. As it turns out, a comparative approach involves extra difficulties. I will here offer a modest and possibly overoptimistic account of comparative conceptual plausibility. It is modest because it is not meant to be the final word on the issue; my aim is only to show that such a comparative approach is minimally feasible. It is possibly overoptimistic because it depends on a couple of assumptions for which I do not really offer arguments.

Let us start by examining the possibilities that arise from conditions (i), (ii) and (iii) in (15). First, the easy cases. If c meets (i) and c′ does not meet (i), for example, then c can be said to be more plausible than c′. Similarly, if c meets (ii) and c′ does not meet (ii), then c is more plausible than c′. This is because we can say that [dinosaur] is more plausible than [parallel universe], for example (assuming that the proposition that parallel universes exist is not known to be plausible, while the proposition that dinosaurs existed is plausible). Finally, if c and c′ do not meet (i) but both meet (ii), then whether c is more plausible than c′ seems to depend on there being a comparative theory of propositional plausibility able to compare the plausibility of the two corresponding propositions.

The complicated cases are the ones where (I) c and c′ both meet (i) and (II) c and c′ are both fruitful but do not meet neither (i) nor (ii). Both cases can benefit from the following comparative analysis of the notion of conceptual fruitfulness. Before going to that, however, I should mention what seems to be an easy special case of (II): if the proposition ‘c is actual is not plausible’ is not known to be true, but the proposition ‘c′ is actual is not plausible’ is known to be true, then c is more plausible than c′. This is because we can say that [parallel universe], for example, is more plausible than [luminiferous aether] and [caloric] (assuming we do not know whether the proposition ‘Parallel universes exist’ is not plausible, but do know that ‘Luminiferous aether exist’ and ‘Caloric exist’ are not plausible).

Having said that, there seems to be six cases where we can compare the fruitfulness of two concepts c and c′. To explain that, let me introduce some harmless notation. Let p and E be such that E explains p; I represent this by E!p. If E!p and I am talking about the explanation for p of which E is the explanans, I write E^p. If in addition to E!p, c is an indispensable conceptual part of E, then I write E_c!p. ℘(c) and ℯ(c) are two sets defined as follows: a phenomenon p belongs to ℘(c) iff there is E such that E_c!p; an explanans E belongs to ℯ(c) iff there is p such that E_c!p. I call ℘(c) the explanatory scope of c.

The first case is where ℘(c) is the same as ℘(c′): the explanatory scopes of both c and c′ are identical. This is likely to happen, for example, if c and c′ belong to the same family resemblance category. In order to deal with this case, I need to introduce the comparative notion of p-fruitfulness. c is more p-fruitful than c′ iff there are E and E′ such that E_c!p and E′_c′!p and E^p is a better explanation than E′^p. With this in hand, we have:

1. (16) In the case where ℘(c) = ℘(c′), if x > y then c is more fruitful than c′, where x is the number of phenomena p ∈ ℘(c) such that c is more p-fruitful than c′, and y is the number of phenomena p ∈ ℘(c) such that c′ is more p-fruitful than c.Footnote ²²

The second case is where ℘(c) ≠ ℘(c′) and the intersection between them is empty. Here we will need to presuppose something perhaps even heavier than the existence of a non-problematic explanatory comparative measure. We need to assume that for two sets of phenomena A and B, we can say whether A is more relevant than B. This involves a qualitative measure, in the sense of the phenomena of A being, overall, more in need of explanation than the phenomena of B, as well as a quantitative one, in the sense of A having more relevant phenomena than B. Once this is granted, we have:

1. (17) In the case where ℘(c) ∩ ℘(c′) = Ø, if ℘(c) is more relevant than ℘(c′) then c is more fruitful than c′.

It might be however that ℘(c) is as relevant as ℘(c′) or that their relevance is incommensurable. In this case an external element comes into play: the extent to which c and c′ are part of superseded explanations. An explanation E^p is superseded iff there is E′ such that E′!p, E and E′ contradict each other, and E′ is known (or non-controversially accepted) to be true. We then we have:

1. (18) In the case where ℘(c) ∩ ℘(c′) = Ø and the relevance of ℘(c) and ℘(c′) are either the same or incommensurable, if w > z then c is more fruitful than c′, where w is the number of explanantia E ∈ ℯ(c) such that E^p is a superseded explanation, for some p ∈ ℘(c), and z is the number of explanantia E ∈ ℯ(c′) such that E^p is a superseded explanation, for some p ∈ ℘(c′).

Also we can now say that the pre-1960 concept of black hole and [parallel universe] are more plausible than [luminiferous aether] and [caloric].

The three remaining cases are cases where ℘(c) is different from ℘(c′) and the intersection between them is not empty. First, it might be that either x = y, where x is the number of phenomena p ∈ ℘(c) ∩ ℘(c′) such that c is more p-fruitful than c′, and y is the number of phenomena p ∈ ℘(c) ∩ ℘(c′) such that c′ is more p-fruitful than c. In this case, c is more fruitful than c′ if the phenomena which are exclusive to the explanatory scope of c are more relevant than the ones which are exclusive to the explanatory scope of c′ (in what follows, x and y are as defined above):

1. (19) In the case where ℘(c) ≠ ℘(c′), ℘(c) ∩ ℘(c′) ≠ Ø and x = y, if ℘(c) − ℘(c) ∩ ℘(c′) is more relevant than ℘(c′) − ℘(c) ∩ ℘(c′) then c is more fruitful than c′.

Second, it might be that x = y and the relevance of ℘(c) − ℘(c) ∩ ℘(c′) and ℘(c′) − ℘(c) ∩ ℘(c′) are either the same or incommensurable. In this case we resort to the number of superseded explanations related to c and c′:

1. (20) In the case where ℘(c) ≠ ℘(c′), ℘(c) ∩ ℘(c′) ≠ Ø, x = y and the relevance of ℘(c) − ℘(c) ∩ ℘(c′) and ℘(c′) − ℘(c) ∩ ℘(c′) are either the same or incommensurable, if w > z then c is more fruitful than c′, where w is the number of explanantia E ∈ ℯ(c) such that E^p is a superseded explanation, for some p ∈ ℘(c) − ℘(c) ∩ ℘(c′), and z is the number of explanantia E ∈ ℯ(c′) such that E^p is a superseded explanation, for some p ∈ ℘(c′) − ℘(c) ∩ ℘(c′).

Third, it might be that x > y. In this case, c is more fruitful than c′ if the phenomena which are exclusive to the explanatory scope of c′ are not more relevant that the ones which are exclusive to the explanatory scope of c:

1. (21) In the case where ℘(c) ≠ ℘(c′), ℘(c) ∩ ℘(c′) ≠ Ø and x > y, if ℘(c′) − ℘(c) ∩ ℘(c′) is not more relevant than ℘(c) − ℘(c) ∩ ℘(c′) then c is more fruitful than c′.

My proposal is that cases are where (I) c and c′ both meet (i) and (II) c and c′ are both fruitful but do not meet neither (i) nor (ii) be resolved by resorting to the above comparative analysis of the notion of fruitfulness (or to a better one). I thus say that, in both cases, c is more plausible than c′ iff c is more fruitful than c′.

There is a fourth possible case where ℘(c) is different from ℘(c′) and the intersection between them is not empty: the case where x > y and ℘(c′) − ℘(c) ∩ ℘(c′) is more relevant than ℘(c) − ℘(c) ∩ ℘(c′). As far as the unpretentious analysis I am doing here is concerned, I say that the fruitfulness of c and c′ here is not commensurable. Consequently, as far as we are dealing with cases (I) and (II) above, the plausibility of c and the plausibility c′ are not commensurable either.

God again

I have argued in the section titled ‘The philosophical import of conceptual plausibility’ that conceptual plausibility is important for the philosophy of religion for at least two reasons. First, it could contribute to the general debate over the rationality of theistic belief. According to an evidentialist-like approach, for example, besides being consistent, a concept of God must also be plausible. Second, it could contribute to the debate about whether a concept of God g is preferable to another concept of God d. This would be done either by showing that g is plausible and d is not plausible, or by showing that g is more plausible than d.

According to (15), in order for a concept c to be (qualitatively) plausible, one of the following conditions should be met: (i) c is actual; (ii) the proposition that c is actual is plausible; (iii) c is explanatorily fruitful. Given the low prospects of arriving at an uncontroversial argument for the claim that God exists, and the not-so-high prospects of arriving at an uncontroversial argument for the claim that ‘God exists’ is plausible, our best chance to show that [God] is plausible seems to be to show that it is fruitful. So, we may ask: Is the concept of God fruitful? Or, putting it in terms of (13), is there a relevant phenomenon p that needs explanation, and a tentative credible explanation for p that has [God] as an indispensable conceptual part?

Given the plurality of concepts of God mentioned earlier, these questions can be answered only when we consider a specific concept of God. As far as the rationality of theistic belief is concerned then, the question we should ask is:

1. (22) Is there a fruitful concept of God? In other words, is there a concept of God g such that there is a relevant phenomenon p and a tentative credible explanation E^p for p such that g as an indispensable conceptual part of E?

A crucial point about (22) is what counts as a relevant phenomenon in the case of [God]. One might think that the following would be a good start:

1. (23) There is evil and suffering in our world.

If this is correct, then a successful theodicy T_g would be enough to show that a specific concept of God g is a fruitful and consequently plausible concept: T_g explains (23) and, we suppose, has g as an indispensable conceptual part. Although this is correct, one might argue that the relevance of (23) depends on, or at least is enhanced by, the theistic assumption that God exists. After all, the aim of a theodicy is to explain why God, minimally conceived as an omnipotent, omniscient, and wholly good being who created the world, allows evil and suffering in the world. The problem of evil is more than anything a problem for theism. Thus, a more neutral phenomenon might be preferred.

Here is one candidate:

1. (24) The world we live in is an orderly word, with scientific laws operating within it, and regularities in the behaviour of medium-sized objects.

It seems pertinent to ask why our world is orderly, so orderly that we can predict in general terms the behaviour of our bodies, as well as of animate and inanimate objects that surround us.

Richard Swinburne argues that (24) is exactly what we would expect in the case God, understood as an essentially all-powerful, all-knowing and perfectly free person, exists:

In other words, (25) below, which has the concept of God as an indispensable conceptual part, supposedly explains (24):

1. (25) God, who is essentially all-powerful, all-knowing and a perfectly free person, exists.

Therefore, by (13) and (14) we can conclude that Swinburne's concept of God is plausible.

Swinburne's project of course does not aim at showing that his concept of God is plausible; it aims at showing that (25) is probably true. He does that through an argument from the best explanation: he struggles to show that (25) is what best explains (24).Footnote ²³ Whether his struggle is successful or not, one cannot deny that (25) does explain (24). That is to say, although it might be questionable that (25) is the best explanation for (24), it is uncontroversial that (25) is an (tentative) explanation for (24). About (25)'s credibility, it depends on the shared background knowledge we choose. If (25) is consistent with twenty-first-century dominant intellectual background knowledge, say, then from this perspective Swinburne's concept of God is a fruitful and consequently plausible concept.

As far as the second contribution of conceptual plausibility to philosophy of religion is concerned, as I said, this could be done through a qualitative approach or through a comparative approach. Although not undoable, from a more rigorous perspective the first approach is problematic, for it would involve arguing for the universal claim that there is no relevant phenomenon p and no explanation E^p such that a specific concept of God g is an indispensable conceptual part of E. Therefore, I will elaborate just on the second approach.

Consider the two concepts of God I mentioned in the section titled ‘The philosophical import of conceptual plausibility’. Let us call the first concept – a tribal and exclusivist deity who demands exclusive worship for itself – g, and the second concept – a forgiving, compassionate and universal deity who loves equally all human beings – g′. Let us also call G and G′ the supposed entities that fall under g and g′, respectively.Footnote ²⁴ The main difference between g and g′ concerns their universality. While G′ directs its love and concern to all human beings, the concern of G is directed only to a distinguished community or social group: either a tribe or ethnical group, the ones chosen by G, say, or the group of people who worship it.

Since g and g′ belong to the same family resemblance category – I am assuming they are both concepts of God –  it is likely, we might suppose, that their explanatory scope is the same. That is to say: ℘(g) = ℘(g′). In this case, according to (16), in order for g′ to be more fruitful than g, for example, the proposition below must be true:

1. (26) x is bigger than y, where x is the number of phenomena p ∈ ℘(g) such that g′ is more p-fruitful than g, and y is the number of phenomena p ∈ ℘(g) such that g is more p-fruitful than g′.

I argue that (26) is true. It seems likely not only that a considerable number of phenomena p within the explanatory scope of g and g′ involve human beings, but also that the explanantia of both ℯ(g) and ℯ(g′) that explain p in one way or other mention human beings. It is hard to imagine theistic explanations for phenomena like the existence of human suffering, human consciousness, and religious experience, or even the order and regularity of the world, which do not mention human beings. But since the attitude of G′ towards human beings is homogenous – it loves all human beings equally –  while G's attitude is heterogenous – it gives special attention to a distinguished group of human beings –  it is likely that for any phenomena p ∈ ℘(g), E′ is simpler than E, where E′ and E are such that E′_{g ′}!p and E_g!p. If we take simplicity as a key characteristic of a good explanation, it is likely that E′^p is a better explanation than E^p. Therefore, it follows that g′ is more p-fruitful than g.

For example, suppose that (24) above is within the explanatory scope of g and g′. E′ might be something along the lines of Swinburne's explanation above: since G′ loves all human beings, he creates an orderly and predictable world in which they might all have the opportunity to learn which actions have more effects, when rocks are likely to fall, predators to pounce, plants to grow, etc. But the attitude of G towards human beings is unbalanced. If E is a story exactly like E′, for example, one could argue that E is not consistent, for G's existence entails that it favours one group of human beings over the rest of humankind. E might contain the basic insight of E′, that G creates an orderly and predictable world because it wants to give to all human beings the opportunity to function in the world. But there must be a justification for why in this situation G treats all humans equally. It might be, for example, that G wants to give to humans who belong to the distinguished group the opportunity to interact with other human beings who behave overall like them, or that G wants to give a chance to the rest of mankind to acknowledge its existence, worship it, and thus become part of its distinguished group. But whatever the justification might be, E will be more complex than E′.

The situation does not change much if we suppose that ℘(g) ≠ ℘(g′). It seems reasonable to suppose that this case fits either (19) or (21), that is to say, that ℘(g) ∩ ℘(g′) ≠ Ø, that the relevance of ℘(c) − ℘(c) ∩ ℘(c′) and ℘(c′) − ℘(c) ∩ ℘(c′) are neither the same nor incommensurable and, given the argumentation above, that it is not the case that x < y, where x is the number of phenomena p ∈ ℘(g) ∩ ℘(g′) such that g′ is more p-fruitful than g, and y is the number of phenomena p ∈ ℘(g) ∩ ℘(g′) such that g is more p-fruitful than g′.

So, in the worst case where x = y, for g′ to be more fruitful than g the proposition below must be true:

1. (27) ℘(g′) − ℘(g) ∩ ℘(g′) is more relevant than ℘(g) − ℘(g) ∩ ℘(g′).

In the best case where x > y, for g′ to be more fruitful than g the proposition below must be true:

1. (28) ℘(g) − ℘(g) ∩ ℘(g′) is not more relevant than ℘(g′) − ℘(g) ∩ ℘(g′).

I argue that (27) is true, which is enough for both cases. Since the attitude of G′ towards human beings is homogenous and universal, while the attitude of G is not, the following is likely to be the case: while most phenomena p belonging only to the explanatory scope of g′ involve all human beings, most phenomena p belonging only to the explanatory scope of g involve only human beings belonging to G's distinguishing group. After all, we agreed that it is likely that most phenomena p within the explanatory scope of g and g′ involve human beings. Given this, it seems reasonable to conclude that ℘(g′) − ℘(g) ∩ ℘(g′) overall is more relevant than ℘(g) − ℘(g) ∩ ℘(g′).