If naturalism is true, then scientific explanation is impossible

Abstract

I begin by retracing an argument from Aristotle for final causes in science. Then, I advance this ancient thought, and defend an argument for a stronger conclusion: that no scientific explanation can succeed, if Naturalism is true. The argument goes like this: (1) Any scientific explanation can be successful only if it crucially involves a natural regularity. Next, I argue that (2) any explanation can be successful only if it crucially involves no element that calls out for explanation but lacks one. From (1) and (2) it follows that (3) a scientific explanation can be successful only if it crucially involves a natural regularity, and this regularity does not call out for explanation while lacking one. I then argue that (4) if Naturalism is true, then all every natural regularity calls out for explanation but lacks one. From (3) and (4) it follows that (5) if Naturalism is true, then no scientific explanation can be successful. If you believe that scientific explanation can be (indeed, often has been) successful, as I do, then this is a reason to reject Naturalism.

Introduction: an Aristotelian insight

In his Physics, Aristotle famously argues for teleology in nature – that nature, at least sometimes, acts for an end, for a goal, for a purpose. Aristotle believes that these ends can serve, at least partly, to explain natural phenomena, and he adds these ‘final causes’ to his other three causes or explanations of natural phenomena – material, efficient, and formal. This much is well known. Less well known is that, in Physics II 8 (198b16–199a8), Aristotle considers an objection to his teleological view of nature, an objection tracing back to the materialist Empedocles. Here's how Aristotle puts the problem (translated by Sedley (2007), 189–190):

There is a puzzle. What prevents nature from producing results not for a purpose or because it is best, but in the way that Zeus rains, not in order to make the crops grow, but of necessity? For what goes up must cool, and what cools must become water and come down; and when this happens, the accidental result is that the crops grow. Similarly if someone's crops rot on the threshing floor, it does not rain in order that this should happen, but it is an accident. So what prevents natural parts from being like this – for example that it is of necessity that teeth grow with the front ones sharp and suitable for cutting, the molars flat and useful for grinding food, because of a coincidental outcome, and not because they happened for this purpose? Likewise in the case of other parts in which purpose seems to be present: where everything accidentally turned out as it would have done also if it were coming about for a purpose, these ones were preserved, having been formed in a suitable way fortuitously, whereas those which did not turn out this way perished, and are still perishing, as Empedocles says about the ‘man-faced ox progeny.’

Aristotle has in mind here a view on which all natural phenomena can be explained via a combination of natural necessity and chance, with no need for teleology, no need for final causes. The rain falls as a result of necessity: heated water must rise, ‘what goes up must cool’, and cooled water must fall. And it's purely accidental whether this rain results in corn growing or crops spoiling. It's just chance. Neither result explains the falling of the rain; the rain didn't fall for the purpose of growing the crops, or for the purpose of spoiling them. In a similar way, as Empedocles proposed in his proto-Darwinian theory, perhaps living things organize themselves with some degree of spontaneity, resulting in a variety of forms. Some are fitting and survive, like the arrangements of our bodies, while others are less fit and do not survive, like Empedocles' ‘man-faced ox progeny’. Either way, as with the rain example, the result is explained by a combination of necessity and chance, not teleology. Our bodies are organized as they are not because it is good for us, nor because they were designed to, but, again, due to a confluence of necessity and chance. Why couldn't all natural phenomena be explained in this way? Why appeal to final causes at all? This is the puzzle Aristotle considers.

And Aristotle gives this reply (Sedley (2007), 190):

Such is the argument which might lead to puzzlement, and there may be others of the kind. But things cannot be that way. For these things, and all natural things, come about as they do either always or for the most part, whereas none of the things that are due to luck and the fortuitous does that. For it does not seem to be due to luck or coincidence that it rains frequently in winter, but it does if it rains in midsummer. Nor do heat waves in midsummer seem due to luck or coincidence, but heat waves in winter do. If then it seems that things are either due to coincidence or for a purpose, then if it is impossible for these things to be due to coincidence or the fortuitous, they must be for a purpose.

He concludes by reaffirming his teleological world-view (translated by Scharle (2008), 149):

But clearly all such things are by nature, as these speakers themselves would say. The ‘for the sake of something’, then, is in things which are and come to be by nature.

Scharle (ibid., 147) calls this discussion, ‘one of the most vexing and important passages in Aristotle's corpus’. It raises many questions.¹ Most importantly, for our purposes: why, in Aristotle's response, does ‘necessity’ not appear as a third possible explanation, in addition to coincidence and for-a-purpose?² This may seem odd, given the context, since Aristotle is responding to an opponent who proposes that all natural phenomena are explicable by chance and necessity. I agree with Falcon (2019, citing Code (1997), 127–134) when he says, ‘Where there is regularity there is also a call for an explanation, and coincidence is no explanation at all . . . Aristotle offers final causality as his explanation for this regular connection . . .’³ In other words, as I understand it, when Aristotle says, ‘it is impossible for these things to be due to coincidence or the fortuitous,’ he's speaking not of rain per se, nor of heat per se, nor of the growth of teeth per se. Rather, ‘these things’ refers to the regularity of rain (in the winter), the regularity of heat (in the summer), and the regularity of tooth growth in humans. He's speaking of those natural patterns.

Aristotle is responding to the claim that all natural phenomena can be explained fully via chance and necessity. The problem Aristotle points out is that chance and necessity are themselves natural phenomena: we see them all throughout nature. So how will Aristotle's opponents explain these natural phenomena, chance and necessity? Chance, Aristotle seems to grant, needs no further explanation; indeed, it seems that to say something happened by chance simply is to say that there is no further explanation. But necessity – regularity – he thinks, does call out for further explanation. Aristotle offers final causes as explanations of regularities: teeth grow as they do for the good of the organism, rain falls perhaps for the good of the crops, etc.⁴

By contrast, the Empedoclean materialist has no theoretical resources by which to explain these necessities, these regularities, or what we would now call ‘the laws of nature’. And that's because, if the Empedoclean has only chance and necessity at his disposal when explaining natural phenomena, and the necessities or regularities themselves cannot be explained by chance – as Aristotle says, ‘these things, and all natural things, come about as they do either always or for the most part, whereas none of the things that are due to luck and the fortuitous does that’ – then they have no explanation at all, on the Empedoclean view.⁵ So, for Empedocles, something that seems to call for explanation in fact has none. That's a cost.

And that's Aristotle's insight in this passage: teleology can explain a widespread type of phenomenon – the patterns we observe in nature – that seem to need explanation, but which have no explanation on the Empedoclean view. Indeed, ultimately, teleology explains all natural phenomena, on Aristotle's view. In Metaphysics (1072b), Aristotle tells us that all nature moves for love of the Prime Mover, whom Aristotle occasionally calls ‘God’. As C. S. Lewis (1964, 113) explains:

[W]e must not imagine Him moving things by any positive action, for that would be to attribute some kind of motion to Himself and we should then not have reached an utterly unmoving Mover. How then does He move things? Aristotle answers, κινɛί ὡς ἐρώμɛνον, ‘He moves as beloved.’ He moves other things, that is, as an object of desire moves those who desire it. The Primum Mobile is moved by its love for God, and, being moved, communicates motion to the rest of the universe.⁶

I think Aristotle is right that his view has a theoretical advantage here. Yet I believe he has underplayed his hand. We can follow the thread of his argument, and take things further. We can show that, by leaving these natural regularities unexplained, the Empedoclean leaves all natural phenomena unexplained. In the end, all scientific explanation fails, on this naturalistic, Empedoclean view.

The main argument

I'd like to defend the following argument:

1. 1. Any scientific explanation can be successful only if it crucially involves a natural regularity.

2. 2. Any explanation can be successful only if it crucially involves no element that calls out for explanation but lacks one.

3. 3. So, a scientific explanation can be successful only if it crucially involves a natural regularity, and this regularity does not call out for explanation while lacking one.

4. 4. If Naturalism is true, then every natural regularity calls out for explanation but lacks one.

5. 5. So, if Naturalism is true, then no scientific explanation can be successful.

Let's begin our defense of this argument with the first premise, defining terms as needed.

Premise 1: naturalism on the sea of scientific explanation

Naturalism

I propose we begin by defining Naturalism. Here, there is disagreement. Rea (2002) says Naturalism is best understood not as a proposition but as a research programme that treats the methods of science, and those methods alone, as basic sources of evidence. Others, like Armstrong (1978, 265) and Danto (1967, 448), take Naturalism to be the claim that the universe is causally closed. Quine (1995, 257) and Devitt (1998, 45) say it's the view that only scientific inquiry produces knowledge, echoing Sellars's (1963, 173) Protagorean mantra that ‘science is the measure of all things: of what is that it is and of what is not that it is not’. Plantinga (2008) defines Naturalism as a vague metaphysical thesis: ‘Naturalism is the idea that there is no such person as God or anything like God; we might think of it as high-octane atheism or perhaps atheism-plus.’ Aristotle, the Stoics, and Hegel may have claims to be atheists, Plantinga says, but Aristotle's Prime Mover, the Stoics' Noûs, and Hegel's Absolute exclude them from the halls of Naturalism.⁷

I believe we can harmonize these answers by taking ‘Naturalism’ to name a collection of views and attitudes that are often held together.⁸ As Oppy (2018, 21) puts it, ‘naturalism is the view that: (a) science is our touchstone for identifying the denizens of causal reality; and (b) there are none but natural causal entities with none but natural causal powers’. The success of the natural sciences may prompt one to adopt, as a research programme justified pragmatically, the austere metaphysical landscape that Plantinga, Armstrong, and Danto describe, as well as the broadly empiricist epistemology that Quine, Devitt, and Sellars endorse, a landscape in which there are none but natural causal entities with natural causal powers. This general package, admittedly vague, is a fair approximation of what philosophers mean when they speak of Naturalism.

The nature and structure of scientific explanations

Now, I wish to support premise 1 in my Main Argument: Any scientific explanation can be successful only if it crucially involves a natural regularity. To see this, let's think about the nature and structure of scientific explanations. A major and still influential contribution to this discussion is Carl Hempel's and Paul Oppenheim's (1948, reprinted in Hempel 1965) Deductive-Nomological Model of scientific explanation. On this model, a scientific explanation consists of two parts: explanandum and explanans. The explanandum is a proposition describing the scientific phenomenon to be explained. The explanans comprises a set of propositions that entail the explanandum, and which must be true for the explanation to succeed. Hence, ‘Deductive-Nomological’ model. And the model is ‘nomological’ because, according to Hempel, for a scientific explanation to succeed, a law of nature must feature crucially in the explanans, that is, it must be essential for the deduction to be valid. In a nutshell, the idea is that science explains a phenomenon by showing how prior (physical) conditions entail that phenomenon, via bridge principles. These bridge principles are, according to this model, laws of nature.

Woodward (2019) gives us this example of a scientific explanation on the Deductive-Nomological Model:

[C]onsider a derivation of the position of Mars at some future time from Newton's laws of motion, the Newtonian inverse square law governing gravity, and information about the mass of the sun, the mass of Mars and the present position and velocity of each. In this derivation the various Newtonian laws figure as essential premises and they are used, in conjunction with appropriate information about initial conditions (the masses of Mars and the sun and so on), to derive the explanandum (the future position of Mars) via a deductively valid argument.

In subsequent decades, there ensued debate over the necessity and sufficiency of the conditions proposed by the Deductive-Nomological Model. Many of these concerns focused on the problem of explanatory asymmetries⁹ as well as explanatory irrelevancies.¹⁰ Attempts to solve these problems all assume that laws of nature – or at least exception-less universal generalizations – will feature crucially in scientific explanation.¹¹ Since it is so important for our purposes, it bears repeating that not one of these proposals challenges the necessity of laws of nature for successful scientific explanations.¹² So, let us turn now to the idea that laws of nature are not in fact necessary for successful scientific explanations, nor are even exception-less universal generalizations necessary.

Woodward (2000, 2019) points out that there are at least some explanations offered in the social sciences appealing to generalizations that admit of exceptions, for example Mendel's Law of Segregation.¹³ To accommodate this suggestion, we'll use the term ‘natural regularity’ to refer to any of these: a law of nature, an exception-less universal generalization describing natural phenomena, or a law-like principle of the special sciences, even if it admits of exceptions. Premise 1 claims only that any successful scientific explanation must feature some natural regularity or other. These regularities may be inviolable laws of nature, or simply exception-less universal generalizations describing natural phenomena, or even, perhaps, principles of the special sciences that admit of exceptions. As for whether the regularity has a further explanation, at present it makes no difference. The point, so far, is simply that, after much philosophical work on the structure of scientific explanation, it seems clear that any scientific explanation must feature some natural regularity or other. The entire scientific enterprise, you might think, is to unearth the deep patterns of the universe, to order the future and the past in the relation of expectation. And the natural regularities are what link the past to the future in this way.

Premise 2: the hole in Naturalism's hull

We've established that any scientific explanation can be successful only if it crucially involves a natural regularity. Let's move now to our second premise in the Main Argument: Any explanation can be successful only if it crucially involves no element that calls out for explanation but lacks one.

First, what is it for something to ‘call out’ for explanation? Recall that Aristotle seemed to think that any natural regularity ‘calls out’ for explanation: it's not the sort of thing that requires no further explanation – because it's obvious, or self-explanatory, etc. – it can be further explained, and ceteris paribus it is a deficiency of a theory if the theory leaves it unexplained.¹⁴

Now, with regard to premise 2, our general question is this: for any phenomenon P, could any putative explanation E of P be successful if E crucially involves some element that calls out for explanation but lacks one?¹⁵ We will wonder below about the particular case in which the phenomenon is a natural regularity. But, with regard to the general form of the question, I believe the answer turns on our judgments concerning cases like this. Imagine we lived in a pre-scientific age, and we wondered how the Earth remained stationary beneath our feet. Why isn't it falling, or rising, or otherwise moving around? One possibility is that there is no explanation of this fact; the Earth is stationary, and that's the end of the story. Our inquiry finds no satisfaction here. But suppose we meet a man who offers this explanation: the Earth is stationary because it rests on the back of a stationary turtle. Now, it may seem as though this would explain why the Earth is stationary: it's held in place by that stable turtle, bless him. But, evidently, it depends. Whether this turtle explains why the Earth is stationary depends on whether there's any explanation of how this turtle remains stationary. For suppose the man says, ‘No, there is no further explanation. The turtle rests on nothing.’ I suggest that the promise of an explanation of the stationary Earth has merely been deferred, but ultimately not fulfilled. A bit of argument in support of this suggestion goes like this: insofar as there's a connection between explanation and understanding – as Woodward (2019) puts it, ‘One ordinarily thinks of an explanation as something that provides understanding’ – this explanation has failed, since we're not in a position to understand why the Earth is stationary. So, if there's no explanation of the turtle's stable position, it turns out that we have, in the end, no explanation of the Earth's stable position. For the same reason, adding another turtle to hold up the first turtle won't help, if that second turtle's position has no further explanation. And this goes no matter how many turtles we put down there, at least so long as that number is finite. (For the infinite case, see below.)

Again, the general principle we're considering in this section is this: for any phenomenon P, any putative explanation E of P can be successful only if E does not crucially involve any element that calls out for explanation but lacks one.¹⁶ And it looks as though, in this case at least, the putative explanation (the support of the turtle) of the phenomenon (the stationary Earth) fails, because the putative explanation crucially involves some element that is itself unexplained (in this case, the turtle's stable position).¹⁷ There seems to be nothing unusual about this instance of the general principle currently under consideration, and the reader can easily supply more. So, we have here the makings of a proof for the universal generalization that is our second premise. If such a principle can be shown to hold with any randomly chosen example, it holds for any example. Of course, my failure to find counterexamples is no guarantee there are none. But what can I do beyond trying my best, and then leaving it to the reader to decide?¹⁸

So far, we've supported our first two premises:

1. 1. A scientific explanation can be successful only if it crucially involves a natural regularity.

2. 2. Any explanation can be successful only if it crucially involves no element that calls out for explanation but lacks one.

From these premises, it follows that:

1. 3. A scientific explanation can be successful only if it crucially involves a natural regularity, and this regularity does not call out for explanation while lacking one.

Now, let us turn to our fourth and final premise.

Premise 4: Naturalism takes on water

Our fourth premise says that, if Naturalism is true, then every natural regularity calls out for explanation but lacks one. To prove this, let's begin by thinking about natural regularities, and possible patterns for their explanation. Take perhaps a law of physics, like the Einstein Field Equations, or Maxwell's Equations. Or take a principle of the special sciences, like Mendel's Law of Segregation, or the Second Law of Thermodynamics, or the Ideal Gas Law, all of which admit of exceptions.¹⁹ Or take even a principle of the folk sciences, like Aristotle's regularity that ‘what goes up must cool, and what cools must become water and come down’, or that it rains frequently in winter. Whichever regularity you choose, let's call it ‘R’. Recall that Aristotle seemed to think that regularities ‘call out’ for explanation: they can be further explained, as they are on his view, and ceteris paribus a theory that explains them is better than one that doesn't. Why would a Naturalist agree? Well, recall that many natural regularities actually do have deeper explanations, on Naturalism. For any natural regularity you choose – even laws that appear to be fundamental, on Naturalism – it is in principle possible to find a further explanation of this law, perhaps in terms of deeper laws, or perhaps by abandoning Naturalism and appealing to supernatural entities. So, for any natural regularity you choose, deeper explanation is at least possible, on Naturalism. And, ceteris paribus, deeper explanation is better.

We'll discuss this more below, but for now let's grant that, at least prima facie, regularities call out for explanation. If a regularity like R has no further explanation, then R is what we'll call ‘brute’. It's not merely that we don't know what the explanation is; on this possibility, there literally is no explanation to be had for R. If, on the other hand, R has some further explanation, then there are three possible options.

The first option is that this regularity R has some further explanation, and this chain of further explanation eventually terminates. Perhaps the explanation of R is a scientific explanation – a derivation of R in terms of other, more fundamental natural regularities – and this process of further scientific explanation eventually terminates.²⁰ Or perhaps non-scientific explanation is involved, for example in terms of God. In any event, on this possibility, the chain of explanation eventually ends. Let's call this ‘Explanatory Foundationalism’, or ‘Foundationalism’ for short. Another possibility is that this process of further explanation continues forever, without repeating. We'll call this ‘Explanatory Infinitism’, or ‘Infinitism’ for short. A final possibility is that this process of further explanation continues forever, but by looping back on itself, as it were, perhaps to include the original regularity, R. We'll call this ‘Explanatory Coherentism’, or ‘Coherentism’ for short.

Within Foundationalism, there are two possibilities. When the chain of scientific explanation of our natural regularity R terminates, the final scientific explanation features a final regularity – call it ‘R_f’ – that has no further scientific explanation. But we might ask whether this final natural regularity R_f – the natural regularity that must feature in the final scientific explanation of R, according to premise 1 – has any further explanation at all. Such an explanation of R_f might take the form of an Aristotelian ‘final cause’, in terms of the good, or perhaps a personal explanation in the tradition of Plato's dēmiourgos, from the Timaeus, the Divine Craftsman, the ‘maker and father of the universe’ (Timaeus 28c, Cooper (1997), 1235). That is, following Aristotle, we may immediately explain R_f in terms of the good, as the Primum Mobile moves for love of the Prime Mover, itself the ultimate good. Or, following Plato, we may explain R_f in terms of the plans and intentions of a Divine Craftsman, which are then, ultimately, explained in terms of the good.²¹ So that's one possibility, on Foundationalism: the final scientific explanation of our regularity, R, has no further scientific explanation, but the natural regularity featuring in that final scientific explanation of R – R_f – has a further explanation nonetheless. As this explanation is ultimately teleological, we'll call this option ‘Teleological Foundationalism’.²²

The alternative is that, though R begins a chain of further scientific explanation, the chain eventually terminates with a final scientific explanation, and this final scientific explanation of R has no further explanation at all. And this would be true even though, qua scientific explanation, this final scientific explanation features another regularity R_f, which prima facie calls out for further explanation, as we've said. Nonetheless, this regularity R_f featuring in the final scientific explanation of R is genuinely brute, on this alternative. We'll call this alternative ‘Brute Foundationalism’. I propose that we also include under this banner the option on which our regularity R has no further explanation at all, and is itself genuinely brute. R is itself R_f, the foundation, on this option, and therefore is the limit case of Brute Foundationalism. However, if we need a name for it, we might call it ‘Simple Brute Foundationalism’, as opposed to ‘Extended Brute Foundationalism’, on which our regularity R has further scientific explanations until we hit the foundational scientific explanation, featuring a distinct, final brute regularity R_f.

The space of possibilities, therefore, looks something like this, where arrows represent the (putative) explanation relation (Figure 1):²³

Figure 1. Possible structures of explanation for natural regularities.

So it looks as though we're in a position to affirm that, if Naturalism is true, the pattern of any putative explanation for any natural regularity must end with something brute, or go on forever, or involve a loop. The only option left out in the consequent here is Teleological Foundationalism. So the claim is that Naturalism is consistent with any pattern of putative explanation for natural regularities, except Teleological Foundationalism. Why think that's true?

Well, we've defined Naturalism as a positive attitude toward the sciences, together with – on the propositional side – a somewhat vague association of the austere metaphysics of, for example, Quine and Armstrong, and a broadly empiricist epistemology.²⁴ Naturalists, as Plantinga put it, don't believe in God, or anything at all like God. Though Naturalism is vague, it clearly seems to rule out a Platonic view on which a Divine Craftsman (very much like God) not only exists, but figures into the explanation of natural regularities. Plantinga also thought it ruled out Aristotle's Prime Mover, the non-physical Noûs that lies beneath and explains the physical world, and this seems right to me.²⁵ Naturalism also finds it hard to square knowledge of these sorts of teleological explanations with empiricism, and the widely alleged banishment of final causes during the Scientific Revolution attests to this. If that's right, then Teleological Foundationalism – either of the Aristotelian or the Platonic variety – is not available for the Naturalist. This leaves, then, either Simple Brute Foundationalism, Extended Brute Foundationalism, Infinitism, or Coherentism. When it comes to explaining natural regularities, those patterns are the only possibilities available to the Naturalist.

Natural regularities call out for explanation, yet cannot explain themselves

Let's think about Brute Foundationalism, either of the Simple or Extended variety. Both patterns feature natural regularities with no further explanation. Would this be acceptable? Or do natural regularities call out for further explanation, being unable to explain themselves? To answer this, we can divide theories of laws of nature – or natural regularities in general – into two broad categories. On a Humean view, so-called ‘laws of nature’ simply are patterns of constant conjunction, patterns of spatio-temporal succession, and there's nothing beyond these patterns that lies behind and explains them. On this view, as Maudlin (2007, 172) put it, ‘the laws are nothing but generic features of the Humean Mosaic’. And these regularities are somewhat paradoxical, on the Humean view: very familiar, and yet immediately mysterious. Scratch the surface of any commonly observed pattern in nature, which constitutes a law, on this view, and you'll find no explanation – not because of any limitation on your part, but because there literally is no explanation for these laws.²⁶ Yet these laws call out for explanation: why are they this way, rather than some other way?²⁷ At least, Aristotle thought so, and you might as well.²⁸

On Non-Humean views, by contrast, there is something that lies behind and explains the patterns of constant conjunction that Hume noticed, and these – not the patterns themselves – are what are properly called ‘laws of nature’. On some Non-Humean views, laws of nature are analysable; on other non-Humean views, they are un-analysable. Perhaps the most prominent theory on which laws of nature are analysable comes from Armstrong (1983), Dretske (1977), and Tooley (1977). On this view, laws of nature are analysable in terms of nomic necessitation relations between universals. Yet this necessity is merely ‘nomic’, not metaphysical or logical. As to why the actual nomic necessitation relations hold between universals rather than other relations, no answer is given – at least, not by the Naturalist. These relations could have been different, and yet they aren't. So, on this view, one can see that laws of nature – understood as contingent nomic necessitation relations between universals – are mysterious. These relations may seem apt to help explain the natural regularities that we observe, yet these relations do not explain themselves, even though they seem to be the sort of things that could have an explanation, and indeed call for one.

On another Non-Humean view (e.g. Harré & Madden, 1975), laws of nature are analysable in terms of substances' causal powers, and liabilities to exercise those powers under certain conditions.²⁹ As Swinburne (2010, 217) puts it, ‘That heated copper expands is a law is just a matter of every piece of copper having the causal power to expand, and the liability to exercise that power when heated.’ For our purposes it is important to note, as Swinburne (ibid.) continues, ‘As a matter of contingent fact substances fall into kinds, such that all objects of the same kind have the same powers and liabilities.’ So, on this type of view, laws of nature are analysed in terms of the powers and liabilities of substances. But, either it's a contingent fact that each substance-type has the powers and liabilities that it does, or, if each substance-type has those powers and liabilities essentially, it's a contingent fact that our universe has those substance-types rather than others, and it's a contingent fact that any particular object is the type of substance that it is. In other words, to take a particular example, either heated copper expands is a contingent truth, since copper could have had different powers and liabilities, or heated copper expands is a necessary truth about copper, yet it's a contingent fact that heated copper expands is true of anything our universe, let alone this particular object before me. (Though it may be necessary that copper expands when heated, it's contingent that this object be copper, and this fact calls out for explanation.) Either way, laws of nature would, on this view, call out for further explanation: either, ‘Why is copper this way rather than some other way?’ or ‘Why do laws about copper describe anything in our universe, rather than laws about schmopper, which is just like copper but with different powers and liabilities?’³⁰ Likewise with the powers and liabilities in terms of which the laws are analysed or explained: they do not explain themselves, and indeed they call out for further explanation.

On a third Non-Humean view (cf. Maudlin, 2007), laws of nature lie behind and explain the patterns of spatio-temporal succession that we observe in nature, and yet these laws are not analysable in any deeper terms. They are primitive. The laws are mysterious ‘frozen accidents’, to use Davies's (2013) evocative expression: constant through time and space, but metaphysically contingent, with no deeper analysis or explanation. They could have been different, and perhaps they even were different at some time in the past. Again, on this view, the laws of nature are posited to help explain the natural regularities that we observe, and yet the laws of nature do not explain themselves. They call out for explanation, but have none.

I think we are now in a position to affirm that natural regularities call out for explanation, and yet no natural regularity can explain itself. This is true of any bona fide fundamental law of nature, and a fortiori true of any principle or regularity of the special sciences. It follows, then, that any natural regularity with no further explanation is left unexplained, and this is a deficiency. The natural regularity calls out for explanation, and cannot explain itself. This will apply, on Simple and Extended Brute Foundationalism, to that final link in the chain of explanations for any natural regularity. For Simple Brute Foundationalism, there's only one link in the chain, and so it follows that, on this pattern, the natural regularity in question calls out for explanation, and yet is unexplained. But let's see if Extended Brute Foundationalism fares any better. Could a natural regularity be explained by an extended chain of explanations in terms of more fundamental natural regularities, if this chain eventually terminates in something brute?

Extended Brute Foundationalism

As we've said, for any scientific explanation you choose, there will feature some natural regularity – call it ‘R’. On Extended Brute Foundationalism, R will call out for explanation, and yet will not explain itself (as we've shown above), but instead will have some deeper scientific explanation, featuring some further natural regularity R₁. This pattern continues until we hit some final, fundamental explanation, featuring some natural regularity R_f. On Extended Brute Foundationalism, R_f is brute; it has no further explanation, and, as we argued in the last section, it cannot explain itself. Now, the question before us is: could R be successfully explained by a pattern like this?

Before answering that question, let me just quickly say that I believe many Naturalists subscribe to scientific explanation in the pattern of Brute Foundationalism, either of the Simple or Extended variety, depending on the regularity. Here's Carroll's (2012, 193) impression of the state of the field: ‘Granted, it is always nice to be able to provide reasons why something is the case. Most scientists, however, suspect that the search for ultimate explanations eventually terminates in some final theory of the world, along with the phrase “and that's just how it is”.’³¹

The alternative to Brute Foundationalism, for the Naturalist, is that there are no fundamental laws of nature: either there are ever more fundamental laws, but no bottom, or the laws circle back on themselves in a loop of explanation. We'll look at reasons against Infinitism and Coherentism below. For now, let's just say that many Naturalists accept Brute Foundationalism, perhaps because they believe that there are some truly fundamental physical particles, and, so, the laws governing them will also be truly fundamental, with no further explanation.³² In a classic work on this question, Oppenheim and Putnam (1958, 9) place a finitude of levels as one of the ‘conditions of adequacy’ of any proposal to unify the sciences via reduction. They appeal to theoretical virtues (ibid., 12ff.) when commending their layered model of the sciences, with elementary particles as the fundamental level, just beneath atoms, which are just beneath molecules, and so on through cells and living things.³³

So, as I say, many Naturalists seem to think of scientific explanation – in particular, the explanatory status of natural regularities that feature therein – along the lines of Brute Foundationalism. Simple Brute Foundationalism for the fundamental laws, Extended Brute Foundationalism for every other natural regularity.

Now, the main question of this section is: on Extended Brute Foundationalism, would any natural regularity R featuring in some scientific explanation be explained? On this view, R is meant to have some further explanation in terms of a deeper regularity R₁, and so on to some fundamental natural regularity R_f, and R_f is truly brute, truly unexplained. I believe we can work backwards, as it were, to see that, on this pattern, R would not be explained. For consider a case with three steps, where R is meant to be explained in terms of R₁, and R₁ in terms of R₂, and R₂ in terms of a final, fundamental natural regularity, R_f. Focus on the last step, where R_f is posited to explain the immediately prior natural regularity R₂. And now recall premise 2, according to which any explanation can be successful only if it crucially involves no element that calls out for explanation but lacks one. Premise 2 entails that, since R_f calls out for explanation but lacks one, and R_f figures crucially in the purported explanation of R₂, this purported explanation of R₂ fails. R₂, it turns out, calls out for explanation, and yet is unexplained (by itself, or by R_f). This argument extends, of course, to R₁, and then further to R itself.

In the end, we conclude that, on Extended Brute Foundationalism, R calls out for explanation, and yet is unexplained. The putative deeper explanations merely offered promissory notes, and the bruteness of R_f means these promissory notes cannot be redeemed. The mystery of the original regularity R is only amplified by these further putative explanations, not diminished, just as we saw with the example above involving a turtle supporting the Earth. So much, then, for explanation of natural regularities in the pattern of Extended Brute Foundationalism.

Infinitism

Let's turn now to Infinitism. Start again with any scientific explanation, which, we've argued, must involve some natural regularity, R. According to Infinitism, R will not explain itself, but instead will have some deeper scientific explanation, featuring some further natural regularity R₁. This pattern continues forever. According to Infinitism, every natural regularity has an explanation in terms of a deeper regularity, and there is no final, fundamental regularity. Now, the question before us is: could R be successfully explained by a pattern like this?

Schaffer (2003) gives a spirited defence of ‘infinite descent’, that is, the idea that there is no fundamental level of reality, at least not one comprised of physical atoms, though his final position seems to be agnosticism (ibid., 505–6).³⁴ Schaffer (2003, 499–500; 2007, 183–184) and Block (2003, 138) cite various scientists expressing support for the possibility of infinite descent, which also counts for something. And Leibniz seems to have actually endorsed the idea, which perhaps counts for more.³⁵

Now, we saw above some reasons from Hempel, Oppenheim, and Cameron to think that there is a fundamental level, and, so, the process of scientific explanation does not go on forever. These reasons had to do with the theoretical virtues of this view as compared to Infinitism. Cameron (2008, 12) reports the intuition against infinitely descending chains of dependence, and denies that this intuition ‘can be justified by any more basic metaphysical principle’. Schaffer (2010, 62) does perhaps a bit more, saying that, if endless dependence were true, ‘[b]eing would be infinitely deferred, never achieved’.

But our question is whether any natural regularity could be explained according to the pattern we call Infinitism. We're not presently concerned with whether there is a fundamental level of physical reality, or even metaphysical dependence. We're wondering, at least with respect to natural regularities, whether there could be an infinite descent of scientific explanation, in terms of ever more basic regularities. There are intuitions in this case analogous to those expressed by Cameron and Schaffer. And I myself am a big fan of intuition.³⁶ But I think we can go further and give good reason to think that Infinitism is impossible, and not merely theoretically vicious in some way. Explanation of natural regularities simply cannot work the way that Infinitism alleges.

One reason to think so borrows from Kim's (1998) and Block's (2003) thoughts on ‘causal drainage’. Kim (ibid., 81) worries that, if there is no bottom level of physics, his famous Causal Exclusion Argument entails that ‘causal powers would drain away into a bottomless pit and there wouldn't be any causation anywhere’. Block agrees there is a tension here, putting it this way:

If there is no bottom level, and if every (putatively) causally efficacious property is supervenient on a lower ‘level’ property . . ., then (arguably) Kim's Causal Exclusion Argument would show, if it is valid, that any claim to causal efficacy of properties is undermined by a claim of a lower level, and thus that there is no causation. (ibid., 138)

Now, Block (ibid., 139) goes on conclude that Kim's Causal Exclusion Argument must be invalid, on the grounds that ‘It is an open question whether there is or is not a bottom level, but it is not an open question whether there is any causation.’ And his reason for thinking that it is an open question whether there is or is not a bottom level is that it is considered to be an open question by at least several prominent physicists (ibid., 138).

With all due respect to those several prominent physicists and their opinions on philosophical questions outside their area of expertise, may I suggest that Block's solution to this tension is not the only one available, or even the most plausible? Another possibility is that Kim's Causal Exclusion Argument is in fact valid, and it does show that, if there is no bottom level of physics, then there would be no causation anywhere, and yet, since there is obviously causation, there must be a bottom level of physics. The fact that physicists have an open mind on this metaphysical question is certainly not conclusive evidence that any argument to the contrary must be invalid. But let me translate these thoughts about causal drainage into terms relevant for our discussion of natural regularities and explanation.

I propose that we modify Kim's Causal Exclusion Argument for our current purposes, and call the result ‘the Explanatory Exclusion Argument against Infinitism’. As we've shown, in any case of a purported scientific explanation, some natural phenomenon, P, is explained in part by some natural regularity or other, R. For simplicity of illustration, let's assume a basic version of the Deductive-Nomological Model of scientific explanation is correct, and R together with some initial conditions are what explain P. Now, if Infinitism is true, then R has a further explanation. It is derivable from one or more deeper, more fundamental natural regularities. Call that natural regularity ‘R₁’ (or, if there be more than one, conjoin them and call the conjunction ‘R₁’). R₁, in turn, will have a deeper explanation in terms of a more fundamental natural regularity R₂, and so on, forever, with no repetition. Using arrows to represent the (putative) explanation relation, things look like this (Figure 2):

Figure 2. The structure of a scientific explanation of a phenomenon, according to Infinitism.

Let's adapt Block's worry to the case at hand. We'll start with the phenomenon P, but we'll extend the reasoning to R. If P is as it is (partly) because of R, and R is as it is because of R₁, then it looks as though R's claim to (partly) explain P is undermined by a lower level, namely by R₁ – R's explanatory role ‘drains away’ to R₁. Really, it's R₁ that, together with the initial conditions, explains P.³⁷ To take a simple example, suppose we wonder why it's frequently raining, and we're given, in reply, Aristotle's folk regularity that it rains frequently in winter, along with the reminder that it's currently winter. A satisfying explanation, at least for common purposes. But, this folk regularity is amenable to deeper explanation in terms of the principles of contemporary meteorology, the angle of Earth's axis relative to the sun, the angle of incidence of the sun's rays to our location during our winter, and so on. And, so, it looks as though these principles (conjoined into a large R₁), together with the initial conditions, are the real explanation of why it's frequently raining. Insofar as there's an explanation here, it's R₁ rather than R that does the explanatory work.

So it goes with the phenomenon P. Yet our question concerned R. Could R be explained by an infinitely descending chain of more fundamental regularities? The same line of reasoning from the previous paragraph applies here. If, on this view, the principles of contemporary meteorology that we're calling ‘R₁’ are explained by even more fundamental natural regularities (call them ‘R₂’), ideally bona fide physical laws of nature, then it seems like those deeper regularities are the real explanation of R, not the ‘higher level’ R₁ regularities of contemporary meteorology. Indeed, you might think the purpose and glory of science is to uncover deeper, ‘more real’ explanations of natural phenomena, in terms of increasingly more fundamental natural regularities.

So, since R₂ is a deeper, ‘more real’ explanation of R than is R₁, R₂ has a better claim to be the true explanation of R. And perhaps now one can see the problem for Infinitism loom into view. If Infinitism is true, every claim of a natural regularity, like R₁, to serve as the explanation of a higher-level natural regularity, like R, is undermined by the claim of a deeper natural regularity, like R₂, which looks to have a better claim to explain R than does R₁. But since, on Infinitism, this undermining goes on forever, we never reach a real, or true, explanation of R. It's turtles all the way down, and a vicious regress: infinite pre-emption, and no explanation. For any regularity you choose as a potential explanation of R, that regularity cannot be the true explanation, since a deeper regularity has a better claim to be R's explanation. Explanation ‘drains away’, on this view, down a bottomless pit. In that case, on Infinitism, no natural regularity explains itself (as we've shown), and no natural regularity is explained by an infinite non-repeating regress of natural regularities. On Infinitism, R calls out for explanation, and yet is not explained by itself, nor by any deeper natural regularity, nor by anything at all.³⁸

Coherentism

If the Explanatory Drainage Argument of the previous section works against Infinitism, it can be redeployed in a straightforward way against Coherentism. On Coherentism, our natural regularity R has a further explanation, and indeed the chain of explanation goes on forever, but in virtue of it looping back upon itself at some point. If the loop includes R itself, the situation would look like this, again with arrows representing the (putative) explanation relation (Figure 3):

Figure 3. The structure of explanation of a natural regularity R, on Coherentism.

Yet if, as we said before, R₁'s claim to explain R is undermined by R₂, then this will continue back through the loop. As with Infinitism, this means that the undermining goes on forever, and we never reach any real, or true, explanation of R. (Indeed, if we did, and if R is itself included in the loop, then R would have as much of a claim to explain itself as any other regularity in the loop would, which is absurd.³⁹) I conclude, then, that, on Coherentism, no natural regularity explains itself (as we've shown), and no natural regularity is explained by an infinite repeating loop of natural regularities.

The final step

Given the foregoing arguments, we're now in a position to affirm premise 4 of our Main Argument: If Naturalism is true, then every natural regularity calls out for explanation but lacks one. On any theory of the laws of nature, they call out for explanation: any natural regularity, however fundamental it seems, could in principle have a deeper explanation, and deeper explanation is better. And, for Naturalism, on any possible pattern of explanation for any natural regularity R, R has no explanation. It's either brute (Simple Brute Foundationalism), or it stands in relations to further regularities in the pattern of Extended Brute Foundationalism, Infinitism, or Coherentism. Yet on none of these patterns can these further regularities successfully explain R.

The final inference in our Main Argument combines this premise 4 with our earlier observations concerning the success conditions for any scientific explanation, in particular the condition that a successful scientific explanation must crucially involve a natural regularity, and yet crucially involve no element that calls out for explanation while having none. Since we now know that, on Naturalism, every natural regularity calls out for explanation but lacks one, we can safely conclude that, on Naturalism, any attempt at scientific explanation fails. That's an interesting result in itself, but especially in light of the enthusiastic attitude towards science that's characteristic of Naturalists, along with their propensity to offer the success of science as reason in favour of Naturalism. If the arguments of this article are sound, then, on the contrary, the remarkable success of science entails that Naturalism is false.

Conclusion

In this article, I've defended the following argument: scientific explanations must involve natural regularities. But no explanation can succeed if it involves an element that calls out for explanation but lacks one. So, a scientific explanation can succeed only if it involves a natural regularity, and this doesn't call out for explanation while lacking one. Yet, on naturalism, every natural regularity calls out for explanation but lacks one. So, if Naturalism is true, then no scientific explanation can be successful. As you might expect, I invite you to run a modus tollens on that conclusion. At least some scientific explanations succeed, obviously. So, it follows that Naturalism is false.

One question lingers: how is scientific explanation possible? How can natural regularities be explained? We've cast doubt upon Brute Foundationalism, both Simple and Extended, as well as Infinitism and Coherentism. The only remaining option we've discussed is Teleological Foundationalism. But how does this account fare better than its rivals?

On Teleological Foundationalism, when the chain of scientific explanation of our natural regularity R terminates – which may be immediately, with R itself – the final scientific explanation features a final regularity – call it ‘R_f’. R_f has no further scientific explanation, but it does have an explanation, perhaps in the form of an Aristotelian ‘final cause’, in terms of the good, or perhaps a personal explanation in the tradition of Plato's dēmiourgos. Even on the latter option, natural regularities are explained, ultimately, in terms of the good. Paraphrasing Socrates from the Phaedo, if one wishes to know the cause of any thing, why it comes to be or perishes or exists, one has to find what was the best way for it to be. Or, if there be no single best way, at least a good way.⁴⁰

Explanations therefore, on this view, terminate with necessary truths about the good. If such truths are discoverable by reason, and reason teaches us that these truths do not stand in need of further explanation (either because they're obvious in themselves and so need no further explanation, or, if you prefer, because they explain themselves), then Teleological Foundationalism does not succumb to the same worries that beset the other possible patterns of explanation.⁴¹ This bears repeating: on Teleological Foundationalism of a Platonic or Aristotelian variety, scientific explanation ultimately rests on foundations that do not call out for explanation. The foundations – necessary truths about the good – are either obvious or self-explanatory. Either way, they do not call out for further explanation. And, so, these necessary moral facts provide a satisfactory stopping point for the scientific enterprise. If you weren't antecedently inclined towards this view of moral facts, perhaps the dim prospects of the alternatives will invite you to take another look at this charming view.

You may have doubts about the possibility of a necessary truth explaining contingent facts. How could a truth of the form it is good for such and such to be explain the fact that such and such is the case? The Aristotelian answer comes quite close to animating the universe, in the literal, etymological sense of ‘animate’ – the Primum Mobile moves for love of the Prime Mover. I admit that this form of Teleological Foundationalism is less clear to me than a broadly Platonic version, on which, to paraphrase Socrates again, ‘it is Mind that directs and is the cause of everything’. For notice that, when it comes to so-called ‘personal’ explanations, which are as familiar and common as the air we breathe, it seems perfectly satisfactory to end an explanation with a necessary truth about the good. For example, I wrote this article in order to better know important truths, and I aim to know important truths because it's good to do so. If, at the bottom of everything, reality is teleological, intentional, goal-oriented, then we should not be surprised to find a similar pattern of explanation underlying all natural phenomena. I believe that Aristotle and Plato were right: this is indeed what we do find. Without it, scientific explanation is impossible.