Explanation in Metaphysics: A Dissertation Prospectus
By Daniel M. Johnson
One of the primary tasks of the philosopher is to explain what it is for something to be the case – what it is for one event (substance, fact) to cause another, what it is for an action to be obligatory, what it is for an object to bear a property, what it is for a proposition to be true necessarily, what it is for a person to know something – there are as many items on this list is as there are topics in philosophy. Some would even say that this kind of explanation is the only task of the philosopher, all that philosophy consists of.[1] I disagree with the stronger claim – it doesn’t do any kind of justice to the diversity of philosophical activity – but it cannot be denied that this sort of explanation permeates the practice of philosophy.
This activity of explaining what something is or what it is for something to be the case is of special importance to metaphysics, since the task of metaphysics generally is to get to the bottom of reality. It is a bit ironic, therefore, that metaphysicians have spent so much more of their time investigating concepts related to this kind of explanation – supervenience, emergence, ontological dependence, and so on – than they have investigating explanation itself. (As we will see, the involved discussion of scientific and causal explanation in the philosophy of science and the philosophy of religion is peripheral to the sort of explanation relevant here, what I will from here on call ontological explanation.) This isn’t to say that metaphysicians and other philosophers haven’t said anything relevant to ontological explanation; indeed, they could hardly have avoided doing so, given how intimately bound up with explanation so many of their projects are. Instead, the concept of ontological explanation remains buried a layer deep in most discussions, and theses about it are either presupposed or clothed as claims about other things. In some cases, this leads to confusion and frustration, and in many other cases the discussion could benefit from a long look at ontological explanation even if that look isn’t strictly necessary to remedy confusion.
My goal is to give ontological explanation that long look, and then use the clarity gained to reinterpret, reorganize, and even make progress on some long-standing disputes in metaphysics.
The two disputes I have particularly in mind are those over a pair of metaphysical infinite regress arguments, Bradley’s Regress and McTaggart’s Paradox. Both have been around for a long time – McTaggart’s argument for over a century and Bradley’s for far longer, since it is a version of Plato’s Third Man argument from the Parmenides – and both remain at the center of peculiarly intractable controversy. It is my contention that the notion of explanation lies buried at the center of the discussion of both arguments. Two consequences follow, which I aim to establish in each case. First, much of the variety of arguments and views surrounding each argument can and should be recast as arguments or views about explanation, either as attempts to motivate (or deny) demands for explanation of certain facts or as restrictions (or denials of restrictions) on explanation. Realizing this can help in evaluating these arguments and views, or at least in clarifying exactly what is at stake. Second, this means that the positions it is permissible to take on these particular arguments are constrained by general truths about explanation: its nature, restrictions on it, and general demands for it.
Because of this, I need first to zoom out and look at ontological explanation itself before I say my piece on the two arguments in question. In the first chapter, I’ll look at the nature of ontological explanation, explore some of its features and its relations to a family of other concepts, and argue that it is important primarily because of its connection to ontological commitment. In the second chapter I’ll defend a proposed restriction on ontological explanation – namely, the claim that infinite regresses of explanations fail to satisfactorily explain – and then explore a couple of general demands for ontological explanations of certain sorts of facts. Finally, in light of all this, I’ll treat Bradley’s Regress and McTaggart’s Paradox in the third and fourth chapters, respectively.
Chapter 1: Ontological Explanation and Ontological Commitment
What is ontological explanation and why is it important? My goal in this first chapter is to argue that it is by means of ontological explanation that we get to the bottom of reality – ontological explanation is the handle of Ockham’s Razor. To be more precise, I’m claiming that the ontological commitment carried by a proposition is determined by features of that proposition’s ultimate ontological explanation. The only way, therefore, to identify a proposition’s ontological commitment is to identify its ultimate explanation. So a proposition’s apparent ontological commitments can be “explained away” – that is, a proposition may appear to carry an ontological commitment that it does not because its ultimate explanation does not carry that commitment. The converse is also true: a proposition may carry more of a commitment than it initially seems to, a commitment revealed only by uncovering its ultimate explanation. In other words, ontological reduction must employ ontological explanation as its tool, and ontological explanation is essentially reductive. Ontological explanation is important, therefore, because of its connection to ontological commitment. First, I’ll begin by identifying a number of features of ontological explanation and discuss the relationship between ontological commitment and a series of connected concepts. Second, I’ll argue for the connection between ontological explanation and ontological commitment. Along the way, I’ll argue that the two major competing accounts of ontological commitment – the quantifier account and the truthmaker account – aren’t really competitors at all, and that they are unified by the notion of explanation. Third and finally, I’ll reply to Roberts’ and Wood’s anti-theoretical challenge to my account of ontological explanation.
Features of ontological explanation. I can’t hope to give a full analysis of explanation or a set of logically necessary and sufficient conditions – an explanation of explanation, if you will – but I do want to point out at least five significant features of ontological explanation. (All of these are features of propositional explanation, because I’ll argue that objectual explanation can be reduced to propositional explanation.) First, if p ontologically explains q, then p is both necessary and sufficient for q. Second, ontological explanation is asymmetric. That is, if p explains q, then q does not explain p. Third, ontological explanation is transitive: if p explains q, and q explains r, then p explains r. Fourth, the relata of ontological explanation are propositions, not states of affairs or sentences. Fifth, ontological explanation is in a certain way objective, independent of human activity. Finally, after identifying these five features of ontological explanation, I will draw two important distinctions, one between partial and full ontological explanations and the other between proximate and ultimate ontological explanations.
These features are not enough to give an explanation of explanation: I haven’t said what ontological explanation is. That is because these features probably aren’t sufficient for explanation (though they are individually necessary). I don’t think I can say what ontological explanation is, but the three features I do identify are important enough that I can use them to say a lot about ontological explanation. All five features are important for the connection I draw between ontological explanation and ontological commitment.
At the end of this section, I will briefly discuss the connections between ontological explanation and a series of related concepts such as conceptual analysis, paraphrase (or translation), ontological dependence, supervenience, and ontological emergence. The interconnections are complex and interesting, but for the most part, the connections are due to these other concepts’ sharing some of the logical properties of ontological explanation (either its asymmetry or its necessity). I’ll discuss the connections mainly to distinguish ontological explanation from these other things.
Ontological explanation and ontological commitment. I will argue, ultimately, that ontological explanation determines ontological commitment: that is, a proposition’s ontological commitment is entirely determined by features of its ultimate ontological explanation. In order to argue this, I need to defend an account of ontological commitment. I will argue that the best versions of the two major competing accounts, the quantifier account and the truthmaker account, are not really competitors at all. In order to show this, I will defend versions of each of the accounts from major objections, then show that the truthmaker account actually entails the quantifier account, which means that those philosophers who proposed the truthmaker account were wrong to consider it a competitor to the quantifier account. Then I’ll show that, on each account, ontological commitment is tied to ontological explanation.
I’ll preface the discussion by clarifying what I mean by ontological commitment. There are at least two possible meanings of ontological commitment. One corresponds with reduction: if I can reduce some type of object to another type, then I am not committed to the first type (though it is still strictly speaking true that the first type of object exists). Another corresponds with elimination: only if I can eliminate a type of object, only if it is strictly speaking false that it exists, can I avoid commitment to that type of object. I will argue that it is the first meaning of ontological commitment that has been primarily at issue in the philosophical discussion, mainly because ontological commitment has come up primarily in the context of Ockham’s Razor-type concerns, and those concerns are reductive, not eliminative. My concern, therefore, is with the sort of ontological commitment that corresponds to reduction. However, some parties to the discussion suffer from some confusion on this score, and I will point this out when it is important. Also, I’ll show that the truthmaker and quantifier accounts of the sort of ontological commitment corresponding to reduction which I will defend give the resources for a derivative account of the other sort of ontological commitment.
I’ll begin with the quantifier account of ontological commitment, coming out of Quine. This view basically says that a proposition carries a commitment to the existence of those entities which must necessarily be among the values of the variables bound by quantifiers in the proposition for the proposition to be true. I’ll argue that the view needs a modification: a proposition only carries a commitment to the existence of those entities which must be among the values of variables bound by quantifiers in the ultimate explanation of that proposition for it (the explanation) to be true. This account can escape the major arguments against the quantifier account, and on this account a proposition’s ontological commitment is determined by features (the existential quantifiers) of its ultimate explanation.
The truthmaker account of ontological commitment says instead that a proposition carries a commitment to the existence of entities necessary to make the proposition true.[2] I’ll argue that this account escapes the major charges brought against it, mainly because the major charges either misunderstand what ontological commitment is or because they misunderstand the nature of the truthmaking relation. Finally, I’ll argue that the truthmaker account entails the quantifier account. The truthmaker account entails the quantifier account because the statement of what is necessary to make the proposition true just will be the ultimate explanation of that proposition, will be existentially quantified, and the truthmakers will be the values of the variables which make that quantified statement true. So the quantifier and truthmaker accounts are not competing accounts of ontological explanation, and on either account, a proposition only carries an ontological commitment determined by features of its ultimate explanation. (The complete statement of this argument will obviously have to be far more complex and detailed; I’ve given only a sketch.)
The anti-theoretical challenge of Roberts and Wood. Robert Roberts and Jay Wood have given a series of arguments against what they call “reductionist” approaches to answering “conceptual why-questions.”[3] Their arguments collectively might fairly be labeled their “anti-theory.” These arguments are a direct challenge to my project, because what they call “answers to conceptual why-questions” are, as far as I can see, equivalent to what I’ve been calling ontological explanations. (The reason I avoided the language of concepts is that it smacks of the a priori or of analyticity, and I don’t think ontological explanation need be a priori or analytic. I doubt that Roberts and Wood mean to say that conceptual analysis is a priori, though, so our differences on this point are probably merely linguistic.) Their anti-theoretical challenge to my project amounts for the most part to a rejection of two of the features I have ascribed to ontological explanation: its necessity and its asymmetry. They deny that, if p explains q, then p must give necessary and sufficient conditions for q; and they deny that, if p explains q, then q may not also explain p.
I reject outright their arguments against the necessity condition on ontological explanation. The data to which they appeal to motivate this denial – basically the data which motivate Wittgensteinian family-resemblance views of concepts – can be accounted for in a variety of other ways, none of which challenge the view that ontological explanation is a necessary relation. One of these ways is the phenomenon of vagueness;[4] another is the linguistic phenomena of equivocation and analogy; a third is the fact that folk concepts may simply be incoherent in various ways. Their arguments against the asymmetry condition, however, reveal something important. Circular analyses are sufficient to accomplish something very important and contribute to our understanding of the world: sometimes all we need is to see a correlation between two things, and this enables us to navigate the world effectively. What a circular analysis doesn’t achieve, though, that a true explanation does, is reveal what is really fundamental about the world. While this may not often be of great practical value, surely revealing what is really fundamental of the world does contribute something valuable to our understanding of it. So while circular analysis is sufficient to achieve something valuable, only true (asymmetrical) explanation, by virtue of its connection to ontological commitment, gets at the fundamental nature of the world.
I may also take a look at a few other challenges to the metaphysician’s goal of getting to the bottom of reality, particularly Bas van Fraasen’s and Hilary Putnam’s. If it turns out that these challenges are significantly related to issues of ontological explanation, I will treat them along with Roberts and Wood’s challenge.
Chapter 2: Constraints On and Demands For Explanation
In the first chapter I will have said quite a bit about the nature and importance of ontological explanation. In this chapter I will discuss general constraints on and demands for explanation. Specifically, I will ascertain whether, first, infinite regresses of ontological explanation are virtuous or vicious, and second, whether there are any general classes of propositions which must have explanations. This investigation mirrors the debate over causal explanation, conducted mainly in connection with the cosmological argument for the existence of God, and I will self-consciously conduct my discussion in parallel with that one. I will look for (and sometimes find) analogues for ontological explanation of arguments pertaining to causal explanation.
Infinite Regresses. Ross Cameron, in a recent paper, claims that there is no reason to think that infinite regresses of explanation are vicious, other than perhaps some (fairly weak) intuitive aversion to them on our part.[5] The only reason we have to avoid infinite regresses, he thinks, is a concern for theoretical simplicity, and the concern for theoretical simplicity can be overridden fairly easily. I disagree; I think that infinite regresses of ontological explanations are vicious, and it is my goal in this section to meet Cameron’s challenge and give an argument beyond a bare appeal to intuition.
My major argument for the viciousness of infinite regresses of ontological explanations is founded on an analogue of a case examined by Alexander Pruss. Pruss’s case involves the flight of a cannonball. If time is dense, then it is possible to give an infinite series of explanations of any given stage of that flight, without ever referring to the actual firing of the cannon. Clearly, though, the flight of the cannonball needs explaining in terms of the firing of the cannon. It follows, then, that the mere existence of an infinite series of explanations for a fact is insufficient to explain that fact. A parallel case can be constructed in the case of ontological explanation.
What does this case show? Well, first, it decisively refutes one possible basis for thinking, as Cameron does, that infinite regresses of explanation don’t have anything more against them than considerations of theoretical simplicity: the Hume-Edwards principle (and its analogue for ontological explanation). The Hume-Edwards principle says that, if each proposition in a series has an explanation, then the series as a whole is sufficiently explained. The cases show this to be false, for though each proposition in the series has an explanation, the series (and the individual propositions in the series) have clearly not been satisfactorily explained.
That isn’t enough to prove Cameron wrong, though, and show that infinite regresses of explanation are vicious. I’ve only so far given a counterexample to a claim that no infinite regresses of explanation are vicious; I haven’t shown that all are vicious. The failure of the Hume-Edwards principle, though, does give some direction for making some general claims about what explanation requires. Infinite regresses of explanation, I suggest, fail to answer the demand for explanation because they fail to achieve the removal of mystery that is attendant on explanation. The cases at least strongly suggest that all infinite regresses of explanation are vicious, not because there isn’t room in our ontology for all those propositions, but because infinite regresses fail to sufficiently explain – so they fail to adequately answer a demand for explanation.
Now, the fan of infinite regresses is free to offer an alternative explanation of the viciousness of the infinite regresses in the examples, but such an explanation would have to rule out the sufficiency of the infinite explanatory regresses in the cases without ruling out all infinite explanatory regresses. (Peter Klein, in defending his epistemological infinitism, gives just the sort of reply the fan of infinite regresses would need to adopt here, and so I’ll take a look at his view to get a model of the necessary reply.) I’ll take a look at a couple of strategies the defender of infinite regresses could take, including one inspired by Graham Oppy’s reply to Pruss, and argue that they all fail. I’ll conclude, then, that it is likely that all infinite regresses of explanation are vicious because they all fail to sufficiently explain.
This major line of argument will be supplemented by a series of more minor arguments – an analogue of another of Pruss’s arguments against the Hume-Edwards principle, a couple of inductive arguments, and an argument from truthmakers.
Demands for Explanation. There are two major candidates for general demands for explanation – claims that certain large classes of propositions have explanations. The first is an analogue of the Principle of Sufficient Reason (PSR): all contingent facts have an ontological explanation. The second is a family of truthmaker principles. I’ll argue that it is only the truthmaker principles which have much chance of being true.
There is a long history of debate over the PSR for causal explanation in connection with the ontological argument, but it is Pruss who has explored it in the most detail in his recent book. Most of the arguments Pruss employs in favor of the causal PSR – and most of the objections to which he replies – simply don’t apply to the ontological PSR. There are two arguments, though, of which analogues can be found for the debate over the ontological version of the PSR: the argument from inference to the best (or only) explanation, and van Inwagen’s modal fatalism objection.
The analogue of the modal fatalism objection is fatal to the ontological version of the PSR. Because of the necessity of the relation of ontological explanation, a PSR for ontological explanation results very obviously in modal fatalism, and Pruss’s favorite ways out of the consequence for the causal form of the PSR (appeals to libertarian free will and to indeterministic causal systems) don’t transfer to the ontological form. Additionally, the fact that we are justified in inferring the truth of the best explanation doesn’t support the ontological PSR as strongly as it does the causal PSR, I’ll argue, because we justifiably resist an inference to the only explanation much more easily in the ontological case than in the causal case. The ontological version of the PSR fails, then, and our practice of inferring the best ontological explanation presupposes only a version of Ockham’s Razor.
The other major candidate for a general demand for explanation is a family of truthmaker principles. In the first chapter, I will have established a connection between truthmaking and ontological explanation, such that any claim that a certain class of facts have truthmakers entails a corresponding claim that those facts have an ontological explanation in terms of existentially quantified statements (or are themselves existentially quantified). I’ll take a look at the major arguments against truthmaker principles and argue that they leave untouched restricted truthmaker principles which still constitute general demands for ontological explanation. Truthmaker principles, then, are the only plausible general demands for explanation.
Chapter 3: Explaining Properties: Bradley’s Regress
The regress with Bradley’s name attached to it is really far older than Bradley; the Third Man argument in Plato’s Parmenides appears to be a version of the same regress, and since Plato the regress has been a major feature in the debates over properties and particularly over universals. Bradley’s Regress, I’ll argue, is a regress of ontological explanation which is started up by demands to explain an object’s having properties (or standing in relations). Since it is most often realists about universals who accept such demands, Bradley’s Regress is most significant as a problem for realists.
The structure of this chapter and the next basically mirrors the structure of the second chapter; I’ll examine those who claim that the regress isn’t vicious and then consider ways to motivate and stop the regress. First, I’ll argue that the regress is in fact vicious. Second, I’ll examine the most powerful way to get the regress up and running: the truthmaker argument. Since most contemporary realists motivate their position by an appeal to truthmakers, they accept a demand sufficient to get the regress up and running. I’ll argue that, once they do what is necessary to get the regress stopped, the three major realist positions collapse into one another and give trope theory a major dialectical advantage. Finally, I’ll consider the two major nominalist theories, trope theory and resemblance nominalism. I’ll argue that trope theory stops the regress while still being able to accept the truthmaker demand, while resemblance nominalism is forced to deny the truthmaker demand for explaining properties.
The Bradley Regress goes something like this. The chair is red. What is it for the chair to be red? Does that fact need explanation? If it does, perhaps the explanation goes something like this: the chair exemplifies the universal redness. But if “the chair is red” needed an explanation, doesn’t “the chair exemplifies redness” also need an explanation? Its explanation would be: the chair exemplifies exemplifying redness. And so on. The regress gets started when there is a demand for explanation of the original fact (the chair is red) which also applies to the explanation of that fact (the chair exemplifies redness), and so a regress gets started. The strategies for avoiding the regress are: deny the demand to explain the original, accept only a demand for explanation of the original which doesn’t apply to all the subsequent explanations, or deny that the regress is vicious.
The infinite regress. A surprising number of philosophers have argued that the Bradley Regress isn’t vicious: Nicholas Wolterstorff, Francesco Orilia, Richard Gaskin, and Philip Keller, to name a few. I’ll argue that each is subject to confusions of various sorts. Wolterstorff, for instance, seems to re-describe the regress so that it isn’t a regress of ontological explanation, and so, I would argue, isn’t the Bradley Regress at all any more. Orilia supports his judgment that the Bradley regress isn’t vicious by giving a criterion for distinguishing vicious from non-vicious infinite regresses. I’ll argue that his criterion is seriously mistaken, and that he’s actually confused as to what an ontological explanation is. The others will receive similar treatment. The Bradley Regress is vicious because it is an infinite regress of ontological explanation.
Truthmaker-motivated realism. The major motivation for realism about universals is some kind of truthmaker principle, a claim that predications need truthmakers. This translates into a demand for explaining predications. Therefore, the realist (or this sort of realist, the one motivated by a truthmaker principle) is committed to accepting a demand for explanation that gets the regress started. Since the regress is vicious, the realist needs to find a way to stop the regress by giving an explanation of predication which itself doesn’t cry out for explanation. I’ll argue that, once this is done, each of the three major versions of realism collapse into one another.
The first major version of realism is substratum theory. I’ll argue that substratum theory is required, in order to stop Bradley’s regress, to accept some particular which functions to tie substrata to universals. I’ll then argue that the substratum theorist is actually required to accept two very different sorts of ties, those which tie the substratum to its necessary properties and those which tie it to its contingent properties. Finally, I’ll argue that, once this is done, the substratum itself is theoretically superfluous: it doesn’t do anything more than the tie which ties its necessary properties together. The result, I’ll argue, looks very much like the third major version of realism, Loux’s neo-Aristotelian substance theory.
The second major version of realism is bundle theory. I’ll argue that the Bradley regress spells the doom of pure bundle theory (according to which only universals exist), but that it actually saves generic bundle theory from the most popular objection to it, the objection from the Identity of Indiscernibles. I’ll argue that the bundle theory is committed to the same two sorts of particular ties to which the substratum theory is committed, and that the resulting theory looks very much like Loux’s substance theory.
The third major version of realism is Loux’s substance theory. I’ll argue that the Bradley regress shows that Loux either needs to make his Aristotelian kinds into particulars themselves, or he needs their instantiation to be a particular entity which necessarily ties the kind down. Also, I’ll argue that Loux is committed to another kind of particular tie which ties the object’s contingent properties to it. The resultant modified version of Loux’s view collapses into the modified substratum and bundle theories.
Finally, I’ll argue that the particular ties to which the realist is committed in order to stop the Bradley Regress just are tropes, and so the pure trope theorist has a major dialectical advantage over the realist. The only way to motivate realism about universals in the face of this disadvantage, I’ll argue, is to find some other motivation than a truthmaker principle about predications. Perhaps universals are important for other reasons, like a theory of causation or of knowledge.
Trope and resemblance nominalism. The two most prominent kinds of nominalism, trope and resemblance nominalism, actually require two very different sorts of replies to the Bradley Regress. The trope theorist is free to accept the truthmaker demand which gets the regress started – in fact, this is a central motivation for trope theory. The trope theorist doesn’t have the difficulties with stopping the regress, though – at least, so I will argue, against William Vallicella’s recent attempt to make trope theory vulnerable to the Bradley Regress. The trope theorist therefore has an advantage of theoretical simplicity over the realist about universals.
Resemblance nominalism and theories in its vicinity (like class nominalism), on the other hand, don’t have the resources to stop Bradley’s regress once it gets started. They are committed to denying the truthmaker principle which motivates it.
Chapter 4: Explaining Time and Change: McTaggart’s Paradox
McTaggart’s Paradox has been a major focus, perhaps the major focus, of discussion about the nature of time for a century. There still isn’t anything like a consensus as to the lessons to be learned from it. In fact, the disagreement over the argument is so radical as to be striking even in the disagreement-prone world of philosophy. D.H. Mellor, in his 1998 book, asserts that the success of McTaggart’s argument (at least the section against A-theory) is “beyond all reasonable doubt” and finds himself compelled to chalk up disagreement over this to a willful blindness.[6] Dean Zimmerman, writing in 2005, reiterates with approval C.D. Broad’s earlier claim that the argument is a “philosophical howler.”[7] Mellor and Zimmerman are both eminent philosophers of time, intelligent and aware of all the arguments in the literature up to their time, writing in the last decade of a century-long discussion of this argument (in which decade, I might add, there hasn’t been anything like a radical development to explain their disagreement) – and still they can disagree to such an extent that one considers the argument not only sound but obviously so, and the other considers it not only fallacious but a “howler.” How is this possible?
This only seems possible if there is some deeper issue lurking just beneath the surface of the debate, and if commitments regarding this issue are both controversial and sufficiently fundamental to render the controversial positions “just obvious” to the various parties to the debate. I think this issue is ontological explanation. Progress can be made in the discussion of McTaggart’s Paradox if we bring the issue of ontological explanation closer to the surface of the debate. That is my aim in this chapter.
McTaggart’s Paradox goes something like this. We have facts employing A-determinations (past, present, future) and tense (which seems to build in A-determinations). If we try to explain these A-facts in terms of non-tensed facts, though, we get a contradiction; so we can only explain them in terms of other tensed facts. If we accept a demand that A-facts need explaining, though, we then get an infinite regress. The only ways out of this argument are, first, to deny that A-facts need an explanation or can be reduced (most A-theorists accept this); second, to accept the demand for explanation but deny that A-facts cannot be reduced (the B-theorist is committed to this); third, to deny that the regress is vicious. McTaggart himself doesn’t take any of these three ways out, and so argues that A-facts must be eliminated – that there aren’t any A-facts. The contemporary discussion of the argument, however, has generally taken this as an argument against the thesis that A-facts can’t be reduced to B-facts.
At the heart of McTaggart’s Paradox lies the issue of explanation – a demand that a certain set of facts (A-facts or tensed facts) have explanations. Because of this, McTaggart’s Paradox unifies most all of the major arguments in the debate between A-theory and B-theory. The A/B debate is an issue of reduction and therefore explanation: B-theorists think A-determinations can be reduced to B-determinations; A-theorists disagree. The dialectic of the debate, then, is this: the B-theorist tries to come up with reasons to think that A-propositions must be explained, while the A-theorist tries to come up with reasons to think that A-propositions need not and cannot be explained, at least not by propositions which don’t themselves employ tense or A-determinations.
I’ll argue, then, that all the major arguments in the debate over A- and B-theory (with the possible exception of the argument from special relativity) are attempts either (on the B-side) to generate demands for explanation sufficient to get McTaggart’s regress started or (on the A-side) to deny that any such demand could be true. McTaggart’s Paradox therefore lies at the heart of the A/B debate.
The famous Williams-Smart “flow” argument, usually listed as a separate argument against A-theory, just is McTaggart’s Paradox (I’ll argue) combined with a clever way to use metaphor to start up the regress. Since nobody has understood the argument in this way, nobody has given a really satisfying treatment of it. I’ll treat this argument in section 2 of this chapter, and argue that it doesn’t end up undermining A-theory.
McTaggart’s own way of motivating the demand for explanation, which William Lane Craig has argued applies to eternalist (and perhaps growing-block) A-theory, is fundamentally the same (I’ll argue) as the prominent grounding objection to presentism. Both are really just applications of the truthmaker demand for explanation. I’ll treat this argument is section 3, and argue that it is fatal to eternalist A-theory, but that presentism may survive it by denying the truthmaker principle involved.
Even if both of these demands for explanation fail, the B-theorist has the dialectical advantage because of Ockham’s Razor. The A-theorist needs some positive reason to resist the reduction of A-propositions to B-propositions. There are two main ways of doing that, the translation argument and the phenomenological argument, which I’ll discuss in sections 4 and 5. I’ll argue that neither is decisive. In particular, the debate over the translation argument exhibits much confusion (on both sides) about ontological commitment, a confusion that my treatment in the first chapter can clear up. I’ll argue that translation isn’t required for avoiding ontological commitment, and so the fact that B-theorists can’t translate A-sentences into B-theoretic language doesn’t mean A-propositions can’t be reduced to B-propositions. B-theory therefore wins by default, because of considerations of theoretical simplicity.
Before I launch into this main discussion of strategies for motivating or denying demands for explanation, I need to first discuss an attempt to play both sides: an attempt to accept a demand for explanation that gets the regress started while denying that the explanation need be reductive. The only way to do that is to deny that the regress is vicious, and Quentin Smith does just that. I’ll treat Smith’s position first, in section 1, and argue that he, like those who think Bradley’s Regress virtuous, is subject to confusions over what makes a regress vicious.
Conclusion
The long look I give to the nature and role of ontological explanation (chapter 1) as well as constraints on and general demands for it (chapter 2) does end up helping to clarify the debates over the two metaphysical infinite regress arguments (Bradley’s and McTaggart’s). Getting straight on ontological explanation helps us to get straight on the dialectical options for the parties to the debate, and the nature of ontological explanation ends up constraining what we can say about the two regress arguments.
[1] For a claim in this vicinity, see Robert C. Roberts and W. Jay Wood, Intellectual Virtues: An Essay in Regulative Epistemology (Oxford: Oxford University Press, 2007), 24.
[2] This statement needs to be made more precise to avoid some unwanted ontological commitments to necessary entities. The process of making it more precise will clutter up this prospectus needlessly, however, so I’ll leave this to the dissertation itself.
[3] Roberts and Wood, 23-30.
[4] I owe my take on this to Jonathan Kvanvig in conversation.
[5] Ross P. Cameron, “Turtles All the Way Down: Regress, Priority, and Fundamentality,” in Philosophical Quarterly 58 (2008), 1-14.
[6] Actually, what he says is that A-theorists have “managed to inoculate themselves against it.” This sounds like willful blindness to me, but perhaps he means something a bit weaker. Still, it is a very strong claim. D.H. Mellor, Real Time II (London: Routledge, 1998), 72-75.
[7] Dean W. Zimmerman, “The A-theory of Time, The B-theory of Time, and ‘Taking Tense Seriously.’” Dialectica 59 (2005), 401-457.