Bayesian Basicality

Suppose that you’re thinking of adopting radical probabilism,[1] or some more moderate form of Bayesianism, as your epistemology, but you’re hesitant because you think there are beliefs which are properly basic (including, perhaps, the belief in God), and you think that Bayesianism won’t make room for such beliefs. Reformed Epistemology,[2] after all, is an externalist epistemology, while Bayesianism appears to be an internalist epistemology. Here’s an obvious way to put these commitments together coherently.

As a preliminary note, I want to call the reader’s attention to the fact, of which I only just became aware while trying to articulate this idea, that Pruss has suggested that (objective) Bayesianism should be regarded as a hybrid epistemology, where belief-updating is an internalist epistemic procedure, but the particular calibration of prior probability assignments is potentially (un/)warranted given an externalist story.[3] I think this account sounds right. I have also been thinking, lately, about a way to fill out an epistemology such that it tells both an internalist and an externalist story (in other words, I’ve been thinking about how to articulate an epistemological commitment which bridges the internalist-externalist divide) and thus, if Pruss is right, it appears that Natural Law Bayesianism can commend itself to us (or to me) in light of this philosophical virtue.[4]

I am increasingly convinced that Natural Law Bayesianism is correct, but what I am about to suggest will hold for any version of objective Bayesianism (and, as we will see, perhaps even for subjective Bayesianism as well). Perhaps we should regard a belief as properly basic if and only if its prior probability is (and ought to be) set at higher than 0.5 (on a scale from 0 to 1). We can then say that we have a defeater D for some properly basic belief H iff:

  1. P(H) >0.5
  2. P(H|D) ≤ 0.5

Recall that a properly basic belief is a belief which one is rational to maintain even in the absence of inferential evidence or rational argument, so long as genuine defeaters are not forthcoming. Take inferential evidence and rational argument to be species of evidence in the Bayesian sense; something E is evidence in the Bayesian sense for hypothesis/proposition H if and only if the probability of H given E is higher than the prior probability of H (prior, that is, relative to the condition ‘E’). Thus, we might have some beliefs the appropriate assignment of whose prior probabilities is in the range 0.5 < x ≤ 1, and these beliefs we will be able to rationally maintain even in the absence of inferential evidence or rational argument.

In fact, if one has coherentist leanings (as opposed to foundationalist leanings), one could even talk about a form of proper-basicality for a coherentist using precisely this language, but just adopt a subjective Bayesianist account of the priors in place of the objective Bayesianist account (mutatis mutandis).


[1] See: Richard Jeffrey, “Radical Probabilism (Prospectus for a User’s manual),” in Philosophical Issues 2 (1992): 193-204.

[2] See: Peter Forrest, “The Epistemology of Religion” in The Stanford Encyclopedia of Philosophy (Summer 2017 Edition), Edited by Edward N. Zalta, (June 15th, 2019):

[3] See: Alexander R. Pruss, “Internalism, Externalism and Bayesianism,” Alexander Pruss’ Blog, (June 15th, 2019):

[4] One might think to suggest that this is more a vice than a virtue, for perhaps an account which is both internalist and externalist inherits all the problems peculiar to either side of that divide. I think this is mistaken; the only way to have an epistemology which is adequate for answering both internalist and externalist concerns is going to be an epistemology whose framework allows us to address puzzles peculiar to each front, and no argument for the indispensability of internalism or externalism will stand as an objection to such an epistemology.

A Moore Bayesian Defense

G. E. Moore famously argued, contra the skeptic, that he had a hand. What he meant by that provocatively simple rebuttal was roughly this: that as sound as one might be inclined to think any argument for skepticism, the fact remains that one should always put more credence in the belief that they have a hand (or some equally evident proposition) than that the argument for skepticism is sound. In other words, people should regard themselves as within their epistemic rights to be more confident that they have a hand than they can ever be that any one (let alone all) of the premises of an abstract philosophical argument for skepticism happen to be true. We ought (meaning any one of us ought), according to Moore (or, at least, my interpretation of Moore), to assign a higher prior probability to the proposition that “I have a hand” than to the proposition that, for instance, “in order to know that P, I have to know that I know P.”[1]

Moore’s response is often thought cute but wanting; it refuses to play by the philosophical rules which the skeptic is taking for granted and it reeks of special pleading, as though the response were really a thinly veiled philosopher’s trick. It seems intuitively attractive to us, but can we really say any more in its defense than that it sounds right?

It occurred to me rather lately that perhaps we can defend a Moorean response to skepticism with a little bit more rigour than merely hand-waving in the general direction of intuitions. Suppose, pace subjective Bayesians, that objective Bayesianism is correct (the difference between subjective Bayesianism and objective Bayesianism being, of course, that subjective Bayesians maintain that nearly any constellation of probability assignments for our priors are appropriate so long as we’re being consistent, and objective Bayesians argue that there are, instead, more (or less) appropriate constellations of probability assignments for our priors).[2] Some might think to do this by appeal to a principle of indifference (for instance, if we have no reason either to think that proposition P is true, nor any to believe P is false, then we ought to assign the prior probability 0.5 to P). I think those who subscribe to what has been called ‘Natural-Law’ Bayesianism actually have a more attractive idea; they suggest, instead, that there are certain appropriate probability assignments we naturally tend to give particular priors. This actually opens the Natural-Law Bayesian to scientific evidence in ways few (or, perhaps, no) other objective Bayesians can be (at least, qua their Bayesian commitments). For instance, one way to roughly obtain information about the approximate prior probability of some proposition, P, is to take the “arithmetic average”[3] of some sufficiently large (so as to be representative) group of human beings’ probability assignment to P. Teasing this out might be complicated, but that can be thought of as a problem for the social scientists and psychologists, rather than philosophers (there’s a division of intellectual labour for a reason). Now, suppose that Natural-Law Bayesianism provides a decision-theory for calibrating our prior-probability assignments. (indeed, we might even update our priors given incoming information about what the more natural assignment of the prior converges towards – though, as Pruss interestingly observes, this wouldn’t be a Bayesian update). It appears likely (let us not read too much into the use of the word here) that one can cash-out the fundamental Moorean claim that we really ought to regard the prior probability that we have a hand as being, while not indefeasibly high (i.e., 1), too much higher than any or all of the premises in any argument for skepticism for our Bayesian-updating procedure upon considering such an argument to leave us affirming skepticism.

Moore’s response is, in some ways, a big ask. Nevertheless, I think that Natural-Law Bayesianism gives us a way to shore up his fundamental claim if only the social science and psychological data turn out to support his supposition. One among many advantages of this is that it opens Moore’s response to skepticism up to experimental (dis)confirmation. I hope to expand on this idea in the future. My preliminary reaction to the thought, though, is that I think it’s right, and I expect that, were the evidence forthcoming, it would support Moore’s move from the perspective of Natural-Law Bayesianism.

Interestingly, this also implies that one may be being perfectly rational to agree that each premise of an argument is extremely plausible (more plausible than not), and that the conclusion follows validly from the premises, but reserve the right to reject the conclusion on the grounds that the conjunction of premises is not as plausible as at least one proposition with which their combination is incompatible.

And there we have it, a more Bayesian defense of Moore’s response to the skeptic.

[1] I borrow this phrasing, as best memory will allow, from W.L. Craig who used it during one (or several) of his lectures on the Defenders podcast. I do not now, however, have an exact citation for it. Here, though, is a useful link in which he explains what he means.

[2] For an excellent article on this, see: William Talbott, “Bayesian Epistemology,” in The Stanford Encyclopedia of Philosophy (Winter 2016 Edition) edited by Edward N. Zalta, accessed March 25th, 2019.

[3] Alexander Pruss, Conciliationism and natural law epistemology, on Alexander Pruss’ Blog, accessed March 25th, 2019.

Perfect Being Theology, Mysterious Superlatives, and God’s Necessary Goodness.

I typically define theism in company with those who, under the enduring influence of St. Anselm, follow him in affirming that God is that than which nothing greater could be conceived. To update the Anselmian lingo in the preferred way of analytic theologians, God is a maximally great being, which is to say that God is the being which exemplifies the uniqualizing[1] property of exemplifying the largest set of compossible categorically great-making attributes.[2] Thus, if omnipotence is a categorically great-making property (i.e., a property which it is in every respect better to be than not), and omnipotence isn’t known to be incompatible with any categorically great-making properties, then God is probably omnipotent (which is to say, omnipotence probably belongs to the set of compossible categorically great-making properties than which no set is greater). This is obviously a shortcut (for, if some property which appears to be categorically great-making was incompatible with the largest set of consistent categorically great-making properties then it would not really be categorically great-making at all), but it is a useful one. Theists who subscribe to this theological/philosophical strategy claim that what we can coherently say about God, at least absent any appeal to revelation, is that for any categorically great-making property P, God has P if and only if P is part of the largest set of categorically great-making properties all of which are compatible with each other. Practically speaking, if omnipotence is compatible with omniscience, omnibenevolence, omnipresence, immutability, divine simplicity, aseity, et cetera, and those are all compatible with each other, then God can be safely said to have all of those properties.

One notoriously difficult problem with this ‘perfect being theology,’ as I’ve laid it out, is that particular superlative attributes are always liable to be rejected on the grounds that they are found, after all, to be incompatible with each other for some philosophically subtle reason. For example, if we found, contrary to current expectations, that omnibenevolence were incompatible with being altogether just, and those were both categorically great-making properties, then one or the other of them would not actually be a property of God (according to the perfect being theologian). So, the perfect being theologian’s approach to defining God actually makes any alleged property of God negotiable in terms of a philosophical trade-off. By applying the right kind of philosophical pressure you can in principle always get perfect being theologians to choose between God’s being immutable and divinely simple on the one hand, and omnisubjective on the other (or any other superlatives in either place). Most of the time this is a purely academic concern; practically speaking the perfect being theologian can get all of the properties the classical theist wants, using perfect being theology, without any serious difficulties. Still, the perfect being theologian operates almost as though her view of God is a hypothesis which could, at any moment, be overturned by the flood of new philosophical considerations. That may not be such a serious problem on its face; after all, the scientist treats the theory of evolution, or atomic theory, or any other theory, as though it might, at any moment, be overturned, but is increasingly confident in these theories as they prove their explanatory worth over time and in the face of multiple challenges. The perfect being theologian may think the very same thing about God as classically construed (e.g., as being omnipotent, and omniscient, et cetera), since it remains philosophically viable in the face of several serious challenges it has faced down through the centuries. A serious challenge to the strategy of the perfect being theologian exists, however, insofar as the perfect being theologian ought to admit the possibility of mysterious superlative attributes.

A mysterious superlative attribute is a categorically great-making property which is in principle out of the intellectual reach of human cognition. In other words, it represents a property which is beyond our ken, and thus unanalyzable (at least as far as we’re concerned). Suppose we have some such property X; for all we know, X is incompatible with many, all, or at least one of the superlative attributes generally ascribed to God. Even should we think that X isn’t likely to be incompatible with these properties and if it were it would, by reason of that, probably not belong to the largest set of compossible superlatives, for all we know there are other equally indiscernible mysterious properties {X1, X2…, Xn}. We have no way of telling how likely it is that there are only a handful of such mysterious superlatives, or even that there are only finitely many such properties, and it seems impossible to dismiss out of hand the possibility that any one of them might be incompatible with any or all of the non-mysterious superlatives. It isn’t hard to see why this poses such a serious challenge to the strategy of perfect being theology. Unless the perfect being theologian is able to give some very impressive reason to think i) that no mysterious superlatives exist, ii) that if they do exist there are few enough of them, and/or they are each so unlikely to be incompatible with non-mysterious superlatives, that they, taken together, are extremely unlikely to imply that any of the non-mysterious superlatives are missing from the largest set of compossible categorically great-making properties, or iii) that no mysterious superlatives are possibly incompatible with the non-mysterious superlatives, then she is in serious trouble. She will be forced to adopt her theology as a useful fiction, however well pragmatically justified. She will end up having to adopt some form of theological anti-realism analogous to (some) versions of scientific anti-realism, and for the purposes of systematic theology that simply will not do.

I’ve been contemplating this problem for a while. I once hoped that the theologian could use some argument from the nature of language to show that any concepts which in principle cannot be given an expression in at least one language possibly comprehensible to us must necessarily be lacking the semantic machinery required for incompatibility with any concept which can in principle be given expression in a language comprehensible to us. While that sounds vaguely promising, I simply have no good ideas about how to cash out that (speculative) claim. It also raises a legitimate question about what we might call quasi-mysterious superlatives (i.e., categorically great-making properties which are in principle intelligible to us, but which are in fact unintelligible to us and/or have never occurred to anybody) which I am not entirely ready to answer.

Nevertheless, it occurred to me recently that we might be able to safeguard at least one of the non-mysterious superlative attributes even in the face of the challenge posed by the possibility of mysterious superlatives which are incompatible with non-mysterious superlative attributes. It seems that God’s being the paradigm of goodness itself (goodness simpliciter – not to be confused with merely moral goodness) is a non-negotiable non-mysterious superlative attribute. In its absence, there wouldn’t even be a standard against which properties could be said to be objectively great-making. Very plausibly, one needs a paradigm of goodness in order to talk meaningfully about greatness (in the relevant sense), and if there is a maximally great being then it must be, among other things, the paradigm of goodness. Therefore, even if God (understood as the maximally great being) has mysterious superlatives which are just beyond our ken, we can know with certainty that whatever they are, they must be compatible with being goodness itself. Thus, the set of compossible categorically great-making properties must necessarily include being identical to the Good. Unless God’s nature serves as the barometer or paradigm of greatness in our ‘great-making’ sense, God cannot necessarily be a maximally great-making being. The whole coherence of perfect being theology hangs on God having the property of being the paradigm of (categorical) greatness.

Supposing this argument is successful, how comforting should its conclusion be for the perfect being theologian? It certainly doesn’t give her everything she wants, so she has plenty of work still cut out for her, but she might be able to use this as an almost Archimedean point from which to make progress. For instance, perhaps some other properties, such as moral goodness, necessarily flow out of an appropriate analysis of being the paradigm of goodness simpliciter. Perhaps, in addition, a parallel argument can be run for other properties, such as being the paradigmatic existent.[3] Ultimately, I think the potential of the arguments I’ve presented, even if successful/sound, is extremely limited. It isn’t good enough to assuage my concerns, but it does feel like a good start. If there is a fatal problem with my argument I suspect it will be caused by some kind of circularity (e.g., God being defined by greatness and greatness being defined by God), but it isn’t clear to me, at present, that there is a non-superficial problem here. Nonetheless, it is a challenge about which I shall have to think carefully in future.


[1] By ‘uniqualizing’ I mean a property which is had, if at all, by at most one being. See: Alexander R. Pruss, “A Gödelian Ontological Argument Improved Even More,” in Ontological Proofs Today 50 (2012): 204.

[2] Thomas V. Morris, “The concept of God,” in Philosophy of Religion: An Anthology, ed. Louis Pojman, Michael C. Rea (Boston: Cengage Learning, 2011): 17.

[3] Obviously, the person to read here is Vallicella; see: William F. Vallicella, A Paradigm Theory of Existence: Onto-Theology Vindicated. Vol. 89. Springer Science & Business Media, 2002.

Anonymous Catholics: Extra Ecclesiam nulla salus, quia seorsum a Christum nulla salus.

What follows is a (very) casual reflection on my view, as a Catholic, of the appropriate ecumenical apologetic Catholics should offer to evangelicals/protestants when asked what we believe about whether they can be saved despite rejecting the Catholic Church’s teachings.

I was recently asked by some very sharp non-Catholic colleagues and friends what Catholics make of the situation in which evangelicals find themselves with respect to salvation. It is well known, of course, that the Catholic Church affirms that extra Ecclesiam nulla salus, (i.e., beyond/outside the Church there is no salvation), but it is also well known that Catholics generally take a more optimistic attitude towards evangelicals and the project of ecumenism. I spouted off the usual apologetic mantra; evangelicals who are baptized are already Catholic, technically (and, perhaps, ‘ontologically’) speaking, even if they aren’t coming to Mass (because they are unaware of any obligation to do so) and that most evangelicals who reject the Catholic Church are actually rejecting a mere caricature of her. When pressed, I detailed the conditions under which an evangelical’s rejection of the Catholic Church would be taken as a bona fide example of rejection, and what that kind of rejection would mean for a person’s salvation from a Catholic point of view. I answered roughly along the following lines: that if one genuinely rejects the Catholic Church then they have, in so doing, rejected Christ himself, for the Catholic Church is his mystical body, her teachings his, her authority inherited or extended from him. If the Catholic Church is what she claims to be, there can no more be salvation outside of her than there can be salvation apart from Christ, for those two things are one and the same.

I was quick to add some necessary caveats, including that a damning rejection of the Catholic Church would have to involve, at least, an intimate knowledge of what the Church actually teaches and why. Some present seemed concerned that in rejecting the teachings of the Catholic Church, to the extent that they were familiar with them, they were putting themselves in the near occasion of damnation from a Catholic perspective. I tried to insist that it would be better to frame such a rejection in terms of sin, rather than in terms of justification/damnation. It was only afterwards, in retrospect, that I felt I could have given a more satisfying response, and I regretted not doing so. Since this issue is of general interest, and since (evidently) even the most intelligent of evangelicals are often unclear what Catholics like me make of their ‘soteriological situation,’ I thought perhaps I’d try my hand offering a brief reflection on it here.

Is there salvation beyond the Catholic Church? The Catechism has a wonderful passage dealing with this question:

“Outside the Church there is no salvation”





(CCC 845-847)[1]

To my way of thinking, there is a theologically perfect analogy between the questions “is there salvation outside the Catholic Church” and “is there salvation apart from Christ” in that, for both questions, the answer will be a (similarly) qualified ‘no.’ Clearly, there can be no salvation apart from Christ (on this, evangelicals will generally agree with Catholics). However, it is not out of the question to think that Christ, by unknown and ‘extra-ordinary’ means, saves those who, through no fault of their own, remain invincibly ignorant of him, but who seek God sincerely and, through grace, have been drawn to God by Christ himself. Karl Rahner S.J., introduced the idea of ‘anonymous Christians’ (i.e., people who were unconsciously Christian) into Catholic theology in the early 1960’s.[2] The same idea was echoed at a much more popular level by C.S. Lewis, who wrote:


These ideas are substantially the same, and they have always seemed right-headed to me, especially given passages such as John 15:22, Acts 10:34-35, Acts 14:17, John 9:41, Numbers 22:9-38, et cetera. The motivations for believing that those who never accept the Gospel through some inability might still be saved are many. One might wonder, for instance, what to make of the mentally disabled who are cognitively unable to accept any theological propositions, or the person who has never been reached with the Gospel, or even the person who has only ever encountered some parody of the real Gospel. Surely a person can only be morally responsible for accepting, failing to accept, rejecting, or failing to reject something if they were acquainted with it, or could easily have been were it not for some fault of their own.

In articulating my view, which takes its cue from Rahner and Lewis (though, I think that you can find early intimations of it in the Ante-Nicene fathers as well), I have made a habit of falling back on one particularly good example from early Church history. Consider Marcus Aurelius, whose virtue and intelligence are virtually unquestioned by Christian historians, but who, in the face of Christianity, not only remained devoutly pagan but made himself a violent enemy of the early Church. Many Christians look back on Marcus Aurelius with a surprisingly warm affection and admiration for him. In the Catholic Encyclopedia’s entry on Marcus Aurelius we read:


Nevertheless, it must be acknowledged that this fondness is not mutual.


Is it to be concluded, therefore, that Marcus Aurelius rejected Christ, and so was damned? It isn’t clear that that’s a foregone conclusion. Catholics, in general, do well to heed the example of the Catholic Church, which at no time has proclaimed anyone definitively reprobate. For a Catholic to claim that anyone in particular is damned is for them to go far beyond anything the Catholic Church teaches, and that presumption seems in equal parts unwholesome and inappropriate for any faithful Catholic. Beyond prudential reasons for being slow to pass judgment as though In Persona Dei, there may be reason to believe that figures like Marcus Aurelius, in rejecting Christianity, rejected a mere caricature of the faith, while simultaneously drawing nearer to the unknown God (Acts 17:23).

Consider what we read of a presumably popular objection to Christianity, roughly contemporaneous[6] with Marcus Aurelius, in a provocative passage from Minucius Felix’ Octavius:



Unfortunately, this passage displays misunderstandings of Christianity which were basically representative of widely circulated misapprehensions at the time. Although riddled with obvious and colossal misrepresentations of Christian liturgy (it sounds almost as though infant baptism and the doctrine of the Eucharist have been conflated, resulting in a confusion which would have been laughable had it not been so serious), there’s no reason to think these were peculiar for the time.

Is it possible that Marcus Aurelius’ understanding of Christianity was filtered through these (or similar) unfair popular characterizations in his day? That is certainly not unlikely. What, then, can we make of his response to Christianity? Had he understood by Christianity something as perverse as what we read above, who could possibly blame him for reacting the way he did? Had he accepted Christianity under this appearance, he would have been thereby rejecting the essence of true Christianity. His attacks on Christianity, on this assumption, are the product not of vice, but of outstanding pagan virtue (indeed, proto-Christian virtue). If this truly was the case, then his apparent rejection of ‘Christianity’ was not a genuine rejection of Christianity at all. For all we know, Marcus Aurelius was unconsciously Christian; an anonymous Christian who, having been led into confusion about the Christian cult, acted against the Church out of love for the good, the true and the beautiful. In other words, out of love for God (the summum bonum), and even for Christ as λόγος, for, as the Shakespearean adage goes, a rose by any other name would smell as sweet.

Marcus Aurelius persecuted the Church, but I think his actions were not motivated by an obstinate rejection of the person of Christ; rather, they were motivated by a rejection of a deplorable caricature which any sufficiently good pagan would surely have been inclined to snuff out for the good of the people. In a sense, his apparent rejection of Christianity may have been no more authentic than the atheism of a man who thought that God was supposed to be a big bearded tyrant walking on the clouds, or a flying spaghetti monster. Depending on what atheists understand to be signified by the term ‘God,’ and depending, more profoundly, upon their unarticulated attitude towards God, they may also qualify, in reality, as anonymous Christians in Rahner’s sense. For all we know, they are – at least, for all we know, they are.

The example of Marcus Aurelius (at least, as I have imagined it) helps to illustrate an important point; namely, that the apparent rejection of Christ is not always a genuine rejection of Christ. I want to suggest that the same holds true with respect to rejecting the Catholic faith. For all we know, the evangelical who rejects the Catholic Church rejects but a caricature of her and may remain, in some deep way, invincibly ignorant of what they appear to reject (presumably they remain ignorant, at least, that the Catholic Church is the true mystical body of Jesus Christ). What I think Catholics like me should say, therefore, is that those who reject the Catholic Church genuinely, and not merely in appearance, are surely rejecting Christ himself, and apart from Christ there is no salvation. However, we find ourselves in precisely the same epistemic quandary when attempting to make a judgment about either whether a person has genuinely rejected Christ, or whether a person has genuinely rejected the Catholic Church. The charitable presumption that Catholics should make in both instances, in my submission, is that people may reject Christ or the Church in appearance only, while being, in reality, anonymous Catholics, unconscious of their being united to the whole communion of saints through incorporation into the mystical body of Christ.



[2] Karl Rahner, S.J., “Membership of the Church According to the Teaching of Pius XII’s Encyclical “Mystici Corporis Christi”,” Theological Investigations 2 (London: Darton, Longman and Todd, 1963): 1-88.
see also: Karl Rahner, S.J., “Salvation,” Sacramentum Mundu, V (New York: Herder and Herder, 1970): 405-409.

[3] C.S. Lewis, Mere Christianity, (Samizdat, 2014), 38.

[4] Patrick Healy, “Marcus Aurelius Antoninus,” In The Catholic Encyclopedia. Vol. 2. (New York: Robert Appleton Company, 1907), accessed July 23, 2018.


[6] Marcus Aurelius’ dates are c. 161-180 A.D., but the dates for Minucius Felix are uncertain, ranging from any times between c. 160-300 A.D.; still, the misunderstandings of Christianity evident in the dialogue published by Minucius Felix may have been in circulation in Marcus Aurelius’ time, and there may have been equally pernicious misunderstandings in circulation in Aurelius’ time regardless.

[7] Minucius Felix, Octavian, Ch. IX,

An Argument Against Newtonian ‘Absolute’ Time From the Identity of Indiscernibles

An interesting thought occurred to me recently while I was reading through the early pages of Bas C. van Fraassen’s An Introduction to the Philosophy of Time and Space. I would not be surprised if this thought is unoriginal (indeed, I might even be slightly surprised if Leibniz himself hadn’t already thought it), but, for what it’s worth, the idea did genuinely occur to me, so, for all I know, it might be original. In any case, I think it may be of some interest, so I’m going to try to briefly flesh it out.

In order to do so, I will have to set the stage by very briefly explaining some of the basics of an Aristotelian view of time (at least, insofar as they are pertinent), and juxtaposing that with a Newtonian view of time as absolute. I will come around, near the end, to a brief reflection on what this argument might tell us, if anything, about the philosophical status of the generic A-theory, or the generic B-theory.

Aristotle is well known for championing a view of time on which time is dependent upon motion. Granted, what Aristotle means by motion bears only mild resemblance to our modern (much more mechanistic) notion. Motion, for Aristotle, is analyzed in terms of potentiality and actuality (which are, for Aristotle, fundamental conceptual categories). Roughly speaking (perhaps very, very roughly speaking), for any property P and being B, (assuming that having property P is compatible with being a B), B either has P actually, or else B has P potentially. For B to have property P actually is just for it to be the case that B has the property P. For B to have property P potentially is just for it to be the case that B could (possibly) have, but does not (now) have, the property P. In other words, potentiality represents non-actualized possibilities. A bowling ball is potentially moving if it is at rest, just as it is potentially moving at 65 mph if it is actually moving at 80 mph. A phrase like ‘the reduction of a thing from potentiality to actuality,’ common coin for medieval metaphysicians, translates roughly to ‘causing a thing to have a property it did not have before.’ This account may be too superficial to make die-hard Aristotelians happy, but I maintain that it will suffice for my purposes here. Aristotle, then, wants to say that in the absence of any reduction from potentiality to actuality, time does not exist. Time, in other words, supervenes upon motion in this broad sense – what we might, in other contexts, simply call change. Without any change of any sort, without the shifting from one set of properties to another, without the reduction of anything from potentiality to actuality, time does not exist.

Newton is well known for postulating absolute time as a constant which depends, in no way, upon motion (either in the mechanical/corpuscularian sense, popular among empiricists of his time, or in the broader Aristotelian sense).[1] In this he was, there is little doubt, infected by the teachings of his mentor, Isaac Barrow, who overtly rejected the Aristotelian view;

“But does time not imply motion? Not at all, I reply, as far as its absolute, intrinsic nature is concerned; no more than rest; the quality of time depends on neither essentially; whether things run or stand still, whether we sleep or wake, time flows in its even tenor. Imagine all the stars to have remained fixed from their birth; nothing would have been lost to time; as long would that stillness have endured as has continued the flow of this motion.”[2]

Newton’s view of time was such that time was absolute in that its passage was entirely independent of motion. It is true, of course, that Newton fell short of thinking that time was absolute per se; indeed, he viewed time as well as space as being non absoluta per se,[3] but, rather, as emanations of the divine nature of God. However, since God was absolute per se, as well as necessary per se (i.e., because existing a se), time flowed equably irregardless of motion, just as space existed irregardless of bodies.

To illustrate the difference, imagine a world in which everything is moving along at its current pace (one imagines cars bustling along the streets of London, a school of whales swimming at 2500 meters below sealevel, planes reddying for landing in Brazil, light being trapped beyond the event horizon in the vicinity of a black hole in the recesses of space, etc.), and, suddenly, everything grinds to a halt. It is as though everything in the world has been paused – there are no moving bodies, the wind does not blow, there are no conscious experiences, light does not propagate, electromagnetic radiation has no effects. Does time pass? On the Newtonian view, it certainly does. This sudden and inexplicable quiescent state might persist for a short amount of time, or a very long time, or it may perdure infinitely. On the Aristotelian view, this is all nonsense; instead, we are simply imagining the world at a time. To imagine that this world persists in this state from one time to another is just to be conceptually confused about the nature of time; time doesn’t merely track change, its relationship to change is logically indissoluble. So, for Aristotle, time cannot flow independently of motion (i.e., of change), while, for Newton, time flows regardless of what, or whether, changes were wrought in the world.

Now, I want to try to construct an argument for thinking that this Newtonian view may be logically impossible. I will start with an appeal to no lesser an authority than Gottfried Leibniz, who was easily Newton’s intellectual superior. He famously championed a principle which has come to be called the identity of indiscernibles (though, McTaggart tried, unsuccessfully, to relabel it as the dissimilarity of the diverse).[4] As Leibniz puts it, “it is never true that two substances are entirely alike, differing only in being two rather than one.”[5] To put it in relatively updated language: “if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic:

∀F(Fx ↔ Fy) → x=y.”[6]

The suggestion was that not only were identicals indiscernible (which is indubitable), but that absolutely indiscernible things must be identical. In other words, if there is not a single level of analysis on which two things can be differentiated, then the two things are really one and the same thing.

‘What is the difference,’ you might ask ‘between this ball here and that ostensibly identical ball over there?’ Well, for one thing, their locations in space (one is here, and the other is there – and this difference suffices to make them logically discernible), to say nothing of which of them is closer to me at this present time, or which one I thought about first when formulating my question (Cambridge properties suffice to make things discernible in the relevant sense). If two things do not differ with respect to their essential properties, they must (if they are genuinely distinct) differ at least in their relational properties, and if not in real relations, at least in some conceptual relations (or, what Aquinas would have called relations of reason).[7] This principle is a corollary, for Leibniz, of the principle of sufficient reason – for, the reason two indiscernible things must be identical is that, if they are truly indiscernible, then there is no sufficient reason for their being distinct. For any set of things you can think of, if they share all and only the very same properties (and, thus, are absolutely indiscernible), then they are identical – they are not a plurality of things at all, but merely all one and the same thing.

Assume that this principle is true (in a few moments, I will explore a powerful challenge to this, but spot me this assumption for the time being). Now, suppose there are two times t1 and t2, such that these two times are absolutely indiscernible. We can help ourselves here to the previous thought experiment of a world grinding to a halt; this perfectly still world is the world at t1, and it is the world at t2. No change of any kind differentiates t1 and t2. There is no discernible difference between them at all. But then, by the identity of indiscernibles, t1 and t2 are identical. To put it formally;

  1. For any two objects of predication x and y, and any property P: ∀P(Px ≡ Py) ⊃ x=y
  2. Times are objects of predication.
  3. Times t1 and t2 share all and only the same properties.
  4. Therefore t1 = t2.

This argument is so straightforward as to require little by way of clarification. I assume that times are objects of predication not to reify them, but simply to justify talking as though times have properties.

There are now two things to consider; first, what implications (if any) this argument’s soundness would have for the generic A-theory of time, and, second, whether this is a powerful argument. With respect to the first, obviously Newton’s view of time was what we would today call A-theoretical. On the A-theory, there is a mind-independent fact about time’s flow – there is a fact about what time it is right now, et cetera. Time, on the A-theory, may continue to flow regardless of the state of affairs in the world. On the B-theory of time, by contrast, there is nothing which can distinguish times apart from change (in particular, change in the dyadic B-relations of earlier-than, simultaneous-with, and later-than between at least two events). It seems confused to imagine a B-series where the total-event E1 (where ‘total-event’ signifies the sum total of all events in a possible world, at a time) is both one minute earlier than total-event E*, and where the total-event E1 is also (simultaneously?) a year earlier than the total-event E*. Indeed, to use any metric conventions to talk about the amount of time E* remained unchanging might be confused (even if one opts for a counterfactual account of how much time would have been calculated to pass had a clock been running, there is still a problem – clearly, had a clock been running, it would have registered absolutely no passage of time for the duration of E*). So, there is just no rational way of speaking about the duration of a total-event E* by giving it some conventional measurement in the terms of some preferred metric.[8] If the B-relations of earlier-than, simultaneous with, and later-than, are not in any way altered from one time to another, then the times under consideration are strictly B-theoretically indiscernible, and, thus, identical. On the A-theory, by contrast, one can provisionally imagine an exhaustively descriptive state of affairs being both past and present.[9] One can imagine its beginning receding into the past while it (i.e., this total-event E*) remains present. I am not sure that every version of the A-theory will countenance this possibility, but it seems right to say that only the A-theory will countenance this possibility.[10] If my argument is right, and the reasoning in this paragraph hasn’t gone wrong, then the A-theory is less likely to be true than it otherwise would have been (we don’t even need to apply a principle of indifference to the different versions of the A-theory, so long as we accept that the epistemic probability of each version of the A-theory is neither zero nor infinitesimal).

In any case, the salient feature of what I’ve presented as the Newtonian view is that time may pass independently of any change in the world at all. I’ve suggested that there is a problem for the Newtonian view (whether or not such a view can be married to the B-theory) in the form of a violation of the principle of the identity of indiscernibles. The Newtonian might, of course, argue that God’s conscious awareness continues regardless of a quiescent world, so that God himself could act as a sort of clock for such a motionless universe. He, at least, would know how long it had been since anything was moving, or changed. In this case, however, the Newtonian is effectively conceding ground to the peripatetic; at least God, then, has to be reduced from potentiality to actuality (this suggestion will, of course, be repugnant, both to Aristotelians as well as to Catholics, but die-hard Newtonians typically aren’t either anyway).

Regardless, this argument may not be as strong as I initially hoped. After all, together with the principle of sufficient reason, the identity of indiscernibles has been the subject of sustained and impressive criticisms. While these criticisms may not present insuperable difficulties for defenders of the principle, they cannot be lightly dismissed. For a fair conceptual counter-example, one might think, in particular, about a perfectly symmetrical world in which there are only two physically identical spheres, neither of which has a single property that the other fails to have. Consider the following passage from Max Black’s ingenious paper, The Identity of Indiscernibles;

“Isn’t it logically possible that the universe should have contained nothing but two exactly similar spheres? We might suppose that each was made of chemically pure iron, had a diameter of one mile, that they had the same temperature, colour, and so on, and that nothing else existed. Then every quality and relational characteristic of the one would also be a property of the other. Now. if what I am describing is logically possible, it is not impossible for two things to have all their properties in common. This seems to me to refute the Principle.”[11]

There are no obvious and attractive ways out of this predicament for the rationalist, as far as I can see. One might be able to say that they have distinct potentialities (i.e., that to scratch or mutilate one would not be to scratch or mutilate the other, so that each one has a distinct potentiality of being scratched or somehow bent into a mere spheroid), but it isn’t clear how useful such a response is. One might argue that each one is identical with itself, and different from its peer, but it isn’t clear that self-identity is a bona-fide property. One may, out of desperation, ask whether God, at least, would know (in such a possible world) which was which, but it may be insisted, in response, that this is a pseudo-question, and that, while they are not identical, God could only know that there were two of them (and, of course, everything else about them), but not which one was which.

In passing, I want to recommend that people read through Black’s paper, which is written in the form of a very accessible and entertaining dialogue between two philosophers (simply named ‘A’ and ‘B’ – yes, yes, philosophers are admittedly terrible at naming things). Here is a small portion which, I feel, is particularly pertinent;

“A. How will this do for an argument? If two things, a and b, are given, the first has the property of being identical with a. Now b cannot have this property, for else b would be a, and we should have only one thing, not two as assumed. Hence a has at least one property, which b does not have, that is to say the property of being identical with a.

B. This is a roundabout way of saying nothing, for ” a has the property of being identical with a “means no more than ” a is a When you begin to say ” a is . . . ” I am supposed to know what thing you are referring to as ‘ a ‘and I expect to be told something about that thing. But when you end the sentence with the words ” . . . is a ” I am left still waiting. The sentence ” a is a ” is a useless tautology.

A. Are you as scornful about difference as about identity ? For a also has, and b does not have, the property of being different from b. This is a second property that the one thing has but not the other.

B. All you are saying is that b is different from a. I think the form of words ” a is different from b ” does have the advantage over ” a is a ” that it might be used to give information. I might learn from hearing it used that ‘ a ‘ and ‘ b ‘ were applied to different things. But this is not what you want to say, since you are trying to use the names, not mention them. When I already know what ‘ a’ and ‘ b ‘ stand for, ” a is different from b ” tells me nothing. It, too, is a useless tautology.

A. I wouldn’t have expected you to treat ‘ tautology’ as a term of abuse. Tautology or not, the sentence has a philosophical use. It expresses the necessary truth that different things have at least one property not in common. Thus different things must be discernible; and hence, by contraposition, indiscernible things must be identical. Q.E.D


B. No, I object to the triviality of the conclusion. If you want to have an interesting principle to defend, you must interpret ” property” more narrowly – enough so, at any rate, for “identity ” and “difference ” not to count as properties.

A. Your notion of an interesting principle seems to be one which I shall have difficulty in establishing.”[12]

And on it goes – but I digress.

Now, if such a world (with two identical spheres) is logically possible, it looks as though the spheres in it are indiscernibles even if they aren’t identical. No fact about their essential properties, or relations, will distinguish them in any way (and this needn’t be a case of bilocation either, for we are supposed to be imagining two different objects that just happen to have all and only the same properties and relations). If that’s correct, then (I take it) the identity of indiscernibles is provably false.

So, my argument will only have, at best, as much persuasive force as does the identity of indiscernibles. It persuades me entirely of the incoherence of imagining a quiescent world perduring in that state, but I doubt whether the argument will be able to persuade anyone who rejects the identity of indiscernibles.

[1] Strictly speaking, I’m not entirely sure that Newton would have said that time can continue to flow independently of any change of any kind, but I do have that impression. Clearly, for Newton, time depends solely on God himself.  Below, I will consider one response a Newtonian could give which suggests that time flows precisely because God continues to change – however, to attribute this to Newton would be gratuitous and irresponsible. I am not a specialist with regards to Newton’s thinking, and I do not know enough about his theology to say whether, or to what extent, he would have been happy to concede that God changes.

[2] The Geometrical Lectures of Isaac Barrow, J.M. Child, Tr. (La Salle, III.: Open Court, 1916), pp. 35-37.

Reproduced in Bas C. van Fraassen An Introduction to the Philosophy of Time and Space, (New York: Columbia University Press, 1941) 22.

[3] William Lane Craig, Time and the Metaphysics of Relativity, Philosophical Studies Series Vol. 84. (Springer Science & Business Media, 2001), 114.

[4] See C.D. Broad, McTaggart’s Principle of the Dissimilarity of the Diverse, Proceedings of the Aristotelian Society, New Series Vol. 32 (1931-1932), pp. 41-52.

[5] G.W. Leibniz, Discourse on Metaphysics, Section 9;

[6] Peter Forrest, “The Identity of Indiscernibles,” in The Stanford Encyclopedia of Philosophy ed. Edward N. Zalta, (Winter 2016 Edition);

[7] See W. Matthews Grant “Must a cause be really related to its effect? The analogy between divine and libertarian agent causality,” in Religious Studies 43, no. 1 (2007): 1-23.

[8] I will not, here, explore the idea of non-metric duration.

[9] Interestingly, McTaggart would likely have begged to disagree. Indeed, one may be able to construct an argument along McTaggart’s lines for the impossibility of a world remaining totally quiescent over time by arguing that the A-properties of pastness and presentness were incompatible determinations.

[10] It is entirely possible, upon reflection, that I am dead wrong about this. Perhaps this is just my B-theoretic prejudice showing itself. Why, if the A-properties of Presentness and Pastness aren’t incompatible determinations of a total-event E*, think that the B-relations of being earlier-than and simultaneous-with are incompatible determinations of a total-event E*? I continue to persuade and dissuade myself that there’s a relevant difference, so I’m not settled on this matter.

[11] Max Black, “The identity of indiscernibles,” in Mind 61, no. 242 (1952): 156.

[12] Max Black, “The identity of indiscernibles,” in Mind 61, no. 242 (1952): 153-4,155.

On (Possibly) Being Unable To Avoid Speaking Falsely

I was thinking yesterday about Thomas Aquinas’ rather strict view on the duty to never lie, even, as he says, when we lie for the sake of a joke. He admits, of course, that lying in the cause of a joke (a jocose lie) is not a mortal sin, but he does insist that it is at least venially sinful.

Ergo mendacium iocosum et officiosum non sunt peccata mortalia.[1]

I thought to myself that Aquinas probably means jokes which only work if the audience accepts a falsehood asserted before the punchline. I am reminded here of a (probably apocryphal) anecdote about Dominican friars teasing Aquinas by saying “look, out the window – flying pigs!” in response to which he looked out the window, to their great amusement. He retorted to their laughter by saying that he would sooner believe that pigs could fly than that his Dominican brethren could lie. Clearly, in such a case, Aquinas would say that what these friars did was sinful (at least venially). However, I don’t think Aquinas would offer the same analysis of sarcastic jokes, where what one says is actually the opposite of what one affirms by saying it. In sarcasm, one expresses a truth P by expressing a token-sentence K which, under normal circumstances, affirms not-P, but which, when used sarcastically, is understood by everyone to affirm P. To utter K sarcastically is to affirm P, and everyone knows this. This got me thinking about a strange situation.

Suppose one is in a court of law and must answer any question with a simple affirmative or negative. Suppose, then, that for some question, the token statement which is an affirmative is true in one language game, and false in another language game, and the token statement which is the negation is true in one language game and false in another. Call these tokens Y and N, and let us suppose that half the audience is playing the first language game, and the other half is playing the other. If one answers Y, then half the audience will believe something true, while the other half of the audience will believe something false, because they are unconsciously playing two different language games. If one answers N, the same situation results. Suppose you are fully aware that Y will communicate a falsehood to some, and that N will communicate a falsehood to others. Suppose, further, it isn’t possible to elaborate on Y or N (you can tell any story you like here – maybe you speak a totally different language, and you have a designated translator in court who is committed to translating whatever you say into simply Y or N – or any other scenario you like, so long as you aren’t able to avoid affirming Y or N).

In such a strange case, would you have to lie? It seems like you would have to communicate something false (imagine, for simplicity, that your silence would be taken as an affirmation of Y, or N, or would be a sort of speech-act by omission which, in any case, would communicate a falsehood), which you knew to be false.

If such a situation arose, it wouldn’t be possible to avoid telling a lie (at least where the sufficient conditions of lying are speaking falsely with a knowledge that what you’re saying is false). Therefore, it wouldn’t be possible to do the right thing (except in terms of telling the lesser lie, whatever that is). Does this pose much of a problem for Aquinas’ view? I’m actually not sure. If we really can construct a situation in which there is no way to avoid sinning, that would plausibly provide us with a reductio ad absurdum and should cause us to carefully review what we think qualifies as a sin. However, it is still open to the especially devout Thomist to bite the bullet here, or to find some way of arguing that the situation I propose arises in no logically possible worlds. It might help our case if we could provide some kind of hypothetical example. Here’s one: consider the question “is God infinite?” Clearly, those speaking the language of Duns Scotus are going to take a rejection of this as a false statement, and they (playing their language game) would be right to do so. On the other hand, those speaking the language of modern mathematicians would recognize the affirmative to be a straightforward falsehood (for God is not infinite in any quantitative sense). There is no unqualified answer (in the form of an affirmation or denial) which does not communicate a falsehood which one knows to be false (presuming one is sufficiently well theologically informed).

[1] ST, II-II, Q. 110, Art. 3, ad. 3.

Arguing that the B-theory (or the A-theory) is a metaphysically necessary truth

I have profound sympathy for the intuition that, for either the A-theory of time, or the B-theory of time, if it is true, then it is necessarily true. It obviously follows, therefore, from either one’s metaphysical possibility, that it is a necessary truth. However, the force with which this intuition imposes itself notwithstanding, it turns out to be extremely difficult to prove this modal thesis, and there may, in fact, be a really good objection to it.

Does it really follow from the A-theory’s being true (supposing it is) that it is necessary, or from the B-theory’s being true (supposing it is) that it is necessary? Suppose our world is an A-theory world; could God really not have created a B-theory world?

Interestingly, while I was rereading a paper today from Joshua Rasmussen, my attention was drawn to one of his footnotes, in which he outlines a sort of modal-ontological argument from the possibility of presentism (typically considered to be a version of the A-theory – though, I note in passing, he was arguing in the paper that presentism is strictly compatible with the B-theory) to its necessity. His argument went roughly as one might imagine (note: he uses ‘Tenseless’ as an abbreviation for the thesis that he argues for in the paper, and which needn’t directly concern us here):

Here’s the argument: (i) suppose it’s possible that Tenseless and presentism are true; (ii) then it’s possible that presentism is true; (iii) necessarily, if presentism is true, then presentism is necessarily true; therefore, (iv) if it’s possible that presentism is true, then it’s possible that presentism is necessarily true; (v) if it’s possible that presentism is necessarily true, then presentism is true (by S5); therefore, (vi) presentism is true.[1]

This caused me to review one of my (many, many) old blog post drafts, in which I tried to argue that if the A-theory is true, then it is a necessary truth, and if the B-theory is true, then it is a necessary truth. Here’s (roughly) what that looked like:

I have been asked, in the past, why I maintain that if the B-theory is true in any possible world, then it is true in all logically possible worlds (from which it follows that it’s true in the actual world), and that the same can be said for the A-theory. Upon reflection, I suppose I was reasoning in something like the following way:

  1. God exists in every possible world (assumption).
  2. If God exists in every possible world then his necessary essence is exemplified in every possible world.
  3. God either is by his necessary essence, or is necessarily not, simple and/or immutable in the classical senses.
  4. The B-theory is true if and only if God is essentially simple and/or immutable.
  5. Either the B-theory is true, or the A-theory is true (and not both).
  6. If the B-theory is true in one logically possible world, it is true in all logically possible worlds.
  7. Therefore, if the A-theory is true in one logically possible world, it is true in all logically possible worlds.

The weakest point of the argument, now that I lay it out and think about it, seems to be premise 4, for although it seems right to say that if God is simple and immutable then the B-theory must be true, it seems wrong to say that if the B-theory is true then God must necessarily be simple and/or immutable. Why think that if God weren’t simple and/or immutable then He couldn’t create a B-theory world? I then tried to construct a more elaborate argument for the conclusion that if the B-theory is true, then it is necessarily true, and if the A-theory is true, then it is necessarily true. It went something like:

  1. God’s existence is possible (assumption).
  2. God is a metaphysically necessary being. (by definition)
  3. For any metaphysically necessary being, if it exists in a single logically possible world it exists in all logically possible worlds.
  4. God exists in every possible world (assumption).
  6. There is a logically possible world in which God’s essence includes being metaphysically simple and immutable. (Assumption)
  7. Therefore, in all logically possible worlds God is metaphysically simple and immutable.
  8. If God is metaphysically simple and immutable, then necessarily: if there is a contingent world, then the B-theory is true.
  9. There is a contingent world.
  10. Therefore, the B-theory is true.

This argument isn’t very good. For one thing, it highlights a really big problem for the idea that the A-theory of time and the B-theory of time are mutually exclusive and logically exhaustive disjuncts. Indeed, if there is no contingent world, there are surely no A-properties, but there are also no B-properties (it is hard to imagine a B-theory on which only ‘atemporal simultaneity’ is preserved – that is so depreciated that it isn’t clear whether it would even qualify as a version of the B-theory). It looks like this problem for Rasmussen’s argument as well (why accept his (iii)?).

I also had some rough notes on a third argument, which went something like this:

  1. God’s existence is metaphysically possible. (assumption).
  2. God is a metaphysically necessary being (and his essence, whatever it is, is metaphysically necessary).
  3. God either is essentially, or essentially is not, simple and immutable in the classical senses.
  4. There is a contingent world. (assumption)
  5. If there is a contingent world, then the A-theory is true, or the B-theory is true (and not both).
  6. The A-theory is true if and only if God stands in real relations to the world which are grounded in himself.
  7. If God stands in real relations to the world grounded in himself, then God is not simple and immutable.
  8. If God possibly stands in real relations to the world which are grounded in himself, then God necessarily stands in real relations to the world which are grounded in himself.
  9. If God necessarily stands in real relations to the world which are grounded in himself then the A-theory is necessarily true.
  10. Therefore, if the A-theory is possibly true, the A-theory is necessarily true.
  11. If the A-theory is not possibly true, then the B-theory is necessarily true.

The reader will have to forgive me for being a little loose as well as slightly enthymematic. I’m not sure this is a good argument. The intuition is supposed to be that God can only be simple and immutable in a B-theory world, that he cannot be simple and immutable in an A-theory world, and that whichever way God is in any possible world (at least with respect to being simple and immutable), that is the way He is in all possible worlds.

Perhaps one will disagree with me that God exists in all logically possible worlds (which is just to say that God does not exist, since, obviously, if a metaphysically necessary being exists in a single possible world it exists in all possible worlds). They will argue that it may seem necessary given theism that whichever theory of time is true of the actual world is true of all logically possible worlds, but that they either reject, or in any case do not accept, theism. It might seem as though we are at a standstill with such a person.

There is, nevertheless, another way to argue that the A-theory is necessarily false (and the B-theory, therefore, necessarily true). Suppose we accept the claims that the (weak-)PSR and the A-theory of time are logically incompatible with each other.[2] Now, take the weak-PSR which says that for any possibly true contingent fact P, P possibly has an explanation. Obviously, if the weak-PSR is true it is a necessary truth. This entails that there is a logically possible world in which P, and the explanation of P, both obtain. Suppose that P is “it is now this particular time.” On the A-theory, this contingent fact does not have an explanation. That means (supposing all we have said so far) that at least one logically possible world is a B-theory world. It follows that there is no logically possible world in which the A-theory is true. However, this reasoning is not likely to be any more compelling than the theistic reasoning explored above.

Can I do any better? Probably not today. (I suppose I could have deployed my argument for thinking that the A-theory is not logically possible because there is no logically possible world in which time flows – an argument I developed a bit in my undergraduate thesis and which, I am beginning to think, may make an appearance in my Master’s thesis – but I’d rather leave it out of this post for the sake of convenience).

[1] Joshua Rasmussen, “Presentists may say goodbye to A-properties,” Analysis 72, no. 2 (2012): 270-276.

[2] For more on this, see