Defining ‘God’

Against the somewhat populist mantra of atheists like Sean Carroll (that the term ‘God’ is not now, nor seemingly ever, clearly defined),[1] I have insisted that analytic theologians, at least, have provided a very clear definition of God which is serviceable for the purposes of philosophical analysis. When(ever) defining theism, therefore, I have been very insistent upon the roughly Anselmian definition (i.e., that God is that than which nothing greater could be conceived – or, put more simply, that God is an altogether perfect being) which is also adopted, in a refined form, by analytic theologians engaged in the project of what is called perfect being theology. Perfect being theology (PBT) suggests that God is that which exemplifies the largest compossible package of great-making (or ‘perfect-making’) properties. For all its philosophical and rhetorical advantages, however, there is an important sense in which this definition dislocates the term ‘God’ from the way it is often used in the real world. For instance, while the monotheistic Hindu, or the (follower of) Bahá’í, or the Muslim, or the deist will, on this definition, be included among the ranks of theists, the Mormon, who professes belief in the God of the Bible, may turn out to be an atheist[2] (this, for those unfamiliar with Mormonism, is because the Mormon concept of the God of the Bible is – to the best of my understanding – of a finite material non-necessary definitely-old humanoid being on a nearby planet who has his own god, and that god, in turn, has his own god (regress ad infinitum)[3] – a being, in short, which is categorically lacking every perfection). Indeed, insisting upon the philosophically sophisticated definition introduced by Anselm and refined by analytic theologians makes the believers in the Roman pantheon of gods (as well as other ancient polytheists) non-theists. Polytheists (of the imagined variety) are something of a rarity in the modern world, which may appear to mitigate the seriousness of the problem they pose, but the fact that our definition can’t make sense of our colloquial language (insofar as we want to call polytheists theists, and certainly don’t want to call them atheists) remains a problem. More seriously, it turns out that several philosophically/theologically high-profile theists in our own time who reject PBT (e.g., open-theists/process-theologians) turn out to be atheists on the definition on which I am in the habit of insisting, even though they believe in a transcendent incontingent intentional/personal omnipotent entity responsible for the existence of everything not identical to itself. More exotically, the Anselmian definition of theism alluded to above will both exclude Wittgensteinian theists[4] and include neo-Meinongian atheists (I’m thinking here of a hypothetical neo-Meinongian who adopts PBT and insists that non-existence is a great-making property; for them, “God exists” is false, but there is really such a thing as the God defined by PBT).

Though the Anselmian definition of God seems, at first blush, intuitive and uncontroversial (it seems to accord well with what theists mean when they use the term ‘God,’ as well as vindicating religious sentiments expressed as worship), the corresponding definitions of theism and atheism tangle us up with especially awkward commitments. How are we to resolve this problem responsibly? One solution might be to regard theism as having no strict definition, no set of necessary and sufficient conditions, but to, instead, regard any instance of ‘theism’ as picked out by a kind of family resemblance (perhaps we could have disjunctive sets of sufficient conditions none of which are necessary for theism). Another strategy is to define theism more than once (offering a wide, and a narrow definition, or some set of definitions running along a scale from widest to narrowest), leaving people to specify in which sense they mean to use the term when deployed in conversation. On this suggestion we could give ‘theism’ a technical definition for the purposes of doing analytic philosophy or natural theology, and then a more general definition in order to accommodate its real-world use. I am open to either strategy. For instance, I would be happy to accept the latter strategy (of defining theism multiple times), allowing its most general meaning to be defined as something like “[that] there is a being to whom religious/unrestricted worship is appropriately directed,” provided only that I could then provide a more philosophically careful definition for the purposes of philosophical interrogation (plug in Anselm’s or PBT’s definition here).

What this reflection is meant to surface to the reader’s attention is that defining theism may actually not be as easy as rhetorical responses to Sean Carroll (and others of his ilk) suggest. Perhaps, in place of being so dismissive of Carroll et alia as illiterate pedestrian theological-invalids, we should, instead, welcome the implicit challenge of defining God clearly and then offer the Anselmian definition as a proposal to be considered seriously.

This, I’m afraid, seems to be the best we can do (without doing serious violence to our normal use of ‘god’-language).

 

[1] For example, Sean Carroll in his very successful debate with William Lane Craig back in 2015, insisted several times that theism is just not sufficiently well defined (e.g., “Theism does not even try to do this because ultimately theism is not well defined[,]” “you do not see graphs like this in the theological papers trying to give God credit for explaining the fine-tuning because theism is not well defined[,]” and, of course: “It’s not hard to come up with ex post facto justifications for why God would have done it that way. Why is it not hard? Because theism is not well defined. That’s what computer scientists call a bug, not a feature.” The popularity of this debate noticeably boosted the popularity of this rhetorical strategy. To his credit, Carroll does say: “… theism is not well defined. I’m going to be emphasizing this… point because if you ask a theist about the definition they will give you some very rigorous sounding definition of what they mean by God. The most perfect being, the ground for all existence, and so forth. There are thousands of such definitions, which is an issue, but the real problem is not with the definition, it’s when you connect the notion of God to the world we observe. That’s where apparently an infinite amount of flexibility comes in and I’m going to be inveighing against using that in cosmology.” He acknowledges, therefore, that there are rigorous(-sounding?) definitions on offer but persists in thinking (and suggesting) that ‘God’ is not sufficiently well defined.
See: William Lane Craig and Sean Carroll, God and Cosmology: The Existence of God in Light of Contemporary Cosmology, accessed February 10^th, 2020. https://www.reasonablefaith.org/media/debates/god-and-cosmology-the-existence-of-god-in-light-of-contemporary-cosmol/

[2] Or, perhaps, the Mormon might turn out to be an agnostic, regarding the question of whether a perfect being exists to be an open question on which the Church of Latter-Day Saints makes no pronouncements either way – or, indeed, some Mormons might be theists, others atheists, others agnostics, others Wittgensteinians, others theological non-cognitivists (and so on) so that Mormonism is strictly not determinative of theism in this widely adopted Anselmian sense.

[3] For instance, see Joseph Smith Junior’s King Follett sermon, where he says, among other things:
“I am going to tell you how God came to be God. We have imagined and supposed that God was God from all eternity. I will refute that idea, and take away the veil, so that you may see.”
“Here, then, is eternal life—to know the only wise and true God; and you have got to learn how to be gods yourselves, and to be kings and priests to God, the same as all gods have done before you, namely, by going from one small degree to another, and from a small capacity to a great one; from grace to grace, from exaltation to exaltation, until you attain to the resurrection of the dead, and are able to dwell in everlasting burnings, and to sit in glory, as do those who sit enthroned in everlasting power.”
However, interestingly, there are parts even of this sermon which appear, on first reading, to make room for an ultimate God, a God who is the head of all gods, and who created the world (though, of course, not ex nihilo: “Now, I ask all who hear me, why the learned men who are preaching salvation, say that God created the heavens and the earth out of nothing? The reason is, that they are unlearned in the things of God, and have not the gift of the Holy Ghost; they account it blasphemy in any one to contradict their idea. If you tell them that God made the world out of something, they will call you a fool. But I am learned, and know more than all the world put together.”). For example: “In the beginning, the head of the Gods called a council of the Gods; and they came together and concocted [prepared] a plan to create the world and people it.”
See: Joseph Smith Jr., The King Follett Sermon, accessed February 10, 2020. https://www.churchofjesuschrist.org/study/ensign/1971/04/the-king-follett-sermon?lang=eng

[4] See: D.Z. Phillips, “Wittgensteinianism: Logic, Reality, and God,” in The Oxford Handbook of Philosophy of Religion, edited by William J. Wainwright, (Oxford: Oxford University Press, 2005): 447-471.

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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 15^th, 2019): https://plato.stanford.edu/entries/religion-epistemology/#RefoEpis

[3] See: Alexander R. Pruss, “Internalism, Externalism and Bayesianism,” Alexander Pruss’ Blog, (June 15^th, 2019): http://alexanderpruss.blogspot.com/2017/03/internalism-externalism-and-bayesianism.html

[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. https://www.reasonablefaith.org/question-answer/P80/does-knowledge-require-certainty

[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 25^th, 2019. https://plato.stanford.edu/archives/win2016/entries/epistemology-bayesian/.

[3] Alexander Pruss, Conciliationism and natural law epistemology, on Alexander Pruss’ Blog, accessed March 25^th, 2019. https://alexanderpruss.blogspot.com/2019/02/conciliationism-and-natural-law.html

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…, X_n}. 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”

846 How are we to understand this affirmation, often repeated by the Church Fathers? Re-formulated positively, it means that all salvation comes from Christ the Head through the Church which is his Body:

Basing itself on Scripture and Tradition, the Council teaches that the Church, a pilgrim now on earth, is necessary for salvation: the one Christ is the mediator and the way of salvation; he is present to us in his body which is the Church. He himself explicitly asserted the necessity of faith and Baptism, and thereby affirmed at the same time the necessity of the Church which men enter through Baptism as through a door. Hence they could not be saved who, knowing that the Catholic Church was founded as necessary by God through Christ, would refuse either to enter it or to remain in it.

847 This affirmation is not aimed at those who, through no fault of their own, do not know Christ and his Church:

Those who, through no fault of their own, do not know the Gospel of Christ or his Church, but who nevertheless seek God with a sincere heart, and, moved by grace, try in their actions to do his will as they know it through the dictates of their conscience – those too may achieve eternal 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:

“Is it not frightfully unfair that this new life should be confined to people who have heard of Christ and been able to believe in Him? But the truth is God has not told us what His arrangements about the other people are. We do know that no man can be saved except through Christ; we do not know that only those who know Him can be saved through Him…”[3]

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:

“Marcus Aurelius was one of the best men of heathen antiquity. Apropos of the Antonines the judicious Montesquieu says that, if we set aside for a moment the contemplation of the Christian verities, we can not read the life of this emperor without a softening feeling of emotion. Niebuhr calls him the noblest character of his time, and M. Martha, the historian of the Roman moralists, says that in Marcus Aurelius “the philosophy of Heathendom grows less proud, draws nearer to a Christianity which it ignored or which it despised, and is ready to fling itself into the arms of the Unknown God.””[4]

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

“In his dealings with the Christians Marcus Aurelius went a step farther than any of his predecessors. Throughout the reigns of Trajan, Hadrian, and Antoninus Pius, the procedure followed by Roman authorities in their treatment of the Christians was that outlined in Trajan’s rescript to Pliny, by which it was ordered that the Christians should not be sought out; if brought before the courts, legal proof of their guilt should be forthcoming. [For the much-disputed rescript “Ad conventum Asiae” (Eusebius, Church History IV.13), see ANTONINUS PIUS]. It is clear that during the reign of Aurelius the comparative leniency of the legislation of Trajan gave way to a more severe temper. In Southern Gaul, at least, an imperial rescript inaugurated an entirely new and much more violent era of persecution (Eusebius, Church History V.1.45). In Asia Minor and in Syria the blood of Christians flowed in torrents (Allard, op. cit. infra. pp. 375, 376, 388, 389). In general the recrudescence of persecution seems to have come immediately through the local action of the provincial governors impelled by the insane outcries of terrified and demoralized city mobs. If any general imperial edict was issued, it has not survived.”[5]

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:

“And now, as wickeder things advance more fruitfully, and abandoned manners creep on day by day, those abominable shrines of an impious assembly are maturing themselves throughout the whole world. Assuredly this confederacy ought to be rooted out and execrated. They know one another by secret marks and insignia, and they love one another almost before they know one another. Everywhere also there is mingled among them a certain religion of lust, and they call one another promiscuously brothers and sisters, that even a not unusual debauchery may by the intervention of that sacred name become incestuous: it is thus that their vain and senseless superstition glories in crimes. Nor, concerning these things, would intelligent report speak of things so great and various, and requiring to be prefaced by an apology, unless truth were at the bottom of it. I hear that they adore the head of an ass, that basest of creatures, consecrated by I know not what silly persuasion,–a worthy and appropriate religion for such manners. Some say that they worship the virilia of their pontiff and priest, and adore the nature, as it were, of their common parent. I know not whether these things are false; certainly suspicion is applicable to secret and nocturnal rites; and he who explains their ceremonies by reference to a man punished by extreme suffering for his wickedness, and to the deadly wood of the cross, appropriates fitting altars for reprobate and wicked men, that they may worship what they deserve. Now the story about the initiation of young novices is as much to be detested as it is well known. An infant covered over with meal, that it may deceive the unwary, is placed before him who is to be stained with their rites: this infant is slain by the young pupil, who has been urged on as if to harmless blows on the surface of the meal, with dark and secret wounds.

Thirstily–O horror!–they lick up its blood; eagerly they divide its limbs. By this victim they are pledged together; with this consciousness of wickedness they are covenanted to mutual silence. Such sacred rites as these are more foul than any sacrileges. And of their banqueting it is well known all men speak of it everywhere; even the speech of our Cirtensian testifies to it. On a solemn day they assemble at the feast, with all their children, sisters, mothers, people of every sex and of every age. There, after much feasting, when the fellowship has grown warm, and the fervour of incestuous lust has grown hot with drunkenness, a dog that has been tied to the chandelier is provoked, by throwing a small piece of offal beyond the length of a line by which he is bound, to rush and spring; and thus the conscious light being overturned and extinguished in the shameless darkness, the connections of abominable lust involve them in the uncertainty of fate. Although not all in fact, yet in consciousness all are alike incestuous, since by the desire of all of them everything is sought for which can happen in the act of each individual.”[7]

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.

 

[1] http://www.vatican.va/archive/ENG0015/_P29.HTM

[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. http://www.newadvent.org/cathen/02109a.htm

[5] Patrick Healy, “Marcus Aurelius Antoninus,” In The Catholic Encyclopedia. Vol. 2. (New York: Robert Appleton Company, 1907), accessed July 23, 2018. http://www.newadvent.org/cathen/02109a.htm

[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,
http://www.earlychristianwritings.com/text/octavius.html

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; http://www.earlymoderntexts.com/assets/pdfs/leibniz1686d.pdf

[6] Peter Forrest, “The Identity of Indiscernibles,” in The Stanford Encyclopedia of Philosophy ed. Edward N. Zalta, (Winter 2016 Edition); https://plato.stanford.edu/entries/identity-indiscernible/

[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. http://home.sandiego.edu/~baber/analytic/blacksballs.pdf

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. http://www.logicmuseum.com/authors/aquinas/summa/Summa-IIb-101-113.htm#q110a1arg1

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).
5. If God exists in every possible world then his necessary essence is exemplified in every possible world.
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 http://alexanderpruss.blogspot.co.uk/2013/01/can-theorists-accept-principle-of.html

Some Problems With Degreed Existence

It was typical for the Medievals to speak of existence as a degreed concept (i.e., as the kind of thing which comes in greater or lesser degrees). Modern philosophers generally balk at this suggestion, insisting instead that a thing either exists, or does not exist, but that it makes no sense to speak in terms of degrees of existence. It is, of course, possible to adopt that bivalent view with respect to the truth conditions for statements like “x exists”, but also indulge a way of speaking which uses ‘exists’ as a dyadic relation (e.g., “x exists more(/less) than y”). There are several ways in which one can try to make sense of this kind of talk, but I have often thought that the most appealing way was in terms of possible worlds. Suppose we say:

x exists more than y iff x populates more possible worlds than y.

This has seemed, to me, to be satisfying for a number of reasons. Obviously, it allows for the medieval convention, and it also obviously places God at the top of the hierarchy of being (and this without, as of yet, even broaching the topic of one’s theory of existence), which is what the Medievals (and I) ultimately want. At the same time, the modern philosopher is going to be hard-pressed to reject the analytic convention of speaking in terms of possible worlds, and it seems sensible to give ‘existence’ a stipulative qualified definition, for particular purposes, running along these lines. In addition, this modal definition of existence (as a degreed concept) plausibly subsumes several other candidate rationales for this kind of talk, including that ‘degreed existence’ measures immutability, contingency, et cetera.

However, perhaps there are some problems with this which I had previously glossed over. I don’t think much of the objection that existence isn’t a predicate, for a few reasons. First, the way in which the Medievals are using the term, here, is clearly predicatory, and idiosyncratic enough that they can help themselves to a specially stipulated (probably onto-theological) definition. Second, existence isn’t usually considered a first-order predicate, but there isn’t much of a problem considering it a second-order predicate. Third, there are systems on which existence really is a first-order predicate, such as Krypke’s quantified modal logic. These and other reasons incline me to dismiss such a facile (Kantian) objection. Nevertheless, there are some real problems here worth thinking about.

For one thing, the cardinal value of possible worlds with any y, so long as y exists in at least two possible worlds, seems to be ℵ₀.[1] It isn’t clear how one thing could exist in more possible worlds than that (I find it hard to imagine the argument for thinking that x exists in ℵ_n where n>0).

– Actually, here is an argument for this: Platonism is true (assumption), and not only natural numbers, but all the reals, are abstract objects. Therefore, there is an non-denumerable infinity of actual things, that infinity’s cardinal value being ℵ₁. Further, we can argue that mathematical functions are abstract objects, and since the set of all real functions in the interval 0 < X < 1 is the non-denumerable ℵ₂,[2] so too will be the number of actual things (given Platonism). In any case, I digress. –

Perhaps if x existed in all worlds where y existed, and also existed in worlds where y did not exist, we could justify retaining this convention (though we would have to give up Cantor’s notion of equivalence in terms of correspondence or, more precisely, bijection), but then there wouldn’t be a (very?) smooth gradation of being. Dream objects, for instance, would not be less real, or have less existence, than the material objects of the external world (consider that mental states are multi-realizable, so that for any mental state, a whole cacophony of physical states suffices to bring it about, even if, given some particular physical state, the mental state must come about – I assume this, here, just for the sake of argument). I had previously hoped that this problem was roughly analogous to the problem with measuring the ‘closeness’ of possible worlds to each other (when we talk about changing only a little bit of a world’s description, technically we are always talking about changing at least ℵ₀ propositions).[3] If the problems were analogous, then their solutions were likely to be analogous, and I was (and remain) supremely confident that there must be a solution to the latter. However, we can apparently solve the latter problem by talking about first-order propositions directly about states of affairs in that world (at least plausibly, there are finitely many of these). That solution doesn’t translate well, as far as I can tell, into a solution for the first problem, so that the problems don’t seem analogous enough to have analogous solutions.

Another problem is that seemingly insignificant beings like atoms are going to be more real (in the sense of having higher/greater existence) than plants, and so human beings have less existence than mosquitoes. The Medievals would not have been thrilled. For them, plausibly, a thing exists to the extent that it succeeds in resembling God.

There is a possible reductio here as well; if some things have more existence than others by the modal measure suggested, then we might wonder whether we can license speech about some things having more unreality than others? Suppose we accept talk of impossible worlds, and suppose we then accept talk of really-impossible worlds. To get an idea what this would look like, refer to Pruss here. Well, then it looks like some things don’t merely not-exist, but some really don’t exist, and they don’t exist even more than other non-existent things.

Not all of these problems are equally troubling, but they are worth taking inventory of regardless. I think the attempted reductio ad absurdum at the end is pretty weak. We can just deny that there are really impossible worlds, or even deny that there really are impossible worlds. In any case, we can just exclude such considerations by fiat, since stipulative definitions can be constrained however we see fit, so we can just constrain the stipulative definition of ‘[degreed] existence’ so as to ignore such puzzles. Still, not all of these are so easy to dismiss. I won’t flesh this out here, but these considerations lead me to suspect that the best way to give an account of ‘degreed existence’ (in the sense the Medievals want to indulge talk about) may be with reference to a well worked out theory of existence after all.

[1] Is this true? Maybe not – maybe there is some y such that y exists only in two (or, in any case, in some finite number of) possible worlds. I have trouble imagining what this would be, but, in any case, for nearly any conceivable y, it will turn out to be true that there are ℵ₀ possible worlds containing it.

[2] William Lane Craig, The Kalam Cosmological Argument, (Oregon, Wipf and Stock publishers, 1979), 80.

[3] Technically, we are changing even more propositions than this. It is widely agreed now that there is no set of all true propositions. Taking the power-set 𝔓(W) of all propositions true at possible world W, you can generate infinitely more propositions, and this actually changes the cardinality of the number of true propositions from ℵ₀ to ℵ₁, the latter of which is a non-denumerable infinity. The process can be repeated indefinitely, leaving us with an indefinitely large set, and there is no way to deal with indefinitely large sets in set theory.

When Absence of Evidence is Evidence of Absence

There is a popular and catchy saying which I myself have been caught repeating in the past, but which, for all its intuitive appeal, is false; namely, that the absence of evidence isn’t evidence of absence. Many a new-atheist has repeated the mantra that there is no evidence for God’s existence, insinuating thereby that this absence of evidence is good evidence for atheism. William Lane Craig, a noted philosopher, theologian and tireless Christian apologist has responded as follows:

“[Atheists] insist that it is precisely the absence of evidence for theism that justifies their claim that God does not exist. The problem with such a position is captured neatly by the aphorism, beloved of forensic scientists, that “absence of evidence is not evidence of absence.” The absence of evidence is evidence of absence only in cases in which, were the postulated entity to exist, we should expect to have more evidence of its existence than we do.”¹

He has reiterated as much more informally (but more elaborately) on his podcast, ReasonableFaith, where he says:

“The absence of evidence will count as evidence of absence when if the thing existed, then having surveyed the grounds, so to speak, we would expect to see evidence of their existence, and we don’t see it. And so, for example, in the case of fairies, if they existed then we ought to be able to find traces of their existence – their dead bodies when they die, their carcasses, other sorts of remains, little clothing factories where they build their clothes, and we ought to detect them flying about just as we detect dragon flies and bumblebees – but we don’t. So this would be a case where I think the absence of evidence would count as evidence of absence.”²

On this view, the absence of evidence only counts as evidence of absence when we have some reason to expect to see the evidence ex hypothesi. This has enormous intuitive appeal; consider the hypothesis that there is at least one tiger in India. Can the fact that I, sitting in Canada, currently see no tiger really count as evidence that there is not at least one tiger in India? Surely not; presumably because that evidence isn’t expected on the assumption of the relevant hypothesis’ truth. Elliott Sober, reflecting on absence of evidence, notes that in the case of arguments from absence “it is easy to see how each can be turned into a valid argument by adding a premise. The arguments have the form:

I do not have any evidence that p is true.
p is false.

Just add the premise

(P1) If p were true, then I’d have evidence that p is true.”³

This further highlights the fact that it is natural for us to think that absence of evidence is evidence of absence only when we expect the evidence ex hypothesi.

For years I found this response intellectually satisfying, but in recent years I have come to think that it is woefully mistaken. It is true that my failure to observe a tiger in Canada provides no evidence against there being at least one tiger in India, but it is not because I wouldn’t have anticipated seeing a tiger in Canada given that there is at least one tiger in India. All my affection and respect for Craig notwithstanding, if Craig means that absence of evidence E for hypothesis H is only evidence of absence (i.e., not-H) when the probability of E on H is greater than 0.5, then he is, I think, incorrect. In what follows I will try to explain why, as well as explore what to me seem interesting corollaries of Bayesianism.⁴

John Hawthorne, speaking about probability theory and the fine-tuning argument at a conference back in 2015, warned:

“Human beings, even intelligent human beings, are terrible at reasoning about probabilities. There’s enormous empirical evidence that human beings are terrible at reasoning about probabilities, and so we have to proceed with care.”⁵

Playfully picking on (presumably) a student in the audience, Hawthorne says: “Justin gave us the kind of awesome sounding principle… [that] if you don’t see something then that can be evidence of its absence only if you expect that you would get evidence were the thing there.”⁶ Not the cleanest off the cuff articulation, but clearly Hawthorne had in mind the principle for which W.L. Craig advocates. He continues; “that’s wrong… and I can prove to you that it’s wrong.”⁷ He proceeds to give an illustration using a hypothetical creature he calls a Dynx, where he stipulates that 75% of Dynx are invisible to the naked eye, and the probability that there is a Dynx in a box placed before us is 50%. We open the box, and we see no Dynx. The probability that there is no Dynx given our background knowledge and this new piece of information (namely that we do not see any Dynx) is approximately 57%. You can satisfy this for yourself by simply dividing up the space of possibilities (i.e., ‘seeing a Dynx in the box,’ ‘not seeing the Dynx in the box,’ and ‘there being no Dynx in the box’), eliminating the possibility of ‘seeing a Dynx in the box,’ and then expressing your updated probability assessment accordingly. So, even though we ought not to expect to see a Dynx in the box if there is one in the box, our failure to observe one is still evidence for their being no Dynx. This simple illustration (and others like it) seems to be entirely compelling. What, then, is the genuinely Bayesian determination of evidence?

On the Bayesian theory of confirmation,⁸ some evidence E will count as evidence for some hypothesis H (given background knowledge B) just in case E (conjoined with B) raises the (prior) conditional probability of H. To put it more formally, E will count as evidence for H just in case: P(H|E&B)>P(H|B). However, [P(H|E&B)>P(H|B)]⊃[P(~H|~E&B)>P(~H|B)]. In other words, if E provides any evidence for H, then ~E provides some evidence against H. It needn’t, of course, be the case that E provides as much evidence for H as ~E does for ~H, but it strictly follows from Bayesianism itself that ~E would be evidence against H just in case E would be evidence for H.

To illustrate with an example, let us take a hypothesis H1: “that aliens exist,” and evidence E1: “I am being abducted by aliens.” Obviously P(H1|E1&B)>>P(H1|B). What is not so obvious is that P(H1|~E1&B)<P(H1|B). The reason it isn’t so obvious is that ~E1 provides negligible evidence for ~H1 (even though E1 would provide compelling evidence of H1). If aliens abduct me, that’s really good evidence that they exist. If aliens do not abduct me that’s really poor evidence that they don’t exist. It may be some evidence, but it isn’t very much evidence.

Not only can the absence of evidence be negligible evidence of absence while the presence of that evidence would be altogether compelling, but the absence of evidence can even be inscrutable evidence of absence while the presence of evidence is scrutable and enormously supportive of the hypothesis in question. Take the example of a miracle, and for simplicity let us use the miracle of the bodily resurrection of Jesus of Nazareth. The bodily resurrection of Jesus, if it did occur, would be relatively good evidence for God’s existence; P(G|R&B)>>P(G|B). However, if Jesus had not been raised from the dead, would that provide any evidence against God’s existence? According to Bayesianism it would, but it seems like it would be not only negligible evidence, but even inscrutable evidence. There is no way one could put a figure (with any justification) on how much more confident it should make us in atheism that some miracle, like Jesus’ resurrection, did not occur. If we could give any estimate of what the probability is that God would perform a miracle when called upon to do so, for instance, then we could make some predictions about how many hospitalized people with terminal diseases (according to medical diagnosis) under observation get better when prayed for. We can’t make these predictions not because there is no actual probability of God doing a miracle, but because we aren’t at an epistemic vantage point from which we can assess that probability with any level of confidence at all.

Further, the evidence may not be merely negligible, but can in special instances be literally infinitesimal (an infinitesimal is a non-zero infinitely small quantity). Consider Hempel’s paradox⁹ for a moment; any observation of a pink shoe provides some evidence for the hypothesis that all ravens are black. The hypothesis that all ravens are black is logically equivalent to the statement that all non-black things are non-ravens. It follows, therefore, that any observation of a black raven is evidence that all non-black things are non-ravens, and any observation of a non-black non-raven is evidence that all ravens are black. An observation can’t be evidence for one without being evidence for the other precisely because they are logically equivalent statements, at least interpreted at face value; this is just what Hempel called “the equivalence condition.”¹⁰ However, it seems as though there are potentially infinitely many things which are non-black non-ravens which, at any moment, we will fail to observe. If this is so, then each of these instances of absence of evidence will count as instances of infinitesimal evidence of absence (or, at least, infinitely many of these instances will count as instances of infinitesimal evidence of absence). One thinks of the infinitely many miracles God could have performed at any given moment (e.g., growing a lost limb, bringing a dead child back to life, parting the Atlantic ocean); is it really the case that every instance of a miracle not happening provides some evidence against God’s existence? If so, and if there are infinitely many opportunities for God to perform a miracle of some kind (in infinitely many of which God decides to perform no miracle), does that not entail that the probability of theism is literally infinitesimal, or else that each instance (or, at least, infinitely many instances) of a non-miracle provides at most infinitesimal evidence against theism? This gets a little tricky, of course, because Bayesian theory isn’t really equipped to deal with cases of what we might call ‘transfinite probabilities,’¹¹ but if we take its implications seriously even in such cases we will plausibly think that at least some things provide literally infinitesimal evidence for a conclusion or hypothesis.

An interesting objection to this suggests that there is not, even potentially, an infinite number of unobserved observables. Given the limited bandwidth of the human body as a kind of measuring apparatus,¹² there may be infinitely many different but observationally indistinguishable events. Imagine, for instance, two pairs of pink shoes whose colours or sizes differ by so little as to make it impossible for any human being to tell the difference between them. For any of the attributes assessed by the five senses, there will be limited empirical bandwidth given the human body as a tool of observation. What this seems to entail is that there is not a potentially infinite number of different possible observations, in which case we needn’t concede the absurdity of infinitesimal probabilities. This objection is appreciably practical, but I’m not entirely confident that it settles the matter. After all, I can imagine a human being with “electron-microscope eyes”¹³ or with any number of other physical alterations which would allow them to observe an apparently potentially infinite number of different events. For any such alteration, I can imagine God miraculously bringing it about that observer S has precisely the alterations necessary to observe some miracle M₁ which would have previously been indistinguishable from miracle M₂, but is not now indistinguishable from M₂ for S. Moreover, I’m not convinced that observational indistinguishability is terribly relevant; there are infinitely many possible pink shoes which I could now be observing, but am not, and even if infinitely many of them would be indistinguishable to me, failing to observe any one provides some evidence against the hypothesis that all ravens are black. So it seems to me that we’re stuck with conceding that at least some things provide literally infinitesimal evidence.

In summary, I think we have seen why the absence of evidence is evidence of absence in all cases except those in which the presence of so-called evidence would do nothing to raise the conditional probability of the hypothesis in question. Thus, my failing to observe a tiger in Canada provides no evidence against the hypothesis that there is at least one tiger in India not because I wouldn’t expect that evidence if there were at least one tiger in India, but because even if I were observing a tiger in Canada it would provide no evidence that there is at least one tiger in India.¹⁴ We have also seen that even when absence of evidence is negligible evidence of absence, or inscrutable evidence of absence, or infinitesimal evidence of absence (or any combination of those three), it will still provide some evidence of absence; if E would have been evidence for H, then the absence of E provides evidence against H.

Post Scriptum: I want to thank Tim Blais, Cale Nearing and Sean Boivin who provided me, in discussions subsequent to the original article, with food for thought without which I would never have made the improvements I have lately introduced above.

1 William Lane Craig, “Theistic Critiques of Atheism” The Cambridge Companion to Atheism. Edited by Michael Martin (Cambridge University Press, 2006): 70.

2 http://www.reasonablefaith.org/objections-to-belief-in-god

3 Elliott Sober, “Absence of Evidence and Evidence of Absence: Evidential Transitivity in Connection with Fossils, Fishing, Fine-Tuning, and Firing Squads,” in Philosophical Studies 143, no. 1 (2009): 64.

4 As a cautionary caveat lector; though I’m pretty confident that what I’m about to say is correct, I have not taken any class on probability theory (yet); if anyone thinks there’s some subtle mistake somewhere, they are encouraged to share it. I am more than open to updating my views.

5 https://youtu.be/3Gl_w1yMgCg?t=16m40s

6 https://youtu.be/3Gl_w1yMgCg?t=20m35s

7 https://youtu.be/3Gl_w1yMgCg?t=20m35s

8 Elliott Sober, “Absence of Evidence and Evidence of Absence: Evidential Transitivity in Connection with Fossils, Fishing, Fine-Tuning, and Firing Squads,” in Philosophical Studies 143, no. 1 (2009): 66.

9 James Fetzer, “Carl Hempel,” in The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta, (Spring 2017 Edition), accessed April 2, 2017. https://plato.stanford.edu/archives/spr2017/entries/hempel/

10 James Fetzer, “Carl Hempel,” in The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta, (Spring 2017 Edition), accessed April 2, 2017. https://plato.stanford.edu/archives/spr2017/entries/hempel/

11 If one dislikes this term because they think that probabilities can be no higher than 1, which makes them finite, I would suggest they think about how the conditions I just stipulated could imply that some hypothesis H is infinitely likely without having probability 1. However, if that doesn’t mollify the critic, I could agree to change the term to ‘non-finite’ probabilities.

12 I borrow here from Bas C. van Fraassen, who notes insightfully that “the human organism is, from the point of view of physics, a certain kind of measuring apparatus.” See: Bas C. van Fraassen, The Scientific Image, (Oxford: Clarendon Press, 1980), 17. 

13 Bas C. van Fraassen, The Scientific Image, (Oxford: Clarendon Press, 1980), 17.

14 If one thinks that observing a tiger somewhere raises the conditional probability that one may be observed anywhere then one will reject this conclusion, but they needn’t, in so doing, reject the principle this example is being employed to illustrate.