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

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

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

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

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

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

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


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

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

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

An Amended Modal-Epistemic Argument for God’s Existence

Several years ago I was introduced to a clever and fascinating argument, developed by a philosopher named Emanuel Rutten, which attempts to demonstrate the existence of God from two key premises: (i) that anything which is possibly true is possibly known, and (ii) that it is not possible to know that God does not exist, from which it logically follows that (iii) God exists. The argument has some intuitive appeal to me, though I was initially skeptical about the second premise (skeptical, that is, that the atheist could be persuaded to accept the second premise). I had also heard certain criticisms of the argument which seemed to present nearly insuperable objections to it; although I started working on responses to those objections, I eventually moved on to other philosophical inquiries leaving this argument (and my many notes on it) to gather proverbial dust on my old hard drive. Recently, however, I decided to revisit the argument and use a variation on it in the context of a semi-formal online debate. I was shocked by my interlocutor’s reaction; although he had not been shy about sinking his teeth into every other argument I had presented for theism (from the cosmological argument from contingency, to the transcendental argument from the laws of logic, to a version of the moral argument, to the modal-ontological argument), I received radio-silence when presenting this argument. After several days of him reflecting upon the argument, he eventually rejoined by saying that he couldn’t think of a single criticism, but that he was convinced the argument was bad for some reason he was unable to articulate. This made me want to revisit the modal-epistemic argument for God’s existence and see if it couldn’t be salvaged in light of certain criticisms of which I am aware.

The basic intuition behind Rutten’s argument is that reality’s being intelligible is somehow connected to, and explained by, the existence of a God-like being. This same intuition seems to lurk behind Bernard Lonergan’s argument for God in the nineteenth chapter of his magnum opus, Insight, where he made the tantalizing claim (for which he argued at great length) that “if the real is completely intelligible, God exists. But the real is completely intelligible. Therefore, God exists.”1 There is also a subliminal connection here, I think, even to C.S. Lewis’ argument from reason. The same intuition is also bolstered, to some extent, by Fitch’s paradox, which is a logical proof developed by the philosopher and logician Frederic Fitch in 1963. Fitch was able to prove, using prima facie uncontroversial assumptions, that “necessarily, if all truths are knowable in principle then all truths are in fact known.”2 This philosophical finding was taken to be paradoxical by many, but it sits exceptionally well with the theist who affirms that omniscience is exemplified by God. What these observations show, I think, is that the intuition behind Rutten’s argument is widely shared (at least among theists) and may be well motivated.

The bare-boned sketch of Rutten’s argument can be outlined as follows:

  1. All possible truths are possibly known (i.e., if there are logically possible worlds in which P is true, then there will always be a subset of such worlds in which P is known).
  2. It is impossible to know that God does not exist.
  3. Therefore, God necessarily exists.

It has to be said straight-away that this is an over-simplified formulation of his argument; we will come, in due course, to his more measured articulation of the argument, but the rough sketch provided by this syllogism will help us lay the groundwork for the actual argument.

Rutten stipulates the following relatively modest definition of God, for the purposes of his argument; God is the personal first-cause of the world (where the world is the whole of contingent reality). Since that logically implies that God is incontingent, I will abbreviate this as ‘IPFC.’ He also specifies that, for the purposes of the argument, he means the following by knowledge: “A conscious being… knows that proposition p is true if and only if p is true and the being, given its cognitive situation, cannot psychologically but believe that p is true.”3 More precisely, for any P, if some conscious being B cannot psychologically help believing that P is true, then P satisfies at least one of the following four conditions for B: “(i) The proposition is logically proven; (ii) the proposition is obviously true, i.e. intuitively self-evident; (iii) the proposition is grounded in indisputable experience; or (iv) the proposition is based on indisputable testimony.”4 This makes it obvious that Rutten means that something is known if and only if (a) it is true, and (b) given some conscious being’s cognitive situation, that being, whose cognitive faculties aren’t malfunctioning, cannot psychologically help believing that it is true. In what follows I will refer to this peculiar kind of knowledge as knowledge*, instances of knowing satisfying these conditions as knowing*, et cetera.

The first premise seems to flow directly out of the perennial philosophical commitment to the world’s intelligibility. Arguably, to be intelligible the world has to be the kind of thing which is knowable* in principle (if not always to us, due to some limitations of our cognitive faculties, then at least to some logically possible intellects with different cognitive faculties). This philosophical presumption has, Rutten hastens to note, “led to extraordinary discoveries”5 in science. In fact, it seems to be a fundamental pillar of science itself, for science is predicated on the assumption of the world’s intelligibility. The second premise also seems prima facie plausible; it is, somewhat ironically, appealed to confidently by many agnostics and some atheists.

The argument is, in its rough form, susceptible to a myriad of informative objections. Consider, for instance, the possibly true proposition: “God understands my reasons for being an atheist.”6 The proposition, although plausibly possibly true, is not knowable – for knowledge requires belief, but no atheist can believe the proposition. Similarly the proposition “there are no conscious beings”7 may be possibly true but is also not rationally believable. To avoid these kinds of counter-examples Rutten stipulates that his first premise should only quantify over rationally believable propositions. He thinks it is reasonable to exclude rationally unbelievable propositions, and that this way of restricting his first premise is not ad hoc, for it seems intuitively plausible that all rationally believable possible truths are knowable. Requiring the propositions of the relevant sort to be both (possibly) true and rationally believable navigates the argument away from obvious counter-examples. There are other counter-examples, however, and Rutten discusses some. First, consider a proposition like “‘John left Amsterdam and nobody knows it.’”8 This seems possibly true and obviously unknowable, even though it could be argued to be rationally believable. To deal with objections like this Rutten introduces a distinction between first-order propositions and second-order propositions; first-order propositions, he says, are directly about the world, whereas second-order propositions are about people’s beliefs about the world. Rutten then decides to limit the first premise of his argument to truths expressed by first-order propositions. In this way he blocks cute objections from propositions like ‘there are no believed propositions.’

Then he states his argument9 more formally in the following way (I have changed the wording very little, and added nothing of consequence):

1. If a rationally believable first order proposition is possibly true, then it is knowable* (first premise),
2. The proposition ‘IPFC does not exist’ is unknowable* (second premise),
3. The proposition ‘IPFC does not exist’ is rationally believable (third premise) ,
4. The proposition ‘IPFC does not exist’ is first order (fourth premise),
5. The proposition ‘IPFC does not exist’ is not possibly true (from 1, 2, 3 and 4),
6. The proposition ‘IPFC does not exist’ is necessarily false (from 5),
7. The proposition ‘IPFC exists’ is necessarily true (conclusion, from 6).

The third premise is either true, or else atheism is irrational. The fourth premise is self-evidently true. The fifth premise follows logically from 1,2,3 and 4. Six follows logically from five. Seven follows logically from six. So the key premises are 1 and 2. The first premise is very plausible insofar as its negation would imply that reality is not intelligible, but to deny that reality is intelligible seems absurd. That reality is intelligible (if not to us then at least in principle) seems to be a fundamental commitment of epistemology. However, if reality is intelligible, then for any first-order rationally believable proposition P, if P is possible then P is possibly known*. Can we know this premise in the strong sense of knowledge used within the argument? Maybe (e.g., perhaps it is obviously true, i.e. intuitively self-evident), but that’s also irrelevant; all we need is to ‘know’ it in the more general sense (i.e., having a true justified belief – allowing for whatever epistemology you’d like to use in order to qualify ‘justified’) in order to know (as opposed to know*) that the conclusion is true. 

The second premise is plausible given that, for the purposes of the argument, ‘knowledge’ is defined as satisfied just in case at least one of the four stipulated conditions are satisfied. However, God’s non-existence cannot be logically proven (if it can, then obviously this and all other arguments for God’s existence are worthless). On atheism, the proposition that God does not exist is not self-evidently true. On atheism, the proposition ‘God does not exist’ cannot be grounded in indisputable experience. On atheism, the proposition ‘God does not exist’ cannot be believed on the basis of indisputable testimony. It follows that the second premise is true. So, the argument looks sound, at least at first blush.

One immediate reaction to this argument is to suggest that it can be parodied by a parallel argument for atheism by substituting the second premise for: 2.* The proposition “God exists” is unknowable*. However, this is naïve; in at least one possible world in which God exists, plausibly God knows* that the IPFC (i.e., himself) exists, but in no possible world where no IPFC exists can anyone know* that no IPFC exists. As Rutten explains:“on the specific notion of knowledge used for the argument… logical proof, intuition, experience and testimony exhaust the range of knowledge sources, and none of them suffices to know that God does not exist.”10

Years ago now I heard one very interesting objection which I will try to reproduce as fairly as my memory and skill will allow. The objection basically maintains that if God could know* that the IPFC (i.e., God) exists, then it is possible for at least one atheist in at least one logically possible world to know* that the IPFC does not exist. Rutten suggests, in the paper, that “God’s knowledge that he is God – if possible – is an instance of (iii) (or (ii)),”11 meaning that it is either “obviously true, i.e. intuitively self-evident; [or]… grounded in indisputable experience.”12 But what experience could possibly establish the indubitability of being the IPFC? For any experience you can imagine having (if you were God), it seems logically possible that it is the result of an even greater being who created you with the purpose of deceiving you into thinking that you are the IPFC. What about intuitive self-evidence? Well, if it is possible for God to simply look inward and, through introspection, discover his relations (for, to be the IPFC is to bear certain relational properties, such as that of being first-cause), then why can’t there be a logically possible world in which an atheist introspects and discovers that she lacks any relation to an IPFC? If it is logically possible for the IPFC to introspectively survey its own relational properties, then why can’t a logically possible atheist do the same?

I think the best answer to this is to note that it may be possible to introspectively discover at least some of one’s essential properties (as opposed to merely accidental properties). I can know, by rational reflection, that I exist (cogito ergo sum), that I am a thinking thing, that I am either contingent or not omniscient, et cetera. I can also deduce from what I discover as self-evident through introspection that other facts happen to be true, such as that there exists something rather than nothing. So, coming back to God, perhaps God can know by introspection that he is incontingent, personal, and has some uniqualizing properties13 (that is, properties which, if had at all, are had by no more than one thing) etc. – and perhaps that means that he can deduce that he is the only being which could be an IPFC in principle, and that he is an IPFC just in case a contingent world exists. But, he could plausibly know* from indisputable experience (of some sort) that a contingent world exists. Therefore, he could deduce and know* that he is the IPFC. If atheism were true, no being would have, as an essential property, a lack of any relation to an IPFC. Lacking a relation cannot be an essential property, so there’s no reason to think it could be introspectively discovered that one lacks a relational property to the IPFC. Moreover, unless the atheist can actually produce (perhaps with the aid of premises introspectively discovered as self-evident) a logical proof that the IPFC does not exist it seems they cannot know* that no IPFC exists. So while this objection is extremely interesting, I do think that it fails; it is reasonable to maintain that, possibly, God knows* that the IPFC exists, and it does not plausibly follow that an atheist possibly knows* that no IPFC exists.

Another objection might come from considering large facts. Take, for instance, what Pruss has called the Big Conjunctive Contingent Fact (BCCF),14 and let’s take the sub-set of that fact which includes only first-order, rationally affirmable facts (for simplicity, I will abbreviate this as the BCCF*). The BCCF* is plausibly comprised of infinitely many conjuncts, and at least is possibly comprised of infinitely many conjuncts. Is this possible truth, the BCCF*, possibly known? I think it is possible so long as there is possibly a being with an infinite capacity for knowledge (or else, perhaps, an actually infinite number of beings with some finite capacity for knowledge not all of which are such that a discrete set of first-order rationally affirmable truths would have been beyond its ken). But, assuming there cannot be an actually infinite number of beings, doesn’t that presuppose something like theism, by presupposing the possible exemplification of omniscience (here we assume that BCCF*⊃BCCF, and that any being which knows the BCCF* also knows all analytic truths)? After all, the Bekenstein bound15 is generally taken to imply “that a Turing Machine with finite physical dimensions and unbounded memory is not physically possible.”16 However, it seems senseless to suggest that there could be a physical object (like a brain, or some other kind of computer) which is actually infinitely large. Therefore, doesn’t the first premise presuppose something like theism insofar as it presupposes the exemplifiability of omniscience or at least an intellect with an actually infinite capacity for knowledge? That would make the argument ostensibly circular.

First, the IPFC needn’t be omniscient even if it knew the BCCF*. Second, and more importantly, the IPFC isn’t being presupposed to be omniscient, or even knowledgeable enough to know the BCCF*. Third, a being’s being omniscient is necessary but insufficient for the truth of theism. Fourth, I’m not sure whether it is senseless to talk about infinitely large physical objects, or (actually) infinitely many beings, but I am relatively sure that most atheists have a vested interest in allowing for those kinds of possibilities in order to avoid conceding important premises in some (Kalaam) cosmological arguments. So this attempted charge of subtle circularity seems wrong.

[I should grant this this last objection could be accused of being a straw man erected by none other than myself; to that I just briefly want to say that I had originally thought that there may be an objection here, but as I tried to write the objection down clearly it seemed to crumble in my hands. Having already written it out, and having found it interesting to reflect upon it whether or not it is a viable objection at all, I decided to keep it in this final draft.]

I’m sure there are other possible objections which I would have been better able to iterate or anticipate had I done so years ago when this argument, and some objections to it, were still fresh in my mind. However, my sense is that that will do for an introduction to the argument. What makes this argument really exciting, I think, is that it, as Rutten notes, “does not fall within one of the traditional categories of arguments for the existence of God. For it is not ontological, cosmological or teleological. And it is not phenomenological either, such as for example the aesthetic or moral argument[s] for God’s existence.”17 The argument, whether sound or unsound, is doing something genuinely novel, at least for the analytic tradition of the philosophy of religion.

Rutten ends his short paper on an optimistic note which may be appropriately appended here, and this is where I will end my short excursus:

As I mentioned in the introduction, I propose to refer to the argument as a modal-epistemic argument. Ways to further improve it may be found, just as has been done with arguments in the other categories. I believe that if this happens, the prospects for the argument are rather promising.”18

1 Bernard Lonergan, Insight: A Study of Human Understanding, Collected Works of Bernard Lonergan, vol. 3, ed. Frederick E. Crowe and Robert M. Doran (Toronto: Toronto University Press, 1992), 695.

2 Brogaard, Berit and Salerno, Joe, “Fitch’s Paradox of Knowability”, The Stanford Encyclopedia of Philosophy (Winter 2013 Edition), Edward N. Zalta (ed.), URL = <;.

3 Emanuel Rutten, “A Modal-Epistemic Argument for the Existence of God.” Faith and Philosophy (2014), 3.

4 Emanuel Rutten, “A Modal-Epistemic Argument for the Existence of God.” Faith and Philosophy (2014), 4.

5 Emanuel Rutten, “A Modal-Epistemic Argument for the Existence of God.” Faith and Philosophy (2014), 14.

6 Emanuel Rutten, “A Modal-Epistemic Argument for the Existence of God.” Faith and Philosophy (2014), 7.

7 Emanuel Rutten, “A Modal-Epistemic Argument for the Existence of God.” Faith and Philosophy (2014), 8.

8 Emanuel Rutten, “A Modal-Epistemic Argument for the Existence of God.” Faith and Philosophy (2014), 9.

9 Emanuel Rutten, “A Modal-Epistemic Argument for the Existence of God.” Faith and Philosophy (2014), 10-11.

10 Emanuel Rutten, “A Modal-Epistemic Argument for the Existence of God.” Faith and Philosophy (2014), 2.

11 Emanuel Rutten, “A Modal-Epistemic Argument for the Existence of God.” Faith and Philosophy (2014), 5.

12 Emanuel Rutten, “A Modal-Epistemic Argument for the Existence of God.” Faith and Philosophy (2014), 4.

13 Alexander R. Pruss, “A Gödelian Ontological Argument Improved Even More.” Ontological Proofs Today 50 (2012): 204.

14 Alexander R. Pruss, “The Leibnizian cosmological argument.” The Blackwell Companion to Natural Theology, ed. W.L. Craig and J.P. Moreland (2009): 24-100.

15 See: “Bekenstein Bound,” Wikipedia, accessed March 24,2017.

16“Bekenstein Bound,” Wikipedia, accessed March 24,2017.

17 Emanuel Rutten, “A Modal-Epistemic Argument for the Existence of God.” Faith and Philosophy (2014), 28.

18 Emanuel Rutten, “A Modal-Epistemic Argument for the Existence of God.” Faith and Philosophy (2014), 28.

Three Trinitarian Theses

Abstract: In this paper I will try to argue that (i) the Trinity is a logically coherent and metaphysically possible way God could be, (ii) that the Trinity, if true, is a great-making feature of God, and (iii) that we can know that the Trinity is true.

St. Anselm classically maintained that God is “that than which nothing greater can be signified,”[1] and the method of perfect being theology, which takes its cue from Anselm, commits one to the view that the word God just means the same thing as Anselm’s famous definition. This definition makes the attribution of the classical ‘omni-’ properties natural, and although varieties exist among ‘Anselmian’ theists on the question of what properties like ‘omnipotence’ and ‘omniscience’ really amount to, this provides the common ground on which these theists stand. The Christian, however, stands out among theists of this variety by making a claim unique to, and distinctive of, Christianity. God, according to the Christian tradition, is a trinity of persons. He is Father, Son, and Holy Spirit, and yet, although He is three co-equal divine persons, “they are not Three Gods, but One God.”[2] There are three challenges which face the Christian theist here, and I aim to address them in turn. First, there is the challenge of addressing how this admittedly “odd arithmetic”[3] is not incoherent, and, therefore, conceptually possible. Second, there is the challenge of showing that the doctrine of the Trinity is, in fact, metaphysically possible. Finally, there is the challenge of showing that the Trinity would, if true, contribute in some way to God’s greatness.

Turning first to the problem of logical coherence, we should observe at the outset that logical coherence is not an altogether well-defined concept. For the purposes of this paper I will take a proposition to be logically coherent if and only if it is conceptually possible, where conceptual possibility means something like ‘involving no prima facie a priori contradiction.’ Conceptual possibility is “closely connected with consistency,”[4] and some thinkers, like Anthony C. Anderson, have elaborated it as being independent of “conceivability, semantical rules, definition, stipulation, or epistemic notions such as provability or deducibility.”[5] The doctrine of the Trinity, then, will count as conceptually possible just in case it presents no contradiction in itself.

It is tempting to think of this species of modality as being somewhere in between metaphysical possibility and merely physical possibility. There are problems with such a characterization, however, for it is not clear that all physical possibilities are either metaphysically or conceptually possible, and it is clear that not all conceptual possibilities are metaphysically possible. For instance, one might maintain that in ontological arguments both for and against the existence of God, the possibility premises are conceptually possible whether or not they are metaphysically possible (surely at least one of them is not). Moreover, if physical possibility is determined by our best scientific theories, and if theories are deemed scientifically better or worse based only on how well they satisfy certain empirical desideratum (like predictive power, explanatory scope, etc.), then it could well be that some scientific theory which is singularly better than its competitors makes claims about the world which are metaphysically and conceptually impossible. One thinks of the way the ‘Schrödinger’s cat’ thought experiment would suggest, interpreted as literally true, that outright contradictions obtain. Moreover, suppose that the infamous ‘principle of sufficient reason’ (henceforth PSR) is true, and that the Copenhagen interpretation of quantum mechanics is our best scientific theory of quantum mechanics. Technically the Copenhagen interpretation of quantum mechanics is not incompatible with the PSR,[6] but the story about quantum mechanics it offers, if taken literally, really is irreconcilable with the PSR, for it suggests that there are entirely indeterminate events for which no sufficient reason exists.

Why, one might ask, should we even care whether the Trinity is conceptually possible if it can be metaphysically possible either way? First, it seems that conceptual coherence is a necessary condition of sensibly affirming anything, and surely the Christian wants to affirm sensibly that the Trinity is true. Second, although a proposition’s conceptual possibility does not imply its metaphysical possibility, a proposition’s conceptual impossibility does imply its metaphysical impossibility, for the law of non-contradiction is not only a law of conceptual modality, but of metaphysical modality as well. How is one to demonstrate that there is no contradiction in the paradoxical assertion that God is three in one? The answer, of course, is ‘by making distinctions.’ God, according to the Trinitarian, is not one x and three x, but is one x and three y (where ‘x’ and ‘y’ stand in place of the predicates ‘being’ and ‘persons’ respectively). Since the doctrine clearly distinguishes the predicates ‘being’ and ‘person,’ it avoids being narrowly logically impossible,[7] and also provides a clue as to how the doctrine is supposed to be understood.

Having established the conceptual possibility of the doctrine of the Trinity, we move on to the much more difficult problem of demonstrating the metaphysical possibility of the Trinity, to which there are at least three contemporary approaches. I will briefly examine these three, argue that two of them seem viable, and that at least one of them demonstrates that the doctrine of the Trinity is metaphysically possible. Although I will take the time to briefly examine three strategies, there are really “two main strategies for solving the problem: the Relative-Identity strategy, and the Social Trinitarian strategy.”[8]

The Social Trinitarian (ST) strategy finds its impetus in some of the early Church Fathers, including Hilary of Poitiers who writes that ““each divine person is in the Unity, yet no person is the one God (On the Trinity 7.2; cf. 7.13, 32).”[9] In modern times such an approach has been prescribed and encouraged by Richard Swinburne, as well as William Lane Craig. This way of thinking about the Trinity takes the Threeness of God to be primitive, and attempts to explain how God could be one (rather than taking God’s oneness to be primitive and attempting to explain how God could be three persons). Attractive analogies for the Trinity abound on this view, and one, from W.L. Craig, is particularly worthy of examination. He writes;

 “In Greco-Roman mythology there is said to stand guarding the gates of Hades a three-headed dog named Cerberus. We may suppose that Cerberus has three brains and therefore three distinct states of consciousness of whatever it is like to be a dog… He has three consciousnesses. We can even assign proper names to each of them: Rover, Bowser, and Spike… Despite the diversity of his mental states, Cerberus is clearly one dog.”[10]

Those less familiar with Greco-Roman mythology than pop culture can replace ‘Cerberus’ with ‘Fluffy,’ the three headed dog from the Harry Potter novels. This analogy has among its benefits the ability to apparently make comprehensible a prima facie incomprehensible doctrine. It has the added advantage of providing a beautiful explanation of how the Trinity is a great-making property, for on this view the Trinity implies that God is a community of persons, and thus that God can be love.[11]

Unfortunately this ST is riddled with severe problems. It makes a mess of many of the divine attributes, such as omnipotence; questions such as whether all three persons are omnipotent, or whether the community of three is omnipotent, (etc.) arise.[12] The most profound problem, however, is that ST seems to imply polytheism, or at least has no principled way of telling polytheism apart from monotheism. Thus, the “Social Trinitarian claim that there are three minds in the Trinity,”[13] threatens to imply a subtle form of polytheism, where the divine nature is a genus, and the persons are each individual specimens belonging to the same species. They each token the divine nature, but remain distinct non-identical beings sharing in that same nature in precisely the same way as three (or more) human beings token, and share in, the same human nature. Indeed, it implies “that the old testament prophets who thundered that God is one (and whose monotheism Christians inherit) meant only that pagans preached a few too many divine beings, and did not know how alike, akin, and in accord all divine beings truly are.”[14]

A second broad approach is to begin by taking as given that God is exactly one being, and that, although the persons are each identical with God, they are not identical with each other, so that the identity relation is not altogether transitive. Although this violates Leibniz’ famous law of the identity of indiscernibles, problems for such a view of identity have already been alternatively motivated. For example, Max Black famously refuted the principle by rhetorically asking: “isn’t it logically possible that the universe should have contained nothing but two exactly similar spheres?”[15] Alternative accounts of identity have therefore arisen, and some of them will allow for exactly the kind of apparently acrobatic-like maneuver that Christians want to make. Peter Geach has maintained, for instance, that identity statements should be cashed out in terms of the general form “x is the same F as y,”[16] and maintains that “x’s being the same F as y does not guarantee that x is indiscernible from y.”[17] On his view, it can turn out that “x is an F, y is an F, x is a G, y is a G, x is the same F as y, but x is not the same G as y.”[18] What is significant here is that such theories of identity are on the market, and that Geach’s own theory isn’t the only one, as thinkers such as Nicholas Griffin and Eddy Zemach[19] also advance theories of identity which, if even possibly true, logically imply that the Trinity is metaphysically possible.

A third solution to the Trinitarian paradox exists which Michael C. Rea and Jeffrey E. Brower insist is the “single most neglected solution to that problem in the contemporary literature.”[20] Brower and Rea attempt to draw on the analogy provided by Aristotelian metaphysics in order to elucidate how the Trinity can be understood; they ask us to imagine that we have before us “a bronze statue of the Greek goddess, Athena,”[21] and insist that, in the same material object, we would also have “the lump of bronze that constitutes it,”[22] with which the statue is not strictly identical. This analogy, and the way Aristotelian metaphysics entreats us to deal with such funny objects, carves out room for “an object a and an object b to be “one in number” – that is, numerically the same – without being strictly identical.”[23] According to Aristotle, things picked out as material entities are actually “hylomorphic compounds”[24] which are comprised of both matter and form. In this way, however, two non-identical substances might be numerically one by being instantiated by the same matter, such as “a fist and a hand.”[25] This relation between two substances bearing a relation of “accidental sameness”[26] is precisely the right analogy on which to conceive of the relation of the persons of the Trinity to the divine nature, according to Brower and Rea. On this analogy, “each person will then be a compound structure whose matter is the divine essence and whose form is one of the three distinctive Trinitarian properties.”[27]

Although this view seems to imply the existence of what Rea and Brower call ‘kooky objects’ such as “seated-Socrates… pale-Socrates, bald-Socrates, barefoot-Socrates, and so on,”[28] it remains an attractive and viable way of thinking about the Trinity which does justice to what the Christian monotheist wants to say. Moreover, it suggests that the Trinity, along with puzzles about accidental sameness, are “special instances of a broader counting problem,[29] which takes some of the sting out of the Trinitarian paradox.

Do such models demonstrate that the Trinity is metaphysically possible, or do they merely demonstrate that the Trinity is conceptually possible? I take it that insofar as these theories can be taken to describe coherent states of affairs (coherent, at least, to all appearances), they give us as solid a reason to think that the Trinity is metaphysically possible as any arguments for the metaphysical possibility of anything can. Thus, we can safely rest the case for the metaphysical possibility of the Trinity.

How, though, are we to make sense of the claim that this odd metaphysically possible scenario of God being exactly three distinct persons each identical with the same being is a great-making feature of God? The best answer to this question is that the Trinity makes intelligible the claim that God is love, and that God is not merely disposed to love (in potentiality) but is by His very nature loving (in act). As Williams put it;

“… love in the literal sense requires more than one person. So if God is love that love must involve the love of one person by another. And if creatures cannot be the only ones who are the object of God’s love, there must be a plurality of persons in the Godhead.”[30]

To the suggestion that God might love himself merely because he is the summum bonum seems incongruent with His nature as moral exemplar, for then he would be perfectly selfish, and also command of us that we be perfectly altruistic (which he exemplifies in Christ), but as St. Anselm writes “it seems inconsistent to enjoin a thing upon us which it is not proper for him to do himself.”[31]

Latent here is actually a cosmological argument for the Trinity which, as far as I know, has not yet been developed by anyone. Bonaventure famously offered four ‘proofs’ for the Trinity in his commentary on the sentences of Peter Lombard,[32] but the argument I have in mind does not figure into any of his four arguments. The argument goes:

  1. If God created the world then He had a rational motivation to do so.
  2. If God had a rational motivation to create the world then it must be an internal, rather than external, motivation (i.e., a motivation arising from his divine nature).
  3. None of the classical divine attributes (omniscience, omnipotence, omnibenevolence, etc.) provide a rational motivation to create the world.
  4. If there is a rational motivation for creating the world then it is love.
  5. If God creates the world out of love then God is love (divine simplicity).
  6. Love is always shared between at least two persons.
  7. Therefore, God is at least two persons.

Another version could go:

  1. If God created the world then He did so out of love – kenosis, a self-giving love.
  2. God did create the world.
  3. Therefore God did so out of love.
  4. If God created the world out of love then love must exist in God’s nature (not merely as a potentiality, but as actuality).
  5. Love (in actuality) is always shared between at least two persons.
  6. Therefore, God in his nature must be at least two persons.

Various other ways of making the same point could no doubt be thought up. The Trinity, from this perspective, becomes something more than a quaint and puzzling theological add-on to the doctrine of God, and instead provides a way to satisfy the PSR which other forms of monotheism simply do not succeed in doing. The Trinity provides a sufficient reason for God’s creative activity, whereas Unitarianism (here understood as the claim that God is one and only one person) seems incapable of giving a comparably good answer (if it can give any answer at all) to the question of why God created the world in the first place.

With respect to the question of whether one can come to know that the Trinity is a great-making property, it seems obvious that one can come to know this. First, even if one cannot clearly articulate why the Trinity adds to the greatness of God, one can come to know that the Trinity is a great-making property of God simply by knowing i) that all God’s essential attributes are great-making, and ii) that an essential attribute of God is that He is a Trinity of divine persons. One can know the former analytically, for it is a tautological truth if one accepts that God just means maximally great being. One can know the latter if one knows the doctrine of the Trinity to be true, for instance by recognizing it to be the conclusion of a sound cosmological argument, or by having religious experiences which provide sufficient confirmation of this truth, or by having a properly basic belief in the truth of the Biblical testimony – or any number of other ways. However, suppose that one wanted more here – suppose one wanted to know why the Trinity increases the greatness of God; some progress can be made here in terms of noting that the doctrine of the Trinity allows God to be essentially loving, which seems like a great-making feature. The problem is that this could be satisfied just as well if God were four persons, or five persons, or infinitely many persons. Bonaventure provided arguments for thinking that the number of divine persons must be exactly three,[33] and so one could appeal to such arguments in combination with the insight that the Trinity allows God to be essentially loving in order to explain just how the Trinity could be a great-making feature. However, even apart from such an argument’s success, there is enough to justify the Christian in believing that the Trinity is a great-making feature of God.

From what has been said it should be clear that the Christian can claim, with due propriety, to know that the Trinity is both true, and a great-making feature of God. The justifications available for both of these (true) beliefs are many and powerful. One can also show that the doctrine of the Trinity is conceptually possible (i.e., involves no inconsistency), and is metaphysically possible. In fact, one can argue from the fact that we have good reason to think that a Christian can have a justified belief in the Trinity’s truth (quite independently from whether the Trinity is in fact true) that it must be metaphysically possible, for nobody can have a justified belief in a metaphysical impossibility. The relative-identity thesis, if viable, provides a way to make sense of the doctrine of the Trinity, and is independently motivated by puzzles plaguing Leibniz’ account of identity.[34] The solution offered by Brower and Rea is also a philosophically live and promising option open to the Christian theist which, if nothing else, helps to strengthen the reasonable conviction that the Trinity is metaphysically possible.



[1] Brian Davies, “Aquinas and Atheism,” The Oxford Handbook of Atheism (2013): 120.

[2] J. Sullivan, “The Athanasian Creed,” in The Catholic Encyclopedia. (New York: Robert Appleton Company: 1907). Retrieved November 17, 2015 from New Advent:

[3] Brian Leftow, “Anti-Social Trinitarianism,” in Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 52.

[4] Marcin Tkaczyk, “A Debate on God: Anselm, Aquinas and Scotus,” Ontological Proofs Today 50 (2012): 117-118.

[5] Anthony C. Anderson, “Conceptual Modality and the Ontological Argument,” in Ontological Proofs Today. Lancaster: Ontos Verlag (2012): 299.

[6] See Alexander R. Pruss, The Principle of Sufficient Reason: A Reassessment,” (Cambridge University Press, 2006): 160-170.

[7] Where by narrowly logically impossible I mean simply “amounts to a contradiction of the form ‘a is B and a is not-B’ where B is used univocally.”

[8] Jeffrey E. Brower, and Michael C. Rea, “Material Constitution and the Trinity,” Faith and Philosophy 22, no. 1 (2005): 57-76.

[9] William Lane Craig, “Toward a Tenable Social Trinitarianism,” Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 96-97.

[10] William Lane Craig, “Toward a Tenable Social Trinitarianism,” Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 98.

[11] 1 John 4:16.

[12] See Brian Leftow, “Anti-Social Trinitarianism,” in Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 62-66.

[13] Brian Leftow, “Anti-Social Trinitarianism,” in Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 60.

[14] Brian Leftow, “Anti-Social Trinitarianism,” in Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 73.

[15] Max Black, “The Identity of Indiscernibles,” Mind (1952): 156.

[16] Michael C. Rea, “Relative Identity and the Doctrine of the Trinity,” Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 252.

[17] Michael C. Rea, “Relative Identity and the Doctrine of the Trinity,” Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 252.

[18] Michael C. Rea, “Relative Identity and the Doctrine of the Trinity,” Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 252.

[19] Michael C. Rea, “Relative Identity and the Doctrine of the Trinity,” Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 252.

[20] Jeffrey E. Brower, and Michael C. Rea, “Material Constitution and the Trinity,” Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 269.

[21] Jeffrey E. Brower, and Michael C. Rea, “Material Constitution and the Trinity,” Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 263.

[22] Jeffrey E. Brower, and Michael C. Rea, “Material Constitution and the Trinity,” Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 263.

[23] Jeffrey E. Brower, and Michael C. Rea, “Material Constitution and the Trinity,” Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 263-4.

[24] Jeffrey E. Brower, and Michael C. Rea, “Material Constitution and the Trinity,” Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 267.

[25] Jeffrey E. Brower, and Michael C. Rea, “Material Constitution and the Trinity,” Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 271.

[26] Jeffrey E. Brower, and Michael C. Rea, “Material Constitution and the Trinity,” Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 269.

[27] Jeffrey E. Brower, and Michael C. Rea, “Material Constitution and the Trinity,” Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 269.

[28] Jeffrey E. Brower, and Michael C. Rea, “Material Constitution and the Trinity,” Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 268.

[29] Jeffrey E. Brower, and Michael C. Rea, “Material Constitution and the Trinity,” Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 280.

[30] C.J.F. Wiliams, “Neither Confounding the Persons nor Dividing the Substance,” in Reason and the Christian Religion (New York: Oxford University Press, 1994): 240. Cited from Brian Leftow, “Anti-Social Trinitarianism,” in Philosophical & Theological Essays on the Trinity edited by Thomas McCall and Michael C. Rea, (Oxford University Press, 2009): 54.

[31] St. Anselm, Cur Deus Homo, 203.

[32] St. Bonaventure of Bagnoregio, Commentaria In Librium Sententiarium, trans. The Franciscan Archive, (n.p.: The Franciscan Archive, 2010), compact disk.

[33] St. Bonaventure of Bagnoregio, Commentaria In Librium Sententiarium, trans. The Franciscan Archive, (n.p.: The Franciscan Archive, 2010), compact disk.

[34] One might think to ask whether a fist and a hand are really indiscernible, for they involve different forms.

Defending Propositional Omniscience: A Way Back to Full Omniscience

Abstract: In this paper I will set out to defend a version of propositional omniscience. In doing so my task will be to establish the conditional that either the difficulties faced by propositional omniscience are not insuperable, or else that, if my general approach to dealing with them fails, no attempt to salvage propositional omniscience will ever succeed. The paper will deal first with challenges to the instantiability of any kind of omniscience, and then move on to dealing with challenges posed specifically to the propositional account of omniscience.

The question concerning the nature and extent of God’s knowledge is one with which analytic theologians have had to grapple, and one on which nothing approaching a general consensus has yet to emerge among them. It has led some to adopt open theism (i.e., to deny that God knows what the future will bring),[1] others to adopt the view that God is omnisubjective,[2] others to adopt the view that God both knows everything (including about the future) and yet is learning new facts every moment of every day,[3] and still others that God is factually omniscient even though there are truths that He can’t possibly know.[4] This diversity is less surprising when one appreciates how riddled the question is with philosophical puzzles about semantics, set theory, the nature of time, the nature of knowledge and the nature of propositional content. What is a little more surprising, perhaps, is that so many philosophical theologians have shrunk back from defending propositional omniscience in light of the proposed difficulties. I will argue that these difficulties are not insuperable and that, therefore, we ought to hold our ground and defend propositional omniscience. This paper can thus be read as an attempt to kick against the goads of the current sensus intellectorum.

Before diving into my defense, a word about motivations for defending the possibility[5] of propositional omniscience may be appropriate. First, propositional omniscience given theism has some strong intuitive appeal, for “being incapable of knowing all there is to know or being capable of knowing all there is to know and knowing less than that are conditions evidently incompatible with absolute perfection.”[6] For the theist, and perhaps especially for the perfect being theologian, this provides strong impetus for preferring propositional omniscience to any ‘weaker’ or more gerrymandered versions of omniscience unless led by necessity to do so. Second, it seems obvious to me that if propositional omniscience can be defended then it not only provides the most elegant solution to Fitch’s paradox,[7] but also (thereby) enriches the funds of natural theology by adding yet another argument for God’s existence to an already impressive deposit. Finally, among the advantages of propositional omniscience we could include that the most plausible alternative version of omniscience, namely ‘factual omniscience,’ follows from it, for “it is not possible to be propositionally but not factually omniscient.”[8] These reasons conjointly provide us with ample motivation for at least exploring how we might go about defending the coherence of propositional omniscience.

Having, I hope, justified my philosophical project to the reader’s satisfaction I will now proceed to offer a defense of propositional omniscience. I will defend a version of propositional omniscience, shortly to be defined, against two general kinds of attack; first, I will defend it against the charge of logical incoherence, and, second, I will defend it against challenges typically raised in the literature from what we might call ‘the problem of indispensable indexicals.’ I will take omniscience to be exemplified by a being S if and only if for any true proposition P, S knows P, and for any untrue proposition Q, S does not believe Q.[9]

Propositional Omniscience (PO)=def. For any proposition P, if P is true then it is known, and if P is not true then P is not believed.

In other words, if a proposition has the property of being true, then a PO-being[10] believes it, and if it either has the property of being false, or in any case does not have the property of being true, then a PO-being does not believe it.[11]

Many arguments against Omniscience have recently been registered in the academic literature, and although I do not have the space or the time to deal with all of them, I will raise at least two such arguments which I feel are particularly troubling. I take them to be the very best arguments against omniscience available, so that if they can be dispelled we have good reason to think that the others probably can be as well. The first such argument comes from Patrick Grim and is often referred to as a ‘cantorian’ argument against omniscience. God’s omniscience, he opines, must consist in his knowing all truths, but since “by Cantor’s power set theorem we know that the power set of any set is larger than the set itself,”[12] we can prove quite easily that there is no such thing as the set of all truths. For any such supposed set of all truths we can take its power set and generate new truths which belong to the set of all truths, and since we can do this indefinitely the set of all truths is not merely infinite, but indefinite, and therefore nonexistent.

Although this objection has a tremendous amount of prima facie force, responses to it abound in the literature, primary among which is the response of Alvin Plantinga who expresses his puzzlement at Grim’s argument by asking why we should think that “the notion of omniscience, or of knowledge having an intrinsic maximum, demands that there be a set of all truths.”[13] Although this response seems to me to be perfectly satisfactory, not everyone has been so easily convinced by it. In particular, Patrick Grim has replied in return that “the only semantics we have for quantification is in terms of sets,”[14] so that giving up the use of them altogether makes ‘omniscience-statements’ inexpressible “within any logic we have.”[15]

Supposing that one feels an inordinate attachment to set-theoretic language, there still remain ways in which omniscience can be safeguarded. Alexander Pruss, for instance, attempts to evade set-theoretic paradoxes by shaving down what he calls the “Big Conjunctive Contingent Fact”[16] or BCCF[17] to a BCCFOF: “let the Big Conjunctive Contingent First-Order Fact (BCCFOF) of a world be the conjunction of all contingent first-order propositions in that world, with any logical redundancies omitted in order to root out set-theoretic paradoxes.”[18] Thus, we might just say that God is first-order propositionally omniscient by knowing the set of true propositions in the BCCFOF (along with the set of all necessary truths), and be satisfied with that. This kind of response steps in the right direction, but on its own it obscures the fact that Grim’s paradox leads to much more severe problems than the (alleged) problem for omniscience, such as how we are to construe logically possible worlds. If logically possible worlds are maximally consistent sets of propositions then, given this cantorian argument, it follows that the actual world isn’t a logically possible world. This constitutes a definitive reductio ad absurdam, and so even in the absence of a solution to the problem, this cantorian argument cannot be accepted.

The typical solution adopted in the literature has become to construe worlds not as sets of propositions, but as “possibly true maximal proposition[s]… [which entail] every proposition with which [they are] consistent.”[19] If this construal of worlds, in response to set-theoretic paradoxes, dissolves the problem of the cantorian challenge, then it does so with the additional advantage of restoring the coherence of omniscience as well. God, to be omniscient, merely has to believe the world-sized-proposition which is true, and not believe anything with which it is inconsistent. In fact, this proposal sits well with the classical line taken by philosophical theologians that God’s knowledge is not discursive (i.e., divided into different regular-proposition-sized beliefs) but is an intuitive grasp of the truth as a simple[20] seamless whole. Immanuel Kant, for instance, writes:

“Now, however, we can also conceive of an understanding which, since it is not discursive like ours but is intuitive, goes from the synthetically universal (of the intuition
of a whole as such) to the particular.”[21]

At this point we have indicated enough philosophical avenues by which to evade the problem that we can rest reasonably assured that Grim’s argument poses no defeater for belief in (the possibility of) omniscience.[22]

A second argument which has invited the attention of philosophers and theologians more recently is the so-called ‘grounding’ argument against omniscience presented by Dennis Whitcomb. He illustrates the problem as follows:

“Suppose for reductio that someone is omniscient. Then his being omniscient is partly grounded by his knowing that he is omniscient (which is one of the knowings that helps make him all-knowing). And his knowing that he is omniscient is partly grounded by his being omniscient (for knowledge is partly grounded by the truth of what is known). Since partial grounding is transitive, it follows that his being omniscient is partly grounded by his being omniscient. But this result is absurd, for nothing can partly ground itself.”[23]

The notion of grounding here, Whitcomb suggests, is not merely one of bearing a supervenience relation, which he points out may hold symmetrically between two facts, just as “the facts about the surface area and the volume of a sphere each supervene on the other,”[24] but one of bearing a relation of dependence. However, it is absurd to think that any fact is (even partly) grounded by itself in the sense of depending upon itself, and therefore no being can be omniscient.

To lay out the argument more precisely, Whitcomb argues that five claims (including omniscience) are incompatible, and then defends the “truth of each of them except the claim that there is an omniscient being.”[25] These claims include transitivity (i.e., that if A grounds B and B grounds C, then A grounds C), irreflexivity (i.e., that if A grounds B then B does not ground A), that truth grounds knowledge, and that every fact of the form ‘∃x∀y’ is grounded by its instances. It turns out that God’s knowing that He is omniscient is an instance of His omniscience, but that His omniscience (at least partly) grounds His knowing that He is omniscient, which implies that His omniscience (at least partly) grounds itself (which is absurd).[26]

This argument has been addressed in at least two ways in the literature. First, Joshua Rasmussen, Andrew Cullison and Daniel Howard-Snyder have co-authored a paper presenting a powerful reductio of Whitcomb’s argument by way of parody. They put forward a “formally identical argument that concludes that one of the present co-authors does not exist”[27] but insist that, since this is absurd, “Whitcomb’s argument is unsound.”[28] They begin by defining a predicate ‘daniscient’ as knowing “all and only whatever propositions Dan Howard-Snyder happens to know.”[29] From here the parody proceeds with perfect parity:

“Suppose for reductio that Dan Howard-Snyder is daniscient. Then his being daniscient is partly grounded by his knowing that he is daniscient (which is one of the knowings that helps make him daniscient). And his knowing that he is daniscient is partly grounded by his being daniscient (for knowledge is partly grounded by the truth of what is known). Since partial grounding is transitive, it follows that his being daniscient is partly grounded by his being daniscient. But this result is absurd, for nothing can partly ground itself. Hence our reductio assumption is false.”[30]

Rik Peels has also contributed similar reductios,[31] though he has done better by being able, in addition, to “provide a diagnosis of where precisely the argument goes wrong.”[32] In his submission, Whitcomb’s argument fumbles because his “notion of grounding actually covers two distinct kinds of [grounding] relations”[33] which he fails to disambiguate.[34]

At this point we can rest assured that omniscience isn’t in as much trouble as one may have imagined if they merely skimmed the literature. A variety of difficulties present themselves, however, for the possibility of PO. Recall that PO is not satisfied by just any old kind of omniscience, but only by omniscience of a peculiar sort; namely, omniscience in the sense that there is no true proposition which an omniscient being fails to know. However, there are very many propositions which it seems are both possibly true, and not possibly (all) known by God (or any other potentially PO-being). For instance, consider propositions like “I am Tyler,” or “I am John.” These pose serious difficulties for PO, for they suggest that there are propositions the meanings of which are bound up with indexicals in such a way that no being could know all such true propositions.

Turning once again to Patrick Grim, we find the problem put succinctly as follows: “only I can use… ‘I’ [in a propositional expression] to index me – no being distinct from me can do so,”[35] and yet since neither he nor any of us are omniscient, it follows that no being is (propositionally) omniscient just in case ‘I’ is essential to the meaning of the proposition in which it figures. The contention here is that propositions like “I am Tyler” are both true and unknowable to anyone other than me. Since there is no way to translate an indexical like ‘I’ in a proposition without thereby changing the very meaning of the proposition, it seems that nobody other than me can know any propositions in which ‘I’ indexes me. Since I am not omniscient, it would follow that no being is propositionally omniscient. This whole argument depends, however, on a crucial assumption which I mean to challenge; namely, that propositions just are meanings.

It is not atypical among analytic philosophers to simply regard propositions as meanings. Pruss, for instance, writes that “propositions have their meanings essentially – indeed, propositions could even be thought of as identical with meanings.”[36] I want, in what follows, to challenge this assumption. I will make a start of doing so by drawing off of Darren Bradley’s defense of two-dimensionalism with respect to objects of belief.[37] On Bradley’s view, objects of belief have two dimensions; first they have content, and second they have a mode, (i.e., “the way in which [what is believed] is believed”[38]) so that on this view beliefs have “a content that is grasped by a role.”[39] Bradley’s concern is to account for belief-change over time, especially in light of “standard confirmation theory,”[40] according to which the only rational rule governing belief-change is conditionalization.[41] This does not account, however, for belief changes such as when the belief that “today is Sunday” becomes the belief that “yesterday was Sunday.” Such changes of belief over time involve no new evidence on which the conditional probability of a belief B changes, but surely that kind of change of beliefs is rational nevertheless.

What we need, Bradley stipulates, is “two rules of belief update – conditionalization and mutation,”[42] where mutation corresponds to the mode of a belief as it changes over time, and conditionalization corresponds to the content of a belief. So, if a present-tensed proposition is uttered at one time, and a past-tense proposition with the same very same truth-conditions is uttered at a later time, “then both sentences express the same belief,”[43] even though they “are apprehended with different roles”[44] by involving different modes. This gracefully explains why the belief that ‘the meeting is now’ can catalyze action in me which ‘the meeting is at noon’ cannot, even if one is true if and only if the other is true. Bradley argues that “the neat bifurcation I defend requires that content only changes by conditionalization… [and] this requires that mutation doesn’t affect content.”[45]

Although, as I have already indicated, Bradley’s purpose is to account for the turnover of tensed beliefs, I see no reason why his response would not work equally as well for the indexical ‘I’ as for any tensed indexical. Moreover, so long as we add that content is propositional content, and admit that some meaning (namely the meaning apprehended by a mode) is extra-propositional, there is no reason why we cannot concede that there will always be some semantic loss in translating “I am tired” to “Tyler is tired,” while maintaining that both of these sentences express the very same proposition.[46] The propositional content of “I am Tyler” as uttered by me, and “yes you are” as uttered by you, is identical; “on the traditional view, the same proposition is expressed in each case.”[47] All this view requires is a commitment to the (very unsurprising) thesis that meaning is, to some extent (and in at least some cases), psychologically determined.

I said at the outset, however, that I would defend a conditional claim; namely that if my approach to defending propositional omniscience fails then no approach will succeed. In order to defend propositional omniscience in light of the problem of semantically essential indexicals it seems that we must either dislocate proposotional content from semantics, or else argue that nothing essential to the meaning of a proposition I might assent to is lost if I fix the context of utterance by getting rid of personal indexicals. I see no hope of successfully doing the latter, so if the former approach does not work it looks like propositional omniscience will turn out to be indefensible after all. Supposing, for the sake of argument, that this were the situation in which we found ourselves, it seems to me that we ought to opt for factual omniscience, according to which “for every truth, God knows the fact which that truth expresses – a claim which does not entail that God knows every truth about every fact.”[48] After all, the difference between PO, as I have defended it, and factual omniscience, is really just a matter of semantics.

Some concluding remarks should figure in at this point. We have seen that the arguments which I suggested were the most powerful against omniscience have failed to pose insuperable difficulties for omniscience, and this should raise our confidence that all arguments against omniscience currently on offer fail to pose a genuine defeater for the belief that at least one being is omniscient. We have also seen that Darren Bradley’s two-dimensionalism concerning objects of belief carves out a dialectical space for preserving propositional omniscience in light of the problem of indispensable indexicals precisely by differentiating the content of a belief and the mode by which the belief is apprehended. If this can be done then we can defend propositional omniscience, and if it cannot then there is no way left for us to defend propositional omniscience (in which case, again, we should be content to adopt factual omniscience).

[1] See William Hasker, God, Time, and Knowledge, (New York: Cornell University Press, 1998).

[2] See Linda Zagzebski, “Omnisubjectivity,” in Oxford Studies in Philosophy of Religion 1 (2008): 231-248.

[3] See William Lane Craig, “Doctrine of God (Part 5),” Lecture, Defender’s Class, March 29, 2010. He states that: “But if God knows these tensed truths, then that means that his knowledge is constantly changing, as future-tense truths become false and the present-tense [version] becomes true.”

[4] See Brian Leftow, Time and Eternity, (New York: Cornell University Press, 2009), 326.

[5] Here, as elsewhere throughout the paper, by ‘possibility’ I mean possibility in any world relevantly similar to our own.

[6] Norman Kretzmann, “Omniscience and Immutability,” in The Journal of Philosophy (1966): 409.

[7] Berit Brogaard and Joe Salerno, “Fitch’s Paradox of Knowability,” in The Stanford Encyclopedia of Philosophy ed. Edward N. Zalta (Winter 2013 Edition), [].

[8] Brian Leftow, Time and Eternity, 318.

[9] This definition has a familiar ring to it, and I wonder if I’ve heard/read something similar to it in the work of either Plantinga or Craig. I could find no such reference, but I note that I have a curious itch here – I want to avoid any semblance of plagiarism, and so I should note that I have an uncomfortable suspicion that I may be, here, unconsciously regurgitating something very similar in prose to what one might find in Craig or Plantinga (or, perhaps, elsewhere?). As I say, I can find no such reference, and in any case the definition as stated really does proceed from my mind.

[10] (i.e., a being satisfying propositional omniscience, or a ‘propositionally omniscient being.’)

[11] If one suggests that within para-consistent logic there may be propositions which are both true and false, and therefore that omniscience is impossible if para-consistent logics possibly describe a world (accurately), my response would be that no logically possible world can be accurately described by a para-consistent logic.

[12] Patrick Grim, “Logic and Limits of Knowledge and Truth,” in Nous (1988): 349.

[13] Alvin Plantinga and Patrick Grim, “Truth, Omniscience, and Cantorian Arguments: An exchange,” in Philosophical Studies 71, no. 3 (1993): 267. I note that it is precisely in anticipation of this problem that PO as I have defined it is articulated in a way which makes no explicit or implicit set-theoretic commitments at all.

[14] Ibid., 269.

[15] Ibid.

[16] Alexander Pruss, The Principle of Sufficient Reason: A Reassessment, (New York: Cambridge University Press, 2006): 284.

[17] Ibid.

[18] Ibid., 238.

[19] William F. Vallicella, A Paradigm Theory of Existence: Onto-Theology Vindicated, Vol. 89. (Dordrecht: Kluwer Academic Publishers, 2002), 23.

[20] ‘Simple’ is here used in the sense of being non-composite.

[21] Immanuel Kant, “The Critique of the Power of Judgment,” translated by Paul Guyer and Eric Matthews, (New York: Cambridge University Press, 2002): 276.

[22] Also see: Keith Simmons, “On an Argument Against Omniscience,” in Noûs (1993): 22-33.

[23] Dennis Whitcomb, “Grounding and Omniscience,” in Oxford Studies in Philosophy of Religion Vol. 4, ed. John Kvanvig OUP (2012): 5.

[24] Ibid., 3.

[25] Ibid., 1.

[26] Ibid., 7.

[27] Joshua Rasmussen, Andrew Cullison and Daniel Howard-Snyder, “On Whitcomb’s Grounding Argument for Atheism,” in Faith and Philosophy 30, no. 2 (2013): 198.

[28] Ibid.

[29] Ibid., 199.

[30] Ibid.

[31] For example, he has argued by beginning with the assumption that “some person S knows that K,” where “‘K’ stands for the fact that < Someone has knowledge >,” but since this assumption is an instance of K, K appears to be grounding itself, from which it follows (given irreflexivity) that no person knows that K.

[32] Rik Peels, “Is Omniscience Impossible?,” in Religious Studies 49, no. 04 (2013): 481.

[33] Ibid., 487.

[34] For want of space I refer readers interested in the details to the paper itself, and in particular to pages 487-489.

[35] Patrick Grim, “Against Omniscience: The Case from Essential Indexicals,” in Nous (1985): 154.

[36] Alexander Pruss, The Principle of Sufficient Reason, 45.

[37] I do not necessarily endorse the particulars of his view, such as the insinuation that all beliefs have both a content and a role, or that

[38] Darren Bradley, “Dynamic Beliefs and the Passage of Time,” in Attitudes De Se, ed. A. Capone & N. Feit  (University of Chicago, 2013): 294.

[39] Ibid., 301.

[40] Ibid., 302.

[41] Ibid.

[42] Ibid., 303.

[43] Ibid., 301.

[44] Ibid., 295.

[45] Ibid., 303.

[46] Just as the B-theorist might concede to the A-theorist that some meaning will inevitably be lost when translating tensed expressions to tenseless expressions without thereby conceding that there are propositions whose truth-makers include a fact about what time it objectively is.

[47] Patrick Grim, “Against Omniscience,” 153.

[48] Brian Leftow, “Time, Actuality and Omniscience,” in Religious studies 26, no. 03 (1990): 309.

Personal Theism and Contingent Persons

I sometimes hear it said that some people are ready to countenance that there exists a being which is necessary, transcends the world, and is related to the world as it’s explanation or cause, and yet for whom the suggestion that this being is ultimately personal is too much to swallow. I have previously noted that there are arguments to think that if there is such a cause of the world, then that being must be (or is much more plausibly than not) personal. Perhaps we can construct a different and additional argument to demonstrate that if Theism is true, then personal Theism is more plausibly true than impersonal Theism.

The conditional probability of their being contingent persons seems to be no greater or lesser on impersonal Theism than it would be on Naturalism. Thus Pr(CP|IT) = Pr(CP|N). Conversely we can infer that, ceteris paribus, Pr(N|CP) = Pr(IT|CP), and assuming that nothing in our background knowledge privileges either Naturalism or Impersonal Theism over one another, we can say that Pr(N|CP&BK) = Pr(IT|CP&BK). Naturalism/Impersonal-Theism gives us no more or less reason to suspect that the actual world would contain contingent persons than Impersonal-Theism/Naturalism (respectively). The rub of it is that contingent persons are surprising on a Naturalist ontology, where contingent persons are beings with intentional states, reflexive self-awareness, who inhabit first-person perspectives, have conscious experience, and introspectively apprehend themselves to be ‘free’ in some sense. On Naturalism these beings are very surprising, since if we gather up all the logically possible worlds at which Naturalism holds true, we should find that very few of them contain contingent persons (as described). Consider a thought experiment offered by John Bergsma:

“I think there is an even deeper problem with the Naturalistic, Materialist evolutionary worldview, which I will call NME,… it is that if NME is true it is unlikely and inexplicable that we would have cognitive processes at all. Restated, if NME is true we would expect a world without creatures that have mental states, however we do have a world with creatures that have mental states… Let’s engage in a mental experiment to show that this is the case. Imagine that we designed a very sophisticated mechanical robot that was able to land on other planets, locate raw materials, refine those materials, build a factory from them and proceed to build copies of itself. Suppose that we land that robot on a distant planet and let it get to work. 50 years later we return and the experiment has been successful, the planet is teeming with copies of our original robot all of them milling about in search of raw materials to make further copies of themselves. So from an evolutionary perspective these robots have been very successful; they have multiplied, exceedingly. However, would the robots have developed sentience? Would they be aware of their own existence? Would they actually think, feel, write poetry? In a science fiction movie maybe they would. But this is the real world, and we know that they would not. Although their behavior is adaptive and they have proliferated, they would not be one wit closer (pun intended) to actually having mental states… Mental states are invisible to evolution because evolution can only act on behavior; the only way mental states would become visible to evolution is if they actually effected behavior, and this is precisely the thing that most academics who hold to naturalist materialist evolution or NME vociferously deny. NME adherents generally deny that mental states have any influence on behavior because they intuitively sense that mental states are not material entities, or at the very least are difficult to analyze as material entities. Therefore, mental states fit uncomfortably into a materialist worldview and materialists want to deny the full reality of mental states.”[1]

However, arguably, contingent persons are more at home in (i.e., less surprising in) possible worlds where personal Theism is true. If God both exists and is personal then a world with contingent persons is, if not to be expected, at least not very surprising (or at least not as surprising as it would be on Naturalism). If we agree that the existence of contingent persons is relatively surprising on Naturalism (and, thus, too, on Impersonal Theism) then we can commit ourselves to: Pr(PT|CP)>>Pr(N|CP), and Pr(PT|CP)>>Pr(IT|CP).

Plausibly, if our background knowledge does nothing to privilege Naturalism over Impersonal Theism (which the Impersonal-Theist is likely to accept), then it does nothing to privilege Naturalism over Personal Theism either. Thus Pr(PT|CP&BK)>>Pr(N|CP&BK), from which it obviously also follows that Pr(PT|CP&BK)>>Pr(IT|CP&BK).

Although I can imagine a number of ways in which the indignant Naturalist might offer objections to this argument (for instance by insisting that our background knowledge really does make Naturalism more plausible than Theism), it seems to me that the Naturalist should find common cause with the (personal-) Theist in arguing that impersonal Theism does nothing to make contingent persons less surprising than they would be, or are, on Naturalism. Moreover, insofar as personal-Theism does make contingent persons less surprising than they otherwise would have been (and thus less surprising than they would have been on either Naturalism or impersonal Theism), the existence of contingent persons, combined with Theism, makes personal Theism more plausible than it otherwise would have been (and more plausible than Impersonal Theism).

Thus, we have a good argument to infer from ‘both Theism and the existence of contingent persons’ that God is personal. If somebody is willing to accept Theism, then it seems like Impersonal-Theism would be the harder pill to swallow.

Maybe this argument could have some interesting extension to pantheism. Pantheism is the view that there is no distinction between ‘God’ and ‘Everything,’ that God is nothing other than the whole of reality, and that all the parts of reality are parts of God. The term itself makes its first appearance “in the writing of the Irish freethinker John Toland (1705) and [is] constructed from the Greek roots pan (all) and theos (God).”[2] There are nuances to be attended to, such as that to which Thomas Aquinas drew his attention in distinguishing “between the doctrine that God is the form of all things (‘formal pantheism’) and the doctrine that God is the matter of all things (‘material pantheism’) (Moran 1989, 86).”[3] However, in general, Pantheism is the view that the terms ‘God’ and ‘the world’ pick out exactly the same thing. Thus Spinoza, perhaps the most famous of Western Pantheists, simply identifies ‘God’ with ‘Nature’ in his philosophical system.

I note that Pantheism is not to be confused with the increasibly popular view called Panentheism. As John Culp explains in the Stanford Encyclopedia of Philosophy:

“Panentheism seeks to avoid either isolating God from the world as traditional theism often does or identifying God with the world as pantheism does. Traditional theistic systems emphasize the difference between God and the world while panentheism stresses God’s active presence in the world. Pantheism emphasizes God’s presence in the world but panentheism maintains the identity and significance of the non-divine.”[4]

Insofar as pantheism (as opposed to Panentheism) also maintains that God is ultimately impersonal, it becomes, pace the argumentation above, less plausible than personal Theism (whether classical monotheism, or Panentheism).

[1] Alvin Plantinga and John Bergsma “Science and Faith Conference” from the Franciscan University of Steubenville

[2] Mander, William, “Pantheism”, The Stanford Encyclopedia of Philosophy (Summer 2013 Edition), Edward N. Zalta (ed.), URL = <;.

[3] Mander, William, “Pantheism”, The Stanford Encyclopedia of Philosophy (Summer 2013 Edition), Edward N. Zalta (ed.), URL = <;.

[4] Culp, John, “Panentheism”, The Stanford Encyclopedia of Philosophy (Spring 2013 Edition), Edward N. Zalta (ed.), URL = <;.

Aren’t worlds comparably better or worse?

Si c’est ici le meilleur des mondes possibles, que sont donc les autres?

I here mean to explore a paradox about comparing worlds with each other insofar as they are supposedly comparably better or worse. On the one hand I will maintain the alethic truism that there is no such thing as a best of all possible worlds, and conversely that there is no such thing as a worst of all possible worlds. To see why, consider that a best of all possible worlds is a world than which no better world could be conceived. However, the concept of a world than which no better could be conceived seems to be incoherent. Stephen T. Davis explains:

Take the notion of the tallest conceivable human. This notion is incoherent because, no matter how tall we conceive a tall human to be, we can always conceptually add another inch and thus prove that this person was not, after all, the tallest conceivable human. Just so, it may be argued, the notion of the best of all possible worlds is incoherent. For any possible world, no matter how much pleasure and happiness it contains, we can always think of a better one, i.e., a world with slightly more pleasure and happiness.[1]

Alvin Plantinga offers a more amusing illustration:

Just as there is no greatest prime number, so perhaps there is no best of all possible worlds. Perhaps for any world you mention, replete with dancing girls and deliriously happy sentient creatures, there is an even better world, containing even more dancing girls and deliriously happy sentient creatures. If so, it seems reasonable to think that the second possible world is better than the first. But then it follows that for any possible world W there is a better world W’, in which case there just isn’t any such thing as the best of all possible worlds.[2]

This truth seems indubitable once it has made its first impression on the mind, but it also leads to a conspicuous problem. To obviate the problem, we should turn first to St. Thomas Aquinas:

“The terms ‘more’ or ‘less’ only make sense if something is the maximum in a genus.”[3]

If there is neither a best nor a worst of all possible worlds, and if Thomas is right, then what sense can we make of calling some worlds better than others? Solutions do not abound. What I intend to do in this article is to survey some candidate solutions, and then share what has become my preferred solution to this problem inspired by St. Thomas Aquinas’ Quinque viæ (five ways), in particular from the fourth argument for God’s existence.

Gottfried Leibniz was the philosopher who introduced logically possible world semantics in the first place, and though he was clearly exceptionally brilliant, contemporary philosophers like Alvin Plantinga have raised their eyebrows high at Leibniz’ suggestion not only that there is a best of all logically possible worlds, but that this is it! Plantinga has, in fact, taken to calling this ‘Leibniz’ lapse.’[4] Although amusing, this charge has been criticized by those attempting to protect Leibniz’ good name. Thus, for example, Dr. George Gale, one of my philosophy professors at Concordia, has attempted an answer to the following effect: he has argued that, at least for Gottfried Leibniz, “this most perfect, best of all possible worlds is so only in accordance with a mathematical formula [relating simplicity of laws to abundance and variety of phenomena], and not in accord with our normal, everyday, Candidate-like notions of perfection, i.e., moral ones.”[5]

Thus, Plantinga’s criticism is guilty of an equivocation, since Plantinga must have something other than Leibniz’ notion of better-making properties in mind. As an aside, it seems to me that Leibniz’ solution is open to a deeper objection from William Lane Craig and possibly also from Alexander Pruss,[6] who have both concluded that it is absurd to posit an actually infinite number of contingent beings. Leibniz needs for the aggregate of all contingent beings, his ‘monads,’ to be actually infinite in number. Leibniz’ eclectic notion of better-making properties notwithstanding, however, unless one is inclined to think that Leibniz is right about better-making properties, it seems that Plantinga, Davis and others like them have posed an indissoluble difficulty. One, at least, for which a plausible and satisfying answer will not be found in Leibniz’ work.

One could, of course, simply bite the bullet and admit that what makes one world better than another is merely a matter of taste, and that the ascriptions ‘better’ or ‘worse’ express nothing more profound than preference. This solution is likely to be only as satisfying as moral nihilism is, and for the same reasons. A world in which a thousand more pregnant women get kicked in the stomach than another world seems, ceteris paribus, a much worse world relative to the other, and its being so isn’t simply a matter of taste or convention, like the way a world with a thousand fewer key-lime pies than ours seems worse than ours to me.

One could object to Plantinga that, though Leibniz does not have the right conception of what properties make worlds better, neither does Plantinga (at least, not as reflected in his thought experiment). Thus one can argue that Utilitarian standards of better-making properties are simply the wrong standards in the same way as Leibniz’ mathematical standards are; a world with more deliriously happy sentient creatures may be no better for it. Perhaps there are some other standards (known or unknown, discernible or indiscernible) which, like Leibniz’ standards, admit of a maximally good (or bad) world. This solution also strains credulity, however, as one need not be a Utilitarian to concede that, all things being equal, a world with more deliriously happy creatures really is better. Moreover, some Utilitarians could argue that two worlds in which the same average happiness obtains are really just as good as each other, so that the addition of more deliriously happy sentient creatures makes no calculable difference to how good a world is. So, Plantinga’s suggestion is about as far from being Utilitarian as he is. Moreover, for just about any standards it seems that one can simply run a parody of the kinds of arguments presented by Plantinga and Davis – perhaps even Leibniz’, if there really are different sizes of infinity and no greatest size of infinity. I am familiar enough with set-theory to know that there are different sizes of infinity, since some infinite sets cannot be bijected into others, but I am not familiar enough with set-theory to know if there is a species among these different ‘sizes’ of infinity than which no greater size exists. Either way, perhaps somebody opting for this Leibnizian avenue could argue, in a fashion similar to our hypothetical Utilitarian above, that once a world has the quality of instantiating an actually infinite number of desideratum it can no longer be meaningfully called ‘worse’ than any other world, even if that other world has ‘more’ desiderata.

This leads to another solution which I find not altogether unattractive. Perhaps instead of talking about a single ‘best’ or ‘worst’ of all possible worlds, one can identify a class of worlds than which no greater world can be conceived, and then speak of this class of worlds as the standard against which the goodness of worlds is measured. Any world with an actually infinite number of desideratum would surely be a world than which no greater could be conceived (I put no stock in any distinction, here, between conceivability and ‘possibility’ simpliciter).

I see two problems with this recommendation. First, due to the looseness of the definition, the set of all possible worlds would qualify as a set of worlds than which there could be no better world. Second, however, in order to isolate a class of worlds than which no better world could be conceived, and other than which every world is worse, seems to require positing an actual infinity of some sort, and we are led straight back to the problem posed by Dr. Craig.

Given that the impossibility of an actually infinite number of beings seems to pose such a problem for talk of best/worst possible worlds, perhaps one could run the following response in the form of an argument:

  1. If there is a best/worst of all possible worlds, then it includes an actually infinite number of beings and/or (better/worse-making) properties.
  2. If there is no best/worst of all possible worlds, then no world is better or worse than any other(s).
  3. But, at least some worlds are better or worse than some other(s).
  4. Therefore, there is a best/worst of all possible worlds.
  5. Therefore, there is at least one world which includes an actually infinite number of beings and/or (better/worse-making) properties.

I don’t find that satisfying myself, but that’s because W.L. Craig has sold me on thinking that it is logically impossible (indeed clearly incoherent) to talk about any actually infinite aggregate of contingent beings (I note in passing that he has not sold me on the idea that there couldn’t be an actually infinite number of events, anymore than there couldn’t be an actually infinite number of true propositions – to reify either of these into quasi-beings is a mistake, and though I would agree that if time were tensed there could not possibly be an actually infinite number of past events, I am adamantly a B-theorist).

A philosopher named Jean David Robert brought one solution to my attention which attempts to show that the objection to there being better or worse possible worlds is based on the presumption that there are better and worse possible worlds, and thus the objection cannot go through. Scilicet, the objection only works if the objection fails. He explains:

If it’s true that “there is no such thing as the best of all possible worlds because one can always conceive of a better world,” then it’s false that “one can never conceive of a better world because there is no such thing as the best of all possible worlds.” […]
Consider the following counterexample: on my desk, I have a potentially infinite number of rulers of different lengths. In other words, I have one potentially infinite ruler. I also have two rulers of different finite lengths. I compare the length of these two rulers using the potentially infinite ruler, and determine that one of the finite rulers is 1 cm longer than the other. Now imagine that the rulers are in fact possible words and the length of the rulers correspond to the objective value of these possible worlds. We can see that it does make sense to speak of one possible world being objectively better than another.

I like this answer; it has an almost Moorean quality to it. An actually Moorean answer may also be provided; perhaps we all know that some worlds are better than others, and we are surer of this truth than we are or can be sure of all the clever arguments against it. However, the trouble with the Moorean answer, and in a subtler way the trouble with J.D. Robert’s answer, is that it doesn’t actually help us make good sense of ‘better’ or ‘worse’ possible worlds. It may help us sleep at night, but it doesn’t get us anywhere. J.D. Robert’s doesn’t precisely because his potentially infinite ruler consists of the indefinite put-together of differently sized rulers, but for any ruler to have a size relative to any other it must be in principle comprised of commensurable units of length. However, to say that there are in principle commensurable units of length is just to say, pace the metaphor, that there is some standard against which these worlds can be compared so as to make one ‘better’ than another.

All of the aforementioned solutions seem to leave me high and dry. None of them seem to me to represent a plausible answer to the question ‘how can we meaningfully say of one world that it is better or worse than any other?’ I have come to think, however, that there may be a natural theological solution to the problem. Once again, I turn to St. Thomas Aquinas:

Among beings there are some more and some less good, true, noble and the like. But “more” and “less” are predicated of different things, according as they resemble in their different ways something which is the maximum, as a thing is said to be hotter according as it more nearly resembles that which is hottest; so that there is something which is truest, something best, something noblest and, consequently, something which is uttermost being; for those things that are greatest in truth are greatest in being, as it is written in Metaph. ii. Now the maximum in any genus is the cause of all in that genus; as fire, which is the maximum heat, is the cause of all hot things. Therefore there must also be something which is to all beings the cause of their being, goodness, and every other perfection; and this we call God.[7]

This may sound appealing to Theists like me, but presumably we shouldn’t be satisfied with merely gesturing in the direction of Theism, as though saying ‘God!’ loudly enough solves every problem. How can one cash-out this solution?

First, it is clear that if God exists, then his nature is identical to ‘the Good.’ In fact, if God exists then it seems like the only way to intelligibly predicate anything of him will have to avoid univocal predication just as much as equivocal (indeed, in God’s case, univocal predication is equivocal). Thus, we can predicate things of God in two ways: either by analogy, or metaphorically. We can say that God is our king metaphorically, while we can say that God exists or is good analogously. I will spare myself the trouble of having, here, to explain St. Thomas’ whole philosophy of language. I will, instead, take the liberty of presuming that the reader is at least relatively familiar with Thomistic philosophy of language.[8] God, ex hypothesi, is clearly the bearer of superlative attributes which serve as the paradigms of those attributes insofar as they are identified as instantiated in the world. In other words, for any predicate P, if P is an intrinsic superlative attribute of God, then God’s nature serves as the paradigm according to which P is predicated of contingent beings. Thus, if a being is good, it is good to the extent that it imitates (or intimates) the nature of God. If a thing is beautiful, it is beautiful to the extent that it intimates the pleasure of ‘seeing God’ (note that beauty is defined by Aquinas as that which, upon being seen, pleases).

I suspect, therefore, that when we say one logically possible world is better or worse than another, we mean that it is better or worse in the very same (or, at least, similar enough) sense as one person may be better or worse than another. Clearly, though, the Theist (at least of the Thomistic variety) will say that one person is good to the extent that they intimate God.[9] They are virtuous to the extent that their character intimates the character of God. A possible world, therefore, is good to the extent that it intimates the nature of God (i.e., to the extent that God’s nature is intimated in that world). This may mean that it reflects God’s moral goodness as well as his justice, his wrath as well as his mercy. Thus, the suggestion is that one possible world W is better than some other world W’ just in case it better intimates the nature of God.

I am convinced that this answer is not only appealing, but exactly right. In fact, I am tempted to make an argument of it for Theism. I will end this article with a brief sketch of how this argument is likely to go:

  1. If some possible worlds are better/worse than others, then either (i) there is a best/worst of all possible worlds which acts as the standard against which the goodness of worlds is measured, or (ii) there is a class of best/worst of all possible worlds which acts as the standard against which the goodness of worlds is measured, or (iii) God’s nature serves as the paradigmatic standard against which the goodness of worlds is measured.
  2. Some possible worlds are better/worse than others.
  3. There is no best/worst of all possible worlds which acts as the standard against which the goodness of worlds is measured.
  4. There is no class of best/worst of all possible worlds to act as the standard against which the goodness of worlds is measured.
  5. Therefore, God’s nature serves as the paradigmatic standard against which the goodness of worlds is measured.
  6. If God’s nature serves as the paradigmatic standard against which the goodness of worlds is measured then God’s nature exists.
  7. Therefore, God’s nature exists.
  8. If God’s nature exists, then God exists.
  9. Therefore, God exists.

Somebody may wish to wiggle out of this argument by splitting the horns of the trilemma in the Major premise, for instance by suggesting that moral Platonism may be a fourth alternative. However, the argument could be appropriately amended by changing the first premise to include the supposed alternative, and then we could insert a ‘premise 4.1’ which denied that moral Platonism is a solution.

[1] Stephen T Davis, ed. Encountering Evil [New Ed]: Live Options in Theodicy. (, 2001): 75.

[2] Alvin Plantinga, God, Freedom, and Evil. (Wm. B. Eerdmans Publishing, 1974): 61.

[3] Apologies to the reader: I can’t seem to find this quote in St. Thomas’ works, and I’m not sure where it came from either – it may not have come from the Summa Theologiae. It’s in one of his writings, somewhere.

[4] Plantinga, Alvin C. “Which worlds could God have created?.” The Journal of Philosophy 70, no. 17 (1973): 548.

[5] Roger Stuart Woolhouse, ed. Gottfried Wilhelm Leibniz: critical assessments. Philosophy of mind, freewill, political philosophy, influences. Vol. 4. (Taylor & Francis, 1994): 453.

[6] Alexander Pruss, “Probability on Infinite Sets and the Kalaam Argument”

[9] Interesting thought: if God had not incarnated setting the paradigmatic standard of a best of all possible persons, could people still be (have been) meaningfully said to be better than others? The answer is, obviously, bound up with the suggestion I am here in the business of elaborating. It could, I think, make sense, even without a best of all possible men, just in case the measure of a man’s goodness is the degree to which he intimates the divine nature.

[10] Alexander Pruss, “One Thing I have Learnt from Hume”