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.


Math, therefore God?

“Monsier! (a+bn)/n=x, donc Dieu existe; répondez!”[1]

Thus (allegedly) spoke the mathematician Leonard Euler when, at the invitation of Russian Empress Catherine the second, he confronted Denis Diderot in a (very short) debate on the existence of God. Diderot, who was not very good at math, was dumbstruck; he had absolutely no idea how to even begin responding to such an argument. In fact, he couldn’t even understand the argument, and Euler knew it! The court laughed him literally out of town (he promptly asked the Empress for leave to return to France). The formula, of course, is entirely meaningless, and may have been sleight of hand on Euler’s part (making his argument mathemagical rather than mathematical). Additionally, the anecdote has survived only in sparse notes (of dubious historical relevance) here and there with probably varying degrees of accuracy, so it is anyone’s guess what Euler actually meant. This amusing anecdote does, however, invite us to think about what arguments there could be, in principle, from mathematics for the existence of God.[2] Without offering much commentary on how promising these arguments are, I want to distinguish three viable (or, at least, viably viable) types of arguments which could be constructed.

The Argument from Mathematical Beauty

Although the formula Euler originally spouted off didn’t signify anything of mathematical (or philosophical) consequence, the beauty of Euler’s equation, eiπ + 1 = 0, gave rise to the apocryphal anecdote that Euler argued “eiπ + 1 = 0, therefore God exists.” There is (mathematicians tell us) a sublime mathematical beauty in this equation, and there is no obvious or intuitive reason why it is true. What is so special about this equation? One savvy commentator I ran across online put it so nicely I feel compelled to quote him:

“It’s a sort of unifying identity in mathematics, containing each of the fundamental operations (additive, multiplicative, exponential) and each of the fundamental constants (e, i, pi, 1, 0) combined in a theorem that united trigonometry, analysis, and algebra and geometry. It’s really an amazing identity, and the proofs for it are diverse and fascinating…”[3]

It has, thus, been called the origin of all mathematics. Keith Devlin is purported to have said:

“like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler’s equation reaches down into the very depths of existence.”[4]

Its elegance cries out for an explanation, but that explanation has proved so elusive that a desperate appeal to God begins to look almost reasonable, even to (some) mathematicians.

What should we make of this sort of argument? It seems on its face to be about as prima facie (in)admissible as any other argument from beauty. However, this argument may have more to recommend it than meets the eye. In particular, mathematical beauty has an uncanny predictive ability, at least in the sense that the more beautiful the mathematical formula, the more likely it is to describe the fundamental structure of the real world. Robin Collins has noted, for instance, that:

“To say that the beauty of the mathematical structure of nature is merely subjective, however, completely fails to account for the amazing success of the criterion of beauty in producing predictively accurate theories, such as Einstein’s general theory of relativity.”[5]

John Polkinghorne, in a lecture I recently had the pleasure of listening to (via podcast), said something similar though with less economy of words:

“It isn’t just [to satisfy] an aesthetic indulgence that theoretical physicists look for beautiful equations; it is because we have found, time and again, that they are the ones which actually do describe… a true aspect of the physical world in which we live. I suppose the greatest physicist I’ve known personally was Paul Dirac, (who held Newton’s old chair… in Cambridge for more than 30 years, who was one of the founding figures of quantum theory, [and] unquestionably the greatest British theoretical physicist of the twentieth century) and he made his great discoveries by a relentless and highly successful lifelong quest for mathematical beauty. Dirac once said ‘it is more important to have beauty in your equations than to have them fit experiment.’ Now he didn’t mean by that that it didn’t matter at the end of the day whether your equations fit the experiments (I know no physicist could possibly mean that), but what he meant was this: ok, you’ve got your new theory, and you use the solution and you find it doesn’t seem to fit what the experimentalist is telling you – now there’s no doubt that’s a setback, but it’s not absolutely necessarily fatal. Almost certainly, you will have solved the equations in some sort of approximation, and maybe you’ve just made the wrong approximation, or maybe the experiments are wrong (we have [known that] to happen even more than once in the history of physics – even in my lifetime I can think of a couple examples of that), so at least there’s some sort of residual hope that with a bit more work and a bit more luck you might have hit the jackpot after all. But, if your equations are ugly, there’s no hope. The whole 300-year history of theoretical physics is against you. Only beautiful equations really describe the fundamental structure of the world. Now that’s a very strange fact about the world… What I am saying to you is that some of the most beautiful (mathematical) patterns that our pure mathematical friends can think up in their studies just thinking abstractly… are found actually to occur, to be instantiated, in the structure of the world around us.”[6]

So mathematical beauty satisfies the empirical desideratum of predictive power in the sense that the more beautiful the mathematical expression, the more likely it is to describe reality.

Interestingly I think this kind of consideration can motivate a scientist (and perhaps even a die-hard empiricist, and/or a naturalist) to believe in the objectivity of aesthetic properties. In fact, unless they find a plausible evolutionary account for why our brains should be calibrated so as to recognize more beauty in the abstract mathematical equations which, it turns out, describe reality, than we find in other equations, there will be a residual mystery about the eerie coincidence of mathematical beauty and accurate mathematical descriptions of physics. An eerie coincidence the queerness of which can perhaps be mitigated by admitting the objectivity of aesthetic qualities.

However, the puzzling queerness of that eerie coincidence can only be (or can most plausibly be) ultimately alleviated if the universe is seen as the product of a (trans-)cosmic artist. If behind the fundamental structure of the universe there lies an intellect with aesthetic sensibilities (in some sense), then that would explain why the world showcases the mathematical-aesthetic qualities it does at the level of fundamental physics even when there is no (obvious?) reason why it should have. That, though, begins to look quite a lot like Theism.

The Argument from the Applicability of Mathematics

This segues into the next kind of argument from mathematics, which concerns the applicability of mathematics to accurate descriptions of the fundamental structure of the physical world. For the purposes of this argument beauty is entirely irrelevant. What is surprising, and in need of an explanation (according to this argument), is that the physical world would turn out to be describable in the language of mathematics (and here we are not simply referring to the basic truths of arithmetic, which are true across all logically possible worlds). William Lane Craig has become the most well-known proponent of this argument, and his articulation of it is relatively succinct.

“Philosophers and scientists have puzzled over what physicist Eugene Wigner called the uncanny effectiveness of mathematics. How is it that a mathematical theorist like Peter Higgs can sit down at his desk and by pouring over mathematical equations predict the existence of a fundamental particle which experimentalists thirty years later after investing millions of dollars and thousands of man-hours are finally able to detect? Mathematics is the language of nature. But, how is this to be explained? If mathematical objects are abstract entities causally isolated from the universe then the applicability of mathematics is, in the words of philosopher of mathematics Penelope Maddy, “a happy coincidence.” On the other hand, if mathematical objects are just useful fictions, how is it that nature is written in the language of these fictions? In his book, Dr. Rosenberg emphasizes that naturalism doesn’t tolerate cosmic coincidences. But the naturalist has no explanation of the uncanny applicability of mathematics to the physical world. By [contrast], the theist has a ready explanation. When God created the physical universe, he designed it on the mathematical structure he had in mind. We can summarize this argument as follows:

  1. If God did not exist, the applicability of mathematics would be a happy coincidence.
  2. The applicability of mathematics is not a happy coincidence.
  3. Therefore, God exists.”[7]

I am not sure of this argument’s philosophical quality, since it seems to me that it may be a metaphysically necessary truth that a logically possible world be amenable to mathematical description of some kind. For instance, it certainly seems true that whatever the geometry of space happens to be, there’s no necessary fact of the matter, but it also seems true that if the geometry of space isn’t Euclidean, it may be hyperbolic, or elliptic, (or maybe something else, je ne sais quoi) but it has got to be something, and what it happens to be may, therefore, not cry out for any more explanation than any other quaint contingent fact about the world.[8] However, maybe I’m mistaken about this; maybe the argument is, in fact, just as viable as other teleological or ‘fine-tuning’ arguments are.

Argument from Mathematical Truth

Finally, the third kind of argument I can think of would go something like this: mathematical truths, like all truths, have truth-makers. These truth-makers will have to be metaphysically necessary on pain of mathematical truths being contingent – but it seems obvious that mathematical truths are necessary truths, that they hold across all logically possible worlds. Now, Nominalism about mathematical objects is incompatible with the commitments we just outlined (unless one adopts Nominalism about modal properties as well), and so seems implausible (or, at least, less plausible than it otherwise would have been in virtue of this incompatibility). Platonism also, however, seems to be problematic. Between Platonism and Nominalism, there is a wide range of views including Divine Conceptualism (according to which mathematical objects exist as necessary thoughts in the necessary mind of God), Theistic Activism, Scholastic Realism[9] and many others besides. In fact, a variety (and perhaps a majority) of the accounts of abstract objects on offer today presuppose the existence of God in different ways.

This opens the way to at least two arguments we could construct for the existence of God. First, we could argue that one of these accounts in particular is most plausibly correct (such as Greg Welty’s Theistic Conceptual Realism),[10] and work our way up from there to the implication that God exists. Second, we could take the disjunction of all the accounts of abstract objects which require the existence of God and argue that (i) if any of them is correct then God exists, but (ii) it is more plausible than not that at least one of them is correct, from which it follows (iii) it is more plausible than not that God exists.

So, there we have it, three kinds of arguments from mathematics for the existence of God; a transcendental argument (from beauty), a teleological argument (from applicability), and an ontological argument (from necessity). Could there be others? Maybe, but I suspect that they will all end up falling into one or another (or maybe at least one) of the general categories I tried to outline here. I admit that I didn’t outline them as general categories very well, but that exercise will have to wait for another day when I have more time to blog to my heart’s content.

As a quick post scriptum; if Euler had any substantive argument in mind and wasn’t merely mocking Diderot for his lack of mathematical aptitude, which of these three kinds of arguments would he most likely have had in mind? It’s hard to say, of course, but my best guess is that if he had anything in mind at all, it would fall into the third category. He may have been thinking that the fact that mathematical and purely abstract (algebraic) ‘structural’ truths exist at all requires some explanation, and this explanation must be found in God. This is just a guess, and I make no apologies for it – I am happy to think that Euler was just teasing Diderot, but I am equally happy to entertain the thought that if Diderot had not immediately asked to leave (because of his embarrassment), Euler may have been able to elucidate his point.

[1] Gillings, Richard J. “The so-called Euler-Diderot incident.” The American Mathematical Monthly 61, no. 2 (1954): 77-80.

[2] Notice that these are not to be confused with mathematical arguments per se; they are merely arguments from mathematics, in the same way as you might have arguments from physics (the argument from cosmological fine-tuning, the Kalam, etc.) for the existence of God which are not intended to be scientific proofs of God’s existence, but scientifically informed philosophical proofs/arguments for God’s existence.

[3] Russel James, Why was Euler’s Identity Supposed to be a Proof for the Existence of God,; Note that he finishes the quoted paragraph with the words “but It has nothing to do with god whatsoever.” I have left this out not because I think he is wrong, or to misrepresent his position, but because it has nothing to do with the formula and everything to do with the propositional attitude he adopts with respect to the question of whether the formula is any kind of reason to think there is a being like God.

[4] Paul J. Nahin, Dr. Euler’s Fabulous Formula: Cures Many Mathematical Ills, (Princeton University Press, 2011), 1.

[5] Robin Collins, The Case for Cosmic Design, (2008),

[6] John Polkinghorne, Science in the Public Sphere,

[7] William Lane Craig, Is Faith in God Reasonable? William Lane Craig vs. Dr. Rosenberg,

[8] I am really, honestly, no more sure of this counter-argument than I am of the argument. For those interested, please do check out the debate between Craig and Daniel Came on the Unbelievable? Podcast, which you can also find here:

[9] J.T. Bridges defends this view:

[10] See: Greg Welty, “Theistic Conceptual Realism,” in Beyond the Control of God: Six views on the Problem of God and Abstract Objects, ed. Paul Gould, (New York: Bloomsbury Academic, 2014), 81-96.

Naturalism and Supernaturalism

What, exactly, is Naturalism? The naïve definition would go: Naturalism is the belief that there are no supernatural entities. What, though, are supernatural entities? The go-to example would be God, but that’s an example rather than a definition. As far as definitions go, a typical place to start is to say that a supernatural entity is anything which is empirically undetectable, or not verifiable/falsifiable by the scientific method. However, plenty of unquestionably scientific beliefs are in things which are not strictly falsifiable (such as the existence of our universe), and a ‘scientific’ view of the world often involves commitment to beliefs which aren’t strictly verifiable (such as the legitimacy of inductive reasoning, or the reality of the past). Moreover, this definition entails that moral values, the laws of logic, the fundamental principles of arithmetic (and all mathematics), aesthetic qualities, facts themselves (as model-independent truth-makers), propositions (whether necessary, contingent, or necessarily false), the (noumenal) external world, and even purely mental phenomena (eg. qualia), will all be supernatural. Science itself, it turns out, is replete with presumptions of supernaturalism according to the stipulated definition.

Alvin Plantinga once defined Naturalism as the belief that there is no such being as God, nor anything like God. I used to think that this definition was serviceable, but I have come to see that it invites some of the most egregious difficulties of all. Buddhists and Mormons may qualify as Naturalists on this definition, and mathematical Platonists may not qualify as Naturalists! Surely that can’t be right. A definition of naturalism on which it turns out that Joseph Smith is a naturalist and Frege a supernaturalist cannot be right. The notorious difficulty of defining Naturalism should now be evident. What once looked like a trivially easy task now appears to be a herculean feat; how are we to draw the line between the natural and the supernatural? To echo (mutatis mutandis) a famous saying of St. Augustine: if nobody asks me what Naturalism is, I know, but if you ask me, I do not know.

One could always suggest that the term ‘Naturalism’ has no definition precisely because concepts have no definitions. Wittgenstein’s famous suggestion that concepts like ‘GAME’ have no definition,[1] and Quine’s famous skepticism about analyticity,[2] are just two of many factors which have contributed to the recent retreat from ‘definitions’ in the philosophy of concepts.[3] This trend has led to the wide embrace of prototype theory, theory-theory, and other alternatives to the classical theory of concepts. If we must give up on definitions, it seems to me that we must largely give up on the project of analytic philosophy, and that makes me considerably uneasy; but then, I’ve always been squeamish about anti-rationalist sentiments. It may turn out we can do no better than to say something like that Naturalists adopt belief systems related by a mere family resemblance, but which cannot be neatly subsumed under one definition. I, however, (stubborn rationalist that I am) will not give up on definitions without a fight.

On the other hand, if Naturalism cannot be defined then those of us who wish to remain analytic philosophers can just cut our losses and accuse self-identifying naturalists of having an unintelligible worldview; one the expression of which involves a fundamental theoretical term for which no clear definition can be given. In other words, when somebody claims that Naturalism is true we can simply retort: “I don’t know what that means, and neither do you.” What kind of rejoinder could they give? Either they will provide us with an acceptable definition (so that we’ll have finally teased it out), or they will have to reconsider the philosophical foundations of everything they believe they believe. Win-win by my count.

In the meantime, let’s try on some definitions for size. Here’s one:

P is a naturalist =def. P is an atheist who believes that all that exists is discoverable by the scientific method.

This definition is bad for several reasons. To begin with, it isn’t clear that a Naturalist need be an atheist; why couldn’t they be a verificationist,[4] or a Wittgensteinian? It seems, at first blush, sufficient that one not believe that “God exists” is a metaphysical truth, but then it also seems wrong to say that an agnostic can be a naturalist. An agnostic is agnostic with respect to supernatural entities, but a naturalist is not. So we’re left in a quandary with respect to the first half of our definition.

The second half doesn’t fair much better. Apart from the fact that scientists routinely commit themselves to the reality of entities which are beyond the scope of strictly empirical discoverability (such as the existence of alternative space-times in a multiverse), there is an puzzle involved in stating what, precisely, qualifies as scientifically discoverable. For instance, many of the fundamental entities in particle physics are not directly empirically observable (they are, in fact, often referred to as ‘unobservable entities’), but we have good reasons to think they exist based on the hypothetico-deductive method (i.e., we know what empirical effects they would have if they did exist, and we can verify those). However, that amounts to having good scientific and empirical motivation for believing in unobservable entities. Is it impossible to have good scientific and empirical motivation for believing in ghosts, or numbers, or God? W.V.O. Quine famously stated that if he saw any empirically justifiable motivation for belief in things like God, or the soul, he would happily accept them into his ontology. In fact, in a move motivated by his commitment to his Naturalized Epistemology,[5] Quine did eventually come to accept the existence of certain abstract objects (namely, sets). Quine leaves us with two choices: either we say that even Quine wasn’t really a (metaphysical) Naturalist in the end, or we find a way to allow Naturalists to believe in things like numbers, moral values, aesthetic facts, and other things which we don’t usually think of as ‘Natural’ entities. I suggest we make use of the notion of scientific/empirical motivation; in other words, we should make room for Naturalists to work out an ontology motivated by a scientific view of the world. The only danger I foresee in that move is that if even belief in abstract objects can be scientifically motivated, it seems as though belief in God, or anything, might turn out to be possibly scientifically motivated. Nevertheless, let us consider a second definition:

P is a naturalist =def. P believes that “God exists,” interpreted as a metaphysical statement, is untrue, and that the only entities which exist are the entities to which the acceptance of a literal interpretation of science commits us.

The first half of this definition seems fine to me, so that’s some progress. The second half is problematic because it implies that constructive empiricists, for instance, are not naturalists; the constructive empiricist agrees with the scientific realist that the statements of science should be literally construed/interpreted, but that when we accept a scientific theory we commit ourselves only to (i) the observable entities posited by the theory, and (ii) the empirical adequacy of the theory. Since the constructive empiricist adopts an agnostic attitude towards unobservable entities, none of them would qualify as naturalists on the above definition. In fact, anyone who adopts any version of scientific anti-realism (including the model-dependent realism of Stephen Hawking and Leonard Mlodinow, or even structural realism) will be disqualified from the running for candidate naturalists.

Let’s try a third:

P is a naturalist =def. P believes that “God exists,” interpreted as a metaphysical statement, is untrue, and P believes in some of, and only, the entities to which a literal interpretation of science commits us.

A possible problem with this definition might be that it threatens to include solipsists (though it isn’t clear what in science, interpreted literally, would commit anyone to the existence of persons). Perhaps we should replace “entities to which the acceptance of a literal interpretation of science commits us” with something like “entities to which our best understanding of science commits us.” That might be problematic since what the best understanding of science is seems up for debate. Perhaps it should be changed to: “entities to which a legitimate interpretation of science commits us.”

P is a naturalist =def. P believes that “God exists,” interpreted as a metaphysical statement, is untrue; P believes in some of the entities to which a legitimate understanding of science commits us; P does not believe in any entities belief in which cannot be motivated by a scientific view of the world (with the possible exception of God – caveat in casu necessitas).

This definition isn’t obviously problematic. It looks to be about as good as I can do, off the top of my head. Note that if this definition is successful, then we have also found the definition of supernaturalism, since (obviously) the definition of naturalism and the definition of supernaturalism bear a symmetrical relation of dependence to one another. This still has some notable disadvantages, including that naturalists will not be able to justify believing in moral facts unless they can generate motivation for believing in them given the resources of a scientific worldview. However, those disadvantages may just come with the territory; they may be the disadvantages not of our definition, but of the philosophy of metaphysical naturalism.

One final note; the term ‘supernaturalism’ has a bit of a bad rep because it is popularly associated with things like ghosts, energies, auras, mind-reading, witchcraft and (for better or worse) a variety of religious beliefs. Because of this many philosophers have opted for using synonyms such as ‘ultra-mundane’ to refer to things like moral facts, possible worlds, necessary beings, et alia. I don’t much mind which term is used, but one advantage to retaining the use of the term ‘supernatural’ is that it helps focus our attempt to define ‘natural’ and its cognates. If we had to define the terms ‘natural’ and ‘ultra-mundane’ it might be less apparent that whatever qualifies as unnatural is going to qualify as ultra-mundane, and vice versa.

[1] Ludwig Wittgenstein, Philosophical Investigations second edition, transl. G.E.M. Anscombe (Blackwell Publishers, 1999).

[2] W.V.O. Quine, “Two Dogmas of Empiricism,” in The Philosophical Review vol. 60, no.1 (1951): 20-43.

[3] For more see: Stephen Laurence and Eric Margolis, “Concepts and Cognitive Science,” in Concepts: Core Readings (1999): 3-81.

[4] A verificationist, I mean, ‘about’ Theism.


Two Too Simple Objections to Open Theism

First, let’s agree to reject dialetheic logics out of hand; it will be taken as a non-starter for me, and, I hope, for you, if any argument were to proceed on the assumption that a proposition can be both true and false at the same time and in the same sense. It may be useful, at times, to proceed as though this were the case (I’m not denying the usefulness of paraconsistent logics), but it certainly cannot be literally correct. Such logical systems do not (and, by implication granting S5, cannot) describe the extra-mental structure of modality.  

Can God know the future on open theism? It is typically assumed that open theism involves a commitment to Presentism about time (according to which future events are not real, and so propositions about the future are not literally true). I am not sure that this is correct, since they may, perhaps, accept the growing-block theory of time instead, but that will land them in precisely the same predicament as Presentism will as far as my following objections are concerned. In any case, the open theist must accept some version of the A-theory other than the moving-spotlight theory of time (or other more esoteric theories of time which will allow for the reality of future events or states of affairs). God, on the open theist view, shouldn’t be able to know the future because there is no future to know.

It seems undeniable that if “P” is true, and if “P⊃Q” is true, then “Q” is true; that’s just good old Modus Ponens. Now, let’s take P to represent the tripartite conjunction: “the state of affairs S1 in the world will entail the subsequent state of affairs S2 just in case God does not intervene in the world at some time between S1 and S2 (inclusive of S1, not inclusive of S2) and God will not intervene in the world at any time between S1 and S2, and S1 describes the current state of affairs.” Let Q represent the proposition “in the future, S2 will be the case.”

Let us say that God knows P, and God knows that P⊃Q. Does God know Q? If not, He has a deficient grasp of logic. If so, then He knows at least some fact(s) about the future.

  1. If open theism is true, God cannot know the future.
  2. Possibly, God can know propositions like “P” and “P⊃Q.”
  3. If God can know propositions like “P&(P⊃Q),” then God can know propositions like Q.
  4. If God can know propositions like Q, then God can know propositions about the future.
  5. If God can know propositions about the future, then God can know the future.
  6. Therefore, open theism is false.

What will the open theist say? The most plausible response open to them, I think, is to deny premise 5. Generally we think of propositions about the future as having truth-makers which are future states of affairs, but it is conceivable that there be true propositions about the future which have, as their truth-makers, nothing beyond present truth-makers. Perhaps P is presently true, while Modus Ponens and P⊃Q are true presently (they may be timeless truths, so we avoid saying that they are ‘presently’ true, even if they are true presently). That might be a sufficient response. A second response might go like this: premise 1 should be restated as 1*: “if open theism is true, God cannot know the whole future,” and premise 5 should be restated as 5*: “If God can know propositions about the future, then God can know at least some of the future.” Obviously 6 does not logically follow from 1*-5*.

Here’s a second argument:

  1. If a proposition is meaningful, then it cannot fail to be true or false (where the ‘or’ is exclusive).
  2. There are meaningful propositions about the future which are not entailed by any presently available truths.
  3. Therefore, there are true propositions about the future which are not entailed by any presently available truths (they cannot all be false, for if P is false, then “P is false” is true).
  4. God is omniscient.
  5. A being is not omniscient if there are truths (i.e., meaningful true propositions) it fails to know.
  6. If open theism is true, there are meaningful true propositions about the future which God fails to know.
  7. Therefore, open theism is false.

The best responses to this argument which I have heard include (i) denying premise 2 altogether, or (ii) denying premise 1. The denial of premise 1 (given our assumed rejection of dialetheic logics) amounts to a rejection of the law of excluded middle (LEM), and that, my friends, is as good as a reductio against open theism. Rather, it is a reductio of open theism! Alternatively, to deny premise 2 (by denying the meaningfulness of propositions about future states of affairs not entailed by presently available truths), seems implausible given the fact that we all apprehend the meaning of sentences like “tomorrow Julie will eat worms in the playground again.” So, we have at least one relatively good, though simple, argument against open theism.

… Maybe there’s time for a quick third: suppose that epistemic justification means something like ‘true justified belief’ (and let’s, for the moment, ignore Gettier cases, just for simplicity). Now it looks like I can know propositions like P:”tomorrow I will finally propose to her,” even though it looks like God cannot know P! That’s another reductio ad absurdam to add to our growing list of reasons to reject open theism.

My mistake; obviously this last argument presupposes the ‘truth’ of propositions like P, but that’s the very object of contention, so my argument runs in, as they say, a circle of embarrassingly short diameter.

As to whether either of the former arguments will work, it seems to me that if the open theism is too deeply entrenched then the open theist will simply bite the bullet and accept the consequences of my arguments while maintaining open theism. However, at least the arguments can act as a warning to others to avoid the philosophical pit that is open theism.



It was in an article written by Stephen Torre which I read very recently that I was introduced to a very intriguing idea; namely, that tokens, and not propositions, are the fundamental bearers of truth-values. The usual view, of course, is that propositions (whatever one thinks of them) are those things to which the categories/properties ‘true’ and ‘false’ exclusively apply. Tokens, then, merely express truths insofar as (and just in case) they express propositions which are true. On the alternative story, which Torre refers to as the “Token View,” it is tokens which are the fundamental truth-bearers. This alternative story is as indifferent to different theories of truth (eg. correspondence, coherence, pragmatist) as the usual story. Turning to Torre, we read:

“There are different views regarding what the fundamental bearers of truth are. One view is that truth applies fundamentally to tokens. On this view, the predicate ‘is true’ is properly applied only to tokens. Such a view is committed to denying that there are token-independent truths. I will refer to this view as the ‘Token View’. A rival view takes truth to apply fundamentally to propositions. On this view, tokens are true or false only derivatively: tokens express propositions and a token is true iff it expresses a true proposition. This view does allow for the existence of token-independent truths.”[1]

I think it is worth having a bit of fun thinking about what the consequences of this prima facie absurd view would be. As it turns out, the view might have some theologically welcome consequences. For instance, it seems clear that the alleged set-theoretic problems for the doctrine of omniscience are evaporated of significance; even if there is no such thing as the set of all (true) propositions, there is clearly[2] such a thing as the set of all (true) tokens, at least if tokens are created by finitely many minds with finite capacities/abilities.

Tokens, like propositions, may require facts (i.e., extra-mental and extra-linguistic truth-makers), but God could be omniscient either factually (i.e., by having direct unmediated acquaintance with the facts, rather than their representations to the discursive intellect in the form of tokens or propositions), or else God can be token-omniscient. What is it, precisely, to be token-omniscient? Let us stipulate a definition:

G is token-omniscient =def. G knows all true tokens, and believes no false tokens.

Suppose that this view is correct quarum gratia argumentum, and suppose that God’s mental activity produces tokens. In this case it looks as though an old adage of Christian theology is more literally true than it seemed at first glance: to think truly is to think God’s thoughts after Him.

Objection 1: Surely quantification over tokens isn’t problematic unless there are indefinitely many of them. However, it is difficult to imagine a finite mind tokening a truth as of yet not tokened by God, even in any logically possible world. It seems plausible to say, then, that if God tokens any truths then he tokens all truths, but the set of all truths is indefinitely large. Set-theorists have no problem quantifying over infinite sets; the problem was always with quantifying over ‘indefinite’ sets, which are not sets at all. If the set of all true tokens is indefinitely large then the problem recurs.

Response 1: Perhaps we should make a distinction analogous to the distinction between first-order propositions (propositions about the world) and second-order propositions (propositions about propositions about the world), and restrict God’s knowledge to first-order tokens.

G is first-order token-omniscient =def. G knows all true first-order tokens, and believes no false tokens.

God would, of course, still know all first-order tokens about second/third/quadruple/etc-order tokens which occur to finite minds, and that seems sufficient for omniscience.

Objection 2: suppose that (logically/explanatorily) prior to God’s creating anything, He realizes that there are no tokens, and, in realizing this (and being always first-order token omniscient), mentally produces the first-order token T1: “there are no tokens.” This is false, and (being a token), is necessarily false. God would not only not be Token-Omniscient, but wouldn’t even have (all and) only true beliefs.

Response 2: It might not be logically possible for God to token T1, but perhaps it is possible, and inevitable (given the assumptions upon which we are now working in this thought experiment), that God token T2: “There are no (other) tokens” or, rephrased more elaborately, T2’:“there are no tokens other than this one.” Perhaps to avoid self-reference paradoxes we should say of tokens, as I am inclined to say of propositions, that (unless they pick out a universal quality, such as the disjunctive property of being true or false or meaningless) they all come with a caveat de aliis implicite (i.e., with an implicit caveat that they are ‘about’ others). Such stand-alone sentences as “the set of all things I say in this sentence is imponderable” are not true, they are entirely bereft of truth-apt content! Pseudo-meaningful sentence constructions. So also, it seems to me, “this sentence is true” is meaningless, and “there are no sentences” is meaningless. [I am not sure I’m right about this; this is just a knee-jerk reaction on my part to self-reference paradoxes].

What are the downsides of this view (other, of course, than that it seems crazy)? I’m not sure I can think of any unanswerable objections to it, and that alone may make it worth pondering, at least for fun.


Edit: Ok, here’s an obvious objection to Token-Omniscience which I, for whatever reason, didn’t think of previously: suppose I token the following: “I am Tyler.” The token’s content is irreducibly bound up with the sense of the indexical ‘I’ in such a way that nobody distinct from me could recognize that token as true, even if they could have recognized the propositional content to be true. The token, per se, is unknowable to any being distinct from me. Therefore, if tokens are the fundamental truth-bearers, and any more than one being ever uses a personal pronoun to index themselves in tokening a truth, no being can be (first-order) token-omniscient. That seems like a pretty definitive defeater to token-omniscience to me.


[1] Torre, Stephan. “Truth-conditions, truth-bearers and the new B-theory of time.” Philosophical Studies 142, no. 3 (2009): 325-344.

[2] I assume that it is logically impossible to have an actually infinite set of tokens created by finitely many finite minds. This can be challenged, of course, by either insisting that there is no absurdity, contra apparentiam, in positing actual infinities, or else that the absurdities do not arise for tokens. If such suggestions are to be taken seriously, then I would have to weaken my claim here from ‘clearly’ to ‘plausibly,’ but all else would remain the same.

Thomism is preferable to Molinism

Abstract: In this paper I will examine two competing theories of God’s providence, namely Molinism and Thomism, and argue that of the two Thomism is theologically preferable. I will show that Thomism can help itself to all the advantages of Molinism without inheriting its distinctive disadvantages. I will not have space to deal at length with the supposed disadvantages of Thomism, but I will suggest that the supposed disadvantages of the Thomistic view can be avoided or greatly mitigated, and that even if they could not Thomism would remain theologically preferable.

Molinism is the theological model, first put forward by the sixteenth century Jesuit theologian Luis de Molina, which attempts to preserve an extremely strong view of God’s providential control over the history and nature of the world while also maintaining that people have genuinely categorical, or ‘libertarian,’ freedom. The way Molina does this is to argue that in addition to God’s natural knowledge (of all necessary modal truths),[1] and his knowledge of contingent facts about the actual world, he has a ‘middle’ knowledge (scientia media) of what people would have freely done in any non-actual[2] metaphysically possible circumstance. God has access to the objects of his so-called middle knowledge logically/explanatorily prior to his choosing to create a world, and it is in light of these objects of his knowledge that he sets the world up precisely as he does, so as to bring about the best of all logically feasible[3] worlds. A world is logically feasible just in case it is both logically possible and, in addition, is possibly instantiated (by God’s creative activity) in light of the true contingent[4] subjunctive counterfactual conditionals of creaturely freedom (henceforth SCCs). The Molinist maintains that these SCCs are either entirely brute facts (contingent facts for which no sufficient explanation exists), or are grounded somehow in something other than God’s intentional assignment.

Molinism, it has been said, is “one of the most brilliant constructions in the history of philosophical theology,”[5] and has sweeping theological utility. It not only tidily explains how to put together genuine free will with God’s providential control over historical contingencies, but it also offers a stunning answer to the so-called problem of evil precisely because the morally sufficient reasons for evils in the world are grounded in objects of God’s knowledge which we have good reason to believe we are in no epistemic position to know, nor even in a position to guess! Molinism even provides an apparently promising way to defend the logical possibility of the classical doctrine of hell against objections to the effect that infinite (read here ‘everlasting’) punishment for finite crimes is incompatible with God’s justice.[6] All its notable advantages notwithstanding, Molinism also presents profound challenges to God’s sovereignty, His divine simplicity and to His impassivity. Moreover, Molinism is incompatible with the principle of sufficient reason, which provides a good reason for rejecting it. Where Molinism fails, however, Thomism can succeed.

The Thomist parts company with the Molinist on the question of the nature of God’s providence by stipulating that that SCCs must, somehow, be determined by God. Robert Koons explains that “the Thomist is supposed to believe that God knows… [subjunctive counterfactual conditionals] by having decided Himself what [they] should be.”[7] Some critics have complained that if God makes these counterfactuals true then people would not have the ‘power’ to do otherwise than they do,[8] but this objection seems confused. After all, supposing that SCCs are indeterministically assigned a truth-value, or that their truth value is in any case not the result of any deterministic process of truth-value assignment, no problem is supposed to arise for the Molinist. If our apparently free actions turned out to result from what, at bottom, can be described as a mindless indifferent unintentional indeterministic process[9] then they would be as unfree as if they were strictly causally determined by antecedent conditions entirely out of our control. However, the Molinist will deny that just because the SCCs (together with facts about what world God has elected to create) both logically entail that people will act precisely as they do and result from some unintentional indeterminism, the actions of creatures are not free. The Molinist can hold this consistently because they recognize that logical entailment is not to be confused with causal necessitation, and it is not true that if it is logically entailed that A do Y, then A is unfree with respect to Y.[10] The fact is that God does not cause a person to act as they do on either the Thomistic or the Molinist view, even if He sets up the world in such a way as to logically ensure that they act precisely as they do. This is a point to which we shall return.

In the first place among the many arguments against Molinism comes the argument from William Hasker, which was polished and improved upon by Robert Adams, and deserves special attention. Hasker’s argument was that Molinists need for the truth of SCC’s to be explanatorily prior to the existence of libertarian-free agents and their libertarian-free actions, but, Hasker thinks, Molinism will commit one to the belief that SCC’s are grounded in a libertarian-free agents free activity. He suggests that there is a contradiction between the claim that some free agent ‘A’ can freely bring Y about, and the claim that there is a ‘hard fact’ about the past history of the world, explanatorily prior to A’s bringing Y about, which broadly logically entails that Y be brought about by A. Hasker assumes that if A can freely bring Y about then A has the power to refrain from bringing Y about. For Hasker, “A [freely] brings it about that Y iff: For some X, A causes it to be the case that X, and (X & H) =>[11]Y, and ~(H =>Y), where ‘H’ represents the history of the world [causally] prior to its coming to be the case that X.”[12] Since it is a condition of A’s being free with respect to bringing Y about that H apart from X not logically entail that Y, if there is an SCC entailed by H which, in turn, entails Y, A cannot be free with respect to Y. The history of the world cannot include an SCC which entails that Y unless A is not free with respect to bringing it about that Y. Therefore, A’s bringing Y about freely requires that the SCC entailing that A bring Y about be grounded in A’s bringing X about, rather than grounded in H. To ground SCCs in the actions of libertarian free agents, however, would entirely undo Molinism as an explanation of God’s providential control over the free decisions of His creatures.

Unfortunately I am not convinced that this argument against Molinism is any good. In fact, I am convinced that it is no good. The trouble here is that for H to broadly logically entail Y does not seem (to me) to entail that A did not freely bring it about that Y, or that A couldn’t have refrained from bringing Y about in the relevant sense. A, to be free, need only be free in the sense that nothing in H causally necessitates Y. However, for H to broadly logically entail Y is not incompatible with A’s ability to freely bring Y about. Suppose, for instance, that the A-theory of time is true, and suppose further that the history of the world has included the fact that “at t (where t is some future time) A will freely do B.” If this fact is part of the makeup of facts true in the past history of the world (and presumably it would be, since it is future-tensed), then there would be facts in the past history of the world which would broadly logically entail that A do B, but this would do absolutely nothing to negate A’s freedom with respect to doing B. One should not confuse broadly logical entailment with causal determinism. Libertarian freedom and causal determinism[13] really are incompatible, but there’s no good reason to think that libertarian free will is incompatible with free choices being broadly logically entailed by facts which have no causal influence on the free choices they entail. A can be causally free to refrain from bringing Y about even if it is broadly logically entailed by some contingent fact H that A bring Y about.

Robert Adams has articulated a similar argument, but couches the key commitment to which he invites us in the language of explanatory priority. He suggests that “if I freely do A in C, no truth that is strictly inconsistent with my refraining from A in C is explanatorily prior to my choosing and acting as I do in C.”[14] His argument operates on the crucial assumptions that explanatory priority is (i) transitive, and (ii) asymmetrical. It must be transitive because Adams wants to say that SCC’s are explanatorily prior to our free choices (because they are explanatorily prior to our very existence, which is itself explanatorily prior to our free choices), and it must be asymmetrical because otherwise our free choices could be explanatorily prior to SCCs which are explanatorily prior to our free choices. Unfortunately Adams makes the very same mistake as Hasker made when he insists that “the truth of [an SCC] (which says that if I were in C then I would do A) is strictly inconsistent with my refraining from A in C.” [15] In addition, W.L. Craig has argued that the notion of explanatory priority used in Adam’s argument may be equivocal, and that, if it isn’t, “there is no reason to expect it to be transitive”[16] in the way required by the argument. Adam’s argument, therefore, seems plagued with difficulties.

There are, however, some genuine problems with Molinism. Problems to which Thomism seems immune. The first such problem is that Molinism seriously threatens God’s divine simplicity in a subtle but profound way. According to the doctrine of divine simplicity God’s knowing is (somehow) identical with His willing, which is (somehow) identical with His being. One of the chief motivations of the Thomistic view of providence is that it satisfies “a concern to preserve the doctrine of the simplicity of God,”[17] precisely because God’s knowing and his willing amount to the very same thing.[18] By contrast Molinism suggests that God is affected by the objects of his middle-knowledge in such a way that His knowing cannot amount to the same thing as His willing, and this presents a fundamental threat to the doctrine of divine simplicity. It also threatens the doctrine of God’s impassability, according to which “God’s relation to [the world][19] is always one of cause-to-effect and never effect-to-cause.”[20] If Molinism is true then God bears an effect-to-cause relation to SCCs, which are uncreated contingent features of the world.

Another difficulty with Molinism is that it may not only fail to provide a promising theodicy, but may present its own form of the problem of evil. According to a standard Molinist theodicy, God has minimized the evil and maximized the good in this world by creating the best of all logically feasible worlds in light of the SCCs which happen to obtain. For illustration, we can imagine that if two logically feasible worlds W and W’ are indistinguishable (mutatis mutandis) except insofar as W involves one more person than W’ coming to freely accept God, then W will be a better feasible world than W’. However, given the indeterminate nature of SCCs, it may be the case that there are two worlds W1 and W2, such that W1 and W2 are indistinguishable in all respects except (mutatis mutandis) that W1 involves the salvation of Susie and Jim, and the damnation of Thomas, whereas W2 involves the salvation of Thomas and Jim, but the damnation of Susie. Given this situation, it seems as though an omnibenevolent God would be stuck with a classic buridan’s ass paradox. In this case God would have to arbitrarily choose to create one world rather than the other (assuming He wouldn’t just create both), but this leaves God with no morally sufficient reason for allowing the damnation of Thomas/Susie (depending on the world selected, or for the damnation of Thomas1 and Susie2 if God created both worlds). Suppose further that there is no better logically feasible world than either W1 or W2. That would mean that there is no such thing as the best of all feasible worlds, in which case God has not created the best of all feasible worlds.

Perhaps the Molinist will argue that were SCCs to have presented God with such a dilemma (or trilemma, or quadrilemma, etc.), then God would have refrained from creating any world at all. The fact that God has created a world can, therefore, be taken as an indication that the SCCs were not set-up such that God could not have had morally sufficient reason for allowing any and all actual instances of evil. The trouble here is that if Molinism requires that SCCs not present this predicament to God, then Molinism may turn out to be intolerably unlikely to be true, for of all the possible ways the SCCs could have turned out, it seems immensely (perhaps infinitely) more probable that God be faced with just such a predicament than not. For any SCC-set1 which allows for a best of all feasible worlds, there is a set [SCC-set2, SCC-set3… SCC-setn] every member of which precludes there being a best of all feasible worlds and represents a ‘closer’ logically possible SCC-set to SCC-set1 than any SCC-setx which also allows for a(nother) best of all feasible worlds.

The Molinist may object that probabilities aren’t what they seem here, since one might naïvely assume that given a randomly selected number from the set of all numbers, one is more likely to get an even number than a prime, but this is demonstrably false.[21] However, the key here is the relative closeness of the SCC-sets which morally prohibit God’s creating any world at all. For every cluster of SCCs related by family resemblance, the majority of possible SCC-sets in the vicinity will be creation-prohibiting. Imagine throwing a dart from an infinite distance in the direction of an infinite set of floor tiles each of which had one minuscule red spot, and having the dart land precisely on one of those red spots; this is what it would be like for God to happen-upon an SCC-set which isn’t creation-prohibiting.[22]

Moreover, even if the possible ‘SCC’ sets made it no more likely than unlikely that a best of all logically feasible worlds is instantiable, the fact that Molinism in principle allows the set of SCCs to proscribe God’s creating the world means that the conditional probability of Molinism given that a world exists is (significantly?) less than the conditional probability of Thomism; Pr(M|World)<<Pr(T|World).

Molinism also fails to preserve as strong a notion of God’s sovereignty as Thomism because it suggests that there are contingent objects/elements in the world over which God has absolutely no control. God is, as it were, simply confronted with SCCs which are beyond his power to do anything about, and He must make due as best He can with them. God’s omnipotence is also apparently undermined (or unnecessarily restricted) for, on standard Molinism, if it is true that ‘S if placed in C would freely do A’ then “even God in His omnipotence cannot bring it about that S would freely refrain from A if he were placed in C.”[23] In an attempt to evade such difficulties thinkers like Kvanvig have defended what is referred to as ‘maverick Molinism,’ according to which “though counterfactuals of freedom have their truth-value logically prior to God’s acts of will, God could have so acted that these counterfactuals would have had a different truth value from that which they actually have.”[24] This view, however, retains the rest of the disadvantages of Molinism, along with inviting the disadvantages which are supposed to attach themselves to the Thomistic view, such as that God becomes the author of sin. So, the Molinist’s only way out of this objection turns out to be less attractive than abandoning Molinism altogether (and embracing Thomism).

Another problem with Molinism is that it seems incompatible with the principle of sufficient reason (PSR), according to which for every true proposition there is available some sufficient explanation of why it is true. This principle has fallen into disrepute among many philosophers today, but there are very good reasons for being reluctant to abandon it. First, the PSR seems extremely plausible at first blush, and is even considered by many to be self-evident.[25] Second, no principle should be considered philosophically proscribed by a philosophical commitment with comparably less intuitive plausibility, but Molinism and its constitutive philosophical commitments seem less intuitively plausible than the PSR. Third, although the PSR faces some impressive philosophical challenges, none of these are insuperable.[26] Finally, Pruss has offered impressive arguments for thinking that if the PSR is rejected then this would undermine not only “the practice of science,”[27] but also philosophical argumentation itself.[28]

The inconsistency between Molinism and the PSR is that whereas the PSR entails that there exists some sufficient reason for the truth of the SCCs which God knows, Molinism seems to require[29] that these truths be without any sufficient explanation. The SCCs are not determined by God, nor can they be determined by the properties of the actual world, including properties of actual persons, since these counterfactuals are explanatorily prior to the existence of the actual created world and its denizens.

Perhaps the Molinist can offer some arguments here in response; the Molinist can say, for instance, that statements of the general form “had S been in circumstance C, S would freely have done A” seem meaningful, and, if meaningful, must be either true or false. Many have argued this way by appealing to a “subjunctive conditional law of excluded middle (SCLEM),”[30] though I think one can erect an equally good argument on the basis of the law of excluded middle (LEM) itself. Since any SCC statement about what libertarian free persons would do in non-actual circumstances is true or false if and only if it is meaningful (by LEM), one need only maintain that it is meaningful in order to draw out the conclusion that it is true or false. For any SCC*, and its negation ‘~SCC*’ at least one of them will be true, whether it has a sufficient reason or not. This method of argument attempts to offset the implausibility of rejecting the PSR with the implausibility of rejecting the LEM. Moreover the Molinist can perhaps hold to a weakened, and yet still intuitively plausible, version of the principle of sufficient reason. Timothy O’Connor suggests, for instance, that “one should seek explanation for every fact other than those for which there is an explanation of why there can be no explanation of those facts.[31] This weakened principle salvages some of the intuitive appeal of the PSR, but also allows wiggle-room for the Molinist to get away with positing brute facts, so long as the Molinist can come up with some plausible story about why there can be no explanation of a subjunctive counterfactual conditional’s truth.

Although this line of argument appears to allow the Molinist to eschew uncomfortable questions about what sufficient reason there could be for SCCs, in order to argue that this weakened principle will excuse the Molinist from having to explain why the true SCCs are true, the Molinist will have to provide some explanation of why the Thomistic alternative is not (broadly) logically possible. This is not merely a tall order, it is to all appearances hopeless. In fact, the Thomist can offer an argument from ‘LEM & PSR’ for Thomism by noting first that SCCs are meaningful, and that, if true, they must have an explanation (by PSR). Thomism offers an explanation for them in terms of God’s will, and Molinism offers no explanation for them at all. Because Thomism finds no obstacle in the PSR, it has this quintessential philosophical advantage over Molinism.

The most significant difficulties, and perhaps the only real difficulties, with the Thomistic view are (i) that it appears to make God the author of sin, along with (ii) making it difficult, at best, to use a free-will defense against the problem of evil. Let us note, before offering some brief remarks about how to possibly avoid these problems, that on balance one should prefer these two difficulties to the set of difficulties Molinism comes with. Thus, even if all the ways Thomists have proposed to deal with this fail (and even fail miserably) Thomism would still be on balance preferable to Molinism. Turning to the first problem, there may be hope for the Thomist to mitigate it if he maintains that “although there is coequal responsibility for the existence of sin [between God and creature], it does not follow that there is coequal blame for sin… [for] blame attaches to actions, and actions are characterized by intentions,”[32] but God and man perform intentionally different actions in bringing it about that X. Second, one can safeguard genuine freedom if “the truth-values of the conditionals are shaped by God’s activity of willing… and yet these truth-values not be “up to God” in the relevant sense[.]”[33] However, even if such problems cannot be solved, Thomism remains preferable, on balance, to Molinism.

[1] I am not sure if it makes sense to talk about ‘nearer’ or ‘farther’ logically impossible worlds, but if it does then I will want to say that God’s natural knowledge will include this as well, and that the nearness and farness of logically impossible worlds from each other, or from possible worlds, or from the actual world, will all be necessary truths to which God has unbridled access.

[2] I am here tacitly assuming a B-theory of time. A-theorists can rephrase as ‘neither actual, nor to be actual, nor previously actual.’

[3] The term is borrowed from William Lane Craig, who explains that some worlds, even if logically possible, are not feasible for God to create in light of the fact that the relevant subjunctive counterfactual conditionals effectively prohibit such a world from being actual. See William Lane Craig, “Yet Another Failed Anti-Molinist Argument,” in Molinism: The Contemporary Debate (2012): 144-62.

[4] I say contingent because there are clearly some logically necessary subjunctive counterfactual conditionals if (i) Theism is true and (ii) God has free will. For instance, consider: “If Tara had freely chosen to reject God, then God would have (freely) chosen to allow her to damn herself.

[5] Robert Merrihew Adams, “An Anti-Molinist argument,” in Philosophical Perspectives (1991): 345.

[6] See William Lane Craig’s debate with Ray Bradley,

[7] Robert C. Koons, “Dual Agency: A Thomistic Account of Providence and Human Freedom,” in Philosophia Christi 4, no. 2 (2002): 3.

[8] See Jonathan L. Kvanvig, “On Behalf of Maverick Molinism,” in Faith and Philosophy 19, no. 3 (2002): 1.

[9] I will take it that if any stage in an explanatory sequence involves mindless unintentional indeterminism, and if it, in turn, strictly entails all the explanatorily posterior elements in that explanatory sequence, then the explanandum in that sequence can be said to result from a mindless unintentional indeterministic process.

[10] Which is just to say that free actions cannot be logically entailed.

[11] This symbol, for Hasker, indicates broadly logical entailment/necessitation.

[12] Thomas P. Flint, “A New Anti-Anti-Molinist Argument,” in Religious studies 35, no. 03 (1999): 299.

[13] Where by causal determinism I mean that for any event, either all subsequent events are causally necessitated by it, or it is causally necessitated by antecedent events.

[14] Robert Merrihew Adams, “An Anti-Molinist argument,” in Philosophical Perspectives (1991): 350.

[15] Robert Merrihew Adams, “An Anti-Molinist argument,” in Philosophical Perspectives (1991): 350.

[16] William Lane Craig, “Robert Adams’s New Anti-Molinist Argument,” in Philosophy and Phenomenological Research 54, no. 4 (1994): 858.

[17] Robert C. Koons, “Dual Agency: A Thomistic Account of Providence and Human Freedom,” in Philosophia Christi 4, no. 2 (2002): 5.

[18] Robert C. Koons, “Dual Agency: A Thomistic Account of Providence and Human Freedom,” in Philosophia Christi 4, no. 2 (2002): 5.

[19] I replaced Koons’ “the creature” with “the world” because it seems wrong to say that SCCs are ‘creatures’ on the Molinist view, but the way Koons’ argument proceeds seems to treat SCCs as a threat to God’s impassibility for this reason (i.e., the reason cited in the quotation).

[20] Robert C. Koons, “Dual Agency: A Thomistic Account of Providence and Human Freedom,” in Philosophia Christi 4, no. 2 (2002): 6.

[21] I would have to confer with a mathematician, or a philosopher specializing in the philosophy of mathematics, in order to verify this, but to the best of my knowledge mathematicians can prove, and have proven, that the infinite set of even numbers and the infinite set of prime numbers can be bijected (without remainder) so that the probabilistic resources in either case is mathematically equivalent, and, therefore, the odds of getting either a prime number, or an even number, would be the same. Supposing I am wrong about this (and it’s entirely possible that I am), then the argument works in my favor (against Molinism) even more conspicuously, for there seem to necessarily be proportionally more SCC-sets which present God with a dilemma, trilemma, quadrilemma (etc.) than SCC-sets which do not.

[22] I don’t know if this is right, but I’m trying to suggest that the relative closeness of creation-prohibiting SCC-sets (as compared to the creation-permitting SCC-sets) gives us reason to think that the Molinist story is improbable. Also, note that if Intelligent Design theorists are right about our ability to make a rational inference to design on the basis of something like specified complexity, it seems reasonable to say that the apparent fine-tuning of the actually true SCC-set cries out for an explanation, but this explanation cannot be given by Molinism (though it can be provided by Thomism).

[23] William Lane Craig, “Yet Another Failed Anti-Molinist Argument,” in Molinism: The Contemporary Debate (2012): 127.

[24] Jonathan L. Kvanvig, “On Behalf of Maverick Molinism,” in Faith and Philosophy 19, no. 3 (2002): 1.

[25] Alexander R. Pruss, “The Leibnizian Cosmological Argument,” in The Blackwell Companion to Natural Theology (2009): 26-28.

[26] I do not have the space to argue this here, but I would refer readers to: Alexander R. Pruss The Principle of Sufficient Reason: A Reassessment Cambridge University Press, 2006.

[27] Alexander R. Pruss The Principle of Sufficient Reason: A Reassessment (Cambridge University Press, 2006): 255.

[28] Alexander R. Pruss, “The Leibnizian Cosmological Argument,” in The Blackwell Companion to Natural Theology (2009): 45.

[29] Flint does apparently argue that SCCs are within our volitional control. See Robert C. Koons, “Dual Agency: A Thomistic Account of Providence and Human Freedom,” in Philosophia Christi 4, no. 2 (2002): 12. This is, perhaps, an exception to the rule, but it also seems convoluted for reasons Koons deals with in his paper.

[30] Alexander R. Pruss, “The subjunctive conditional law of excluded middle,”

[31] Timothy O’Connor, Theism and Ultimate Explanation: The Necessary Shape of Contingency. John Wiley & Sons, 2012: 84.

[32] Robert C. Koons, “Dual Agency: A Thomistic Account of Providence and Human Freedom,” in Philosophia Christi 4, no. 2 (2002): 23.

[33] Robert C. Koons, “Dual Agency: A Thomistic Account of Providence and Human Freedom,” in Philosophia Christi 4, no. 2 (2002): 7.