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 = <https://plato.stanford.edu/archives/win2013/entries/fitch-paradox/&gt;.

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. https://en.wikipedia.org/wiki/Bekenstein_bound

16“Bekenstein Bound,” Wikipedia, accessed March 24,2017. https://en.wikipedia.org/wiki/Bekenstein_bound

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.

Banach-Tarski paradox, א Infinities, Infinitesimals, and the A-theory

I will offer an analysis of what is going wrong with the Banach-Tarski paradox suggesting that points, construed as infinitesimal surface areas, are nothing more than mathematically useful fictions. I will suggest that infinitesimals raise the same kinds of modally-prohibitive paradoxes in metaphysics as positing actually infinite quantities does (and for the same or similar reasons), and then consider an argument against the A-theory (in most of its forms) which can be purchased from these insights. I will then scout out some philosophical avenues available to the A-theorist.

The Banach-Tarski paradox is a famous mathematical paradox according to which it can be proved that if you divide the surface area of a sphere into little bits, and simply rearrange the bits appropriately, you can reconstruct two spheres each with the same surface area as the original sphere. In layman’s terms, you can prove (something just a shocking as) that 1=2.[1] To explain how it works, it may be worth calling to mind the various paradoxes associated with actual infinities.

Consider what it would be like to count upwards from -7 to infinity and stop only once you’ve arrived. Even if given an infinite amount of time you would never arrive, because no finite additions can sum up to a transfinite quantity. Subtract infinity from infinity, and what do you have? You have zero, but you also have infinity, and you also have 18.9801 (and every other real number); all of these are not just legitimate answers, they are mathematically correct answers. However, clearly 18.9801 is not equal to either zero, infinity, or anything else! Have a (Hilbert) hotel with an infinite number of rooms, all of which are occupied, and you want to check in an infinite number of new guests? No problem, just move every person from the room they are in (n) to the room with a room number equivalent to two times the original room’s room number (2n). Done; you’ve managed to move people around in such a way as to create an infinite number of vacant rooms without asking anyone to leave. Most of us (who are interested in this sort of thing) know the myriad paradoxes which arise from postulating even the possibility of an actual infinity. It seems relatively philosophically secure that there cannot be an א number of things (where א represents the first transfinite number, not to be confused with ∞ which symbolizes infinity taken as a limit rather than a quantity). If there are philosophically sophisticated caveats then so be it, but the point will remain that there are plenty of examples of things for which having an א number of them is clearly (broadly logically) impossible.

Let’s return, for a moment, to Hilbert’s Hotel, because it’s a particularly useful illustration. Suppose that the guest in room 3 checks out, while all the (infinitely many) other rooms remain occupied. The desk clerk decides that they want every room occupied, so they ask each person in room n (where n>3) to move one room over; that is, from room n to room n-1. That will fill up room 3, but the process will also leave no room empty because there is no room number n for which there is not an occupied room n+1. This works equally well for two dimensional shapes, such as circles; remove one ‘point’ from the circumference of a circle and you may have an infinitesimal gap, but simply move every other point along the circumference over (uniformly) by an infinitesimal amount and, voila, the gap is plugged and there will be no new gap. The trick in the case of the Banach-Tarski paradox is to apply the same reasoning to three-dimensional objects. For the best explanation of this paradox I’ve ever seen, (especially for readers who aren’t familiar with it, please make your life better and) check out Vsauce.

Alexander Pruss has noted on his blog that this result “is taken by some to be an argument against the Axiom of Choice.”[2] However, he argues that you can get the same paradoxical result in similar cases (and even in the same case) without the axiom of choice, so that the axiom of choice should be cleared of all suspicions. I agree (though I’m certainly no expert). Richard Feynman is purported to have said, upon being shown the proof, that “it’s fine you can do it with ‘continuous spheres’, since there’s no such thing. The important thing is you can’t do it with oranges, because oranges are made of a finite number of indivisible parts.” I think he is wrong about oranges (being actually comprised of indivisible finite parts, at least if the ‘parts’ are extended in three spatial dimensions), but his sentiment is appreciably insightful nonetheless.

The problem with the paradox, in my submission, is that it divides the surface of the sphere up into points. However, points on a sphere, like points on a line segment, are infinitesimals. This is precisely why (Aristotelians) say that line segments are not composed of points the way walls are composed of bricks, but, instead, points act as the limits between which a line segment is continuously extended. An infinitesimal is a quantity which is infinitely small. It is non-zero, but it is also smaller than any finite quantity. Sure infinitesimals are useful for doing things like infinitesimal calculus, developed by one of my all time favorite philosophers Gottfried Wilhelm Leibniz, but they remain, I believe, nothing more than useful fictions. To borrow a phrase from W.L. Craig;

“They are akin to ideal gases, frictionless planes, points at infinity, and other useful fictions employed in scientific theories.”[3]

If we are to accept the possibility of infinitesimal quantities in reality, then we will quickly run into paradoxes like the Banach-Tarski paradox (which, quite apart from being obnoxious to the rational intellect, seems to violate the law of conservation of matter and energy). Positing infinitesimals is just as paradoxical as positing sets of actually infinitely many discrete things (where ‘things’ is an ontologically loaded term). I am suggesting that infinitesimals are just as paradoxical as actual infinities, and, at bottom, for the same reason(s). In fact, I have this intuition that every argument for thinking that there cannot be any actual infinities (as opposed to potential infinities, where ‘infinity’ merely acts as a limit), admits of a parody for an argument against the existence of infinitesimals. I’m not sure I can rigorously prove it, but I think it’s very plausible.

It seems to me that there’s something conceptually parasitic about infinitesimals relative to infinities. They each conceptually supervene on each other symmetrically. To visualize this symmetry, consider plotting the function ƒ(x)=  1/x which will look like this:

[http://mathworld.wolfram.com/images/eps-gif/AsymptotesOneOverX_1000.gif]

The distance between the curved line and the x-axis (i.e., y=0) as x approaches (positive or negative) infinity is shrinking (or, at least, its absolute value is shrinking), and approaching an infinitely small non-zero measure. When X is infinite, the absolute value of the y-axis coordinate of the curved line (i.e., the distance between the curved line and it’s asymptote, here being the x axis) is infinitesimally small. This example helps to illustrate the point that the concept of an infinitesimal is bound up with the concept of infinity, so that in the absence of one the other would be inconceivable. That at least motivates the suspicion that if one turns out to be metaphysically impossible, so will the other.

What relevance does this have for the philosophy of time? Well, consider that on the A-theory there is such a time as the present. How long does the present last? What, precisely, is its magnitude, its duration? Let’s consider the following argument:

  1. If the A-theory is true, then the present is either infinitesimal in duration, or it is finite in duration.
  2. The present cannot be infinitesimal in duration.
  3. The present cannot be finite in duration.
  4. Therefore, the A-theory is false

Premise 3 can be established with Leibniz’ argument against the (logical) possibility of a physically indivisible element, or ‘atom’ (in the etymologically literal sense). For anything extended in three-dimensional space, however small, it will always be logically possible for me to divine it in two, even if I am physically incapable of doing so (due to some constraint, such as not having the appropriate equipment for the job, or maybe not even being able to develop any tool which could do the job). Physical impossibilities are not (all) logical impossibilities, and logically there is no constraint on how many times I could divide an object extended in space. To say that there is an object extended in space which is not logically possibly divided up into smaller constituent pieces is, according to Leibniz, incoherent. The exact same argument, mutatis mutandis, works against there being chronons (i.e., atomic chunks of time).

The denial of premise 2 is absurd given our observations that positing infinitesimals leads to modally unconscionable paradoxes like Banach-Tarski.

Ways out: I see four ways, not all of them equally viable, for an A-theorist to escape the conclusion of this argument.

First, they could challenge premise 3 on the grounds that, if there are chronons, then by definition they are entities which cannot be physically divided. The suggestion would be that the prima facie absurdity of a Chronon de dicto doesn’t entail the impossibility of a chronon de re. This dangerously dislocates rational intuition from epistemic reliability, but I can imagine extreme empiricists embracing this response.

Second, they could challenge premise 2 by arguing that positing any more than one real infinitesimal of any kind might be problematic, but that there’s no way to derive similar paradoxes from positing a maximum of one infinitesimal. In other words, perhaps paradoxes involving infinitesimals only arise when there are n infinitesimals, where n ∈ ℕ, and n>1. Multiply an infinitesimal by any natural number, or even a transfinite number, and you will still get an infinitesimal result, so it seems harder to show that from one infinitesimal you could derive some kind of contradiction.

Quick thought: Perhaps if there are rules/axioms such as (i) no infinitesimal can be larger or smaller than any other infinitesimal, but (ii) anything (other than 1) to the power of itself is larger than itself, you could derive a contradiction by taking an infinitesimal X, running it through Xx=Y, and then asking whether Y is larger than X, or the same size (it appears to be both). However, I don’t have the kind of facility in mathematics to be able to produce a rigorous proof that even a single infinitesimal would lead to some kind of contradiction or unconscionable paradox. Moreover, it isn’t entirely clear to me what relevance that kind of mathematical paradox would have for the metaphysical consideration at hand. In any case, the second challenge to premise 2 cannot be lightly dismissed.

Third, one could adopt a really wild philosophy of time, such as the Apresentism I wrote about in the last post (thus denying the first premise).

Fourth, one could deny the first premise by adopting what has been called a non-metric view of the present. This is the view preferred by William Lane Craig.[4] I have more than expended my allotted time for blogging and casual writing today, so I will leave this post here for now. I may return to the idea of non-metric present in the (near) future in another post.

[Ha, I don’t presently have time to write more. Get it?]

[1] For fun, check out and try to find the mistake in the following mathematical proof that 1=2 here: https://www.math.toronto.edu/mathnet/falseProofs/first1eq2.html

[2] http://alexanderpruss.blogspot.ca/2013/06/the-banach-tarski-paradox-and-axiom-of.html

[3] William Lane Craig, “Response to Greg Welty,” in Beyond the Control of God: Six Views on the Problem of God and Abstract Objects, ed. Paul Gould (A&C Black, 2014), 102.

[4] See: Craig, William. “The extent of the present.” International Studies in the Philosophy of Science 14, no. 2 (2000): 165-185.

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, http://www.reasonablefaith.org/can-a-loving-god-send-people-to-hell-the-craig-bradley-debate#section_1

[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,” http://alexanderpruss.com/papers/SCLEM.html

[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.

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: http://www.newadvent.org/cathen/02033b.htm

[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.” http://www.reasonablefaith.org/defenders-2-podcast/transcript/s3-5#ixzz3oMoGGJIJ

[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), [http://plato.stanford.edu/archives/win2013/entries/fitch-paradox/].

[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.

A Scientistic argument for Determinism, and some related thoughts

I would like to write a little bit, today, about Determinism. First, I want to try to give another argument for determinism which occurred to me recently (though I think it is a very poor argument, but may be worth mentioning if for no other reason than that it is some kind of argument for determinism). Following this I wish to draw on a thought experiment presented by Alexander Pruss to show that libertarian free will can be consistently combined with physical determinism.

What arguments are there for determinism? Let us take determinism to be the thesis that for any even E, E either follows of causal necessity from some prior (or posterior) event(s), or else from E every event follows of causal necessity. To avoid trouble, let us stipulate that no two events are both simultaneous and non-identical (i.e., events are complete states of affairs at a moment). Obviously the reason I used ‘causal’ necessity in the definition, as opposed to logical necessity, is that at any time t1, plausibly there is a future-tense (or past-tense) fact about any time t1+n (where n can be negative), so that at least one proposition at any time (and thus for any E) will logically entail every other proposition at every other time. Even the libertarian accepts that, so we should be careful not to conflate that with determinism.

I have said previously that I can think of one argument for a modest kind of determinism which would still be strong enough to rule out libertarian free will; 1) that human beings are entirely material entities, 2) that all material entities are governed entirely by deterministic physical laws, and therefore 3) human beings are determined to act and think exactly as they do act and think. I mentioned that this argument seems implausible to me for two reasons; first, that human beings are not plausibly entirely material entities,[1] and second that the laws of physics are not actually deterministic.[2] However, notice that this argument, even if it were sound, would not go as far as to entail that determinism per se is true (but only that physical determinism is true), nor would it give us any justificatory reason(s) for believing that determinism is true. Additionally, the restriction to physical determinism may actually undermine determinism per se. On determinism per se, even the universe is deterministically caused to begin to exist (assuming it does so), but on physical determinism there is no physical determinant responsible for the beginning of space, time, energy and matter. Physical determinism would, then, imply that materialism (and anything like it) is false, or that determinism per se is false. That’s a hard bullet for the champion of scientism to bite.

Here’s a more ambitious argument for determinism:

  1. Determinism is a necessary presupposition of the scientific method.
  2. The scientific method is the only, or in any case the best, avenue to genuine discovery (i.e., the finding of truth, since a discovery of something false is not a genuine discovery).
  3. Therefore, the presupposition of determinism is a necessary condition of the only, or in any case the best, avenue to genuine discovery (i.e., to the truth).
  4. For any P, if P is a presupposition necessary for the only, or in any case the best, avenue to genuine discovery, then P ought to be believed.
  5. Therefore, determinism ought to be believed.
  6. For any P, if P ought to be believed then P is true (i.e., nothing untrue ought to be believed).
  7. Therefore, determinism is true.

We might call this a presuppositionalist argument for determinism. If it were sound then it would provide us with a good reason to believe that determinism is true.[3]

Is this argument any good? Unsurprisingly, I think not. To start off, the first premise seems dubious, especially in light of the same points I made in response to the last argument for determinism which I examined – namely that quantum mechanics may not be deterministic (and yet clearly indeterministic theories of quantum mechanics are scientific, whether or not they are possibly true), and even Newtonian mechanics is certainly not deterministic (and yet, again, is clearly scientific, regardless of whether it is true, or even possibly true – scientific theories can suggest metaphysical impossibilities without ceasing to be scientific). The second premise is also problematic in my view, since it seems to me to simply enunciate the prejudice of scientism, which we have no good reasons for accepting, along with very good reasons for rejecting. So, I outright reject both of the first two premises of this argument.

I also think there are significant problems with the sixth premise which, even though I accept it, seems dubious on the assumptions of determinism and scientism. If determinism is correct, that seriously threatens the possibility of genuine ethics, including the ethics of belief, and if scientism is true then we have no good reason for believing that there are no false beliefs which we ought to adopt (for instance, if scientism and determinism are true, maybe I ought to believe that I am free in a morally relevant sense, even though, in fact, I am not and cannot be – or, paradoxically, if determinism/scientism are true, then, possibly, I ought not to believe that they are true). The whole reason for thinking that a belief ought to be believed if and only if it is true is based on a kind of metaphysical conception of truth on which truth, beauty and goodness are, we might say, ‘natural siblings.’ This makes perfect sense on the Christian way of seeing things, as well as many (perhaps most) other worldviews, but it does not make much sense on materialism or naturalism (which scientism enjoins on us). I’m not even sure it makes much sense on any non-materialist, but yet deterministic, view of the world (like the Calvinist worldview).[4]

Returning to the topic of physical determinism, I would now like to talk about an illustration I found in Pruss’ writing which helps to show that physical determinism is logically compatible with libertarian free will. Pruss uses the image of a cannonball flying through the air to clarify the difference between the Principle of Sufficient Reason (PSR) and what he calls the “Hume-Edwards-Campbell Principle” (HECP). According to the HECP, if each member of an infinite set could be explained in terms of the preceding member(s) then (i) every member of the set would be explained, and (ii) the set itself would stand in need of no additional explanation. The HECP is sometimes used as a response to cosmological arguments from contingency, for obvious reasons. Hume, for instance, writes:

Add to this that in tracing an eternal succession of objects it seems absurd to inquire for a general cause or first author. How can anything that exists from eternity have a cause[?]… In such a chain, too, or succession of objects, each part is caused by that which preceded it and causes that which succeeds it. Where then is the difficulty? But the whole, you say, wants a cause. I answer that the uniting of these parts into a whole, like the uniting of several distinct countries into one kingdom or several distinct members into one body, is performed merely by an arbitrary act of the mind and has no influence on the nature of things. Did I show you the particular causes of each individual in a collection of twenty particles of matter, I should think it very unreasonable, should you afterwards ask me, what was the cause of the whole twenty. This is sufficiently explained in explaining the cause of the parts”[5]

This principle is, I believe, demonstrably wrong for several reasons, though my favorite demonstration is provided by Pruss who proves that an infinite series of successive explanations is logically equivalent to one great big viciously circular explanation. However, my interest here is not to find out whether the HECP is correct, but how thinking through the HECP can help make clear how physical determinism is compatible with libertarian free will.

To illustrate the difference, let’s imagine that there were a cannonball flying through the air in a logically possible world where there was no time at which the cannonball was not flying through the air. Every point in time at which the cannonball was in a certain place, going a certain speed in a particular direction, those facts could all be explained by pointing to facts about where a cannonball was (how fast it was going, and in what direction it was moving) at a preceding point in time (at least presuming the regularity of its motion, which is to say that its motion is governed by certain laws). For Hume (et al) it would make no sense to ask for an explanation over and above this for the fact that there is a cannonball flying through the air; we can explain why the cannonball exists, why it is moving as fast as it is, and why it is going in this direction rather than that direction, all by referring to facts about the laws governing its movement along with the fact that it existed, where it was, how fast it was moving, and in what direction it was going at some previous time. Where the HECP makes any further explanation unnecessary, the PSR demands that there be an explanation for why there is a cannonball at all, for the PSR demands that there be an explanation of any contingent fact.

Keeping this distinction in mind, let us imagine a logically possible world W which had no beginning, but was just stretched out temporally infinitely in its past, and in which physical determinism is true. At any point in time in W, W could be said to have existed for an infinite number of some unit of temporal length (hours, days, milliseconds, etc.), call this unit T, so that it had no beginning in the sense that there is no first T in W.[6] Now, for any state of affairs in W picked out by any time tn, all the facts about that state of affairs can be explained by the facts which obtain in W at a slightly earlier time tn-1. So, for any state of affairs at any time in W, there is an adequate explanation for that state of affairs in terms of some other state of affairs at another time which deterministically brings it about. In W, the HECP is satisfied by the facts we have laid out, whereas the PSR requires a deeper explanation for the existence of W, and for contingent facts obtaining in W. The PSR reminds us that such explanations are possible, and this will help us to see that libertarian free will possibly coincides with physical determinism.

Bear in mind that all we need to do in order to demonstrate the compossibility of two propositions is to show that there is a logically possible world out there which satisfies both propositions. In W, physical determinism is satisfied. If in/at W there is at least one libertarian-free act (or, technically, even just one libertarian-free agent), then the compossibility of libertarian free will and physical determinism will have been logically demonstrated. Clearly, however, it is logically possible that the existence of W is explained by the voluntary election of a libertarian-free divine agent (i.e., God). If God, in a libertarian-free capacity, chose to create such a world, then the world and all of its happenings would ultimately be explained in terms of God’s acting freely to create it. Thus, physical determinism is clearly logically compatible with libertarian free will. This is because God is, ex hypothesi, not a material entity. Suppose, further, that people are not merely material entities (i.e., the mind is immaterial), but that epiphenomenalism is true of all embodied people, and the mind, which persists after bodily death, becomes libertarian free once freed of the body. So long as this is logically possible its very possibility goes to show that physical determinism is demonstrably logically compatible with libertarian freedom.

However, there may be another way in which libertarian free will is compatible with physical determinism, at least on the B-theory of time. Suppose that there is a set of physical states of affairs P, consisting of {P1, P2, P3… Pn}. Now, suppose that any Pn+1 follows from Pn of causal necessity (for closed physical systems).  Every physical state of affairs in P is causally explained by some other physical state of affairs in P. Nevertheless, it is logically possible that the sufficient reason for a state of affairs in P involves the fact that a libertarian-free agent in that world makes a libertarian-free decision Fn at some time tn. Here, we might schematize this relationship as follows:

P1 → P2 → P3 → P4
↑↑↑↑       ↑↑↑↑
F1           F2

So, although P2 is physically-causally explained (i.e., HECP explained) by P1, P1 and P2 may only be sufficiently explained (i.e., PSR explained) by appeal to F1 (which itself is sufficiently explained just in case it is logically possible that facts about libertarian-free acts can be sufficiently explained).[7] It may seem strange to talk about libertarian-free acts which occur, in some sense, independently of their space-time context (for, if they occurred within that context, then physics, as we’re imagining it, would provide the context and impetus for the decision, along with determining the decision), but certainly that’s no stranger than thinking of God’s choices as libertarian free even though they are independent of any space-time context.

There is also, perhaps, a stranger way in which we can conceive of this relationship of free choices in a space-time context and a physically deterministic world. I should note that I’m not entirely sure whether this is coherent (it may run into unforeseen problems which more extensive analysis could tease out), but my suspicion is that it is coherent (and, therefore, logically possible). We might imagine that the context in which a libertarian free choice is made is physically under-determinative, but that, once a free decision is made, the result is that the world is supplied physical properties which make that decision appear physically determined. Here we have to imagine that free decisions occur with a limited space-time context (an under-determinative one), and that backwards causation is possible (i.e., events from the future can cause things in the past). Then, we might imagine that even though a temporally antecedent state of affairs P1 causally determines that P2 occurs next, a person’s free choice after the time at which P1 is the case, and before the time at which P2 is the case, is the sufficient reason P1 has the causally determinative features it has for bringing P2 about. On this view, a libertarian free agent makes a decision in light of an under-determinative slice of P1, and their making a decision has temporally backwards-reaching effects which supply P1 with all the physical features necessary for it to deterministically bring P2 about. On this view, a libertarian free decision can be the sufficient reason why P1 deterministically brings P2 about, even though P2 is HECP explained adequately in terms of P1 alone. This view is strange only because we generally think of causal sequences as parallel with temporal sequences, but, at least on the B-theory of time, there is no reason causal antecedence and temporal antecedence need to go hand-in-hand; my free decision may (atemporally) cause features of the past, and maybe those features physically-deterministically cause events in the future.

The Temporal Sequence: P1 → Fn → P2

The (atemporal) Causal Sequence: P1* → Fn → P1 → P2

In conclusion then, we still have no good arguments for believing either in determinism per se, nor in physical determinism. Moreover, even if physical determinism were true, we would have, it seems, no good reasons to doubt the fact that we are libertarian free, at least if we accept the possibility of temporally backwards causation (and, therefore, the B-theory). This can more easily be seen when we distinguish the HECP from the PSR, and note the two different levels of explanations which satisfy them. The PSR needn’t be true, but explanations of the kind it demands, if even possible, carve out a space for libertarian-free decisions even in a physically deterministic world.

[1] For further reading on this point, see Koons, Robert C., and George Bealer, eds. The Waning of Materialism. Oxford University Press, 2010.

[2] I cited the Copenhagen theory of quantum mechanics, as well as John Norton’s now famous example of a ball on a dome (in the comments section, in response to a reader), which illustrates that even Newtonian mechanics is not entirely deterministic. I could easily have added (though I did not think to) that Newton’s laws were all stipulated for closed systems anyway, and it is no part of those laws as such to stipulate that the physical universe as a whole is a closed system, so that his laws cannot imply physical determinism. Newtonian physics did not preclude God’s intervention in the world, for instance, and this is precisely why Newton was not being inconsistent when he maintained both that his laws were true, and that God occasionally intervened in the physical world (for instance by providing the planets with an extra ‘push’ every now and again). This demonstrates clearly that Newton’s laws, even if they were deterministic for closed systems (which the ball-on-dome example disproves), wouldn’t come anywhere near to entailing physical determinism.

[3] Not all sound arguments are good arguments, for the soundness of an argument is neither a necessary, nor sufficient, condition of the goodness of an argument (just as the goodness of an argument is neither necessary nor sufficient for soundness). I will discuss this distinction in more detail in an upcoming post. For now, however, observe that if this argument were sound, then it would give us good reasons for accepting its conclusion, or at least for accepting premise 5.

[4] Calvinism requires a compatibilist view of free will and determinism in order to allow normative statements about what one ought or ought not to believe, but I’m not convinced that such accounts are even coherent. In fact, I am convinced they are not.

[5] Pruss quoted a passage from Hume, but I have provided a more extended excerpt of the same passage from Hume. David Hume, “Dialogues Concerning Natural Religion” in Modern Philosophy: An Anthology (Second Edition), Edited by Roger Ariew and Eric Watkins (Indianapolis: Hackett Publishing Company, 2009), 622.

[6] At first I thought, in passing, that if somebody had trouble with the idea of an infinite past I could just say that there was a world W* in which temporally backward causation (i.e., causation from future events to past ones) is the only kind of causal relation which obtains, and where every event is deterministically caused by some posterior event, and although the world has a temporal beginning, it has no temporal end. However, one should only be concerned with actually infinite regresses of past events if one is i) an A-theorist, or ii) worried about infinite chains of causes. If one is an A-theorist, they will not likely accept the possibility of backward causation anyway, and if one is, like me, worried about infinite chains of causes, then they will have the same problem with W* as they had with W. If you, like me, do have a problem with accepting that W is logically possible then either suspend your modal suspicions here for the sake of argument, or just notice that any length of time can be infinitely subdivided, so that over any measurable length of time it is logically possible that an infinite number of causes are at play just in case it is true that there is no particular time tn at which no cause can logically possibly obtain.

[7] I strongly believe they can be sufficiently explained, and this is because I adamantly reject the assumption that all explanations can be reduced to, or expressed by, entailments. However, I will leave off giving an account of this highly contentious position for now; the reader who disagrees with me is invited to accept the weaker conditional claim that if facts about libertarian free actions could be sufficiently explained, then any combination of libertarian free acts might figure into a sufficient explanation for precisely why the physical states of the universe are precisely as they are. However, notice that, for the purposes of my argument, the PSR needn’t be true, it just needs to be possible that there be an underlying explanation which goes beyond the demands of the HECP.