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

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

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

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

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

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

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

 

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

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

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

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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.

Math, therefore God?

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

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

The Argument from Mathematical Beauty

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

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

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

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

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

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

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

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

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

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

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

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

The Argument from the Applicability of Mathematics

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

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

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

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

Argument from Mathematical Truth

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

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

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

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

[1] Gillings, Richard J. “The so-called Euler-Diderot incident.” The American Mathematical Monthly 61, no. 2 (1954): 77-80. http://www.fen.bilkent.edu.tr/~franz/M300/bell2.pdf

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

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

[4] Paul J. Nahin, Dr. Euler’s Fabulous Formula: Cures Many Mathematical Ills, (Princeton University Press, 2011), 1. https://books.google.co.uk/books?id=GvSg5HQ7WPcC&pg=PA1&redir_esc=y#v=onepage&q&f=false

[5] Robin Collins, The Case for Cosmic Design, (2008), http://infidels.org/library/modern/robin_collins/design.html

[6] John Polkinghorne, Science in the Public Sphere, http://www.veritas.org/science-public-sphere/

[7] William Lane Craig, Is Faith in God Reasonable? William Lane Craig vs. Dr. Rosenberg, http://www.reasonablefaith.org/debate-transcript-is-faith-in-god-reasonable

[8] I am really, honestly, no more sure of this counter-argument than I am of the argument. For those interested, please do check out the debate between Craig and Daniel Came on the Unbelievable? Podcast, which you can also find here: https://www.youtube.com/watch?v=nn4ocx316dk

[9] J.T. Bridges defends this view: https://www.youtube.com/watch?v=eFU1BKxJf1k

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

Naturalism and Supernaturalism

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

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

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

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

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

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

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

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

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

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

Let’s try a third:

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

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

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

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

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

[1] Ludwig Wittgenstein, Philosophical Investigations second edition, transl. G.E.M. Anscombe (Blackwell Publishers, 1999). http://lab404.com/lang/wittgenstein.pdf

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

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

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

[5] http://iweb.langara.bc.ca/rjohns/files/2015/03/Quine_selection.pdf

Two Too Simple Objections to Open Theism

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

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

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

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

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

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

Here’s a second argument:

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

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

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

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

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

 

Token-Omniscience?

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

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

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

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

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

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

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

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

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

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

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

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

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

 

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

 

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

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