When Absence of Evidence is Evidence of Absence

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

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

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

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

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

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

Just add the premise

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Easing your way into a Worldview

I want to offer a brief reflection on a phenomenon I see often which strikes me as curious; namely, the phenomenon of easing your way into a worldview by piecemeal steps.

In certain religious traditions (most commonly in those traditions typically referred to derogatorily as ‘cults’), there is a proselytic strategy of conveying certain articles of the faith (which may seem intuitive, wholesome, or otherwise welcome) but keeping information about other articles of faith hidden or secret except to the appropriately initiated. Underlying this practice is this unarticulated recognition that several of that religion’s teachings are so outlandish and counterintuitive that to even admit them in public (or in the presence of the uninitiated) would do damage to the cause of winning people over to their faith. As slimy as I’m inclined to think this practice is, there is perhaps something shrewd about it in light of the way most of us form our worldview-sized beliefs. In fact, it may be the case that for most major worldviews (worldviews which, in the free marketplace of ideas, do exceptionally well at winning over a great portion of the human race) people naturally ease their way into them by finding good reasons to affirm them and then making counter-intuitive adjustments along the way to accommodate them. We can illustrate this, in my submission, even by taking a critical look at metaphysical naturalism.

Take naturalism to be, approximately, the belief that (i) ‘God exists’ is not true, (ii) there exist at least some of the theoretical entities postulated by our best science, and (iii) that there exist no entities belief in which cannot be motivated in principle by a scientific view of the world (with the possible exception of God, caveat in casu necessitas). Perhaps naturalism sounds prima facie plausible to many people; the tremendous success of the scientific project of making sense of the world, the apparent superiority of scientific explanations over pre-scientific explanations, the relative implausibility of worldviews competing with naturalism given our new scientifically updated background knowledge about the world, all seem to lend some credence to metaphysical naturalism. One might be led, for these reasons, to adopt a naturalistic worldview and then slowly adjust their auxiliary beliefs accordingly one at a time. First, they may give up robust (or at least traditional) moral realism. Second, they may give up on affirming that there are objectively true (in the correspondence sense) mathematical propositions, or even analytic ones.1 Next they may give up correspondence theory, and then finally they end up denying things like qualia and conscious states.2 Before too long the naturalist will go from sounding soberingly sane to talking about “the illusion that thought is about stuff,”3 and insisting that there are no true sentences (including this one). The conclusions to which one arrives end up being so obnoxious to common sense, so ludicrous to the man on the street, that no sane person could ever agree to them without being eased into accepting them one small step at a time. Just as the frog who remains in slowly warming water until it boils her alive, so too the stubborn naturalist complacently gives in, incrementally, to ostensible insanity; the more comprehensive the atheist’s guide to reality gets, the more it looks like a guide to the surreal.

The very same happens with (some popular versions of) fundamentalism; one begins by finding the Christian worldview plausible for a variety of reasons ranging, perhaps, from natural theology to historical biblical scholarship, from cute arguments (like C.S. Lewis’ trilemma)4 to (Josh McDowell’s)5 systematic apologetics. However, before long one is arguing that the light of supernovae, which has taken millions of years to reach us, was created by God merely a few thousand years ago in order to create the appearance of now-dead stars, or that cancer exists because a talking snake fooled our most primitive human ancestor, or that carbon-dating is so inaccurate that it doesn’t preclude the possibility that dinosaurs were roughly contemporaneous with mankind. In this manner one slides from apparently reasonable starting points to what may as well be Alice’s wonderland.

A similar pattern holds true for lone-wolf thinkers whose worldviews end up being hodge-podge syntheses which hardly anyone else will ever find plausible or intellectually satisfying. Original thinkers from Zeno to Berkeley, from Diogenes to David Lewis put forward philosophies regarded by most to be laughable grandiloquent fictions. It is not surprising, then, that so many should regard the history of philosophy as a museum of the absurd. Even the man who abandons philosophical inquiry altogether creates for himself a view of the world riddled with inconsistencies and idiocies to which he remains blind thanks only to his refusal to reflect critically upon them.

Given this situation, it seems reasonable to ask: is there any stopping the flood of myriad derisory beliefs? The question of how plausible a worldview is seems irrelevant to the assessment of its truth unless the presumption that reality is not too counterintuitive turns out to be correct. If reality turns out to be massively counter-intuitive, then plausibility provides no guide to truth. However, if plausibility is the primary litmus test for believability (after logical coherence, etc.), then we are proverbially up the faecal creek without a paddle.

My reaction to this line of thought is as follows; just as parsimony should be regarded as a signpost of truth in the sense that between any two views, ceteris paribus, the more parsimonious is more likely to be true, so closer alignment with common sense makes a view, ceteris paribus, more likely to be correct. What qualifies as common sense may not be so easily answered, but something like nearly universally shared intuitions about plausibility will qualify (we can leave the details to be worked out elsewhere). Obviously most people are prejudiced, to some degree, in advance of the following exercise, but I think one of the most valuable procedures when it comes to worldview-selection is to take inventory of a (prima facie sufficiently plausible) worldview’s most counter-intuitive consequences and compare them to the most counter-intuitive consequences of competing worldviews. This exercise won’t provide us the means for any definitive doxastic adjudication, but I think it remains one of the best approaches we have to comparing competing worldviews.

The alternative, realistically, is for us to unreflectively slide comfortably into a worldview by taking incremental steps towards the absurd, readjusting our plausibility assignments slowly and surely, and ending up with beliefs we would never have consented to accept had we seen clearly precisely to what it was we were inevitably committing ourselves when we adopted the overarching paradigm in question.

1 See: W.V.O. Quine, “Two Dogmas of Empiricism,” Perspectives in the Philosophy of Language (2000): 189-210.

2 See: William Ramsey, “Eliminative Materialism”, The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta (2016), accessed March 27, 2017. https://plato.stanford.edu/archives/win2016/entries/materialism-eliminative/

3 Alexander Rosenberg, The Atheist’s Guide to Reality: Enjoying Life without Illusions. (WW Norton & Company, 2011), 95.

4 See: C.S. Lewis, Mere Christianity, (Samizdat, 2014): 29-32.

5 Josh McDowell, The New Evidence that Demands a Verdict: Evidence I & II Fully Updated in One Volume to Answer Questions Challenging Christians in the 21 st Century, (Thomas Nelson, 1999).

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.

Notes on a Transcendental Argument from Logic

Nearly ever since I was first exposed to transcendental argumentation through listening to that famous debate between Greg Bahnsen and Gordon Stein,1 I have retained the intuition that there is an interesting potential argument from the fact that there are necessary propositions (necessary, that is, simpliciter) to the conclusion that there is a necessary mind. While the analysis of what it means to be a necessary mind will fall short of the God of perfect being theology or classical theism, it will still provide a being which so resembles God that it significantly undermines atheism. This being may not have all the superlative attributes, but it will be a metaphysically necessary immaterial spaceless timeless being with an intellect (and whatever that entails), et hoc omnes intelligunt Deum. However, to avoid the charge of using St. Thomas’ famous phrase in order to paper-over the chasm between my conclusion and full-blown theism, I will state the conclusion more modestly in terms of which the good old reverend Bayes would approve. Enjoy;

1) There are laws of logic.
2) Logical laws are identical to necessary propositions (exempli gratia [P v ~P])
3) Therefore, there are necessary propositions.
4) Propositions are not real entities which exist mind-independently, but are mind-dependent (i.e., there is no proposition for which there is not at least one subvenient mind).
5) A necessary truth is a truth which obtains in all logically possible worlds.
6) Necessary truths are either grounded in at least one contingent mind, or at least one incontingent mind.
7) There are logically possible worlds without any contingent minds.
8) Therefore, there must be at least one necessary mind.
9) If there is at least one necessary mind then it is a being with intellect (plausibly knowing all necessary truths), which is immaterial (spaceless, timeless) in nature.
10) The conditional probability of theism is, ceteris paribus, greater than the conditional probability of not-theism on the condition that there is at least one metaphysically necessary immaterial being with intellect. 
11) Therefore, theism is probably true, 
ceteris paribus.

There are plenty of points at which one could still object to this argument, but it seems to me that most objections are philosophically more costly than the conclusion. One might also just accept the conclusion but deny that, in fact, things really are equal (i.e., cetera non sunt pariba) in this case. For instance, the objector could insist that there are no propositions which are ‘necessary’ in the sense required here (that is, necessary simpliciter – not a merely model-dependent necessity). They might also insist, for some odd reason, that there are not possible worlds without contingent minds, or that those worlds are possible in a merely model-dependent way while other possible worlds are possible simpliciter. That would be pretty wild. Another might argue that the existence of a metaphysically necessary immaterial mind doesn’t raise the conditional probability of theism at all (maybe because the probability of theism is ‘0’ – or because it is ‘1’). Somebody could, of course, deny the major premise, that there are laws of logic. Somebody may also insist that laws of logic are not identical to the propositions which express them (though that seems to reify them so much as to put the objector, for other reasons, in the near occasion of belief in theism anyway). Alternatively one may think that each premise on its own seems more plausibly true than false, but that the collection of them together seems to have a upper-bounded probability of lower than or equal to 0.5, and that would be a principled way to object.

Edit*: it occurs to me that there’s no way of which I’m aware to really set an upper-bound on the probability of a conclusion. What the objector could say, then, is either that the conclusion just seems to be no more likely than 0.5 (notwithstanding the plausibility of the individual premises), or that the premises collectively set a lower-bounded probability on the conclusion of less than or equal to 0.5, in which case the argument fails to be compelling.

To be fair, this argument of mine very likely draws significantly from the influence of James N. Anderson and Greg Welty,2 whose argument seems, to me, much better than what often passes for responsible argument among presuppositionalists (among whom, I should take a moment to clarify, I adamantly do not count myself).

1 For those interested, you can find the audio of the debate, and the transcript (because the audio is really not great) at the following two links: https://youtu.be/ZLZdOGCE5KQ?t=34s and http://www.brianauten.com/Apologetics/apol_bahnsen_stein_debate_transcript.pdf

2 James N. Anderson and Greg Welty, “The Lord of Non-Contradiction: An Argument for God from Logic” Philosophia Christi 13:2 (2011). http://www.proginosko.com/docs/The_Lord_of_Non-Contradiction.pdf

An Amended Minimal Principle of Contradiction

The law of non-contradiction seems self-evidently true, but it has its opponents (or, at least, opponents of its being necessary (de dicto) simpliciter). W.V.O. Quine is perhaps the most well known philosopher to call the principle into question by calling analyticity itself into question in his famous essay “Two Dogmas of Empiricism,” and suggesting that, if we’re to be thoroughgoing empiricists, we ought to adopt a principle of universal revisability (that is to say, we adopt a principle according to which absolutely any of our beliefs, however indubitable to us, should be regarded as revisable in principle, including the principle of revisability). Quine imagined that our beliefs were networked together like parts of a web in that we have beliefs to which we aren’t strongly committed, which we imagine as near the periphery of the web, which are much less costly to change than the beliefs to which we are most strongly committed, which we imagine as near the center of that web. Changing parts of the web nearer to the periphery does less to change the overall structure of the network than changing beliefs at the center of the web. Evolution has, in operating upon our cognitive faculties, selected for our tendency towards epistemic conservatism.

This, he thinks, is why we don’t mind changing our peripheral beliefs (for instance, beliefs about whether there is milk in the fridge or whether a certain economic plan would better conduce to long-term increases in GDP than a competing plan) but we stubbornly hold onto our beliefs about things like mathematics, logic, and even some basic intuitive metaphysical principles (like Parmenides’ ex nihilo nihil fit). Nevertheless, indubitability notwithstanding, if all our knowledge is empirical in principle, then everything we believe is subject to revision, according to Quine. He boldly states:

… no statement is immune to revision. Revision even of the logical law of the excluded middle has been proposed as a means of simplifying quantum mechanics; and what difference is there in principle between such a shift and the shift whereby Kepler superseded Ptolemy, or Einstein Newton, or Darwin Aristotle?1

This statement is far from short-sighted on Quine’s part. Those who defend his view have suggested that even the law of non-contradiction should be regarded as revisable, especially in light of paraconsistent systems of logic in which the law of non-contradiction is neither axiomatic, nor derivable as a theorem operating within those systems. This is why Chalmers calls attention to the fact that many regard Quine’s essay “as the most important critique of the notion of the a priori, with the potential to undermine the whole program of conceptual analysis.”2 In one fell swoop Quine undermined not only Carnap’s logical positivism, but analyticity itself, and with it a host of philosophical dogmas ranging from the classical theory of concepts to almost every foundationalist epistemological system. The force and scope of his argument was breathtaking, and it continues to plague and perplex philosophers today.

More surprising still is the fact that Quine isn’t alone in thinking that every belief is revisable. Indeed, there is a significant faction of philosophers committed to naturalism and naturalized epistemology, but who think that a fully naturalized epistemology will render all knowledge empirical, and, therefore, subject to revision in principle. Michael Devitt, for instance, defines naturalism epistemologically (rather than metaphysically):

“It is overwhelmingly plausible that some knowledge is empirical, justified by experience. The attractive thesis of naturalism is that all knowledge is; there is only one way of knowing”3

Philosophical attractiveness, I suppose, is in the eye of the beholder. It should be noted, in passing, that metaphysical naturalism and epistemological naturalism are not identical. Metaphysical naturalism does not entail epistemological naturalism, and neither does epistemological naturalism entail metaphysical naturalism. I have argued elsewhere that there may not even be a coherent way to define naturalism, but at least some idea of a naturalized metaphysic can be intuitively extrapolated from science; there is, though, no intuitive way to extrapolate a naturalized epistemology from science. As Putnam puts it:

“The fact that the naturalized epistemologist is trying to reconstruct what he can of an enterprise that few philosophers of any persuasion regard as unflawed is perhaps the explanation of the fact that the naturalistic tendency in epistemology expresses itself in so many incompatible and mutually divergent ways, while the naturalistic tendency in metaphysics appears to be, and regards itself as, a unified movement.”4

Another note in passing; strictly speaking Devitt’s statement could simply entail that we do not ‘know’ any analytic truths (perhaps given some qualified conditions on knowledge), rather than that there are no analytic truths, or even that there are no knowable analytic truths. Quine, I think, is more radical insofar as he seems to suggest that there are no analytic truths at all, and at least suggests that none are possibly known. Devitt’s statement, on the other hand, would be correct even if it just contingently happened to be the case that not a single person satisfied the sufficient conditions for knowing any analytic truth.

Hilary Putnam, unfortunately writing shortly after W.V.O. Quine passed away, provided a principle which is allegedly a priori, and which, it seems, even Quine could not have regarded as revisable. Calling this the minimal principle of contradiction, he states it as:

Not every statement is both true and false”5

Putnam himself thought that this principle establishes that there is at least one incorrigible a priori truth which is believed, if at all, infallibly. Putnam shares in his own intellectual autobiography that he had objected to himself, in his notes, as follows:

“I think it is right to say that, within our present conceptual scheme, the minimal principle of contradiction is so basic that it cannot significantly be ‘explained’ at all. But that does not make it an ‘absolutely a priori truth’ in the sense of an absolutely unrevisable truth. Mathematical intuitionism, for example, represents one proposal for revising the minimal principle of contradiction: not by saying that it is false, but by denying the applicability of the classical concepts of truth and falsity at all. Of course, then there would be a new ‘minimal principle of contradiction’: for example, ‘no statement is both proved and disproved’ (where ‘proof’ is taken to be a concept which does not presuppose the classical notion of truth by the intuitionists); but this is not the minimal principle of contradiction. Every statement is subject to revision; but not in every way.”6

He writes, shortly after recounting this, that he had objected to his own objection by suggesting that “if the classical notions of truth and falsity do not have to be given up, then not every statement is both true and false.”7 This, then, had, he thought, to be absolutely unrevisable.

This minimal principle of contradiction, or some version of it, has seemed, to me, nearly indubitable, and this despite my sincerest philosophical efforts. However, as I was reflecting more deeply upon it recently I realized that it is possible to enunciate an even weaker or more minimalist (that is to say, all things being equal, more indubitable) principle. As a propaedeutic note, I observe that not everyone is agreed upon what the fundamental truth-bearers are (whether propositions, tokens, tokenings, etc.), so one’s statement, ideally, shouldn’t tacitly presuppose any particular view. Putnam’s statement seems non-committal, but I think it is possible to read some relevance into his use of the word ‘statement’ such that the skeptic may quizzaciously opine that the principle isn’t beyond contention after all. In what follows, I will use the term ‘proposition*’ to refer to any truth-bearing element in a system.

Consider that there are fuzzy logics, systems in which bivalence is denied. A fuzzy logic, briefly, is just a system in which propositions are not regarded (necessarily) as straightforwardly true or false, but as what we might think of as ‘true’ to some degree. For instance, what is the degree to which Michael is bald? How many hairs, precisely, does Michael have to have left in order to be considered one hair away from being bald? Well, it seems like for predicates like ‘bald’ there is some ambiguity about their necessary conditions. Fuzzy logic is intended to deal with that fuzziness by allowing us to assign values in a way best illustrated by example: “Michael is 0.78 bald.” That is, it is 0.78 true that Michael is bald (something like 78% true). Obviously we can always ask the fuzzy logician whether her fuzzy statement is 1.0 true (and here she either admits that fuzzy logic is embedded in something like a more conventional bivalent logic, or she winds up stuck with infinite regresses of the partiality of truths), but I digress. Let’s accept, counter-possibly, that fuzzy logics provide a viable way to deny bivalence, and thus allow us to give a principled rejection of Putnam’s principle.

Even so, I think we can amend the principle to make it stronger. Here is my proposal for an amended principle of minimal contradiction:

“Not every single proposition* has every truth value.”

I think that this is as bedrock an analytic statement as one can hope to come by. It is indubitable, incorrigible, indubitably incorrigible, and it holds true across all possible systems/logics/languages. It seems, therefore, as though it is proof-positive of analyticity in an impressively strong sense; namely, in the sense that necessity is not always model-dependent. At least one proposition* is true across all possible systems, so that it is necessary in a stronger sense than something’s merely being necessary as regarded from within some logic or system of analysis.


As a post-script, here are some principles I was thinking about as a result of the above lines of thought. First, consider the principle:

At least one proposition* has at least one truth-value.

To deny this is to deny oneself a system altogether. No logic, however esoteric or unconventional or counter-intuitive, can get off the ground without this presupposition.

Consider another one:

For any proposition* P, if we know/assume only about P that it is a proposition*, then P more probably than not has at least one truth-value.

I’m not certain about this last principle, but it does seem intuitive. The way to deny it, I suppose, would be to suggest that even if most propositions* were without truth-values, one could identify a sub-class of propositions with an extremely high probability of having a truth-value, and that will allow one to operate on an alternative assumption.

[Note: some of the following footnotes may be wrong and in need of fixing. Unfortunately I would need several of my books, currently in Oxford with a friend, to adequately check each reference. I usually try to be careful with my references, but here I make special note of my inability to do due diligence.]

1 W.V.O. Quine, “Two Dogmas of Empiricism,” in The Philosophical Review, Vol. 60, No.1 (Jan., 1951), 40.

2 David J. Chalmers, “Revisability and Conceptual Change in “Two Dogmas of Empiricism”.” The Journal of Philosophy 108, no. 8 (2011): 387.

3 Louise Antony, “A Naturalized Approach to the A Priori,Epistemology: An Anthology. Second Edition, Edited by Ernest Sosa, Jaegwon Kim, Jeremy Fantl and Matthew McGrath. (Oxford: Blackwell publishing, 2000), 1.

4 Hilary Putnam, “Why Reason can’t be Naturalized,” Epistemology: An Anthology. Second Edition, Edited by Ernest Sosa, Jaegwon Kim, Jeremy Fantl and Matthew McGrath. (Oxford: Blackwell publishing, 2000), 314.

5 Hilary Putnam, “There is at least one a priori Truth” Epistemology: An Anthology. Second Edition, Edited by Ernest Sosa, Jaegwon Kim, Jeremy Fantl and Matthew McGrath. (Blackwell: 2000): 585-594.

6 Auxier, Randall E., Douglas R. Anderson, and Lewis Edwin Hahn, eds. The Philosophy of Hilary Putnam. Vol. 34. (Open Court, 2015): 71.

7 Auxier, Randall E., Douglas R. Anderson, and Lewis Edwin Hahn, eds. The Philosophy of Hilary Putnam. Vol. 34. (Open Court, 2015): 71.

A Semantic Problem with Platonism

Previously noted sympathies notwithstanding, I have grave and seemingly intractable problems with Platonism. Perhaps the most severe of these follows from Christian Theism, which suggests that there is one necessary being, God, without whom nothing which exists would exist (in the sense that all other things which exist are ontologically dependent upon God). This is the confession of the central creeds of the faith, starting with the Nicene-Constantinopolitan creed (325-381 A.D.), referred to affectionately by Catholics simply as the symbol of faith. There are, of course, (in my view, quisling) children of the Church who argue that the “all” in “all things visible and invisible” does not quantify over universals, but I think that interpretation exceptionally dubious. However, this is inside baseball at its worst, and bound to leave those uninterested in theological minutia bored or irritated, if not entirely lost.

There is, however, one problem I have with Platonism which is at once subtler, less indirect and more accessible than my principal objection. I have not yet developed this line of thought, and I am unacquainted with any literature which successfully fledges this out into a respectable argument (on that note, if anyone is aware of sources which further develop the thought I am about to present, I would welcome their reading recommendations), but I mean, here, merely to register a suspicion; to gesture, in a vague and lackadaisical way, in the general direction of a possibly indissoluble difficulty. As such, I abandon any pretense to having found a proof (in the form of a compelling falsifier) of anything and submit the comparably modest suggestion that I think I have found a problem. With that caveat, let me invite the reader into the weeds.

There is, I suspect, an under-appreciated difficulty with the Platonist’s claim that universals ‘exist.’ This, as I interpret it, is the central claim of Platonism; Platonism, if it signifies anything, signifies that for any x, if x is a universal then x exists. Symbolically:


(Where Ux means “x is a universal” and Ex means “x exists.”) This helps to differentiate Platonism from other competing views, such as neo-Meinongianism.[1][2] The definition of full-blooded Platonism goes further than this, perhaps, but it certainly signifies no less than this.

Let us bracket, for the moment, concerns about using ‘exists’ as though it were a (first-order) predicate. I note in passing, however, that if one insists on existence being a second-order predicate indicating that the thing to which it applies has at least one first-order property, then platonic forms will have properties, and there an interesting puzzle arises, for all (first-order non-vacuous standalone) properties are universals, thus implying that universals may be properties of universals. Indeed, there may be cases where two (or more) universals are symmetrically related to each other as each other’s properties (each one being a property of the other(s)).[3] This is all both interesting and moot, for even if all properties are universals, not all universals are properties, and the argument is, as far as I can see, compatible with any (metaphysical or semantic) analysis of ‘existence.’

It should also be appreciated that some views on universals may carry the implication that existence is a first-order predicate after all. I am not an expert on neo-Meinongianism, but it seems, on its face, to entail that existence is a property (for it maintains that there are actual non-existent objects, as well as actual existent objects).[4] The Stanford Encyclopedia of Philosophy entry under Alexius Meinong does, however, note the following:

“Meinong’s distinction between judgments of so-being and judgments of being, combined with the indifference principle that being does not belong to the object’s nature (so-being), reminds one of Kant’s dictum that being is not a real predicate. Meinong did not accept the ontological argument either, and argued that “being existing” is a determination of so-being and can in a certain sense be properly accepted even of the object “existing golden mountain,” and, say, even of the object “existing round square,” whereas “existence”, which is a determination of being, will no more belong to the one than it does to the other (1907, §3; 1910, §20, 141 [105]).”[5]

So perhaps it is unclear whether Meinong’s view, properly interpreted, does imply that existence is a first-order predicate. In any case, it may have this implication, and that suffices for maintaining that, for all we now, Platonism may have this implication as well. For the purposes of this post, therefore, I ask that the reader give me some leeway in allowing me to speak as though existence is a property.

A Platonist, as here understood, is committed to the existence of universals, and universals are those things which can be said of many. Existence, however, can be said of many. Existence is, therefore, a universal, and the Platonist is committed to its existence. But now we draw nearer to the problem. How is it that one platonic form can be a constitutive property of itself? Can existence be a property of existence? If existence must be said to exist, either it will be said to exist in some non-univocal sense, or else the statement will become transparently bankrupt of propositional content. In the first case, something may be said to exist either equivocally or analogously (the only alternatives to univocity). If equivocally, I defy (with nearly hubristic confidence) anyone to make heads or tails of the statement. On the other hand, analogous predication, being already difficult to make good sense of, leaves me, here, feeling as nauseous as I imagine it must feel to be lost at sea. At least with Theism I can make some headway with this philosophically abstruse doctrine, since there is a paradigmatic exemplar to be intimated (along with some reasons for suspecting that the created order would intimate its creator, in much like the way structural realists in the philosophy of science believe scientific theories intimate reality). How, though, can we make sense of analogously predicating predicates of predicates, much less predicating predicates of themselves? How can first-order properties have first-order properties which, themselves, have their subjects as first-order properties? Analogy does nothing to lubricate the discussion at this point.

Am I too infected with Theism to see what sense this could make? Even if we turn to a close (and theistic) cousin of Platonism, namely ‘absolute creationism,’[6] (according to which platonic forms do exist, but (necessarily?!) proceed necessarily from God as creatures), we find nothing which alleviates the perplexity. In fact, it adds to the perplexity by introducing the so-called bootstrapping problem, for there are properties which, in order for God to create them, God would already have to possess (if existence is a property, then it serves as a fine example; another example is the property of powerfulness, which God would need in order to create the property of powerfulness).

So where does all this leave us? Here, I’m afraid, my thinking proceeds with less precision than I am comfortable with, and with embarrassing, though seemingly unavoidable, obviousness. This is precisely why I proceed with such caution, as though clumsily feeling my way through a thick fog. I avoid committing myself with any rigidity to this point. Nevertheless, if I am right then Platonism turns out to be highly sophisticated gobbledygook. At least this will be true of wholesale Platonism (as opposed to constrained or qualified forms of Platonism, such as those prefixed with terms like ‘mathematical,’ ‘prepositional,’ ‘evolutionary,’ et cetera).

Commentaria welcome.

[1] Maria Reicher, “Nonexistent Objects,” in The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta (2015), accessed November 26, 2016. http://plato.stanford.edu/archives/win2015/entries/nonexistent-objects/

[2] Johann Marek, “Alexius Meinong,” in The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta (2013): http://plato.stanford.edu/archives/fall2013/entries/meinong/  adds: “… in the appendix to his 1915 (p. 739–40) Meinong himself interprets such incomplete objects as platonic universals without being (see also 1978, 368), and he also states there: “what words mean [bedeuten] is the auxiliary object, and what they designate [nennen] is the target object” (1915, 741).”

[3] Existence is a property of Being, and Being is a property of Existence, no? This is unclear due to my total lack of clarification (through conceptual analysis) of these terms, but it seems intuitive enough for the moment. I cannot see why there couldn’t be some relatively clear-cut case of this pernicious symmetry.

[4] I believe Vallicella argues that it does somewhere in: William F. Vallicella, A Paradigm Theory of Existence: Onto-theology Vindicated. Vol. 89. Springer Science & Business Media, 2002.

[5] Johann Marek, “Alexius Meinong,” in The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta (2013): http://plato.stanford.edu/archives/fall2013/entries/meinong/

[6] Thomas V. Morris and Christopher Menzel. “Absolute creation.” In American Philosophical Quarterly 23, no. 4 (1986): 353-362.

The Inclination to Believe

Man, it seems, has a natural inclination towards religion, or at least to belief in God or something very much like God. The scriptures say;

“From the greatness and beauty of created things comes a corresponding perception of their Creator.”
~Wisdom 13:5

This isn’t merely a theological point, but a fairly well attested point of psychological fact about which there needn’t be any disagreement between Christian theists and atheistic naturalists; human beings seem naturally inclined towards belief in a transcendent creator, a locus of moral value, and summum bonum. Almost all peoples across almost all times have had something like religion, and almost all of these (to greater or lesser extents) have directed man to God or something like God.

Some atheists might suggest that once we know we have a predisposition (emotional or otherwise) to believe in God or something like God, we have acquired a reason to be skeptical of our belief in God or something like God. After all, if our belief is not formed under the influence of rational deliberation then it seems unlikely that it would be reliable. The analogy of seeing patterns where there aren’t any is often raised; we make out an octopus in the clouds, we make out a portrait of the virgin Mary on a piece of toast, we connect conspiratorial dots leading us to conclude that 9/11 was an inside job or that aliens built the pyramids, et cetera. Once we know that we are-appeared-to-patternly as an intellectual knee-jerk reaction even when not presented with any actual pattern, we have acquired a reason to be skeptical of any prima facie beliefs about patterns. It follows (so the suggestion goes) that if we know we have a natural tendency to believe in God, or something like God, we ought to be skeptical of that belief.

I think the Christian here can both argue that the (hypothetical) atheist is wrong to advance such an argument, and that, in fact, (perhaps surprisingly) just the opposite is true. First, what’s wrong with the argument? Well, obviously in the case of our prima facie beliefs about patterns, we are regularly confronted with defeaters of our beliefs. We have good reason to think, for instance, that no cloud’s shape is due to its tendency to conform to shapes like those of cars, or octopuses. However, in the absence of such a defeater we would be well within our epistemic rights to believe that we were confronted with a pattern when being appeared-to-patternly. After all, the inclination we have to believe in patterns is broadly reliable; evolution wouldn’t have selected for it (we presume) if it weren’t at least reliable enough to be an aid to survival and reproduction. So, we are justified (at least if reliability of a belief forming process is a sufficient condition of justification) in retaining our belief in the absence of a defeater. We rightly give up our beliefs in a set of patterns when presented with a defeater for our beliefs, and this happens regularly. Do we have any similar defeater in the case of our belief in God, or something like God? It doesn’t seem so (unless one is inclined to think that some argument for atheism is sound, such as the argument from the evidential problem of evil). Thus, in the absence of an apparently sound argument for atheism, we seem to have no defeater for our belief in God or something like God, even if that belief were formed not as a result of doing sophisticated natural theology, but formed just by looking up at the heavens and reacting to the beauty of it all by forming the belief in God or something like God. If the (hypothetical) atheist wishes to convince us that this belief-forming process isn’t reliable, they will have to provide us with some reason (any reason) for believing so without begging the question.

We might also advance a tu quoque argument against the atheist here, noting that there seem to be plenty of beliefs for which we (the Christian and atheist both) have no justification beyond our psychological disposition for believing it. This seems to be true for our fundamental moral judgments, which are not as such open to empirical verification or falsification. This seems to be true of our belief in an extra-mental extra-linguistic external world (as opposed to, say, subjective idealism). It seems to be true of our belief in the reality of the past (as opposed to the most unpalatable version of presentism imaginable). There are many examples of beliefs which we have a natural inclination to form and which we all (or, nearly all) believe, but for which it is difficult to see what non-circular or non-question-begging argument(s) we could present in their defense. If this is right, then the atheist is in exactly the same position (with respect to many of her beliefs) she is accusing the Christian of being in (with respect to his belief in God). This does nothing to indict the atheist’s argument, but at least it gives the atheist some reason to pause and reconsider the objection.

Finally, I don’t think we’re stuck with a stalemate between the Christian and the atheist here. In fact, I think that our having an inclination to believe in God or something like God is itself evidence for the reliability of this disposition. Consider the conditional probability that we would have such an inclination on atheism (along with background knowledge); it may not be astronomically low, but it certainly isn’t very high prima facie. Now consider the conditional probability that we would have such an inclination (to believe in God, or something like God) on theism (along with background knowledge); it may not be astronomically high, but it certainly isn’t very low, and it is obviously at least higher than it would have been on atheism. Therefore, the fact that we have a natural tendency to believe in God actually gives us a reason to think that this tendency is ‘reliable’ (i.e., conducive to the formation of true beliefs). Even if it isn’t much more likely that this disposition is reliable, it is certainly marginally more likely (prima facie) that this disposition is reliable. In the absence of a defeater or other relevant considerations, that’s enough to tip the scales slightly in the favour of the Christian.

Finally, the disposition to believe in God is not only evidence of its reliability, but also serves equally well (or equally poorly) as evidence for the truth of theism or something like theism. Thus, the natural inclination in man to believe in God provides evidence both for its own reliability, and for the existence of God.