On (Possibly) Being Unable To Avoid Speaking Falsely

I was thinking yesterday about Thomas Aquinas’ rather strict view on the duty to never lie, even, as he says, when we lie for the sake of a joke. He admits, of course, that lying in the cause of a joke (a jocose lie) is not a mortal sin, but he does insist that it is at least venially sinful.

Ergo mendacium iocosum et officiosum non sunt peccata mortalia.[1]

I thought to myself that Aquinas probably means jokes which only work if the audience accepts a falsehood asserted before the punchline. I am reminded here of a (probably apocryphal) anecdote about Dominican friars teasing Aquinas by saying “look, out the window – flying pigs!” in response to which he looked out the window, to their great amusement. He retorted to their laughter by saying that he would sooner believe that pigs could fly than that his Dominican brethren could lie. Clearly, in such a case, Aquinas would say that what these friars did was sinful (at least venially). However, I don’t think Aquinas would offer the same analysis of sarcastic jokes, where what one says is actually the opposite of one affirms by saying it. In sarcasm, one expresses a truth P by expressing a token-sentence K which, under normal circumstances, affirms not-P, but which, when used sarcastically, is understood by everyone to affirm P. To utter K sarcastically is to affirm P, and everyone knows this. This got me thinking about a strange situation.

Suppose one is in a court of law and must answer any question with a simple affirmative of negative. Suppose, then, that for some question, the token statement which is an affirmative is true in one language game, and false in another language game, and the token statement which is the negation is true in one language game and false in another. Call these tokens Y and N, and let us suppose that half the audience is playing the first language game, and the other half is playing the other. If one answers Y, then half the audience will believe something true, while the other half of the audience will believe something false, because they are unconsciously playing two different language games. If one answers N, the same situation results. Suppose you are fully aware that Y will communicate a falsehood to some, and that N will communicate a falsehood to others. Suppose, further, it isn’t possible to elaborate on Y or N (you can tell any story you like here – maybe you speak a totally different language, and you have a designated translator in court who is committed to translating whatever you say into simply Y or N – or any other scenario you like, so long as you aren’t able to avoid affirming Y or N).

In such a strange case, would you have to lie? It seems like you would have to communicate something false (imagine, for simplicity, that your silence would be taken as an affirmation of Y, or N, or would be a sort of speech-act by omission which, in any case, would communicate a falsehood).

If such a situation arose, it wouldn’t be possible to avoid telling a lie. Therefore, it wouldn’t be possible to do the right thing (except in terms of telling the lesser lie, whatever that is). Does this pose much of a problem for Aquinas’ view? I’m actually not sure. If we really can construct a situation in which there is no way to avoid sinning, that would plausibly provide us with a reductio ad absurdum and should cause us to carefully review what we think qualifies as a sin. However, it is still open to the especially devout Thomist to bite the bullet here, or to find some way of arguing that the situation I propose arises in no logically possible worlds. It might help our case if we could provide some kind of hypothetical example. Here’s one: consider the question “is God infinite?” Clearly, those speaking the language of Duns Scotus are going to take a rejection of this as a false statement, and they (playing their language game) would be right to do so. On the other hand, those speaking the language of modern mathematicians would recognize the affirmative to be a straightforward falsehood (for God is not infinite in any quantitative sense). There is no unqualified answer (in the form of an affirmation or denial) which does not communicate a falsehood which one knows to be false (presuming one is sufficiently well theologically informed).

[1] ST, II-II, Q. 110, Art. 3, ad. 3. http://www.logicmuseum.com/authors/aquinas/summa/Summa-IIb-101-113.htm#q110a1arg1


Arguing that the B-theory (or the A-theory) is a metaphysically necessary truth

I have profound sympathy for the intuition that, for either the A-theory of time, or the B-theory of time, if it is true, then it is necessarily true. It obviously follows, therefore, from either one’s metaphysical possibility, that it is a necessary truth. However, the force with which this intuition imposes itself notwithstanding, it turns out to be extremely difficult to prove this modal thesis, and there may, in fact, be a really good objection to it.

Does it really follow from the A-theory’s being true (supposing it is) that it is necessary, or from the B-theory’s being true (supposing it is) that it is necessary? Suppose our world is an A-theory world; could God really not have created a B-theory world?

Interestingly, while I was rereading a paper today from Joshua Rasmussen, my attention was drawn to one of his footnotes, in which he outlines a sort of modal-ontological argument from the possibility of presentism (typically considered to be a version of the A-theory – though, I note in passing, he was arguing in the paper that presentism is strictly compatible with the B-theory) to its necessity. His argument went roughly as one might imagine (note: he uses ‘Tenseless’ as an abbreviation for the thesis that he argues for in the paper, and which needn’t directly concern us here):

Here’s the argument: (i) suppose it’s possible that Tenseless and presentism are true; (ii) then it’s possible that presentism is true; (iii) necessarily, if presentism is true, then presentism is necessarily true; therefore, (iv) if it’s possible that presentism is true, then it’s possible that presentism is necessarily true; (v) if it’s possible that presentism is necessarily true, then presentism is true (by S5); therefore, (vi) presentism is true.[1]

This caused me to review one of my (many, many) old blog post drafts, in which I tried to argue that if the A-theory is true, then it is a necessary truth, and if the B-theory is true, then it is a necessary truth. Here’s (roughly) what that looked like:

I have been asked, in the past, why I maintain that if the B-theory is true in any possible world, then it is true in all logically possible worlds (from which it follows that it’s true in the actual world), and that the same can be said for the A-theory. Upon reflection, I suppose I was reasoning in something like the following way:

  1. God exists in every possible world (assumption).
  2. If God exists in every possible world then his necessary essence is exemplified in every possible world.
  3. God either is by his necessary essence, or is necessarily not, simple and/or immutable in the classical senses.
  4. The B-theory is true if and only if God is essentially simple and/or immutable.
  5. Either the B-theory is true, or the A-theory is true (and not both).
  6. If the B-theory is true in one logically possible world, it is true in all logically possible worlds.
  7. Therefore, if the A-theory is true in one logically possible world, it is true in all logically possible worlds.

The weakest point of the argument, now that I lay it out and think about it, seems to be premise 4, for although it seems right to say that if God is simple and immutable then the B-theory must be true, it seems wrong to say that if the B-theory is true then God must necessarily be simple and/or immutable. Why think that if God weren’t simple and/or immutable then He couldn’t create a B-theory world? I then tried to construct a more elaborate argument for the conclusion that if the B-theory is true, then it is necessarily true, and if the A-theory is true, then it is necessarily true. It went something like:

  1. God’s existence is possible (assumption).
  2. God is a metaphysically necessary being. (by definition)
  3. For any metaphysically necessary being, if it exists in a single logically possible world it exists in all logically possible worlds.
  4. God exists in every possible world (assumption).
  5. If God exists in every possible world then his necessary essence is exemplified in every possible world.
  6. There is a logically possible world in which God’s essence includes being metaphysically simple and immutable. (Assumption)
  7. Therefore, in all logically possible worlds God is metaphysically simple and immutable.
  8. If God is metaphysically simple and immutable, then necessarily: if there is a contingent world, then the B-theory is true.
  9. There is a contingent world.
  10. Therefore, the B-theory is true.

This argument isn’t very good. For one thing, it highlights a really big problem for the idea that the A-theory of time and the B-theory of time are mutually exclusive and logically exhaustive disjuncts. Indeed, if there is no contingent world, there are surely no A-properties, but there are also no B-properties (it is hard to imagine a B-theory on which only ‘atemporal simultaneity’ is preserved – that is so depreciated that it isn’t clear whether it would even qualify as a version of the B-theory). It looks like this problem for Rasmussen’s argument as well (why accept his (iii)?).

I also had some rough notes on a third argument, which went something like this:

  1. God’s existence is metaphysically possible. (assumption).
  2. God is a metaphysically necessary being (and his essence, whatever it is, is metaphysically necessary).
  3. God either is essentially, or essentially is not, simple and immutable in the classical senses.
  4. There is a contingent world. (assumption)
  5. If there is a contingent world, then the A-theory is true, or the B-theory is true (and not both).
  6. The A-theory is true if and only if God stands in real relations to the world which are grounded in himself.
  7. If God stands in real relations to the world grounded in himself, then God is not simple and immutable.
  8. If God possibly stands in real relations to the world which are grounded in himself, then God necessarily stands in real relations to the world which are grounded in himself.
  9. If God necessarily stands in real relations to the world which are grounded in himself then the A-theory is necessarily true.
  10. Therefore, if the A-theory is possibly true, the A-theory is necessarily true.
  11. If the A-theory is not possibly true, then the B-theory is necessarily true.

The reader will have to forgive me for being a little loose as well as slightly enthymematic. I’m not sure this is a good argument. The intuition is supposed to be that God can only be simple and immutable in a B-theory world, that he cannot be simple and immutable in an A-theory world, and that whichever way God is in any possible world (at least with respect to being simple and immutable), that is the way He is in all possible worlds.

Perhaps one will disagree with me that God exists in all logically possible worlds (which is just to say that God does not exist, since, obviously, if a metaphysically necessary being exists in a single possible world it exists in all possible worlds). They will argue that it may seem necessary given theism that whichever theory of time is true of the actual world is true of all logically possible worlds, but that they either reject, or in any case do not accept, theism. It might seem as though we are at a standstill with such a person.

There is, nevertheless, another way to argue that the A-theory is necessarily false (and the B-theory, therefore, necessarily true). Suppose we accept the claims that the (weak-)PSR and the A-theory of time are logically incompatible with each other.[2] Now, take the weak-PSR which says that for any possibly true contingent fact P, P possibly has an explanation. Obviously, if the weak-PSR is true it is a necessary truth. This entails that there is a logically possible world in which P, and the explanation of P, both obtain. Suppose that P is “it is now this particular time.” On the A-theory, this contingent fact does not have an explanation. That means (supposing all we have said so far) that at least one logically possible world is a B-theory world. It follows that there is no logically possible world in which the A-theory is true. However, this reasoning is not likely to be any more compelling than the theistic reasoning explored above.

Can I do any better? Probably not today. (I suppose I could have deployed my argument for thinking that the A-theory is not logically possible because there is no logically possible world in which time flows – an argument I developed a bit in my undergraduate thesis and which, I am beginning to think, may make an appearance in my Master’s thesis – but I’d rather leave it out of this post for the sake of convenience).

[1] Joshua Rasmussen, “Presentists may say goodbye to A-properties,” Analysis 72, no. 2 (2012): 270-276.

[2] For more on this, see http://alexanderpruss.blogspot.co.uk/2013/01/can-theorists-accept-principle-of.html

Some Problems With Degreed Existence

It was typical for the Medievals to speak of existence as a degreed concept (i.e., as the kind of thing which comes in greater or lesser degrees). Modern philosophers generally balk at this suggestion, insisting instead that a thing either exists, or does not exist, but that it makes no sense to speak in terms of degrees of existence. It is, of course, possible to adopt that bivalent view with respect to the truth conditions for statements like “x exists”, but also indulge a way of speaking which uses ‘exists’ as a dyadic relation (e.g., “x exists more(/less) than y”). There are several ways in which one can try to make sense of this kind of talk, but I have often thought that the most appealing way was in terms of possible worlds. Suppose we say:

x exists more than y iff x populates more possible worlds than y.

This has seemed, to me, to be satisfying for a number of reasons. Obviously, it allows for the medieval convention, and it also obviously places God at the top of the hierarchy of being (and this without, as of yet, even broaching the topic of one’s theory of existence), which is what the Medievals (and I) ultimately want. At the same time, the modern philosopher is going to be hard-pressed to reject the analytic convention of speaking in terms of possible worlds, and it seems sensible to give ‘existence’ a stipulative qualified definition, for particular purposes, running along these lines. In addition, this modal definition of existence (as a degreed concept) plausibly subsumes several other candidate rationales for this kind of talk, including that ‘degreed existence’ measures immutability, contingency, et cetera.

However, perhaps there are some problems with this which I had previously glossed over. I don’t think much of the objection that existence isn’t a predicate, for a few reasons. First, the way in which the Medievals are using the term, here, is clearly predicatory, and idiosyncratic enough that they can help themselves to a specially stipulated (probably onto-theological) definition. Second, existence isn’t usually considered a first-order predicate, but there isn’t much of a problem considering it a second-order predicate. Third, there are systems on which existence really is a first-order predicate, such as Krypke’s quantified modal logic. These and other reasons incline me to dismiss such a facile (Kantian) objection. Nevertheless, there are some real problems here worth thinking about.

For one thing, the cardinal value of possible worlds with any y, so long as y exists in at least two possible worlds, seems to be ℵ0.[1] It isn’t clear how one thing could exist in more possible worlds than that (I find it hard to imagine the argument for thinking that x exists in ℵn where n>0).

– Actually, here is an argument for this: Platonism is true (assumption), and not only natural numbers, but all the reals, are abstract objects. Therefore, there is an non-denumerable infinity of actual things, that infinity’s cardinal value being ℵ1. Further, we can argue that mathematical functions are abstract objects, and since the set of all real functions in the interval 0 < X < 1 is the non-denumerable ℵ2,[2] so too will be the number of actual things (given Platonism). In any case, I digress. –

Perhaps if x existed in all worlds where y existed, and also existed in worlds where y did not exist, we could justify retaining this convention (though we would have to give up Cantor’s notion of equivalence in terms of correspondence or, more precisely, bijection), but then there wouldn’t be a (very?) smooth gradation of being. Dream objects, for instance, would not be less real, or have less existence, than the material objects of the external world (consider that mental states are multi-realizable, so that for any mental state, a whole cacophony of physical states suffices to bring it about, even if, given some particular physical state, the mental state must come about – I assume this, here, just for the sake of argument). I had previously hoped that this problem was roughly analogous to the problem with measuring the ‘closeness’ of possible worlds to each other (when we talk about changing only a little bit of a world’s description, technically we are always talking about changing at least ℵ0 propositions).[3] If the problems were analogous, then their solutions were likely to be analogous, and I was (and remain) supremely confident that there must be a solution to the latter. However, we can apparently solve the latter problem by talking about first-order propositions directly about states of affairs in that world (at least plausibly, there are finitely many of these). That solution doesn’t translate well, as far as I can tell, into a solution for the first problem, so that the problems don’t seem analogous enough to have analogous solutions.

Another problem is that seemingly insignificant beings like atoms are going to be more real (in the sense of having higher/greater existence) than plants, and so human beings have less existence than mosquitoes. The Medievals would not have been thrilled. For them, plausibly, a thing exists to the extent that it succeeds in resembling God.

There is a possible reductio here as well; if some things have more existence than others by the modal measure suggested, then we might wonder whether we can license speech about some things having more unreality than others? Suppose we accept talk of impossible worlds, and suppose we then accept talk of really-impossible worlds. To get an idea what this would look like, refer to Pruss here. Well, then it looks like some things don’t merely not-exist, but some really don’t exist, and they don’t exist even more than other non-existent things.

Not all of these problems are equally troubling, but they are worth taking inventory of regardless. I think the attempted reductio ad absurdum at the end is pretty weak. We can just deny that there are really impossible worlds, or even deny that there really are impossible worlds. In any case, we can just exclude such considerations by fiat, since stipulative definitions can be constrained however we see fit, so we can just constrain the stipulative definition of ‘[degreed] existence’ so as to ignore such puzzles. Still, not all of these are so easy to dismiss. I won’t flesh this out here, but these considerations lead me to suspect that the best way to give an account of ‘degreed existence’ (in the sense the Medievals want to indulge talk about) may be with reference to a well worked out theory of existence after all.

[1] Is this true? Maybe not – maybe there is some y such that y exists only in two (or, in any case, in some finite number of) possible worlds. I have trouble imagining what this would be, but, in any case, for nearly any conceivable y, it will turn out to be true that there are ℵ0 possible worlds containing it.

[2] William Lane Craig, The Kalam Cosmological Argument, (Oregon, Wipf and Stock publishers, 1979), 80.

[3] Technically, we are changing even more propositions than this. It is widely agreed now that there is no set of all true propositions. Taking the power-set 𝔓(W) of all propositions true at possible world W, you can generate infinitely more propositions, and this actually changes the cardinality of the number of true propositions from ℵ0 to ℵ1, the latter of which is a non-denumerable infinity. The process can be repeated indefinitely, leaving us with an indefinitely large set, and there is no way to deal with indefinitely large sets in set theory.

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 only entities belief in which can 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).

Some Miscellaneous Reactions to Some of Robert Price’s Points in Favour of Mythicism

In a not so recent debate1 between Bart Ehrman and Robert Price the topic of whether Jesus of Nazareth historically existed was explored. This provides us with one of the first and few high-profile debates with at least one bona-fide scholar where the participants are directly arguing about mythicism. Unfortunately, the debate was a disappointment in several respects in that neither Ehrman nor Price gave performances of the quality many, who were anticipating an outstanding debate, were expecting. However, Price did say a few interesting things which I thought I’d pick up on and say a few words about. This is not intended to be a comprehensive dismantling of Price’s view (I have not the time to be so ambitious), but just intended to provide a registry of some of my miscellaneous reactions to various points.

Price, in his opening speech, provided at least three examples of evidence which may insinuate that one early objection to Christianity was that Jesus never existed. First, he cites a statement which Justin Martyr puts into the mouth of his interlocutor Trypho in his famous Dialogue with Trypho. Second, he cites a statement which Origen is at pains to refute from an anti-Christian polemicist of the second century, Celsus. Third, he calls into evidence the words of 2 Peter 1:16-18 as though they indicate an implicit awareness that there was an allegation already circulating within the first century that Jesus of Nazareth may not have existed at all.

Let us begin with the passage from the Dialogue with Trypho, according to which Trypho, (a Jewish intellectual who, in the dialogue, claims to have been a pupil of Corinthus the Socratic in Argos,2 and may possibly be the second century rabbi Tarfon,3 though that is not widely accepted) makes the following provocative charge:

But Christ—if He has indeed been born, and exists anywhere—is unknown, and does not even know Himself, and has no power until Elias come to anoint Him, and make Him manifest to all. And you, having accepted a groundless report, invent a Christ for yourselves, and for his sake are inconsiderately perishing.”4

Does this passage contain a veiled insinuation that Jesus did not exist? It doesn’t seem so. At very least we gather from the way Justin Martyr proceeds to respond to this comment that he doesn’t have that accusation in mind. Justin promises Trypho that “I will prove to you, here and now, that we do not believe in groundless myths nor in teachings not based on reason, but in doctrines that are inspired by the Divine Spirit, abundant with power, and teeming with grace.”5 However, Justin Martyr goes on to give argument after argument from prophecy to demonstrate that Jesus is a good ‘fit’ for the anticipated messiah of the Tanakh. He never goes on to argue that Jesus of Nazareth existed; he argues on the clear presumption that he and Trypho are agreed that Jesus of Nazareth existed. The likelihood is relatively high that Justin Martyr is writing a largely or entirely fictitious dialogue, but whether it was fictitious or not there is no way to read Trypho’s (alleged) statement as an insinuation that Jesus didn’t exist. That isn’t what Justin Martyr thought the statement insinuated, and it isn’t plausible that a historical Trypho intended to insinuate that the historical Jesus didn’t exist but just let that point drop entirely for the rest of the dialogue with Justin.

My verdict, therefore, is that this provides absolutely no evidence of any early anti-Christian polemic which insinuated that Jesus never existed.

What of Price’s second example, from the second century anti-Christian polemicist Celsus? Well, Price points out that Celsus says: “it is clear to me that the writings of the Christians are a lie and that your fables have not been well enough constructed to conceal this monstrous fiction.”6 However, to read this as a veiled charge that Jesus never existed is implausible for a variety of reasons. First, consider how the passage from Celsus continues: “it is clear to me that the writings of the Christians are a lie and that your fables have not been well enough constructed to conceal this monstrous fiction. I have heard that some of your interpreters…are on to the inconsistencies and, pen in hand, alter the originals writings, three, four and several more times over in order to be able to deny the contradictions in the face of criticism.”7 That is clearly an accusation of embellishment and selective redaction; it is clearly not an accusation of having invented the historical Jesus whole-cloth. Second, consider that Celsus elsewhere argues that Jesus is a bastard child; according to Origen in his Contra Celsus, “[Celsus was] speaking of the mother of Jesus, and saying that “when she was pregnant she was turned out of doors by the carpenter to whom she had been betrothed, as having been guilty of adultery, and that she bore a child to a certain soldier named Panthera.”89 Clearly, however, if Celsus thought that Jesus was born of illegitimate relations between Mary and a Roman soldier named Panthera, then Celsus could not have also believed that Jesus never existed. Those beliefs are so obviously logically incompatible that even an imbecile (as Origen thought) like Celsus could not plausibly have entertained both.

Finally, what of the words in 2 Peter 1:16-18? They read:

For we did not follow cleverly devised myths when we made known to you the power and coming of our Lord Jesus Christ, but we had been eyewitnesses of his majesty. For he received honor and glory from God the Father when that voice was conveyed to him by the Majestic Glory, saying, “This is my Son, my Beloved, with whom I am well pleased.” We ourselves heard this voice come from heaven, while we were with him on the holy mountain.”
(2 Peter 1:16-18, NRSV).

I consider it obvious that the author gives us an indication of what the allegation of ‘cleverly devised myths’ comes to by the way he responds to the charge. Clearly, however, he spends all his time emphasizing not that he was an eyewitness (or that there were eyewitnesses) of Jesus of Nazareth, but that he was one of many eyewitnesses of the majesty of Christ which was attested to and illustrated by miracles. It is the majesty and/or the miracles which the author believes are being alleged to be cleverly devised myths, not the historicity of the person, Jesus of Nazareth; we know this by inferring it from the way the author responds to the allegations he has in mind.

So, in my opinion, all three of these evidences of some early objection to Christianity to the effect that Jesus of Nazareth did not historically exist are completely bunk.

I want to end this reflection on some points brought out by Price in the debate with a few positive notes. There are some areas where I actually agree with Price over against the majority of New Testament scholars. For instance, Price maintains (and this came out in parts of the debate) that there is no more reason to think that Paul wrote Galatians than there is to think that Paul wrote 1st Timothy. Price’s conclusion is that we have reason to believe that Paul did not write any of the epistles traditionally ascribed to him. My conclusion is that Paul plausibly wrote all of the epistles traditionally ascribed to him. This was somewhat tangential to the debate, but it is a point of interesting qualified agreement nevertheless. More interesting still, Price argued that if we strip away all of the miraculous claims made about Christ, we are left with a first-century Jewish Rabbi about whom nothing would have been worth writing in the first place. He says, at one point, that if Clark Kent existed and superman didn’t, there would be no gradual embellishment of stories about Clark Kent because there would be no reason for anyone to remember any stories about Clark Kent in the first place. There either has to have been something about the Jesus of Nazareth of history which made him worth writing (talking, etc.) so much about in the first place, or else the stories about him were mythological from the beginning.

This, I think, is a very interesting point. If historians are intent on whittling down the Jesus of the Gospels to the point where he was an utterly unremarkable first century Jewish rabbi then there is no explanation for why he caused such a stir in the first place. Obviously most historians will respond, here, by conceding that Jesus claimed to be a miracle worker, and performed exorcism ceremonies in a way which presumed an immense and unprecedented amount of authority for himself. It was his innovative preaching along with what W.L. Craig has called the historical Jesus’ “unprecedented sense of divine authority,”10 which sufficiently explain why there were any stories about him in the first place. So, on the one hand, Price has, I think, failed to take inventory of what most New Testament scholars believe we can say with enormous confidence about the historical Jesus of Nazareth. On the other hand, though, Price does well to remind us that if scholars aren’t careful to preserve something remarkable and unique about the historical Jesus, if they reconstruct only a version of Jesus wholly sanitized by the presumption of naturalism, and about whom there was really nothing terribly special, they may be proverbially cutting the tree branch from which they hang.


1 Anyone interested can find the debate, at least currently, at the following link: https://www.youtube.com/watch?v=oIxxDfkaXVY

2 Justin Martyr, Dialogue with Trypho, Ch. 1, http://www.newadvent.org/fathers/01281.htm

3 Claudia Setzer, Jewish Responses to Early Christians,Fortress Press, 1994: 215.

4 Justin Martyr, Dialogue with Trypho, Ch. 8, http://www.newadvent.org/fathers/01281.htm

5 Justin Martyr, Dialogue with Trypho, Ch. 9, http://www.newadvent.org/fathers/01281.htm

6 Celsus, On the True Doctrine, translated by R. Joseph Hoffman, Oxford University Press, 1987: 37. See: http://www.earlychristianwritings.com/text/celsus3.html

7 Celsus, On the True Doctrine, translated by R. Joseph Hoffman, Oxford University Press, 1987: 37. See: http://www.earlychristianwritings.com/text/celsus3.html

8 Origen, Contra Celsus, Book 1, chapter 32. http://www.newadvent.org/fathers/04161.htm

9 I have written a little bit on this before, a long time ago. Those interested may see: https://thirdmillennialtemplar.wordpress.com/2012/02/13/celsus-attack-on-the-holy-mother/

10 http://www.reasonablefaith.org/does-god-exist-1

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.