A Dilemma for Ambitious Modal Epistemology

1. Modest vs. Ambitious Modal Epistemologies

Many strong efforts have been made in recent years to reduce the mystery of modal knowledge. One key area of such efforts has the modest aim of explaining our knowledge of “nearby” or humdrum possibilities. Clear examples of humdrum possibilities include those regarding the possibility of sipping water, painting houses, crossing roads, and cutting limes.  Call accounts that aim to explain possibilities of this sort, modest modal epistemologies.  

However, some accounts of modal epistemology have higher aspirations. Such accounts aim to justify “far out” or exotic possibilities remote from ordinary experience. Clear examples of far out or exotic possibility claims remote from ordinary experience include those about disembodied souls, zombies, personal fission, and maximally perfect gods. Call modal epistemologies that aim to justify possibilities of this sort, ambitious modal epistemologies.

Now of course many philosophers — myself included — would be very happy to discover that we can peer into the modal stratosphere and settle disputes about disembodied souls, philosophical zombies, personal fission, and Anselmian beings. However, as I will argue in the remainder of the paper, there are grounds for pessimism on that front. In particular, I’ll argue that ambitious modal epistemologies are subject to a fatal dilemma: either they’re too permissive, in that too many possibility claims count as known or justifiedly believed, or they’re too restrictive, in that not enough possibility claims their proponents want to know about — specifically, claims about possibilities remote from ordinary experience — count as known or justifiedly believed. Space does not permit me to cover all ambitious modal epistemologies that have been proposed. In lieu of such a project, therefore, I will discuss a representative sampling of the most popular ones to date: a naïve and popular permissive account, Stephen Yablo’s account, David Chalmers’ account, and Peter Kung’s account. For each of these four accounts, I will show that they impale themselves on one horn or the other of the dilemma. I’ll proceed by starting with the most permissive and lax account and work my way down to the strictest and most demanding account.

2. Permissive Ambitious Modal Epistemology

How lax can we get when it comes to constraints on plausible accounts of ambitious modal epistemology?  Perhaps we’d all agree that mere logical possibility is too permissive a guide to possibility. As Alvin Plantinga has pointed out, such an account would allow for the possibility of prime numbers that are prime ministers.  However, one might think that a slightly more conservative account of possibility knowledge is acceptable: a possibility-claim is justified for you if you fail to see, or are unable to rule out, that such a thing is metaphysically impossible; that is, that a modalized kind of epistemic possibility is a guide to metaphysical possibility. 

However, besides the problem that such an approach makes metaphysical possibility a function of one’s ignorance -- the less you know, the more possibilities there are -- such an account admits too many false positives. So, for example, consider Plantinga’s modal ontological argument . The key premise is that there is a possible world at which a necessarily existent individual exists. But given that premise and Axiom S5 – the one that says that what’s possibly necessary is necessary simpliciter – if follows that an Anelmian god exists. Now even on reflection, I fail to find any incoherence in the concept of God as described by Plantinga. So if modalized epistemic possibility justifies claims about metaphysical possibility, I should conclude that Plantinga’s God exists. But so far as I have been able to tell, there have been few takers on Plantinga’s ontological argument — including Plantinga himself, according to his own recent reckoning.

Perhaps that’s bad enough. But the same goes for a maximally excellent being’s possible non-existence. Thus, consider Peter van Inwagen’s “knownos” . A knowno is a being that knows there are no necessary beings. Now I fail to see any incoherence in the notion of a knowno. Alternatively, I see no incoherence in a purely physical, contingent, yet metaphysically independent or “free-standing” universe: there are the fundamental particles, and all else logically supervenes on that. So if epistemic possibility is a guide to metaphysical possibility, then it’s also reasonable for me to believe that there are no necessary beings. But, necessarily, only one of the two claims can be true: an Anselmian being is possible iff a godless world is impossible. Thus, the assumption that epistemic possibility is a guide to metaphysical possibility is too permissive.  

3. Restrictive Ambitous Modal Epistemology

3.1 Yablo

What about restrictive ambitious accounts of modal epistemology? Stephen Yablo’s account is representative of such accounts. The core idea of his account is that possibility-claims are prima facie justified in virtue of imagining possible worlds  at which their de-modalized counterparts are true. So, for example, the claim that, possibly, a ball is stuck on a roof is justified if I can imagine a world at which ‘a ball is stuck on a roof’ is true. We can think of Yablo’s account as a “modal telescope” account: one’s faculty of imagination is like a telescope that can look into other possible worlds; imagining a world is like looking at another possible world through the modal telescope; and if you’re able to imagine a world that would make the de-modalized target claim true in it, then you have, in effect, spied a possible world through the modal telescope that vindicates the target possibility claim.

It’s important to be clear about the sort of imagining Yablo has in mind. As the telescope metaphor suggests, the relevant sort of imagining on his account is not that of entertaining a coherent proposition or narrative – what Yablo calls propositional imagining. Rather, it is (roughly) that of having phenomenal imagery of a distribution of objects and properties – what Yablo calls objectual imagining. There is thus a world of difference between understanding the proposition that, possibly, a pit bull bites my arm, and imagining a pit bull biting my arm.  And imaginings of the latter sort are what Yablo’s account requires for justifying possibility-claims.

So far, we’ve said that Yablo’s account of verifying a possibility-claim involves imagining a world at which the de-modalized target claim is true, where imagining a world involves imagining, roughly, a distribution of objects and properties. However, not just any such imagining counts as verifying a modal claim. Rather, such imaginings must meet two conditions: (i) the imagined scenario must appear to one as metaphysically possible (as opposed to merely failing to appear to one as impossible), and (ii) it must appear to one that the relevant de-modalized claim is true in that scenario (as opposed to merely failing to appear false).  To get a better grasp of Yablo’s two conditions of verification for possibility-claims, let’s look at some concrete examples of success and failure with respect to verification.

First, consider the claim that, possibly, the thing that looks just like a flower before me sprouts new petals. Now I can imagine a world in which this appears to me as true. Unfortunately, that world doesn’t appear to me as possible; rather, it neither appears as possible nor as impossible – its modal status is left undecided. For as it turns out, the object it sits next to it is perceptually indiscriminable from it, and while I don’t know which one is which, I do know that one of the two is a mere flower-facsimile. And given that real flowers can sprout petals while facsimiles cannot, I’m not at all confident that what I imagine is metaphysically possible. Thus, while it passes Yablo’s second condition of verifying a possibility-claim, it fails the first condition. 

Next, consider the claim that, possibly, Goldbach’s Conjecture is false. Now I can imagine a world in which I find an article in a leading mathematical journal with the title “A Refutation of Goldbach’s Conjecture”. This world appears to me as metaphysically possible. However, absent imagining the proof itself within the pages of the article, this imagined world is compatible with the truth of Goldbach’s Conjecture. For my imagining leaves it open that (e.g.) the attempted proof contains a subtle error within it. So while the case passes Yablo’s first condition of verifying a possibility-claim, it fails the second.

Finally, consider the claim that, possibly, a ball is stuck on a roof. I can imagine a world at which there is a ball lying against the back side of a chimney on a slanted roof.  In this case, the world imagined doesn’t just fail to appear to me as impossible; it positively appears to me as metaphysically possible. Furthermore, the imagined world doesn’t leave it ambiguous or undecided that a ball is stuck on the roof; rather, it positively appears to me as one in which a ball is stuck on a roof – I imagine it there, wedged behind the chimney. This case thus satisfies both of Yablo’s conditions of verifying a possibility-claim; the claim is therefore prima facie justified for me.

So that’s Yablo’s account in a nutshell. The problem is that it’s of no help in justifying possibility-claims remote from ordinary experience.  

To see this, consider the claim that, possibly, there is an alien substance that perfectly plays the water role. Now to evaluate this claim via Yablo’s method, we need to objectually imagine a world that meets the following two conditions: (i) it appears to us as metaphysically possible, and (ii) it appears to us that ‘there is an alien substance that perfectly plays the water role’ is true in it. Unfortunately, while I’m able to objectually imagine a world in a way that meets either one of Yablo’s two conditions, I’m unable to objectually imagine a world in a way that simultaneously meets both. 

Thus, suppose I objectually imagine a world W in which I’m standing in front of a swimming pool full of gently undulating clear liquid on Twin Earth. Suppose further that I imagine a chemist in a lab coat in W pointing to the pool and saying, “Don’t be fooled: that watery stuff is XYZ, not H2O”. Would that count as verifying the possibility of twin water? Pretty clearly not.  For what I imagine of W is compatible with the claim that the chemist mistakenly or deceptively refers to the liquid in the pool as XYZ. Therefore, while W appears to me as metaphysically possible, and thus passes on (i), the de-modalized target claim, viz., ‘there is an alien substance that perfectly plays the water role’, neither appears to me as true nor as false in W, but rather as undecided. My objectual imagining thus fails on (ii).

Now you might say that the only problem with the imagined world is the bit about the chemist. For if I take him out of the scenario, I remove the dubious intermediary between my judgment and the objectual representation of XYZ. However, this merely replaces one dubious judge for another. For consider a world W’ just like W, but with the chemist removed. So now it’s just the pool of undulating clear liquid and I. How am I to decide, just by objectually imagining the liquid in the pool, whether it’s XYZ? For the objectual content of the scenario regarding what’s in the pool does not represent itself to me as XYZ. Rather, it merely represents itself to me as clear liquid. But if so, then since this aspect of the imagined world is all I have to go on in determining whether the stuff in the pool is XYZ (as opposed to, say, ordinary H2O), my labeling it as XYZ is nothing more than a shot in the dark.  Thus, my competence in correctly labeling the liquid is no more to be trusted than the word of the imagined chemist. Therefore, as with W, my objectual imagining of W’ passes on (i), but fails on (ii).

On the other hand, suppose we try to cut to the chase and just stipulate that the stuff in the pool in W’ is XYZ, and not water. Given this stipulation, satisfying (ii) is trivial. However, the problem now is that I can’t objectually imagine W’ in a way that satisfies (i). For in this case, the non-XYZ watery stuff in W’ appears to me as neither possible nor as impossible, but rather leaves its modal status undecided. 

3.2 Chalmers to the rescue?

Chalmers’ account is similar to Yablo’s, in that he views imagination as an independent source of justification for modal beliefs, and that he accepts a similar account of verifying a possibility-claim: imagining a possible world at which the de-modalized target claim is true. Chalmers’ primary innovation lies in his wedding of Yablo’s account with the two-dimensionalist distinction between considering a world as actual and considering a world as counterfactual. To give a rough and brief illustration: Suppose I imagine an XYZ-world – i.e., a world at which XYZ is the stuff that plays the watery role. If I consider the imagined world as actual, I consider it as a hypothesis about how the actual world could turn out to be for all I know a priori -- I suppose that XYZ, and not H2O, turns out to be the actual occupant of the watery role. Call this counteractual conceivability. On Chalmers’ view, the counteractual conceivability of XYZ watery stuff is prima facie evidence for the metaphysical possibility of XYZ watery stuff. Call this counteractual possibility. By contrast, when I consider the imagined XYZ world as counterfactual, I hold the actual, H2O world fixed, and imagine (or attempt to imagine) that XYZ is water.  Call this counterfactual conceivability. Of course, XYZ water seems to be counterfactually impossible, but when something is counterfactually conceivable, that’s evidence that it’s a counterfactual possibility.

Chalmers’ main motivation for the two-dimensionalist twist on Yablo-style modal epistemology is to handle the problem of a posteriori necessities raised by Kripke and Putnam. Thus, Chalmers’ diagnosis of the problem of a posteriori necessities is that one is liable to modal error when one illicitly uses counteractual conceivability as a guide to counterfactual possibility, as when one imagines a world with XYZ as the occupant of the watery role and mistakenly takes it as depicting a world with XYZ water. And Chalmers’ solution to the problem of a posteriori necessities is to use counteractual conceivability only as a guide to counteractual possibility, and to use counterfactual conceivability only as a guide to counterfactual possibility.

Now while Chalmers’ account is clearly an advance over Yablo’s in virtue of handling the problem of a posteriori necessities, it nonetheless succumbs to the same criticisms that apply to Yablo’s account. Thus, consider the claim that, possibly, there is XYZ watery stuff. Now if we apply the relevant sort of conceiving to evaluate this claim – counteractual conceiving – we are to verify a world at which XYZ plays the watery role. The problem is that we reach a dilemma at this point. For either we include the stipulation that the clear liquid we imagine is XYZ or we don’t. If we do, then while the de-modalized claim appears true to us, the scenario fails to appear possible (nor does it appear impossible; it’s undecided). But if we don’t add the stipulation, then while the world with clear liquid appears possible, the de-modalized claim that there is XYZ watery stuff doesn’t appear true; rather, only the weaker claim that there is watery stuff (whether water or XYZ or…) appears true.

To see this, consider the following claim: Possibly, there is XYZ watery stuff. Now if we are to evaluate this claim via Chalmers’ account, it is counteractual conceivability that is relevant. Thus, to evaluate this claim, we are to consider an XYZ world – i.e., a world at which XYZ is the occupant of the watery role -- as actual.  And as we’ve seen, this act does not count as justifying the claim in question unless it involves an objectual imagining of a certain sort. Can we objectually imagine a scenario at which the claim is true? 

Well, I can objectually imagine a world at which there is some gently undulating clear liquid in a pool. Furthermore, this world appears metaphysically possible to me; so far, so good.  However, does it also appear to me that the claim, ‘there is XYZ watery stuff’, is true in that objectually imagined world? No, it doesn’t. For again, all I have to go on is the content captured by the relevant objectual imagining – the phenomenal imagery of the undulating clear liquid in a pool. True enough: this imagining does make the claim ‘there is watery stuff’ appear to me as true in that world. But what it doesn’t get me is an appearance that ‘there is XYZ watery stuff’ is true in that world: for all I’m given in the objectual content of my imagining, the watery stuff imagined is H2O, and not XYZ. Thus, it fails the second condition of Chalmers’ Yablo-style modal verification test.

On the other hand, suppose I just stipulate that the watery stuff objectually imagined is XYZ, and not H2O.  The problem now is that while my imagining passes the second condition of verifying a possibility claim, it fails the first condition. For the XYZ-world now no longer appears to me as possible, but rather as undecidable, like the key premise in Plantinga’s modal ontological argument. 

4. Concluding Thoughts

We seem to have surfaced a dilemma. For if an ambitious modal epistemology is viable, then it’s either a restrictive account or a permissive account. But permissive ambitious accounts are too permissive. For while they allow for the twin water modal claim to count as justified, they allow for too many other things to count as justified besides. 

On the other hand, restrictive ambitious accounts are too restrictive. For while they rule out the problematic cases allowed by permissive accounts, they rule out the justification of remote possibility claims as well. Therefore, on either a restrictive or a permissive ambitious account, the epistemic credentials of even modestly remote possibility claims — such as the one about twin water — are dubious.  But of course if the twin water claim can’t be justified, a fortiori are a host of other even more exotic possibility-claims in the literature unjustified: claims about the possibility of (e.g.) disembodied souls, personal fission, swampman, zombies, and maximally excellent Gods. 

Is this a sad result? Perhaps. But it’s one that philosophers can live with. For as we saw in an earlier section, even if the prospects for an ambitious modal epistemology are bleak, modest modal epistemology is in excellent shape, and it’s sufficient to account for the justification of possibility claims at the heart of the most forceful and philosophically significant thought experiments.  As philosophers, it’s natural to want more, and thus to stay in the modal telescope construction business. But as I’ve tried to indicate, our track record for building telescopes that peer beyond our local modal galaxy is humbling. Perhaps the advice goes down better when coming from Mick Jagger and Keith Richards: “You can’t always get what you want. But if you try sometimes, you just might find, you get what you need.”