According to Hill (1997), the strategy of redescribing imagined wannabe-impossibilities as imagined possibilities + misidentification ‘is fundamentally misguided’ because ‘in non-pathological circumstances introspection gives us pretty accurate access to the contents of our own states of imagination’ (p. 83); thus, it is implausible to assume, as the error theory needs to do, that we are systematically mistaken whenever we think we are imagining the impossible. But even if we were mistaken in some or even many cases, the Kripkean redescription strategy just won’t work in all cases. One example, proposed in Wright (2002), is that of first-person counterpossible imagining.

If Kripke is right, Wright claims, I am essentially a human being, and necessarily tied to my actual biological originators. But I can imagine myself as having been born from different parents. I can also imagine myself, say by putting myself at center stage in a fantasy story, as being an elf, an alien, a monkey. Can my imagining these scenarios be explained away as my imagining possible situations involving an intentional doppelgänger of mine, which I mistakenly identify with myself? It seems not, says Wright. For I do not individuate myself qua thinking subject by means of phenomenal, surface appearances, as I individuate water by its external appearances of colorless, tasteless liquid. When I imagine myself in a clearly possible counterfactual situation, such as my being in the Grand Canyon instead of Europe, ‘no mode of presentation of the self need feature in the exercise before it can count as presenting a scenario in which I am in the Grand Canyon’ (Wright 2002, p. 436). The same holds for my counterpossible imagining myself as a monkey: this is not easily redescribable as my imagining a doppelgänger which is a monkey, and mistakenly taking the substitute to be me. I imagine myself in this case as well.

Kripkean redescription also doesn’t appear to be available with mathematical conjectures and impossibilities. If we can imagine in the relevant sense mathematical conjectures whose truth value we ignore, we can, in general, equally easily imagine that they are true, and that they are false.Footnote 16 A mathematician may imagine that Goldbach’s Conjecture fails. She may try to see what would follow from this. Suppose that the conjecture is true. If mathematical necessity is absolute, then it is absolutely impossible for some even number (larger than two) not to be the sum of two primes. Still, we cannot easily redescribe the mathematician’s imagining the relevant impossibility as the conceiving of a false doppelgänger of the content of the conjecture. What could such a doppelgänger be?

Proven conjectures, such as Fermat’s Last Theorem, make the case more vivid. Take a competent, but skeptic mathematician, who imagines she can find some mistake in Andrew Wiles’ proof, or even direct counterexamples to the theorem. The person understands the content of the theorem pretty well: it’s a simple claim on Diophantine equations. It is implausible to redescribe the situation as the mathematician’s imagining counterexamples to an intentional duplicate of the content of Fermat’s Theorem. There appears to be no content-misidentification going on here. Wright concludes from similar cases that ‘for a large class of impossibilities, there are still determinate ways things would seem if they obtained’ (Wright 2002, p. 437).

Aside from problems of generality, it seems to us that the Kripkean error theory comes, to use a label borrowed from Kung (2014), with a ‘telescopic view’ of the imagination at issue in HOP: when we imagine a scenario where P, we look with a metaphorical mental telescope at a situation making P true. What cannot happen is that such mental telescope has us look at the impossible: if the scenario shows up, it is there to be seen. What can happen is that we fail to appreciate what scenario we are looking at.

Talk of ‘telescopic view’ by Kung is meant to remind us of Kripke arguing against a telescopic view of our access to worlds in the aforementioned objections to Lewis. The context is the problem of transworld identification in the philosophy of possible worlds, which, as far as we know, is originally due to Kaplan (1969). This is an epistemic issue, not to be confused with the problem of transworld identity, which as far as we know is due to Chisholm (1967). The latter can itself be phrased in different ways (Divers 2002, Ch. 16, makes the relevant distinctions), but it is in any case an issue of (modal) metaphysics. The former has to do with how can we know whether we have a case of transworld identity in some sense or other.

In Kaplanian terms: which of the individuals in a possible world w is the ‘transworld heir’ of an individual in a different possible world (say, the actual one, @)? Given our own David Lewis at @, we are supposed to carry out some investigation among the individuals in w, with the aim of locating the Lewis-representative there. The problem seems intractable, insofar as w may include several individuals who resemble Lewis in various respects and can compete for the role. Here is one individual whose fingerprints and facial expression are indiscernible from those of our own David, but who never did philosophy and had a career as a drug dealer. Here’s another one who does not quite look like David, but who has written a book called On the Plurality of Worlds, where he defends the view that possible worlds are disconnected spacetimes largely filled with concrete stuff, etc.

Scholars usually consider transworld identity as a real issue (unless one is a counterpart theorist, which few want to be anyway), and transworld identification as a pseudo-problem, precisely under the influence of Kripke. This pseudo-problem comes, for Kripke, from a purely qualitative view of how worlds represent possibilities. Other worlds, says Kripke, are not something we glance at via the famous telescope. We need not represent alternative situations in purely qualitative terms: ‘generally, things aren’t “found out” about a counterfactual situation, they are stipulated.’ (Kripke 1980, p. 49), et cetera: the story is so well known that it hardly needs rehearsing (see also Plantinga 1974, p. 95; Chihara 1998).Footnote 17

Now if the kind of conceivability of P invoked by Humeans is the imaginability of a world or situation verifying P, and this involves having pictorial mental representations, such representations must make for pictorial-cum-labeling imagination on pain of being of very limited use for modal epistemology. Then they work, we suggest, more like Kripkean stipulation than, as presupposed in Kripkean error theory, as a Kripkean telescope. Kung (2014) claims that its stipulative component is what gives to (what we have called) pictorial-cum-labeling imagination its power to access the impossible. In particular, the identity of the represented objects in an exercise of imagination can in general be stipulated—it does not need to be discovered.

One imagines John kissing Mary. The phenomenology of the mental imagery can be such that the represented figures are relevantly similar to John and Mary: hair color, eyes, bodies. But what makes the imagining count as a representation of a scenario in which John kisses Mary is that one takes one figure as representing John and the other as representing Mary. And just as one can imagine John kissing Mary—a possible scenario—so can one imagine John as a cleverly disguised robot: one labels the person-lookalike one is imagining, which turns out, on inspection, to be filled with circuits and transistors instead of flesh and blood, as old John. But the latter scenario, if Kripke is right, is metaphysically impossible.

The need for labeling of this kind can be appreciated also by considering qualitatively indiscernible imaginings which are about different scenarios. One imagines two mono-zygotic twins one knows, standing next to each other, John on the left and Paul on the right, to the level of detail in which the two are qualitatively indiscernible in the scenario. What makes the one on the left John, and the one on the right Paul, is that they are so labeled. Had the label been inverted, we would have had qualitatively identical imagery representing a different situation: one in which John is standing on the right, and Paul on the left.

Once one accepts that the identity of the objects involved in such exercises of imagination is settled arbitrarily, one easily grants the imaginability of situations where the identity of objects is other than what it actually is: one can imagine Mohammed Ali punching Cassius Clay, and Hesperus as distinct from Phosphorus.Footnote 18

If one now retorts that it may then be in our powers to also stipulate, in imagining a world w that makes P true, that w be possible, one is then doomed to trivialize the role of conceivability-as-imagination as a tool for the discovery of possibility: for HOP can then be secured as true by definition. One is, in effect, characterizing the relevant imagination as one that entails possibility by fiat, begging the question against anyone who does not already agree with HOP to begin with.Footnote 19