The Appearance of Skepticism: Possibility, Conceivability and Infinite Ascent

Abstract The paper articulates a novel strategy against external world skepticism. It shows that a modal assumption of the skeptical argument cannot be justified.


Introduction
In proposing a skeptical scenario, the Skeptic challenges us to contemplate a situation in which things appear to be the way they do now, and yet nothing is as it appears to be. This can be illustrated in a variety of ways-by invoking the Cartesian Evil Genius or by Putnam's well-known setup, wherein some mad scientists place one's brain in a vat with nutrients and hook it to a supercomputer.
There have been many attempts to refute such skeptical scenarios (sks henceforth). This is notoriously hard to do, if not impossible, since the result of any test meant to rule out this frightening prospect can be simulated as well. So, the antiskeptical strategy I shall sketch here does not propose yet another such test. 1 The central idea is different: to articulate what can be called a (Carrollian) modal "neutralization" of the skeptical argument. 2 I isolate a less-discussed modal assumption of this argument, and draw on the resources of contemporary modal epistemology to show that the Skeptic cannot justify it. The moral is that there is actually no skeptical threat to confront.

A modal assumption
Traditionally, external world skepticism is not explicitly construed in modal terms. To see how considerations in the epistemology of modality become relevant to it, let us begin with what has become the standard version of the skeptical argument. Suppose that the Skeptic presents the modus 1 Or, instead of a test, one may (equally hopelessly) propose other means to rule out the skeptical hypothesis, e.g., as not the best explanation of one's perceptions. See Vogel (1990) and the many replies it elicited, especially Beebe (2009). 2 The similarities between the strategy here and Lewis Carroll's famous regress puzzle in What the Tortoise Said to Achilles will become evident soon. tollens below and I become worried by its conclusion-that I am not justified to hold even my most mundane beliefs, e.g., that I have hands.

Argument SK:
What can be done now? Since the validity of the argument is unassailable, responses to it have concentrated on its soundness. 4 An antiskeptical strategy tried in the past has been to show that the premises of the argument SK are actually problematic. 5 Here, I shall pursue a somewhat similar idea. However, I will not deal with any of the premises directly; instead, I shall challenge the first one indirectly. The challenge to SK-1 will be indirect since my concern will be the following modal proposition: The focus on this proposition-in which I take modality to be metaphysical 7 -is motivated by the observation that a most natural rendering of the first premise of the skeptical argument would be "Assuming that you accept that it is possible that you are the subject of a sks, you are not justified to believe that you are not in such a situation"; or, "Assuming SKP-0, SK-1." 8 So, one wonders, what happens if I do not make this assumption? The answer, I take it, is that, in this case, nothing further can be said. In particular, one is no longer in the position to evaluate SK-1 at all. Similarly, if we recall the presuppositional analysis of the famous example involving the present king of France, if there is no such king, the issue of his baldness does not arise; hence, the proposition "The present king of France is bald" lacks a truth-value. I suggest that we face the same situation here. Once I doubt that SKP-0 holds, the justification issue raised in SK-1 does not actually arise, i.e., SK-1 lacks a truthvalue. Thus, SKP-0 should be understood as a (Strawsonian) presupposition of premise SK-1. (A proposition p presupposes another proposition q iff p lacks a truth-value unless q is true. 9 Here, p = SK-1 and q = SKP-0). Therefore, SKP-0 has a special status in this debate: argument SK poses a threat only to someone who accepts it. So, if the Skeptic wants me, her opponent, to accept that SK-1 has a truth-value (i.e., that it is true), then I must first believe that SKP-0 holds.

SK-1
You are not justified to believe that you are not the subject of a sks (e.g., that you are not a brain in a vat).

SK-2
If you are justified to believe that you have hands, then you are justified to believe that you are not the subject of a sks (e.g., that you are not a brain in a vat). SKC Therefore, you are not justified to believe you have hands. 3 (SKP-0) It is possible that I am the subject of a sks. 6 3 This version of the argument-in terms of justification, not knowledge per se-follows Klein (2015). See also Klein (1995). 4 It has been noted that premise SK-2 relies on the Closure Principle (formulated in terms of justification; see Klein [1995Klein [ , 2015) and some authors took issue with this principle, hence with SK-2. Since I think that this principle is unproblematic, I will not discuss the attempts to respond to SK by rejecting it. I will also set aside contextualist strategies as well as a related strategy, according to which the attempt to defend Closure (and thus SK-2) leaves one unable to defend premise SK-1. See Huemer (2000) for discussion. 5 As M. Williams put it, "the skeptic [trades] on theoretical commitments that [s]he either does not acknowledge or tries to pass off as commonsense platitudes" (1999,50). This idea is echoed in Pritchard (2016, 172). 6 Hereafter, I shall take SKP-0 to be equivalent to the formulations above: it is possible that I am a brain in a vat/that nothing is as it appears to be, etc. 7 For convincing arguments that the modality involved cannot be epistemic see Levin (2000), Kung (2011), and Echeverri (2017). 8 As I clarify below, here I treat SKP-0 as a presupposition, so my treatment of it differs from Levin's, who calls it a "premise" (2000, 423) of the skeptical argument. There are other reconstructions of the Skeptic's position that treat SKP-0 (or something close enough) as a premise too. Graham (2007, 29), for instance, takes the first premise of the skeptical argument to be modal: "Massive error is possible about the external world." 9 Locus classicus is Strawson (1950); the definition I use here is van Fraassen's (1968, 137). Simons (2006) and Blome-Tillman (2014) are more recent discussions of this notion. At this point, there are two dialectical options left to explore. The first is that the Skeptic will ask me to provide the reason for which I doubt proposition SKP-0. The second is that the Skeptic will try to justify it herself in order to remove my doubt and, thus, to advance SK-1. As we shall see, neither option is satisfactory for the Skeptic.
The first move amounts to shifting the burden of proof on me, her opponent. This raises the further question about whether the Skeptic is entitled to do this, and, moreover, about how this new question should be answered and by whom. 10 So, let us ask what kind of proposition is SKP-0. It surely isn't an a priori/necessary truth. Is it a "natural intuition" we have? 11 Or, is it part of the background knowledge about the world? If any of these were the case, the Skeptic would be entitled to ask me for a reason to doubt such a proposition. Yet SKP-0 clearly does not share this status with "2 + 2 = 4," "Stones do not feel pain," or "Humans need food to survive," and other similar propositions. SKP-0 is nothing of this kind; it is an unusual, strange thought, a bizarre possibility indeed. 12 But, on reflection, things are even more difficult for the Skeptic since-somewhat ironically-the obligation to justify SKP-0 stems from within her own stance. By the Skeptic's own admission (embedded, as we recall, in the very proposal of a sks), it is uncontroversial that the appears-is gap exists in the perceptual domain: things may only appear a certain way without actually being that way. Applied to the present context, the appears-is distinction becomes a distinction between the genuine possibility that I am the subject of a sks and the situation in which this merely appears possible. Thus, the further challenge to the Skeptic is raised on the grounds that, contrary to what SKP-0 claims, it may only appear possible that I am the subject of a sks. 13 This challenge amounts, in the end, to the obligation to provide reasons to believe SKP-0, i.e., reasons which would a fortiori remove my suspicion that the possibility I contemplate is not genuine.
Before we move on, let me spell out the distinction between the appearance of possibility and genuine possibility. The epistemic phenomenon relevant here has been identified in different contexts and examined under the broad label of "modal error": 14 modality/possibility judgments are quite often unreliable, even wrong, and there are many cases when certain states of affairs appear/ed possible, while they are/were not possible to exist. These cases show that we are entitled to be suspicious 15 when it comes to distinguishing between "it is possible that p" and "it appears 10 Here, I volunteer to offer a reason that she is not entitled, but I do this just for the sake of moving on with the debate. It does not mean that I accept that I am under the obligation to offer this reason; in fact, it may well be the case that the Skeptic herself has to provide such a reason. This is not a settled matter and opening it may lead to yet another debate with the Skeptic. If this were to happen, the gain for the Skeptic's opponent is that the Skeptic would be diverted from her main target-conclusion SKC. As it will become clear later, this is actually compatible with the line of thinking proposed here. 11 A term used in Pritchard (2016, 24). 12 As called by Greco (2012, 318). Hereafter, I shall use this word as a quasitechnical term to refer to (modal) propositions that require justification. Echeverri (2017, 1301) also draws attention to the "the uncontroversial fact that the layperson may be reluctant to believe that she could be in a radical skeptical scenario." While this is true, we will see in a moment that not only laypeople, but also the more reflective/learned people, are in the same situation as soon as they realize that there are cases in the history of mathematics when what was taken to be possible turned out not to be so. 13 One can wonder whether embracing a suitably formulated version of "dogmatism," may help here-since the doctrine states, roughly, that if it appears to S that p, then, in the absence of defeaters, S thereby has justification to believe p. (See Tucker's [2013] collection and the authors therein for recent discussion.) Yet this does not actually help since if dogmatism were to work, the Skeptic would be defeated anyway.
14 See Yablo (1993Yablo ( , 2004Yablo ( , 2006 and van Inwagen (1998). For more recent takes on van Inwagen's views, see Geirsson (2005) and Hawke (2011). The appearance of possibility is most recently discussed by Fischer (2017, chap. 6) and by Berto and Schoonen (2018). Hartl (2016) is a critical discussion of van Inwagen (1998) and Hawke (2011); Hartl rejects the idea that Yablo's and van Inwagen and Hawke's views are compatible (2016, 273); however, the way I intend to use their views here is immune to this criticism. 15 Note that this point holds under the reasonable assumption that an extremely weak version of inductive inference works: not that our past fallibility manifests itself again in the future, but only that it could so manifest. possible that p." Yet, importantly, in what follows, this is not a matter of exceptionless principle, but applies only to what we called above bizarre propositions (like SKP-0). 16 To close this argument, it is crucial to realize that the position we start from is by no means one in which I should believe SKP-0 (by default, as it were), and hence I need to justify why I doubt it. On the contrary, since SKP-0 is at best located in a grey area on the spectrum of plausibility, 17 it is the Skeptic who has to present a justification for it.
I take these considerations to show that the Skeptic has no choice but to appeal to the second option-to (try to) justify SKP-0. Thus, the burden of proof is on her; she has to adduce reasons to believe that being the subject of a sks is a genuine possibility indeed. And now the thesis I shall defend below can be formulated simply as this: the Skeptic is not able to present such reasons.
An immediate reaction here may be that, on the contrary, the Skeptic is able to justify SKP-0, and in two ways. Call the first strategy the "Positive Conceivability" strategy. SKP-0 holds, the Skeptic maintains, simply because it is conceivable that I am the subject of a sks (be it the brain in a vat scenario or any other scenario). And, since what is conceivable is possible, SKP-0 follows. Just in case this first strategy fails, she may appeal to a second, alternative strategy. Let us label it the "Default" strategy. According to it, the Skeptic asserts that SKP-0 holds because I cannot rule out the possibility that I am the subject of a sks. We shall examine these two strategies below. 18 Both failand, it turns out, for virtually the same reason.
One more remark is in order before we move on to discussing the first strategy in detail. 19 A look at the literature reveals that SKP-0 has not received the attention it deserves, 20 and a possible explanation for this lacuna is, perhaps, the initial plausibility of the two strategies mentioned above.
With only a few but notable exceptions, 21 this proposition has not been investigated, even though it is a modal claim and there has been substantial debate around the justification of modal claims. 22

Positive conceivability
A traditional strategy to justify SKP-0 is to invoke conceivability considerations. By appealing to the venerable Conceivability Principle-that, roughly, "conceivability entails possibility"-the Skeptic may claim that the statement "It is conceivable that one is the subject of a sks" 23 entails SKP-0 ("It is possible that one is the subject of a sks"). Let us abbreviate this (Cartesian) principle of inference as SKP-1; moreover, let us grant that the Skeptic has identified a suitable version of it, which bypasses its well-known problems. 24 16 This is in contrast with Albritton's (2011) more radical form of modal skepticism. I return to this issue in section 5. 17 I agree with Echeverri (2017, 1301) who calls it an "open question" whether one should accept SKP-0. 18 The first label is from Chalmers (2004). The second strategy is related to his idea of "negative" conceivability (149); it is also alluded to by DeRose and Warfield (1999, 1): "(…) we can't rule out her hypothesis, that it's possible that [the skeptical] hypothesis is true (…)" 19 A caveat: I only deal with one kind of skeptical argument, the one involving universal simulation. A narrower skeptical argument-a "dreaming" argument according to which it is possible that I am dreaming right now-requires separate treatment, although I suspect along the same lines. (This other argument has it that it is always possible that I am being deceived, not that it is possible that I am always being deceived, as in the argument SK.) 20 SKP-0, or something like it, is acknowledged, but not discussed in, for example, DeRose and Warfield (1999), BonJour (2002), Pryor (2000), Graham (2007), etc. 21 Some of these authors have been mentioned already; see also Clarke (1972), Levin (2000) (criticized in Maitzen [2014]), Beebe (2010), Kung (2011), Albritton (2011), Pritchard (2016) and Echeverri (2017), who address the possibility claim labelled here as SKP-0. Although the present paper shares some of their insights, it does not tackle the issue in the same way. 22 It has been revamped by the influential van Inwagen (1998); I shall discuss more recent takes on it below. Vaidya (2017) contains an updated discussion. 23 Let us assume for the time being that SKP-0 is conceivable by a regular epistemic subject, not by an ideal one. This kind of subject will be discussed later. 24 See Yablo (1993) and Chalmers (2004) for comprehensive analyses of this principle.
Facing this threat, I will immediately note that this principle is a conditional. Thus, SKP-1 is inert unless its antecedent is shown to hold. So, the question to ask the Skeptic is: What is the justification to believe this antecedent? Note, once again, that I am entitled to place the burden of proof on her, since the antecedent is surely neither an intuition we all share nor a piece of established knowledge about the world. The question then is why should I accept the bizarre possibility that it is conceivable that I am the subject of a sks? 25 Let us label the relevant claim here (the antecedent of SKP-1) as Moreover, as we recall, this challenge (to justify SKP-2) is entirely compatible with the Skeptic's own perspective. If things may only appear a certain way without actually being that way, then, in the present context, what appears conceivable may not be genuinely conceivable. Let us abbreviate the former claim as SKP-3: The issue of "modal error" becomes relevant once again in the form of the distinction between cases when certain states of affairs appear/ed possible to conceive (conceivable), while they are/were not possible to conceive. It is the occurrence of these situations in the past that gives us the right to be distrustful when it comes to distinguishing between "it is conceivable that p" and "it appears conceivable that p." 26 (As we also recall, this guarded attitude applies only to bizarre propositions, and SKP-2 is among them).
But, what is it to be conceivable? My understanding of this notion here relies on a recent analysis due to Chalmers (2004). According to this analysis, naturally enough, By substituting "I am the subject of a sks" for p in the biconditional (CON), another equivalence that we will need later-call it (CONsk)-follows immediately: From (CON), through negating both sides, it follows that: It is conceivable that p iff it is not a priori true that~p. 27 (SKP-2) It is conceivable that I am the subject of a sks.
(SKP-3) It appears conceivable that I am the subject of a sks.
(CONsk). It is conceivable that [I am the subject of a sks] iff it is not a priori true that [I am not the subject of a sks].
It is not conceivable that p iff it is a priori true that~p.
Furthermore, we can also introduce the correlate notion of "appearance of conceivability" as follows: Thus, the worry here is, again, that since we can document cases of bizarre propositions p for which we have made the mistake of not distinguishing "it appears conceivable that p" from "it is conceivable that p," 28 the Skeptic needs a reason to justify the claim that the (bizarre) proposition "I am the subject of a sks" is not one of them. That is, she needs a reason to hold the stronger SKP-2, and not only the weaker SKP-3. Now, before we continue to develop this line of reasoning, we need to take a short detour. Consider the following objection. One may remark that according to the principle (CON) above, the Skeptic could immediately show that it is conceivable that I am the subject of a sks-i.e., SKP-2, the left-hand of (CONsk) above. This is so since its equivalent holds, i.e., the right-hand term in (CONsk), namely that But this is too quick. I reply to the Skeptic that she is in fact entitled to accept only a weaker claim, namely (This does appear so given how we understand apriority, and also given what we take ourselves to know about brains, vats, computers, etc.) To justify the claim that there is a difference between proposition (CONsk-rh) and proposition (a-CONsk-rh), I reiterate the argument I have already given above for the notion of conceivability: there are situations in which a proposition appears (or appeared) to hold a priori, and yet, it turns out, it does not (did not) hold a priori. There are actually many such cases 29 when it is reasonable to say that for a (bizarre) proposition p, it appears that [it is not a priori that p], but it is a priori that p. 30 This gap mirrors exactly the contrast between "it appears/ed conceivable that p", and "it is/was conceivable that p." Then, the conclusion of this detour is as stated above, that we can continue the discussion either in terms of conceivability or by spelling this notion in terms of apriority-it will not matter.
(We can see this even more clearly by substituting "I am the subject of a sks" for p in [ACON] above. This yields the following equivalence: (ACON) It appears to be conceivable that p iff it appears that [it is not a priori that~p].

(CONsk-rh)
It is not a priori that I am not subject of a sks.
(a-CONsk-rh) It appears that it is not a priori that [I am not subject of a sks]. Here is an example. For many centuries, it appeared to be an a priori truth that -1 does not have a square root, and yet we now know that it has (AEi). There are other examples, including, e.g., impossible geometrical constructions, the Naïve Comprehension Axiom, or even Goedel's incompleteness theorems. While the construction of a regular heptagon or the trisection of an angle using only compass and straightedge appeared (and perhaps still appear) to be a priori doable (conceivable), it turns out that they are not so because they amount to mathematical (a priori) impossibilities. 30 More explicitly, in the case of the Naïve Comprehension Axiom: although it appeared, and maybe still appears, that it is not a priori false (it is conceivable) that for any property we can form the set of objects that have that property (because we can indicate many properties in this situation), it turns out that it is (and it was) a priori false that this is so (hence it is not conceivable), as Russell's proof showed.
Since the right-hand side of this equivalence is granted, then, as objected, the Skeptic can assert, again, only the left-hand, namely Now the detour has ended, and we are back to where we left off. Returning to the main thread, let us reiterate the conclusion: the Skeptic can only assert the weaker SKP-3 and not the stronger SKP-2. And this is of no use to her.
At this point, it looks like the Skeptic faces a trilemma. The first horn is to say that although the example from set theory works fine, and although the gap between appears-that-p and is-p needs to be bridged for bizarre p's, in the situation under consideration here, there is no such gap because asserting SKP-3 amounts to asserting SKP-2.
The second horn is to show that she can infer SKP-2 from SKP-3. The third horn is a way out not yet discussed, but still available: justify SKP-2 on grounds independent of SKP-3.
All three horns present serious difficulties for the Skeptic, as follows.
According to the first horn, the Skeptic claims that, in the present case, the two notions overlap. If it appears (to me) that the state of affairs in which I am a brain in a vat (say) is conceivable, then it is so, i.e., it is conceivable (by me)-just as if it appears to me that I am in pain, then I am in pain. On this view, we, the individual epistemic subjects, are the ultimate authority in both matters. Thus, the concept "being conceivable" would behave like (or, as Wittgenstein would say, would have the same grammar as) "being in pain"-and unlike, for instance, "being provable." (It is an obvious falsehood to say, for a mathematical proposition q: if it appears to me that q is provable, then q is provable.) But the suggestion of an overlap is implausible on conceptual/"grammatical" grounds. Conceivability is, by definition, a capacity: one's ability (capacity) to conceive something. It thus has clear rational-discursive, objective, and public connotations, just like provability. We saw that it is only natural to say "it appears/ed (to me) conceivable that p, but, upon reflection, turns out it is/was not." So, although it is admittedly not entirely transparent what claiming that "p appears conceivable" amounts to, "p is conceivable" amounts to more. 31 To take stock: we saw that when it comes to the conceivability of bizarre propositions, there are two categories to consider. First, cases of genuine conceivability, when what appears conceivable is so; second, cases of modal error, when it is not so. Hence, the Skeptic was under the obligation to provide reasons that SKP-2 belongs to the first category. However, her first attempt to do this (the first horn) is not convincing.
Let us now discuss the third horn of the trilemma. (We will return to the second horn below). Can the Skeptic justify SKP-2 on grounds independent of SKP-3? It is rather hard to see how, but one proposal could be the following. Imagine that she asserts this: p is conceivable because there is an epistemic subject who actually conceives p (Since, unquestionably, what is actual is also possible). As is immediate, this helps only provided that she also indicates a concrete epistemic subject who does conceive a sks-that is, someone who not only utters the words "I am conceiving a sks," but does the conceiving, as it were. And, moreover, suppose the Skeptic finds someone, call him Mr. P, prepared to declare that I, Mr. P, am conceiving a sks here and now!

(SKP-3) It appears conceivable that [I am the subject of a sks]).
This is perplexing but let us assume that the Skeptic finds someone willing to sincerely declare that. Yet, when queried about a specific skeptical scenario, Mr. P will have to concede that he does not have that much to tell us. Unsurprisingly, he is not in the position to offer (publicly verifiable) details about how the perfect simulation mechanism is supposed to work. 32 For instance, if we consider the specific brain-in-a-vat skeptical scenario, Mr. P cannot tell us where to place the electrodes in the brain, or how to write the software for the supercomputer, and so on. Thus, for any such concrete person that the Skeptic brings forward, I, her opponent, will point out that, absent these relevant, publicly ascertainable details, even if this person is totally sincere, it may only appear to them that they conceive a sks, while in fact they do not conceive it.
Despite that, the Skeptic may be tempted by the further thought that Mr. P's actual failure is irrelevant-since, she claims, it is possible that such details be provided (by Mr. P, or someone else) in the future. But the same problem arises right away: namely, that this may only appear to be possible without it, in fact, being possible. This is the same difficulty once again, which, we now see, the Skeptic cannot avoid. Just as above, the absence of details functions one more time as a defeater of the "is possible" claim.
A complication has to be considered here, however. The Skeptic may insist that such (currently missing) details can be filled in, yet not by a regular person like Mr. P, but by a more powerful intellect, a superhuman one: by an Ideal Mind. 33 Note that this is yet another bizarre possibility claim. The problem with it is evident: the very notion of such an Ideal Mind is unfathomable. It may well appear conceivable that such a mind (i.e., one possessing infinite memory, infinite computational speed, etc.) exists without this being conceivable: we just cannot tell. Moreover, is such a Mind, simply by virtue of being a mind, still subject to modal error? As these hesitations reveal, we are on very shaky ground when it comes to judging this situation. What appears conceivable to such a Mind may or may not be genuinely so (e.g., to conceive a sks). All in all, then, since the very notion of an Ideal Mind is extremely foggy, the Skeptic cannot appeal to it without begging the question.
Finally, let us consider the second horn. The Skeptic may try to show that the inference from SKP-3 to SKP-2 goes through. Now things get complicated slightly, since the Skeptic realizes that she is within her rights to refuse to take on the quite difficult task to provide such a justification. That is, she notes that she is not under the obligation to accomplish this task-namely, to indicate concretely a reason why this inference holds. She observes that she is only committed to something that prima facie looks significantly less demanding: to justify the modal proposition that it is possible to provide such a justification: This is a legitimate move. But I will immediately note, in light of our discussion so far, that even though SKP-4 asserts only a possibility, it will still need justification-because, once again, SKP-4 is a bizarre proposition, hence modal error becomes a threat. What we want, after all, is to show that a proof of the entailment SKP-3 à SKP-2 is conceivable, and all this while being aware that there are many cases when although it may (have) appear/ed conceivable to establish a certain entailment, it is/was not possible/conceivable to do it (since it is/was a priori false that the entailment holds). 34  It is possible to establish that SKP-3 entails SKP-2.
32 See Yablo (1993), van Inwagen (1998), and Chalmers (2004 for the requirement that a certain amount of relevant detail has to be provided to be in the position to speak about a genuine possibility. More recent discussions of this are Geirsson (2005) and Hawke (2011). 33 See a related discussion of "ideal rational reflection" in Chalmers (2004, 147). Note also that in Descartes's version of the skeptical challenge, the Evil Genius is supposed to possess such a Mind. 34 There are such cases, and a well-known illustration may be Cantor's proof that if two sets are such that one is a proper subset of the other (e.g., the even numbers and the natural numbers), it doesn't follow that they have different cardinalities (both sets have cardinality aleph zero).
At this point, it becomes clear that this attempted modal escape launches a (Carrollian) infinite justificatory regress-upward, so to speak. The Skeptic now realizes that propositions SKP-0 and SK-1 are getting further and further "away" from her-and thus, fortunately, from us too. It turns out that SK-1 is based not only on SKP-0, but also, indirectly, on SKP-1, SKP-2, and SKP-3, as well as on yet another modal proposition, SKP-4. And a justification for the bizarre SKP-4 possibility claim is needed. It will consist, presumably, in offering yet another conceivability argument. 35 This is to be piled up on top of what we have amassed so far. So, more and more steps will have to be added to justify SKP-4. Since there is no end in sight for this exercise, the justificatory "tower" grows infinitely high, as follows. (One should read the argument below upward from line 1 and downward from line SK-1): I take this to establish that the worrisome SK argument is beyond the Skeptic's reach, so to speak; hence, it poses no threat to us. This is so since premise SK-1 may not be available to the Skeptic, since its presupposition SKP-0 becomes accessible to her only as the limit of an infinite series of justifications; that is, not at all. 37 Moreover, since we recall that the specific form of the sks discussed here did not matter at all (the brain-in-a-vat scenario served only as a more vivid illustration), the conclusion is entirely general.
Yet, as announced at the outset, this is only half of the story. The Skeptic can appeal to another strategy to justify SKP-0. But it will fail as well, and the failure shares the same structure (the infinite ascent) as the failure of the first strategy. … 5. It is possible to establish that SKP-3 entails SKP-2, i.e., that "It appears conceivable that you are the subject of a sks" entails "It is conceivable that you are the subject of a sks." -Still to be justified by the Skeptic If it is possible to establish that SKP-3 entails SKP-2, then SKP-3 entails SKP-2. 36 4. It appears conceivable that you are the subject of a sks.
-Accepted by both sides 3. It is conceivable that you are the subject of a sks.
-From 5 and 4, by modus ponens 2. If it is conceivable that you are the subject of a sks, then it is possible that you are the subject of a sks.
-The Conceivability principle, accepted by both sides (SKP-1) 1. It is possible that you are the subject of a sks.
-From 3 and 2, by modus ponens (SKP-0) SK You are not justified to believe that you are not the subject of a sks. (SK-1) If you are justified to believe that you have hands, then you are justified to believe that you are not the subject of a sks. (SK-2) You are not justified to believe that you have hands.
(SKC) 35 Note that this is so since we are now within the Positive Conceivability strategy, according to which this is the principled method to justify possibility claims. The next section explores a different way to justify this kind of claims. 36 This is a familiar situation in logic and mathematics (constructivist scruples aside). If it is somehow established (via a metaproof) that it is possible to prove p (even without actually proving it), i.e., that p is provable (in whatever system), then p is considered to be proved (in that system). 37 The present strategy differs from Strawson's (1985) Humean idea (that skeptical doubt is psychologically unrealizable) in that it is, in the sense explicated here, deductively unreachable-a stronger claim.

The Default strategy
Now the Skeptic's idea is to claim that SKP-0 holds simply because I, her opponent, am unable to rule out the possibility described in it; that is, because I cannot conceive reasons against the possibility that I am the subject of a sks. 38 However, this move will fail as well. The root of all the forthcoming difficulties for the Skeptic is easy to identify: the claim supposed to justify SKP-0 is itself modal.
To begin with, note that here the Skeptic is supposed to rely on what can be called a Default Principle of Modal Justification roughly stated as: Suppose that I accept this principle. 40 Yet, since it is a conditional, it is effective only if its antecedent is shown to hold. The antecedent of interest here is: As is clear, (~p 1 SKP-0) and DPMJ together entail p=SKP-0, by modus ponens. Then, the next challenge I raise for the Skeptic is to justify (~p 1 SKP-0). But, must she accept it? Yes, she must. The challenge brings in the idea of modal error one more time: although it may appear that reasons to rule out the possibility described by SKP-0 are not conceivable, maybe it is, after all, possible to conceive reasons to rule out this possibility. The relation between these claims is hard to fathom, since the propositions involved are on all accounts bizarre. Moreover, this need for justification arises since, as we recall, there are many cases when what appeared as not being possible to rule out turned out to be possible to rule out, and vice versa; we cannot tell whether we are in one of these situations right now. Hence, the burden of proof is on the Skeptic, indeed, to specify what entitles her to make the stronger claim ("it is not possible …"), rather than the corresponding weaker claim, that "it appears that reasons to rule out SKP-0 are not conceivable." Although this latter claim is unproblematic, the Skeptic cannot substitute it as an antecedent in the DPMJ. Now the Skeptic realizes that she may still have a way out. She may point out that she is not under the obligation to show, concretely, that what does not appear possible to do is indeed not possible to do. Instead, all she needs to establish is a weaker modal claim, namely that If such reasons are conceivable, then, as always in logic, we can say that what was needed to be shown is in fact shown 42 ; namely, that reasons to rule out SKP-0 are not conceivable.

(DPMJ)
If reasons to rule out p are not conceivable, then p. 39 (~p 1 SKP-0) Reasons to rule out SKP-0 are not conceivable. 41 (p 2~p1 SKP-0) It is possible to conceive reasons showing that what appears not to be possible (i.e., to conceive reasons ruling out SKP-0) is not possible.
38 I take conceivability to be elucidated by the (CON) principle, and thus the argument below can be spelled out in terms of apriority; but, as we saw, this is not needed. 39 This formulation is slightly contrived, yet preferable to the more natural but more verbose "if it is not possible to conceive reasons to rule out p, then p." 40 The DPMJ principle may strike one as too strong. Consider, for instance, the currently unproven Goldbach conjecture G, that every even number larger than two is the sum of two primes. It may look like the principle warrants that G is true: we have no reasons to rule G out (no counterexamples have been found), hence G. Yet, note the crucial difference. The antecedent of DPMJ requires that it not be possible to conceive (or find) such reasons/counterexamples-and this is something that is not established. In fact, it is something we do not believe to be the case: we believe that it is possible to conceive (find) either a counterexample, or a proof, otherwise mathematicians would not keep looking for them. The only situation when we would be entitled to say that it is not possible to conceive (find) a counterexample would be when we had a proof of G. Then, G would be true indeed. 41 Recall that SKP-0 states that "It is possible that I am the subject of a sks." 42 We encountered the same situation above. If p is provable, then we can take p to be proved.
The Skeptic realizes very well that she could help herself with (p 2~p1 SKP-0), but she also understands right away that she is not in that position yet because she still has to offer a justification for the bizarre modal claim above i.e., (p 2~p1 SKP-0). Why is it possible to show that? Why is that a genuine possibility?
Now, in line with the Default strategy, the Skeptic will say that such a claim is justified because, again, it is not possible to conceive reasons to rule out the possibility described in it, i.e., in proposition (p 2~p1 SKP-0). But this very claim (that it is not possible to conceive …) is a bizarre modal claim serving as the antecedent for a new application of the DPMJ principle. To say that it is not possible for someone to conceive reasons to rule out (p 2~p1 SKP-0) is to say that, as far as that subject is concerned: We notice that the indices increase, and this shows where we are heading. The (Carrollian) iterative infinite ascent we already encountered is gradually building up once again. The Skeptic realizes that she is not automatically entitled to claim that (~p 3 p 2~p1 SKP-0), but, at most, the weaker (and useless) version of this proposition-that it only appears that reasons to rule out (p 2~p1 SKP-0) are not conceivable. In order to be in the position to hold (~p 3 p 2~p1 SKP-0), she needs further justification, and so on. SKP-0 and, thus, SK-1 are, just as in the case of the first strategy, getting farther and farther away from the Skeptic-and from us, her opponents.
More explicitly, in order to present SK-1 to us, the Skeptic has to "climb down" the stairs of the infinitely high justificatory "tower" below. (Recall that this is to be read upward from 1 to 4, and then downward from SK-1 to SKC; also, recall the DPMJ principle: "If reasons to rule out p are not conceivable, then p."): (~p 3 p 2~p1 SKP-0) Reasons to rule out (p 2~p1 SKP-0) are not conceivable. So, reasons to rule out SKP-0 are not conceivable. 43 Hence, 2. Reasons to rule out SKP-0 are not conceivable.
-From 3; a restatement (~p 1 SKP-0) To close the discussion of this second strategy: argument SK is devastating, indeed-if the Skeptic presents it to us. But she cannot do this. The conclusion drawn at the end of the examination of the first strategy holds here as well. Since the SK argument's presupposition SKP-0 turns out to be infinitely far away from the Skeptic, the argument is actually not available to her. Thus, despite strong appearances to the contrary, we, her opponents, do not get to confront it.

Further clarifications and concluding remarks
In this final section, I shall take up two issues that may be raised in regard to the line of thinking articulated above. Both difficulties result from a kind of cost-benefit analysis. On one hand, it is not hard to accept that this debate should be governed by the methodological principle that no response to radical skepticism should have major damaging collateral effects. 44 On the other hand, the worry is that the strategy developed here seems to have two such unwelcome effects.
The first effect arises because of the oft-repeated requests made on the skeptic to justify her commitments. Yet, the objection goes, this is unfair: if one is required to justify all their commitments, then one becomes a victim of an infinite regress of justification. 45 And this, in turn, leads to a radical form of skepticism. Hence, the end result is that the cost of responding to skepticism about the external world in this way is too high: the deployment of another form of radical skepticism.
The side effect identified above is worrisome, indeed-and fair, since I do aim to neutralize the Skeptic in this manner. But, on reflection, it is not much of a concern in the present attempt to deal with skepticism. Recall that the strategy proposed here relied on the idea that I, the epistemic subject haunted by the specter of skepticism, should not lose sight of the (skeptical!) distinction between the modal appears-that-p claims and the modal is-p claims; and, what is more, I should ask for justifications of the latter claims when the propositions p in question were what we called "bizarre," i.e., strange, far removed from our familiar epistemic environment. Specifically, these were the kind of justifications that (indeed) launched the infinite regress and, thus, rendered the argument SK "unreachable." The antiskeptical strategy articulated here does not impose the requirement to justify each and every commitment one (the Skeptic, in particular) makes, but only a certain category of them; for instance, there was no obligation on any of the parties to justify some important claims, i.e., SKP-1 or DPMJ, as well as any of the "appears-so" statements.
The second side effect is somewhat similar to the first. By asking for a justification of SKP-0 (a modal claim), I seem to endorse another form of skepticism-about modality. So, again, the cost of the asymptotic kind of victory claimed here seems too high: defeat external world skepticism by embracing another form of skepticism. This is, again, a legitimate concern, and what hopefully answers it is that the suspicion about modality adopted here is quite limited in scope. The strategies above are compatible with the view that many of the modal claims we make in vernacular are, in fact, entirely unproblematic, since they regard familiar matters (e.g., it is possible to find beer in the fridge/to find who shot JFK/to count to 1 billion, and so on, are perfectly acceptable). Only some modal claims should be scrutinized, and SKP-0 belongs to this category given how bizarre, even fantastic, it is. Also, note that the antiskeptical conclusion was drawn without questioning any of the modal claims in the "appears-so" category (e.g., appears possible, appears conceivable, etc.). 44 I paraphrase Echeverri (201744 I paraphrase Echeverri ( , 1310. 45 As it is perhaps already clear, I do not take infinitism about justification to be a viable idea. For discussion, see Post (1980) and Turri (2009). To conclude: in devising the present strategy, I did not aim to show that there is something wrong with the skeptical argument SK per se. The fact that it relies on a certain presupposition (even a modal one) is not in itself a problem since all arguments have presuppositions. Nor did I try to provide a test whose result will tell us whether we are the subjects of a skeptical scenario. The novel idea was to pay close attention to where we stand in relation to skepticism; more precisely, to show that such a threat is infinitely far from us, so to speak. Thus, although impeccable, the Skeptic's argument only appears threatening, without being so. The Skeptic cannot ask us, her opponents, to accept the first premise of her argument without first accepting its bizarre presupposition SKP-0. But once we ask the Skeptic to justify it (since she has to do this, not us), and once she sets out to provide this justification, we saw that she will never be able to "return" to us-unless she performs the impossible (super-)task of climbing down an infinitely high justificatory tower.