Erkenn (2010) 72:177–204 DOI 10.1007/s10670-009-9198-2 ORIGINAL ARTICLE

Skeptical Conclusions Linton Wang • Oliver Tai

Received: 4 July 2008 / Accepted: 14 October 2009 / Published online: 24 November 2009 Ó Springer Science+Business Media B.V. 2009

Abstract For a putative knower S and a proposition P, two types of skepticism can be distinguished, depending on the conclusions they draw: outer skepticism, which concludes that S does not know that P, and inner skepticism, which concludes that S does not know whether P. This paper begins by showing that outer skepticism has undesirable consequences because that S does not know that P presupposes P, and inner skepticism does not have this undesirable consequence since that S does not know whether P does not presuppose P. We indicate that the two types of skepticism aim to different loci of doubts: while outer skepticism doubts whether we can gain an epistemic warrant for the actuality, inner skepticism doubts whether we can gain epistemic identification of the actuality. It is further indicated that responses to skepticism from externalist theories, as well as from fallibilist internalist theories, can only respond to outer skepticism but not to inner skepticism.

1 Introduction For a putative knower S and a proposition P, two types of skepticism can be distinguished depending on the conclusions they draw: outer skepticism, which concludes that S does not know that P, and inner skepticism, which concludes that S does not know whether P. While different qualifications on P can differentiate different types of skepticism—for instance, specifying P as propositions about the external world can give rise to skepticism about the external world—we shall focus on the two types of conclusion in their general form. This paper begins by showing L. Wang (&)
O. Tai Department of Philosophy, National Chung Cheng University, 168 University Road, Min-Hsiung, Chia Yi 621, Taiwan, ROC e-mail: [email protected] O. Tai e-mail: [email protected]

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that outer skepticism has undesirable consequences, but that those undesirable consequences do not follow from inner skepticism. We can distinguish two types of outer skepticism by the qualifications on applicable propositions they introduce. Universal outer skepticism holds the universal form of the outer skeptical conclusion: for a putative knower S, S does not know that P for any proposition P. Consider the propositions P and not-P and a putative knower S. Applying a skeptical argument on P and S, it follows that S does not know that P. On the other hand, from a skeptical argument on not-P and S, it follows that S does not know that not-P. That S knows that P presupposes P, and that S does not know that P presupposes P, for presupposition persists under embedding under negation.1 By similar reasoning, that S does not know that not-P presupposes not-P. As a result, universal outer skepticism has contradictory presuppositions. Further, what is presupposed is also implied, so universal outer skepticism implies contradictions, and thus is undesirable. However, the contradictory presuppositions do not arise from inner skepticism: that S does not know whether P does not presuppose P, and neither does that S does not know whether not-P presuppose not- P. To avoid the contradictory result from outer skepticism in its universal form, one may suggest limited outer skepticism, which arises from holding a qualified outer skeptical conclusion: for a putative knower S, S does not know that P for any true proposition P. Limited outer skepticism is not a thesis in the conditional form that, for any P, if P is true, then S does not know that P, for limited outer skepticism still aims at the spirit of outer skepticism: it simply aims at asserting a non-conditional negative knowledge attribution. Since limited outer skepticism limits the application of skepticism only to true propositions rather than all propositions, no contradiction follows. Nonetheless, this does not make the situation for outer skepticism any better, since it requires a skeptic to pick out the true propositions before they can apply their skeptical arguments. We consider two ways of picking out true propositions. First, a skeptic may use good reasons, e.g. evidence, to pick out a true proposition. Nonetheless, if the reason is good enough to guarantee the truth of a proposition, the skeptic already knows the true proposition; but this is what the skeptic intends to argue against. Second, a skeptic may simply presuppose a proposition and thereby take the truth of the proposition to be granted. But this is unsatisfactory, for why not presuppose the negation of the presupposed proposition? However, given that the first strategy is unavailable, presupposing a proposition and thereby taking it to be true is something that a skeptic has to live with. This will lead to some undesirable consequences for limited outer skepticism. To see the undesirability of limited outer skepticism, consider the following case. Imagine that we are working on epistemology in an isolated classroom, where the door is closed, there is no window, a perfect soundproofing system is installed, etc., so that we have no way to access what is happening outside of the classroom. It is time for us to talk about what skepticism might say about John, one of our crew members in the classroom, and the proposition that it is raining outside, a proposition that we have no way to confirm or disconfirm in the classroom. There is 1

Section 2 elaborates more on the issue of presupposition.

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no way that Jane, another crew member and a skeptic, can appropriately conclude that John does not know that it is raining outside, since the presupposition conveyed by the conclusion requires ‘us’ to confirm the truth of that it is raining outside before Jane can felicitously claim that John does not know that it is raining outside. Similarly, neither can Jane appropriately conclude that John does not know that it is not raining outside. Nonetheless, Jane is free to conclude that John does not know whether it is raining outside since this conclusion does not carry any presupposition about the truth of that it is raining outside. Jane is also free to conclude that John does not know whether it is not raining outside since this conclusion does not carry the presupposition about the truth of that it is not raining outside. Thus, it is better for Jane to be an inner skeptic than a limited outer skeptic. We can also understand outer and inner skeptical conclusions from the perspective of responding to epistemic inquiries or knowledge attributions. For example, consider outer and inner skeptical conclusions as negative answers to two different epistemic inquiries proposed in Williams (1970, 1972, 1995).2 The first inquiry is to ask ‘‘Does S know that P?’’ Williams tracks the inquiry back to Plato’s Theaetetus and identifies this inquiry to originate in the examiner’s stance, i.e. by asking the question, the inquirer assumes himself to know that P. Williams further indicates that the real epistemic concern in the inquiry is that ‘‘we are asking whether the true belief we know him to have has adequate warrant; our stance towards A is that of an examiner.’’ (Williams 1995: 204) Limited outer skeptical conclusions can be understood as responding to the first inquiry negatively for the reason that the required warrant for that S knows that P cannot be satisfiable. The second inquiry, without assuming our knowing that P is true at all, is to ask ‘‘Does S knows whether P?’’,3 and Williams tracks the inquiry back to Plato’s Republic, which is followed by Decartes. Inner skeptical conclusions can be understood as responding to the second inquiry negatively in that the required warrant for anyone to know whether p cannot be satisfiable. The comparison between outer and inner skeptical conclusions with respect to the two inquiries can also be extended to the knowledge attributions that S knows that P and that S knows whether P, respectively. So much for a quick preview for the difference between the two types of skeptical conclusions and the outer and inner skepticism arising from them. Due to the contradictory result from universal outer skepticism, we shall focus our attention on limited outer skepticism. In the rest of this paper, we shall argue that the two types of skepticism, as represented by the two types of skeptical conclusions, engage two different ways of doubting. Limited outer skepticism, to conclude that S does not know that P, engages doubts about whether one’s epistemic position can epistemically warrant the presupposed P, i.e. it doubts whether one’s epistemic state, in a certain degree, can ‘discriminate’ between the presupposed and the negation of the presupposed. In other words, given that what is presupposed is what 2

For a recent discussion on Williams’ distinction of the two inquiries and their epistemological significance, see Wong (2005).

3 Williams’ original inquiry is ‘‘who knows whether P?’’, which is used to characterize the information seeking characteristic of knowing.

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is presupposed to be part of the actual, limited outer skepticism engages doubts about whether one’s epistemic position can epistemically warrant the actual. On the other hand, inner skepticism has no presupposition about the actual in its conclusions, so the doubt is not about whether one’s epistemic position can warrant the presupposed, or the actual. Instead, it challenges whether one can epistemically identify the truth of a given proposition P, and thus engages the doubt on whether one’s epistemic position can epistemically identify the actual, i.e. it doubts whether one’s epistemic state can identify a proposition as true (about the actual). This paper does not intend, or even try, to provide a detailed analysis of the full spectrum of skepticism and possible responses to skepticism. Instead, this paper, by examining the difference between two types of skeptical conclusions in detail, focuses on the difference between the epistemological significance of two types of skepticism that the literature has not given much attention, and at the same time indicates a proper understanding of externalist responses to skepticism and the nature of knowledge arising from externalist epistemology. Section 2 shall clarify the difference in the presuppositions of knowing that P and knowing whether P. Section 3 argues that there are two interpretations of skeptical possibilities. The distinction is further used in Section 4 to differentiate the role of skeptical possibilities in the construction of limited outer and inner skeptical arguments. In Section 5, we shall show that the two types of skepticism aim at two different loci of doubts, and also that the two different doubts concern two different notions of knowledge. It is also indicated that externalist responses to skepticism only respond to limited outer skepticism rather than inner skepticism.

2 Knowing and Presupposition The bottom-line for a linguistic distinction of outer and inner skeptical conclusions is that the verb know is factive in the sense of being able to trigger presuppositions (e.g. Grice 1989, p. 274; Partee 2004, p. 154), and that knowing that P presupposes P rather than simply implying P. ... in which to say that somebody did know that so-and-so was the case and to say that he did not know that so-and-so was the case both imply that it was the case. This is a specimen, I think, of the kind of verb that has been called factive. (Grice 1989, p. 279) The view that knowing that P presupposes P has both its proponents and opponents in philosophical and linguistic circles. In this section, we shall first review the literature showing that knowing that P presupposes P rather than simply implying (entailing) P, and that knowing whether P does not presuppose P, though know is a presupposition trigger. 2.1 Knowing That and Presupposition Many epistemologists take the truth of P to be a necessary condition rather than a presupposition of that S knows that P. We call this the implication account of

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knowing that P, to be contrasted with the presupposition account of knowing that P, which calls for taking know a presupposition trigger. We would like to introduce two major difficulties for the implication account. In the literature, the identifying feature of presupposition is the following: u presupposes w only if u implies w and w is also implied when u is embedded under various logical operators including negation, e.g. :u implies w. The first difficulty for the implication account is that it does not explain the persistence of the implication of P across the battery of tests produced by embedding S knows that P under various logical operators. For example, that it is raining outside is implied by it being true that John knows that it is raining outside, John does not know that it is raining outside, Bill believes that John knows that it is raining outside, John might know that it is raining outside, as well as that if John knows that it is raining outside, then he will bring an umbrella (cf. Geurts 1999). This is mysterious for the implication account. Nonetheless, this persistence of implication can be easily explained in the presupposition account by the projection of presupposition under various logical operators (cf. van der Sandt 1992; Geurts 1999). According to the implication account, the implication of P does not persist when S knows that P is embedded under negation: the truth of P does not follow from it being true that S does not know that P, since S’s knowing that P implies not only the truth of P but also something else. Thus, that S does not know P can follow from that P is false.4 This result gives rise to the second difficulty of the implication account: according to our intuitions, it is quite unnatural that the truth of that S does not know that P follows from the falsity of P, but the implication account does not explain how this intuition arises. Imagine that someone says, ‘‘I do not know that P because P is false.’’ What he says sounds pretty weird. The implication account does not explain the weirdness. If one buys the implication account, it should naturally follow that we do not know false statements. It should naturally follow that we do not know that the sun rises from the west, we do not know that earth is the center of the universe, we do not know that Socrates is Chinese, etc. But none of these statements sounds natural at all. People fail to know things for reasons, but falsity does not naturally count as such a reason. Of course we do not attribute someone knowledge of false statements. But it is not because doing so would be to say something false. It is simply that doing so is unnatural, and there is no (epistemic) reason to say such a thing. We can account for this eccentric situation easily using the presupposition account of that S does not know that P: that S does not know that P presupposes P. Thus, it is weird to say that I do not know that P because P is false, for it is a case of presupposition failure. This is similar to the case that, in case that we all believe that France has no king now, it is weird for someone among us to say that the present king of France is not bald, for saying that the present king of France is not bald presupposes that there is a present king of France. Taking P as a presupposition of that S knows that P accounts for the eccentric situation of saying that S does not know P given that P is false: it is infelicitous to say that S does not know that P because P is false, since the presupposition of P is unsatisfied. In other words, it is 4

For example, Lycan (1999, p. 3) clearly endorses this view.

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infelicitous to talk about whether or not S knows that P if P is false, though it is felicitous to say that S does not know that P because S does not believe that P or S’s belief of P is not justified nor warranted.5 A detailed account for the inappropriateness of attributing that S does not know that P because P is false comes from two ways in which that a presupposition may affect assertions. The first aspect concerns whether a sentence containing a presupposition can be felicitously asserted. According to Lewis (1979), if the presupposition is not in the common ground of conversation, and the presupposition is consistent with our beliefs, we may accommodate the presupposition into our belief systems so that the common ground will include P. However, if a presupposition is incompatible with our belief, a sentence containing the presupposition cannot be felicitously asserted. Thus, in order to assert that S knows P felicitously, it is necessary that we do not believe P to be false. Second, even if a sentence containing a presupposition can be felicitously asserted, there is still a worry about whether it has an intuitively available truthvalue. Strawson (1950), as well as others, has the intuition that a proposition which contains an unsatisfied presupposition lacks an intuitive truth-value, i.e. it is intuitively truth-valueless. This leads to the result that, if P is not true, then the proposition that S does not know that P is truth-valueless. So we can see that, in order to obtain the conclusion that S does not know that P, P must be already established as a true premise in the argument, if a skeptical argument is meant to be valid.6 As indicated in Strawson (1950), that an expression is meaningful and that an expression is felicitously used or has a truth-value should be distinguished. For example, according to Strawson (1950), while The present king of France is bald is a meaningful sentence, but, when we say it right now, it is infelicitously used and truth-valueless, since there is no king of France. Thus, in case that a skeptical conclusion that S does not know that P is infelicitously used and truth-valueless, the presupposition account can still hold that S knows that P to be meaningful.7 5

One may suggest that knowing that P does not even entail P, but only pragmatically implicates P. We find this proposal even less plausible. The standard test for implicatures is by that they can be canceled (defeated), as shown by (1a), where the generalized conversational implicature that not all students failed the test is canceled by the following sentence in fact, all students failed the test. (1) a. Some students failed the test. In fact, all students failed the test. b. John knows that it is raining outside. In fact, it is not raining. If that S knows that P only implicates that P, we would expect (1b) to be consistent, but it is not (See also Williamson 2000, p. 35 for a similar argument).

6

One may question the presupposition account for the following reason. Given that what is presupposed is also entailed, that S knows that P entails that P. In case that P is false, by modus tollens, it follows that it is not the case that S knows that P, and this is a result that the presupposition account does not seem to like. The presupposition account can respond to the objection by the following. Given that the presupposition of that S knows that P is not satisfied, either that S knows that P cannot be felicitously expressed or that S knows that P is truth-valueless, so modus tollens cannot even be applied. 7

Saying that knowing that P presupposes P does not make asserting that I do not know that P equal to asserting that P and I do not know that P, which leads to Moore’s paradox. Saying that I do not know that P is to presuppose P and assert that I do not know it. It gives rise to infelicity when P is not the case, but nothing paradoxical arises.

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Now we turn to some possible objections to the presupposition account of that S does not know P. The general strategy of the objections is to show that (a) there is some interpretation of S does not know that P that does not seem to presuppose P, and (b) the lack of presupposition in that kind of interpretation shows that the presupposition account of that S does not know that P is incorrect. While we accept (a), we reject (b). We do agree that S does not know that P can receive some interpretation that does not presuppose P. Nonetheless, given the fact that there is some interpretation of S does not know that P that fails to presuppose P, we shall argue that it does not follow that know is not an inherent presupposition trigger. Moreover, neither does it follow that there is no interpretation of S does not know that P that presupposes P. Methodologically speaking, the presupposition account aims only at a certain usual and natural interpretation of S does not know that P that presupposes P; the presupposition account does not require every interpretation of S does not know that P to presuppose P. So our strategy to respond to the objections is to distinguish the interpretation of S does not know that P that does not presuppose P from the usual and natural interpretation of S does not know that P that does presuppose P. Consider first some examples to challenge the presupposition account of that S does not know P from Williamson (2000). (2)

a. I did not know that he was guilty, for he was innocent. b. I did not know that he was guilty, and you did not know that he was innocent. (Williamson 2000, p. 35)

Williamson takes both (2a, b) to be linguistically acceptable, and noncontradictory; so that S does not know that P does not presuppose P. Examples like (2a, b) have long been noticed in the linguistic literature under the name of meta-linguistic negation, which can function as canceling presuppositions. As we shall show, if the negation not is interpreted meta-linguistically, that S does not know that P does not presuppose P, since the meta-linguistically used negation functions as canceling the presupposition of that S knows that P.8 On the other hand, in its usual and natural interpretation, the negation not in S does not know that P is interpreted truth functionally as to negate the assertive content of that S knows that P, and thus the presupposition P persists in that S does not know that P. It turns out that these examples cannot be used to show that S does not know that P under its usual and natural interpretation is not presuppositional. The notion of meta-linguistic negation identifies cases where negations like not are not used as a truth functional operator in the usual way (cf. Horn 1985, 1989; Carston 1996, 1998, 1999), and is instead used as ‘‘ ... a device for objecting to a previous utterance on any grounds whatever, including the conventional or conversational implicate it potentially induces, its morphology, its style or register, or its phonetic realization.’’ (Horn 1989, p. 363) For example, consider the following comparisons.

8

The meta-linguistically interpreted not in S does not know that P cancels the presupposition of that S knows that P rather than the presupposition of that S does not know that P.

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(3)

a. It is not the case that John is in New York or John is in Boston, and it is the case that John is in DC. b. It is not the case that John is in New York or John is in Boston—it is the case that John is in New York or John is in DC. a. It is not the case that John falls in love with Mary and marries Mary, for John does not marry Mary. b. It is not the case that John falls in love with Mary and marries Mary—it is the case that John marries Mary and falls in love with her.

(4)

For (3a), the negation it is not the case receives a truth functional interpretation, so the first sentence is equivalent to that John is not in New York and John is not in Boston. The second sentence of (3a) further elaborates by asserting that John is in DC. Nonetheless, if the negation it is not the case is interpreted as a truth functional negation in the first sentence of (3b), given the second part of (3b), one can infer that John is in DC. Nonetheless, this is not entailed by the salient interpretation of (3b). One way to account for the salient interpretation of (3b) is to take the negation in (3b) to be applied to the implicature, following from that John is in New York or John is in Boston, that it is possible that John is in New York and it is possible that John is in Boston, so the entailment does not follow. In this interpretation of the negation, we say that the negation is used meta-linguistically. On the other hand, for (4a), the negation receives a truth conditional interpretation, so the first sentence is equivalent to that John does not fall in love with Mary or John does not marry Mary, and the second sentence explains the case by asserting that John does not marry Mary. However, if the negation it is not the case is understood as a truth functional negation in (4b), the first sentence contradicts the second sentence of (4b). Nonetheless, the contradiction does not follow from the salient interpretation of (4b). Meta-linguistic negation can give an explanation for the absence of contradiction: the negation is applied on the derived (pragmatic) interpretation, from that John falls in love with Mary and marries Mary, that John first falls in love with Mary and then marries her. Similar meta-linguistically used negations also appear in the case of ‘coerced’ presupposition canceling (denying, or rejecting). Consider examples as follows. (5)

a. The king of France isn’t bald—there is no king of France. b. I don’t regret inviting him—he jolly well gate-crashed. c. I haven’t stopped smoking—I’ve never smoked in my life. (Carston 1998)

In examples (5a, b, c), on the salient interpretations, the negation does not apply to the assertive content, but applies to the presupposition arising from those sentences, and echoed by the following sentences. Given the presupposition is canceled, the assertion is no longer under consideration by the presupposition failure. Consider, for example, (5a). If we take the negation to be applied to its assertion, given the presuppositional account of definite descriptions, the presupposition that there is a king of France is preserved and contradicts the following sentence that there is no king of France. Nonetheless, no such contradiction is saliently detected, so the negation is better understood as canceling the presupposition, and thus the negation is understood metalinguistically and the assertive content is no longer under consideration. However, it

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does not follow from the suggestion that the negation in (5a) is understood as canceling the presupposition that the negation of the presupposition that there is no king of France is asserted, since the canceling can arise simply from one’s accepting the possibility that there is no king of France, i.e. it might be the case that there is no king of France. To account for the availability of the coerced meta-linguistic negation, we appeal to Gricean maxims: given the Gricean maxim of quality, i.e. being truthful, the non-contradictory interpretation is preferred. The meta-linguistic negation in sentences containing presuppositional terms can easily explain examples (2a, b) without giving up the presupposition of that S does not know that P. In case (2a), the negation is coerced to be understood as canceling the presupposition that he was guilty and echoed by the claim that he was innocent; thus no contradiction arises from (2a). In case (2b), the negation in the first sentence is coerced to be understood as canceling the presupposition that he was guilty, and the negation in the second sentence is coerced to be understood as denying the presupposition that he was innocent. Thus, the sentence says that it might be the case that he was not guilty and that it might be the case that he was not innocent, and no contradiction arises from (2b) either. The assertive content is out of the question. We are not going to provide further analysis of meta-linguistic negation; readers are referred to the relevant literature. What we mean to point out is that examples like (2a, b) from Williamson (2000) are not enough to show that S does not know that P has no presupposition that P. Instead, given a presuppositional framework for knowing and the general phenomenon of meta-linguistic negation, we can account for examples like (2a, b) without appealing to Williamson’s account. Another objection to the presupposition account of that S does not know that P may arise from the following conversation between two agents A and B, concerning whether a coin will land heads in the next toss. (6)

a. A: The next toss will land heads. b. B: That is a bald claim. You do not know that it will land heads. It might not land heads. c. A: You are right. I do not know that it will land heads. I am just having a little bit of fun.

One may be inclined to say that there is an interpretation of A’s claim, that he does not know that it will land heads, that does not presuppose that it will land heads, i.e. an interpretation of A’s claim as that he does not know ‘‘the truth’’ of that it will land heads, which does not seem to presuppose that it will land heads. One may further use the case to show that, in general, that S does not know that P does not presuppose P. We agree that the kind of interpretation of A’s claim is available. However, as we shall show, the interpretation that leads to the lack of presupposition in the utterance of ‘‘I do not know that it will land heads’’ comes from the meta-linguistic interpretation of the utterance. Thus, the interpretation does not challenge the presupposition account. Though there does not seem to be a salient contradiction in A’s claim that coerces us to adopt the meta-linguistic interpretation of not when we interpret A’s utterance of ‘‘I do not know that it will land heads’’, we think that some contextual clue in the

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conversation does allow us to adopt the meta-linguistic interpretation of the utterance. In the conversation, when A admits that he does not know that it will land heads, one may think that A admits (a) that he lacks the appropriate warrant for that it will land heads, but the truth of that it will land heads is presupposed, or (b) that it is possible that it will not land heads (by A’s agreement with B’s claim that it might not land heads), and thus that it will land heads is not presupposed to be true in order to avoid the conflict with the possibility that it might not land heads. We find the proposal (b) more plausible, since it is not reasonable for A or anyone to presuppose that it will land heads (unless A is going to cheat on the toss) and it is more natural to think that A admits that it is possible that it will not land heads. This option also reflects that B’s claim that A does not know that it will land heads is based on B’s taking A’s claim that the next toss will land heads to be a bald claim, given that it might not land heads. What B challenges is the truth of A’s claim that the next toss will land heads from the very beginning, rather than A’s not having sufficient warrant for his belief that the next toss will land heads. Thus what A says is metalinguistically interpreted to deny the presupposition that it will land heads, and the denial makes it compatible with the claim that it might not land heads. Though we argue that the above objections are not successful in challenging the presupposition account of that S does not know that P, they do invite us to provide a more precise formulation of the presupposition account: that S does not know P presupposes P under the usual and natural truth functional interpretation of the negation not. Some may suggest interpreting the negation in the outer skeptical conclusion that S does not know P meta-linguistically, so the undesirable consequence and limitation of outer skepticism can be avoided. As we have said, the meta-linguistic negation is introduced via coercion in order to avoid contradiction. Without the presence of a contradiction, it is unusual and unnatural to interpret the negation in that S does not know P meta-linguistically. Though the meta-linguistic interpretation is not unavailable, not in the outer skeptical conclusions that S does not know that P is usually and naturally understood as used truth functionally rather than meta-linguistically. And it is the usual and natural use of the negation that outer skepticism aims at in its skeptical conclusions. If one still insists on the idea that S does not know P does not presuppose the truth of P, we believe that the intuition may arise from interpreting that S does not know P as that S does not know whether P in order to avoid the presupposition. For example, consider responding to the question ‘‘Did John win the lottery?’’ by that we do not know that John won the lottery. To make sense of the response, either we already take John’s winning the lottery for granted, or we take it to mean that we do not know whether John won the lottery (though responding to the question by that we do not know whether John won the lottery is more natural if we do not take John’s winning the lottery for granted). And it is quite unnatural to interpret the response meta-linguistically as denying that John won the lottery.9 Though it is 9

A standard discourse of the lottery case is as follows: ‘‘Consider that John bought a lottery ticket and believes that he will not win the lottery, given that he finds his chance to win to be quite low. Even if it is the case that he will win the lottery, we still find that John does not know that he will win the lottery, given that there is a chance, counterfactually speaking, for him to win.’’ In this discourse, that John will win the lottery is already presupposed before we attribute that he does not know it.

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possible to interpret that S does not know that P as that S does not know whether P in some context, we still take the distinction between that S does not know P and that S does not know whether P to be a clear one. In the next section, we shall explain why the presupposition of P does not arise from that S does not know whether P, even if know is a presupposition trigger. 2.2 Knowing Whether and Presupposition Contrary to the presupposition of P from knowing that P, that S does not know whether P does not presuppose P: the truth of P is neither implied by that S knows whether P, nor by that S does not know whether not-P; by asserting that S does not know whether P, it is not claimed either that S does not know that P or that S does know that not-P. The conclusion that S does not know whether P in fact presupposes nothing specific about P, and requires no special knowledge of P either. We said earlier that know is a presupposition trigger, but this does not seem to be compatible with saying that S does not know whether P does not presuppose anything specific related to P. A detailed formal analysis of why no specific presupposition arises from that S does not know whether P, given that know is a presupposition trigger, goes beyond the scope of this paper. Instead, we would like to give an informal account for how this seeming conflict can be resolved. Intuitively, that S does not know whether P can be understood as that, if P is true, then S does not know that P, and if P is false, then S does not know that not-P.10 This conditional analysis exploits a nice trick called presupposition filtering (blocking): the antecedents of the conditionals cancel the presupposition of the consequents that S does not know that P and S does not know that not-P (cf. van der Sandt 1992). Thus, the inner skeptical conclusions from Jane, in the earlier scenario in Sect. 1, can be paraphrased as saying that if it is raining outside, then John does not know it is raining outside, and if it is not raining outside, then John does not know that it is not raining outside. It easily follows that there is no need to have any information about the ‘external’ world in order to claim an inner skeptical conclusion. This type of presupposition filtering is pervasive for presuppositional expressions. For example, consider the following examples. (7)

a. If John is bald, John’s children are bald. b. If John has children, John’s children are bald. (van der Sandt 1992)

While that John has children is presupposed in (7a), because of the presence of the definite phrase John’s children, there is no such presupposition in (7b) though John’s children is presuppositional, and the explanation is that the presupposition is blocked by the antecedent of the conditional. Adopting this type of analysis, there is nothing special about the fact that no presupposition arises from that S does not know whether P, though know is a presupposition trigger. 10 We take that bivalence is behind this intuition. This intuition is also captured by the formal analysis of questions in Hintikka (1976). For criticism of Hintikka’s formal analysis of questions, see Karttunen (1977).

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The filtering of presuppositions can arise from taking interrogatives as complements in general, given that know is a presupposition trigger. For example, that S does not know where John is does not have any specific presuppositions about where John is.11 Even if it is the case that John is in New York, which is the true answer for Where John is?, John is in New York is not presupposed in that S does not know where John is. Intuitively, that S does not know where John is can be paraphrased as that, for any place, if John is there, then S does not know that John is there. No presupposition arises from the paraphrase given that the embedded conditional blocks the presupposition.

3 Two Interpretations of Skeptical Possibilities To set up a skeptical argument, skeptical possibilities are often used. Before we go on to introduce how skeptical possibilities are involved in constructing the two types of skepticism and arguing for the two types of skeptical conclusions, we shall first consider two interpretations of the notion of possibilities in general, and then see the applications of the two interpretations on skeptical possibilities in the epistemological literature. 3.1 Counterfactual and Open Possibilities In the literature, the notion of possibilities can be understood as counterfactual possibilities or open (epistemic) possibilities. While the notion of counterfactual possibility is meant to capture, for a certain given actuality, how a possible world is different from the actual world, the notion of open possibility is meant to capture uncertainty, with respect to an agent or a group of agents, about the actual world concerning what the actual world is. The notion of counterfactual possibilities are often expressed by counterfactual interpretations of expressions in subjunctive mood like might have been, e.g. it might have been the case that John is happy.12 The counterfactual interpretation of a subjunctive expression like It might have been the case that John is happy is composed of a presupposition that John is unhappy, and an assertion of a counterfactual possibility, a situation other than the actual, in which John is happy. On the other hand, the notion of open possibilities, also called epistemic possibilities, is often expressed by the epistemic interpretations of modals like it is possible and might, and is basically a notion relative to the epistemic states of an agent or a group of agents. When we claim, for example, that it is possible that John is happy or that John might be happy, whether what we say is true or not is evaluated, with respect to the proposition, on the epistemic status an agent, participants of a conversation, or a group

11 That S does not know where John is does have a presupposition that John is somewhere. But the presupposition arises from the interrogative rather than from know. 12 It has long been noticed that subjunctive expressions have interpretations other than counterfactual interpretations, but those interpretations are not the interest of this paper.

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of relevant epistemic agents (cf. DeRose 1991).13 On an epistemic interpretation of that John might be happy, it does not presuppose that John is unhappy, but introduces the open possibility that John is happy, i.e. that John is happy is not excluded by the epistemic states of the relevant agents under consideration. Sometimes counterfactual and open possibilities are encapsulated in the same modal expressions. For example, modals like could and might are sometimes used to express counterfactual possibilities, though they are often used to express open possibilities. For example, the expression that I could be a brain in a vat can be considered as expressing either the counterfactual possibility that I am a brain in a vat (under the presupposition that I am not a brain in a vat), or the open possibility that I am a brain in a vat. The difference between counterfactual possibilities and open possibilities is also reflected in the difference between subjunctive and indicative conditionals. (8)

a. If John were happy, he would come to our party. b. If John is happy, he will come to our party.

A subjunctive conditional like (8a) is in general taken to have a counterfactual interpretation, and thus presupposes the negation of the antecedent, so that John is not happy is presupposed by (8a), and thus that John is happy is no longer considered an open possibility. This idea is reflected, for example, by the Lewisian semantics for counterfactual conditionals, where the truth of (8a) is evaluated in a certain subset of the counterfactual possibilities where John is happy (cf. Lewis 1973). On the other hand, an indicative conditional like (8b) is in general taken to pragmatically implicate that the antecedent is possibly true, so that it is possible, and thus considered an open possibility, that John is happy is implicated by (8b).14 While modal sentences can receive either counterfactual or epistemic interpretations, whether a possibility is a counterfactual possibility depends on what the actual world really is, i.e. counterfactual possibility is an objective notion, but whether a possibility is an open possibility is determined by what the relevant agents take to be the candidates of the actual world, so open possibility is a subjective notion. Given that open possibilities are what agents take to be the candidates for the actual world, the possibilities excluded from open possibilities are taken to be counterfactual possibilities by the agents. Agents may include counterfactual possibilities in open possibilities, and consider them candidates of the actual. Thus what one takes to be

13 One way to express the idea is to think of open possibilities as an agent-dependent notion, and the dependency is on the common ground (beliefs) among agents: what is openly possible, and thus epistemically possible, is what is not excluded from the common ground of a group of agents. See DeRose (1991) for a more detailed discussion. This idea can formally appeal to the notion that, like NP quantifiers (cf. Stanley and Szabo 2000), epistemic modals, as well as other modals, contain implicit domain restrictors in their logical forms which can be filled in by either overt syntactic element or contextual information (cf. Kratzer 1981; von Fintel and Iatridou 2003). We will not go into the details of the issue any further. 14 The open possibility arising from indicative conditionals is an implicature, for it can be canceled. For example, we can say something like the following: John is unhappy, but if John is happy, he will come to our party. See Gillies (2004) for more details.

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open possibilities does not determine what the counterfactual possibilities really are, but it may give rise to what one thinks the counterfactual possibilities are. On the other hand, agents may not include the actual world in open possibilities, and thus wrongly take the actual world as a counterfactual possibility.15 3.2 Consideration and Elimination The notions of counterfactual possibilities and open possibilities are associated with the notions of epistemic consideration and epistemic elimination in the discourse of epistemology. While the notion of epistemic consideration is to be applied to counterfactual possibilities, the notion of epistemic elimination is to be applied to open possibilities. What we would like to show in the following is that modal-based externalist theories take skeptical possibilities to be counterfactual possibilities, and exploit the notion of epistemic consideration of skeptical possibilities to respond to skepticism, while the Cartesian tradition takes skeptical possibilities as open possibilities in order to raise the skeptical challenge. 3.2.1 Epistemic Consideration The notion of epistemic consideration is a theory dependent notion arising from externalist epistemology, concerning the inclusion of counterfactual possibilities in epistemic evaluation. To understand the details of epistemic consideration, we need to give a bit more background on externalist epistemology. We shall see that three important features are shared by those externalist theories that take the notion of epistemic consideration to be a key element in a theory of knowledge attribution: (a) the presupposition of actuality is taken to be the reference point of determining counterfactual possibilities, and (b) a set of counterfactual possibilities is selected by certain ‘externally construed’ epistemic principles based on the presupposed actuality and the propositions to be attributed as knowledge, and (c) a strategy in arguing against skepticism that takes skeptical possibilities, as counterfactual possibilities, to be excluded from the selected counterfactual possibilities. Given these three features, concerns about the justification of epistemic consideration may focus on the justification for the presupposition and the externally construed epistemic principles. In the following, we shall focus on elaborating the notions of epistemic consideration rather than evaluating it in different externalist theories. To elaboration the notion of epistemic consideration, consider the notion of epistemic consideration from relevance alternative theories (cf. Dretske 1970; Goldman 1976), Nozick’s conditions of knowledge (cf. Nozick 1981), and the contextualism of DeRose (1992, 1995) and Lewis (1996) as representative examples. Here, we assume that for S to know that P, it must be satisfied that P

15 Putnam (1981) argues that the skeptical possibility that we are brains in vats is actually impossible. One may like to consider whether he argues that it is not the case that we might be brains in vats or that it is not the case that we might have been brains in vats.

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is true, S believes that P, and S’s belief in P satisfies certain epistemic constraints that are taken to evaluate the epistemic effect arising from epistemic consideration. We shall see that the theory-dependency of epistemic consideration arises from the choice of external epistemic principles in different theories. To begin arguing that S knows that P, an actual world, which includes the truth of P, is presupposed, assumed, or taken for granted in externalism. For example, concerning whether Henry knows what he is looking at is a barn, Goldman (1976) says, ‘‘... in particular, he has no doubt that the last-mentioned object is a barn, which indeed it is.’’ (Goldman 1976, p. 772). Concerning whether one knows that the bank will open on Saturday, DeRose (1992) says, ‘‘Assume that in both cases that the bank will be open on Saturday ....’’ (DeRose 1992, p. 3) Though an externalist may have some reasons to hold the truth of P (rather than not-P) or to show that holding the truth of P is justified (but not sufficiently to guarantee the truth of P), e.g. by one’s experiences, but whether P is actually true is not under externalist investigation, and thus is simply presupposed. The importance of presupposing the actual and P in arguing for that S knows that P is that the presupposition provides a reference point to determine counterfactual possibilities in order to apply the external epistemic principles based on notions like relevance, salience, etc. To see this, consider the epistemic significance of the presupposition as follows: by presupposing P as representing part of the actual, we ‘turn’ the possibilities that not-P into counterfactual possibilities. In other words, by assuming P, we change our common ground for epistemic consideration. To see how the presupposition of the actuality and P serve as a reference point for epistemic consideration, consider their roles in various externalist epistemologies. As an exemplar of relevant alternative theories, we examine the two barns case in Goldman (1976). In one case, an epistemic agent is in a situation where he is looking at a real barn surrounded by other real barns; in the other case, an epistemic agent is looking at a real barn surrounded by fake barns which look just like real barns. For Goldman (1976), when we evaluate whether an epistemic agent knows that what he is looking at is a barn, we consider different relevant alternatives in the two different situations: in the latter situation, we consider relevant counterfactual possibilities whether the epistemic agent will falsely believe that what he is looking at is a barn, if what he is looking at is a fake barn, but we do not consider these alternatives for the first case. In the two scenarios, what is presupposed for the actuality is not only that what the agent sees is a real barn, but also other things: true barns in the first case and fake barns in the second case, around the real barn. Given that different actualities are presupposed, attribution of knowledge in the two cases depends on the consideration of different counterfactual possibilities. Since the epistemically considered relevant possibilities differ, it can be concluded that one knows in one case but one does not know in the other case. Furthermore, to argue against skepticism, relevant alternative theories take it that the skeptical possibilities, e.g. that there is nothing in front of the epistemic agent and that the agent is simply having an illusion, are counterfactual possibilities but not relevant alternative possibilities, and thus are not in epistemic consideration. In Nozick’s analysis of knowledge, to determine whether S knows that P, the closest counterfactual possibilities are chosen for epistemic consideration based on

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the presupposed actuality and P (cf. Nozick 1981).16 For example, to see whether I know that I have two hands, it is first assumed that I have two hands. Then Nozick invites us, according to his third condition, to consider whether I will still believe that I have two hands in those closest counterfactual possible worlds where I do not have two hands. To escape from skepticism, Nozick takes it that the skeptical counterfactual possibility, when (for instance) I am a brain in a vat and thus do not have any hands, is not one of the closest counterfactual possibilities; so the skeptical possibility is not included in epistemic consideration and does not threaten knowledge.17 For examples of contextualism, we consider the versions of DeRose and Lewis. For DeRose (1992, 1995), two factors determine what the possibilities are in epistemic consideration for attributing that S knows that P. The first factor concerns what the actual world is (the subject factor in DeRose 1992), and the second involves contextual factors (the attributor factor in DeRose 1992). If one is sensitive, following Nozick, to the truth of P in those selected counterfactual worlds, then one knows that P. A counterfactual skeptical possibility is only included in epistemic consideration in those contexts where there is a serious concern about the skeptical possibility. In a common sense context, the skeptical possibility is not a concern and thus is not included in the epistemic consideration. For Lewis (1996), what is included in epistemic consideration is captured by principles for ignorance of counterfactual possibilities. First, the actuality and P are presupposed, and by the rule of actuality, the actual world is not ignored. Additional rules together with this one yield a set of counterfactual possibilities which are not ignored under epistemic consideration. If there are no counterfactual possibilities of error, i.e. the possibility that not-P holds but we believe that P, in the epistemic consideration, we can say that S knows that P. A counterfactual skeptical possibility is included in epistemic consideration, and thus not ignored, only insofar as the skeptical possibility is brought to our attention, by the rule of attention. In common sense contexts, if the skeptical possibility is not brought into our attention, we do not take it into epistemic consideration.18 Putting together the presupposition of the actuality and the external epistemic principles, externalism excludes the skeptical possibility from epistemic consideration in order to avoid the skeptical challenge. Hendricks (2006) nicely summarizes this approach by what he calls epistemological forcing. 16 In Nozick (1981), the notion of counterfactual possibilities is used only to illustrate subjunctive conditionals in his analysis of knowledge. He does not endorse any specific possible-world account of subjunctive conditionals. 17 To see that Nozick (1981) takes skeptical possibilities as counterfactual possibilities, consider the involved subjunctive mood in Nozick (1981): ‘‘If it were true that an evil demon was deceiving us, if we were having a particular dream, if we were floating in a tank with our brains stimulated in a specified way, we would still believe we were not.’’ (Nozick 1981, p. 201). 18 Lewis (1996) adopts a two step strategy to include counterfactual possibilities into epistemic consideration. His first step is to ‘eliminate’ possibilities, which is a notion that we shall talk about later, and the second step is then to ignore worlds by applying his principles of ignorance. As for skeptical worlds, they are not eliminated, but they can be ignored depending on context. Thus, according to Lewis, elimination is an actuality-independent notion, but ignorance, as well as consideration, is an actualitydependent notion.

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The idea of epistemological forcing is as follows: whenever sceptics cite possibilities of error as arguments against knowledge claim, the strategy is to show that, although they are possibilities of error, they fail to be relevant possibilities of error. (Hendricks 2006, p. 2) In order to determine whether a skeptical possibility is relevant, it must be presupposed what the actuality is. That is the essential point we would like to emphasize. The presupposition of actuality and the adaptation of epistemological forcing is also clearly reflected in standard modal-based epistemic logic. In standard epistemic logic, the truth of a knowledge attribution such as that S knows that P, represented as KSP, is evaluated with respect to a given possible world where P is true,19 and thus the presupposition of a given world, the actuality, is essential for the starting point of evaluation. Furthermore, for KSP to be true with respect to a given world, P is required to be true in every epistemically accessible possible world, all of which are indistinguishable from the perspective of S. We can set constraints on the epistemically accessible worlds to exploit the idea of epistemological forcing, e.g. excluding the skeptical possibilities by making them epistemically inaccessible from a given world. But not every externalist theory adopts epistemological forcing to reject skepticism. Consider reliabilism and virtue epistemology. In both reliabilism and reliabilist-based virtue epistemology, for S to know that P, P is presupposed first, and moreover, cognitive faculties reliably lead to the truth of S’s belief in P. To escape from skepticism, Greco (1993) says: ‘‘But virtue epistemology explains that what is important for knowledge is that our cognitive faculties are in fact reliable in the conditions we are in. And so we do have knowledge as long as we are in fact not victims of a Cartesian demon, or brain in a vat.’’ (Greco 1993, p. 415) However, that our cognitive faculties are in fact reliable is actually another presupposition, since that we are not victims of a Cartesian demon relies on the presupposition of actuality. 3.2.2 Epistemic Elimination Epistemic elimination is the process of determining which possibilities are to be excluded from the open possibilities, by determining which possibilities are epistemically impossible. To show how epistemic elimination works, consider the famous Cartesian meditation. As pointed out by Descartes, we are thinking beings, and thus we can eliminate the possibility that we are not thinking beings; the possibility that I am not a thinking being cannot be included in the open possibilities. Nonetheless, simply on the ground that we are thinking beings, we cannot eliminate the skeptical possibilities such as, for example, that we might be dreaming, that we might be deceived by evil demons, etc. Descartes goes on to argue for the existence of God in order to eliminate the open possibilities that we are dreaming, we are deceived by evil demons, etc. We shall not discuss whether 19

Reflexivity of the accessibility relation is required to satisfy this condition.

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Decartes’ argument for the existence of God is correct. The example given here is only to show Decartes’ purpose in presenting the case. In general, there are two ways to eliminate open possibilities. First, we eliminate the possibilities where our mental states are subjectively (reflexively) distinguishable from the mental states we have. Given that I cannot subjectively distinguish my mental states in worlds in which I am not a brain in a vat and worlds in which I am a brain in a vat, I cannot eliminate the worlds in which I am a brain in a vat, and thus it is an open possibility that I am a brain in a vat. The second is a stronger principle of eliminating the possibilities where we do have different mental states: ‘‘Let E have propositional content P. ... Then I say that E eliminates W iff W is a possibility in which the speaker’s experience or memory has content different from P.’’ (Lewis 1996, p. 596) For example, my mental states in the actual world may be different from my mental states in skeptical worlds, e.g. Noe¨ (2005) argues that the mental states of a brain in a vat are different from our mental states (although we doubt that this is correct). By the stronger principle, we can eliminate skeptical possibilities via the difference in content. Nonetheless, the difference in content does not allow us to eliminate the skeptical possibilities by our weaker principle based on subjective distinguishability. The purpose of epistemic elimination is to eliminate counterfactual possibilities from the open possibilities. We thus take correct principles of epistemic elimination to be principles that eliminate only counterfactual possibilities based on the correct identification of counterfactual possibilities. We shall not here evaluate the weak and strong principles of epistemic elimination, and neither shall we introduce other principles of epistemic elimination. But it is worth noting that Descartes’ concern about skeptical possibilities is about whether they are open possibilities, as can be seen from the fact that he expresses skeptical possibilities in indicative mood. Now let us assume that we are [our italics] asleep and that all these particulars, e.g. that we open our eyes, shake our hands, extended our hands, and so on, are but false delusions; and let us reflect that possibly neither our hands nor our whole body are [our italics] such as they appears to us to be.20 (Descartes 1931, p. 146) This observation indicates a doubt on taking externalism to respond to Cartesian skepticism: Cartesian skepticism takes the threat of skeptical possibilities to come from their nature as open possibilities, but externalists adopt skeptical possibilities as counterfactual possibilities in their response to skepticism.21 While externalism responds to versions of skepticism which take skeptical possibilities to be epistemically considered counterfactual possibilities, one might speculate that internalism responds to versions of skepticism which take skeptical hypotheses to be epistemically non-eliminated open possibilities. However, it is not so. Internalism differs from externalism in that it requires an internalist notion of justification, meaning that the factors determining the justification of a belief are 20 As far as we know, Descartes uses indicative mood to express skeptical possibilities in the original Latin version, and the French translation follows. 21

This issue shall get clearer in Sect. 5.

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internally accessible to the putative knower, as a necessary component of knowledge, and maybe adds a fourth condition to handle Gettier cases (c.f. Feldman and Conee 2004, p. 299). Internalist responses to skepticism thus rely on its notion of justification. If the relevant notion of justification requires ‘certainty’ of beliefs, and thus leads to guaranteeing the truth of beliefs by eliminating possibilities, then there is no need to presuppose truth for a putative knower to entertain knowledge. The skepticism it shall face is the skepticism which takes skeptical possibilities to be open possibilities. In general, people take this type of internalism to have difficulty in handling the relevant type of skepticism since one cannot eliminate skeptical possibilities to reach certainty (cf. Unger 1975). On the other hand, if its notion of justification does not require certainty, as in fallibilist internalism, and the justification of beliefs requires only good reasons or warrants, then the presupposition of truth is required for a putative knower to entertain knowledge. The skepticism that this type of internalism has to face is the skepticism which takes skeptical possibilities to be counterfactual possibilities. In general, this type of internalism responds to skepticism by showing that a putative knower’s beliefs are justified in regarding skeptical possibilities as counterfactual possibilities (cf. Feldman and Conee 2004, Chap 12; Wright 2004).

4 Two Types of Skeptical Arguments Given the two interpretations of skeptical possibilities, we are ready to formulate general argument templates for the two types of skepticism: one exploits skeptical possibilities as counterfactual possibilities but the other exploits skeptical possibilities as open possibilities. We shall now illustrate some examples of exploiting the two templates. Consider a limited outer skeptical argument that, explicitly or implicitly, begins with the assumption that P, and at the end concludes that S does not know that P. Since P is assumed in the premise and presupposed in the conclusion, the truth of P is not the target to be overthrown. Moreover, in general, a skeptic would also like to assume that S believes in P, so S’s belief in P is not under attack. What is in question is whether S’s belief in P satisfies certain epistemic constraints. By demonstrating a skeptical possibility, a counterfactual possibility, of not-P, e.g. dreaming or being a brain in a vat, and taking the skeptical possibility into epistemic consideration, a skeptic argues that S does not know that P by, for example, showing that S’s reason for believing that P is not sensitive to, in the sense of Nozick (1981), the truth of P.22 So the conclusion is that S does not know that P, under the presupposition that P is true and also that S believes P.23 22 Fumerton (1995) distinguishes skepticism with respect to knowledge and skepticism with respect to justified or rational beliefs. Limited outer skepticism is better understood as skepticism with respect to the skepticism on knowledge in the sense that the evidence for beliefs cannot ‘guarantee’ or ‘track’ the truth of the believed proposition, rather than his skepticism with respect to justified or rational beliefs. 23

We find limited outer skepticism is already implicit in Dretske (1970). Of course, it may already appear in even earlier literature, such as the work of Hume. But we would like to leave this historical issue open here.

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Now consider how the argument for inner skepticism might go. Inner skepticism can begin with the premise that S believes that P but conclude that S does not know whether P. As with limited outer skepticism, S’s belief in P is assumed so it is not a target of skepticism. An inner skeptic proceeds to challenge whether S can identify that P is actually the case. The challenge concerns whether a skeptical possibility is actually a counterfactual possibility or just an open possibility. Thus, an inner skeptic’s strategy is to show that a skeptical possibility is still an open possibility, e.g. by showing that it is possible that I am dreaming.24 Now, for a skeptic, raising a skeptical possibility, an open possibility with respect to P, indicates that it might be that not-P. This open possibility of not-P can call it into question that P is the case, since if P is the case, not-P cannot be openly possible; we then conclude that S does not know whether P, where P is no longer presupposed. Moreover, once it is challenged that P is actually the case, the notion of epistemic consideration cannot arise since it is required that P actually be the case in order to pick up counterfactual possibilities. This incompatibility of P’s actually being the case and the open possibility of not-P can be exemplified by the following, where the presupposition that P is incompatible with the open possibility that not-P. (9)

John’s son is happy. But John might not have a son.

(9) sounds contradictory if might receives the epistemic interpretation: since that John has a son is presupposed given the definite phrase John’s son in the first sentence, we are no longer open to the possibility that John does not have a son. We take this incompatibility to be the essential point that gives rise to inner skepticism. Challenging presuppositions is not unique to skeptics, but is quite natural in our daily conversation. Consider someone saying that the present king of France is bald. By saying that, the speaker presupposes that there is a unique present king of France. However, a listener may naturally raise the concern: wait a minute, there is no king of France! (cf. von Fintel 2004). Given the challenge to the presupposition, the evaluation of the assertion is out of the question, but this situation does not lead to the conclusion that the king of France is not bald. While, conceptually speaking, we can distinguish two types of skeptical arguments, it does not mean that these two types of skepticism need to be represented in different argumentation structures. Actually, in the literature, the two types of skeptical arguments are sometimes represented in the same skeptical arguments. It is necessary to distinguish between the different interpretations of the modal terms involved in the arguments in order to differentiate the two types of skeptical arguments. Moreover, the occasional conflation of the two types of skeptical arguments in one argument representation may partially explain why the two types of skeptical arguments are not clearly distinguished in the literature. For example, consider how two types of skeptical argument can arise from distinguishing two ways of interpreting the modal could in the following Cartesian skeptical argument from Feldman and Conee (2004). 24 Whether an inner skeptic can be successful in demonstrating a skeptical possibility to be an open possibility is not our concern in this paper.

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The Possibility of Error Argument (PE) (PE-1) (PE-2) (PE-3)

Any belief about the external world could be mistaken. If a belief could be mistaken, then it is not knowledge. Therefore, by (PE-1) and (PE-2), no belief about the external world is knowledge. (Feldman and Conee 2004, p. 277)

There are two ways to interpret the modal could in (PE-1) and (PE-2). The first way is to interpret it as a modal which indicates a counterfactual possibility, in which case limited outer skepticism arises. Given this interpretation, (PE-1) is interpreted as saying that it might have been the case that any true belief about the external world is mistaken, and thus the truth of the belief is presupposed. Strictly speaking, this does not mean that any belief might possibly have been mistaken. Only true beliefs might have been mistaken. (PE-2) is interpreted as: if it might have been the case that a belief is mistaken, then that belief is not knowledge. (PE-3) is interpreted as indicating that, by (PE-1) and (PE-2), no true belief about the external world is knowledge.25 By treating a skeptical possibility as a counterfactual possibility, externalist theories can agree with (PE-1). When externalist theorists try to respond to the argument, based on the first way of interpretation, they deny (PE-2), e.g. by arguing that the counterfactual possibility of errors is ‘irrelevant’ to the consideration of knowledge. On the other hand, the second way is to interpret the modal as indicating open possibilities, in which case inner skepticism arises. (PE-1) is thus interpreted as meaning that it is possible that any belief about the external world is mistaken, and the truth of the belief is not presupposed; (PE-2) is interpreted as meaning that if it is possible that a belief is mistaken, then it is not knowledge; (PE3) then indicates that, by (PE-1) and (PE-2), no belief about the external world is knowledge.26 Given that the truth of a belief is not presupposed, externalists have no reference point to apply external epistemic principles, and thus have no way to consider whether the open skeptical possibility of error is ‘relevant’ or not. Externalists simply do not respond to this type of skepticism. Limited outer skepticism and inner skepticism also differ on whether they can arise from so-called closure arguments. While it is debatable whether limited outer skepticism can arise from closure arguments at all, one substantial feature of inner skepticism is that it obviously cannot arise from closure arguments. Closure arguments take their name from their exploitation of epistemic closure, which is an epistemic principle, for example, of the following form: if S knows that if P, then Q, then if S knows that P, then S is in a position to know that Q, e.g. (10b) follows from (10a).27

25

The phrase true belief indicates that this is a form of limited outer skepticism.

26

On this interpretation of (PE-3), it is no longer required that the beliefs under discussion are true beliefs. 27 A stronger form of epistemic closure is as follows: if S knows that if P, then Q, then if S knows that P, then S knows that Q.

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a. I know that if I have two hands, then I am not a brain in a vat. b. If I know that I have two hands, then I am in a position to know that I am not a brain in a vat.

Whether the epistemic closure, or its variations, is valid is still under debate (cf. Dretske 2005; Hawthorne 2005). Nonetheless, it seems to be very difficult to formulate a counterpart of epistemic closure for knowing whether. One possible candidate is the following: if S knows whether if P, then Q, then if S knows whether P, then S is in a position to know whether Q. However, the proposed candidate is obviously invalid, e.g. (11b) does not follow from (11a). (11)

a. I know whether (it is true that) if I have two hands, then I am not a brain in a vat. b. If I know whether I have two hands, then I am in a position to know whether I am not a brain in a vat.

The reason that (11a) fails to imply (11b) is obvious: (a) What I know is the truth that if I have two hands then I am not a brain in a vat, but (b) if I know that it is actually false that I have two hands (in that I know that I do not have hands), it does not follow that I am in a position to know whether I am not a brain in a vat, since in case I do not have hands, I could be either a brain in a vat or not a brain in a vat.

5 The Loci of Doubts We would like to indicate the loci of doubts arising from the two types of skepticism by exploiting the two different interpretations of skeptical possibilities as follows: one is on doubting whether one can epistemically warrant the presupposed, the other is on doubting whether one can epistemically identify the actual, as well as the presupposed. In limited outer skepticism, given what is actual, the consideration of skeptical possibilities as counterfactual possibilities is introduced to destroy our justification (or warrant, etc.) for beliefs in the presupposed truth. In inner skepticism, on the other hand, the introduction of skeptical possibilities as open possibilities is done to challenge whether we have a proper identification of the actuality, a concern with what the actuality is, and on how we reach the truth of beliefs. From the skeptical perspective in the Cartesian tradition, introspection or reflection alone does not gives us enough to identify which one of the two possibilities, P versus not-P, is the actual or the skeptical possibility.28 The two ways of skepticism can be further illuminated by the following passage from Nagel (1986). The central problem of epistemology is the first-person problem of what to believe and how to justify one’s belief – not the impersonal problem of 28

The difference between inner and outer skepticism should not be identified with the difference between metaphysical skepticism and epistemological skepticism. Even though inner skepticism expresses a concern about what the actuality is, it is a concern about our ability to identify it rather than a concern about whether there is an actuality.

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whether, given my belief together with some assumption about their relation to what is actually the case, I can be said to have knowledge. (Nagel 1986, p. 69) The paragraph nicely represents limited outer skepticism as an impersonal problem, and inner skepticism as a first-person problem: skepticism as an impersonal problem can only arise from the presupposition of the actuality; skepticism as a first-person problem concerns how one can eliminate the skeptical possibilities from open possibilities. We hope it becomes clear now that the exploitation of counterfactual skeptical possibilities in the construction of limited outer skepticism shows that externalist responses to skepticism are actually responses to limited outer skepticism. Modalbased externalist theories may differ on how the epistemological forcing strategy is adopted to reject skepticism, but their strategies are the same in taking skeptical possibilities as counterfactual possibilities given a certain presupposition of the actuality. Even externalist theories like reliabilism which do not exploit epistemological forcing to respond to skepticism still take skeptical possibilities to be counterfactual possibilities. Thus, limited outer skepticism, rather than inner skepticism, is the target that they respond to. It is intuitively correct that S knows P implies that S knows whether P. Thus, one may suggest that responding to limited outer skepticism, by showing that S knows that P, is also at the same time responding to inner skepticism, because it then follows that S knows whether P. However, this is incorrect. Though the externalist response does indeed show that S knows P leads to that S knows whether P, this holds only under the presupposition that P is true. However, to respond to inner skepticism, one needs to show that S knows whether P simpliciter, i.e. without the presupposition that P is true. In other words, to show that S knows whether P simpliciter, it is necessary to eliminate the open possibilities that not-P, and this is not demonstrated in the externalist responses. The other way does not go either: showing that S knows whether P does not show that S knows that P, for it might just be the case that not-P. On the other hand, internalist responses to skepticism may be responses to inner skepticism or limited outer skepticism depending on the notion of justification they use. As indicated in Sect. 3.2, if the notion of justification requires certainty, no truth of beliefs is presupposed and it faces the inner skepticism. But if the notion of justification does not require certainty, as in fallibilist internalism, the truth of beliefs is presupposed and it faces limited outer skepticism. The difference in the two types of skepticism also reflects two notions of knowledge in the literature. In one sense, the notion of knowledge is related to the association of beliefs and truth, which is about whether one’s belief can associate with the truth in a certain way. For example, in terms of Nozick (1981), knowledge requires truth tracking, i.e. for a belief of P to track the truth of P, it is required to believe P in certain P worlds and not to believe P in certain not-P worlds. And this notion of knowledge is about whether an epistemic agent’s epistemic status can guarantee that the agent tracks truth in a certain subset of counterfactual worlds. Skepticism about this type of knowledge, represented in the form of limited outer skepticism, challenges knowledge by one’s inability to track truth in skeptical

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worlds. On the other hand, a different notion of knowledge is related to certainty, which is about how an epistemic agent can be certain about whether his belief that P is true or false. To reach the certainty of P, it is necessary to eliminate possibilities where one believes P although P is false. Corresponding to this notion of knowledge, inner skepticism arises, similar to what is proposed by Decartes and Unger (1975), who emphasize that knowledge requires certainty. Knowledge is thus challenged by one’s inability to eliminate the skeptical possibilities from the open possibilities, leading to uncertainty. The two notions of knowledge are nonetheless related: to acquire certainty-based knowledge is to acquire truth association-based knowledge, but not vice versa. When one is certain about P, he believes P and the possibility that he is in a not-P world is eliminated. By eliminating not-P worlds, he can identify the difference between P worlds and not-P worlds and thus will not believe P in not-P worlds. So his belief that P can associate with the truth of P whenever a world is taken into epistemic consideration. Nonetheless, even if one’s belief that P can associate with the truth of P in all counterfactual worlds, there is no guarantee that one can eliminate, for example, skeptical possibilities, and thus one can fail to reach certainty about P. The point is that an agent’s certainty that P indicates that the epistemic agent can reflectively distinguish P worlds from not-P worlds. On the other hand, an agent cannot reflectively access whether he can associate with the truth of P, even if he is actually associating with the truth of P. Finally, we would like to associate the two types of skepticism with Pritchard’s notion of epistemic angst. Pritchard (2005) indicates, based on meta-epistemological considerations, that externalist responses to skepticism leave out epistemic angst: that, roughly speaking, the external epistemic conditions are not reflectively accessible from the first-person perspective, i.e. the irrelevance of skeptical possibilities determined by external epistemic principles is not reflectively accessible from the first-person perspective. Epistemic angst has long been recognized from the meta-epistemological perspective. From the perspective of Pritchard (2005), Fumerton (1995) presents a case of epistemic angst for reliabilist notion of justification. Perception, memory, and induction may be reliable processes in Goldman’s sense and thus given his meta-epistemological position we may be justified in having the beliefs they produce, but, the sceptic can argue, we have no reason to believe that these processes are reliable, and thus, even if we accept reliabilism, we have no reason to think that the beliefs they produce are justified. (Fumerton 1995, p. 174) Pritchard (2005) further proposes to formulate the epistemic angst in terms of reflective luck. Reflective Luck. For all S, the truth of S’s belief in a contingent proposition, u, is reflectively lucky if, and only if, S’s belief that u is true in the actual world, but, given only what S is able to know by reflection alone, false in most near-by possible worlds in which the belief is formed in the same manner as in the actual world. (Pritchard 2005, p. 198)

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By reflection alone, one is incapable of determining whether the skeptical possibilities are irrelevant, and thus one’s knowing that he has two hands (for example) is reflectively lucky. This unavoidable reflective luck is epistemic angst.29 Nonetheless, Pritchard (2005) does not take epistemic angst to be a skeptical position, but rather a meta-epistemological position that states a meta-epistemological anxiety for the external conditions given by externalism.30 Given that externalists respond only to limited outer skepticism, we can see how epistemic angst arises from a different perspective: externalists respond to limited outer skepticism by relying on the presupposition of actuality, because actuality is not reflectively accessible. On the other hand, the consideration of inner skepticism extends epistemic angst one step further: it is not only that the external conditions are reflectively inaccessible, and thus that one’s satisfaction of epistemic constraints (e.g. truth tracking) is not reflectively accessible, but also that the presupposed truth and actuality is not reflectively identifiable. We call this extended epistemic angst. Unlike epistemic angst, extended epistemic angst does not represent unavoidable reflective luck, since the denial of the presupposition of actuality makes the notion of reflective luck inapplicable, since this notion presupposes the identification of actuality. Moreover, extended epistemic angst is actually a skeptical position, giving rise to inner skepticism, based on challenging the presupposition of any truth and rejecting any claim of S knowing that P, by concluding that S does not know whether P. Without presupposing any truth, externalism loses its reference point, and thus external epistemic principles can no longer be applied and external conditions cannot be obtained.

6 Concluding Remarks Beginning with two types of skeptical conclusions, this paper argues that the two corresponding types of skepticism, limited outer skepticism and inner skepticism, locate different loci of doubts by exploiting two different interpretations of skeptical possibilities: by treating skeptical possibilities as counterfactual possibilities, one raises doubt about the epistemic warrant of actuality by challenging whether an epistemic agent’s belief satisfies epistemic constraints on knowledge, and the other raises doubt, by treating skeptical possibilities as open possibilities, about the epistemic identification of actuality by challenging the presupposition of truth in knowledge attributions. It is also indicated that externalist theories and fallibilist internalist theories respond only to limited outer skepticism but not inner skepticism, since their responses to skepticism are under the presupposition of what the actuality is, but inner skepticism aims exactly at countering this presupposition. This result leaves those theories with no position to answer the 29

Pritchard (2005) remarks that externalist theories, nonetheless, can avoid what he calls veritic luck defined as ‘‘For all S, the truth of S’s belief in a contingent proposition, u, is veritically lucky if, and only if, S’s belief that u is true in the actual world, but false in most near-by possible worlds in which the belief is formed in the same manner as in the actual world.’’ (Pritchard 2005, p. 196)

30 For the relation between reflective luck and the Pyrrhonian challenge to externalism, see Pritchard (2006).

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presupposition-free question ‘‘Does S know whether P?’’ raised by inner skeptics, since those theories lack proper machinery to identify whether the actuality is that P or that not-P from the very beginning. In the end, those theories fail to capture the certainty-based notion of knowledge targeted by inner skepticism, and thus are incomplete accounts of knowledge. Up to this point, this paper has not said much about how inner skepticism can be refuted, and we have also not provided a division between those responses to skepticism in the literature which can only respond to limited outer skepticism and those that can also respond to inner skepticism. The full spectrum of analysis has to wait for future work. This paper indicates that some kind of infallibilist internalism, which aims at pursuing certainty, can respond to inner skepticism. Since we do not see how infallibilist internalism is possible, we think that inner skepticism is difficult to reject, and we even tend to believe that inner skepticism is not rejectable. However, we also tend to think that the situation is harmless, since that inner skepticism is not rejectable implies only that an agent cannot entertain knowledge requiring certainty. But it leaves open the possibility that an agent can entertain knowledge as a notion of requiring a certain association between beliefs and truth, especially when we have various available externalist theories to respond to limited outer skepticism associated with this type of knowledge. One may complain that knowledge as a notion of truth association requires a putative knower to live with presupposition. Given the failure to reject inner skepticism, to some extent, this result might be just unavoidable: as putative epistemic agents, the knowledge attributions on us may have to be inevitably under presuppositions, and thus we may have only ‘‘presupposed’’ knowledge.31 There may be no room for appropriate knowledge attributions to us without presuppositions, and that is something that epistemic agents have to live with. In general, I believe that skepticism is revealing and not refutable, but that it does not vitiate the pursuit of objectivity. It is worth trying to bring one’s belief, one’s action, and one’s value more under the influence of an impersonal standpoint even without the assurance that this could not be revealed from a still more external standpoint as an illusion. In any case, we seem to have no choice but to make the attempt. (Nagel 1986, p. 7) Given that presupposition is unavoidable for epistemic agents, externalist epistemology does contribute to the understanding of knowledge from the perspective that, under presupposition of the actuality, knowledge goes beyond true beliefs by the requirement for epistemic warrant. Acknowledgments The authors would like to thank Xiang-Min Sen and two anonymous reviewers for very helpful comments. Thanks are also due to audiences at the 2007 annual conference of Taiwan Philosophical Association. The first author gratefully acknowledges the support from Taiwan National Science Council under the project number 95-2411-H-194-015-MY2, 97-2628-H-194-063-MY3, and 982410-H-031-002-MY3.

31 The complaint that skepticism raises the epistemic standard too high can only be based on this presupposed knowledge. Nonetheless, what inner skepticism aims for is non-presupposed knowledge. Thus the complaint cannot be that inner skepticism raises the epistemic standard.

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