Abstract
Skeptical puzzles and arguments often employ knowledge-closure principles (e.g. If S knows that P, and knows that P entails Q, then S knows that Q). Epistemologists widely believe that an adequate reply to the skeptic should explain why her reasoning is appealing albeit misleading; but it’s unclear what would explain the appeal of the skeptic’s closure principle, if not for its truth. In this paper, I aim to challenge the widespread commitment to knowledge-closure. But I proceed by first examining a new puzzle about failing to know—what I call the New Ignorance Puzzle (Sects. 1–3). This puzzle resembles to the Old Ignorance Puzzle (i.e. the closure-based skeptical puzzle), although it does not involve a closure principle. It instead centers on the standard view of ignorance, a highly intuitive principle stating that ignorance is merely a failure to know. In Sects. 2 and 3, I argue that the best way to solve the New Ignorance Puzzle is to reject the standard view of ignorance and to explain away its appeal via conversational implicature. I then use this solution to the New Ignorance Puzzle as a way of explaining why knowledge-closure principles would seem true, and why abominable conjunctions would seem abominable, even if such principles were false (Sect. 4). The upshot is a new way of explaining why the skeptic’s reasoning is appealing albeit misleading.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Unless otherwise specified, I use the phrase ‘knowledge-closure’ to refer to general closure principles, like [Closure], as well as particular instances of such principles (e.g. If Moore knows he has hands then he knows he’s not a BIV). My claims in this paper apply to any version of knowledge-closure no matter how it’s formulated, but I shall focus on simpler versions, like [Closure], for brevity’s sake. Closure principles whose consequents do not involve knowledge attributions (e.g. ones stating that justified belief is closed) are left unaffected by my arguments.
Unlike some theorists (e.g. Goldman and Olsson 2009), I find it more natural to speak of ignorance as a relation to facts rather than to propositions or states of affairs. But this makes no substantive difference in what follows. When I make claims like ‘S is ignorant of the fact that snow is white’ the reader is welcome to rephrase these claims as either ‘S is ignorant that snow is white’ or ‘S is ignorant of snow’s being white’.
To be fair, Williamson could instead be relying on this principle—if S is not in a position to know that P, then S is ignorant of the fact that P. Even so, the issues raised in this paper arise similarly for this weaker principle. For other philosophers who implicitly assume the standard view, see Driver (1989, p. 373ff), Flanagan (1990, p. 420ff), and Engel (2004, pp. 204 and 212).
The case description does not by itself require us to understand the doctor as withholding belief. Perhaps she only withholds diagnosis, but not belief. Nevertheless, the point is that the case can be interpreted in the way I have proposed without altering our initial intuition about her lacking ignorance.
Some may not share these intuitions. But universal assent is unlikely for any intuitive claim (indeed, I do not have the intuition that the standard view is true). Still, lack of universal assent shouldn’t deter us. Those who don’t share the conflicting intuitions assumed in this paper can still consider whether the intuitions of others can be adequately explained away.
An alternative to the standard view has been defended by Peels (2011, p. 345): For any truth P, S is ignorant of the fact that P if and only if S does not believe that P. However, Doctor Visit is equally a problem for Peels’ view, because Ontoit lacks belief in the fact that you have strep without being ignorant of that fact. I do not here focus on Peels’ view because it lacks the intuitive support had by the standard view—i.e. it’s not so initially appealing that people feel comfortable assuming it without argument. So, it cannot be featured within a puzzle like the one below.
Although it’s possible to interpret Doctor Visit in other ways, I shall interpret it as an instance of (i)–(iv). It might be thought that (i) and (iii) jointly entail belief, and thereby exclude (ii). But this is surely false. If anything, (i) and (iii) only entail that S has some degree of confidence that P, but this need not be enough confidence for outright belief—thus (ii) is not excluded by (i) and (iii). An example may help: Suppose I believe it’s probable that this lottery ticket is a loser—satisfying (i)—and for that reason I sell my ticket to the highest bidder—satisfying (iii). I may still fail to believe outright that this ticket is a loser—satisfying (ii)—even if I have some confidence that it’s a loser.
Instead of citing the negative evaluation, one may hold that ‘ignorant’ connotes (without entailing) that the subject significantly lacks information or evidence. This too could explain why we are reluctant to call Ontoit ‘ignorant’. My reply to this alternative would be parallel to what I say below—it doesn’t explain why we’re inclined to assert the negation. So I do not discuss this alternative directly.
One might claim that we’re inclined to assert [Not-Ignorant] because we mistakenly believe it’s true. But this only shifts the problem: we now need an explanation for why we mistakenly believe [Not-Ignorant]. And our reluctance to assert its corresponding affirmative is not enough to explain this. By analogy, the mere fact that you’re reluctant to call Max ‘fat’ doesn’t predict that you’ll mistakenly come to believe he’s not fat.
Since Ontoit withholds belief, this view is feasible only if low-grade knowledge does not entail belief. I allow this for the sake of argument, although many proponents of the present view hold that low-grade knowledge entails belief (e.g. see Goldman and Olsson 2009, p. 20; Engel Jr. 2004, p. 229, fn 24).
In this section, I ignore what Cruse calls “indirect tests for ambiguity”—tests that find two occurrences of a word with different meaning relations (e.g. synonymy, oppositeness) to other words. As Cruse notes, these tests are not reliable in distinguishing ambiguity from lack of specificity (1986, pp. 54–57). I also ignore the definitional test, which would presuppose that we can give necessary and sufficient conditions for knowledge (Lewandowska-Tomaszczyk 2007, p. 143).
Henceforth, let ‘#’ indicate that the sentence in question is linguistically awkward. For conjunction–reduction and ellipsis tests, the awkwardness is supposed to be of a particular kind, known as zeugma, which occurs when a single occurrence of a word must be interpreted in two distinct ways.
Although ‘know’ fails the contradiction test, ambiguity theorists may reply. Steup claims that “‘know’ is an instance of hidden ambiguity because ordinary speakers are not even aware of the distinction between [low-] and [high-grade knowledge]. It’s only after some exposure to epistemology that people grasp that there is a difference here” (2005, p. 7). This would explain why (6) seems contradictory to ordinary speakers, even if it’s not. However, if ordinary speakers don’t recognize the putative difference between weak and strong senses of ‘know’, this suggests that at least one sense is not an established sense. If there are two senses at all, then one of them is likely a non-established, technical usage, and thereby cannot help solve puzzles that arise in ordinary language. Moreover, there are many people, including me, who have had exposure to epistemology but do not recognize the putative ambiguity of ‘know’. Thus, neither competence in English nor exposure to epistemology is sufficient to grasp this putative difference between senses. Why then should we think there is a difference?
See Hazlett (2007, p. 674) for a similar version.
The contextualist theory discussed in this section is attributor-contextualism, where the proposition expressed by a knowledge-utterance is dependent upon features within the attributor’s psychology and conversational or practical situation. For a consideration of certain variants on attributor-contextualism, see Footnote 20.
I assume the antecedent and consequent of [Sufficiency] are to be evaluated with respect to the same context.
To see this in detail, let’s first suppose that ‘ignorant’ is context sensitive, but ‘know’ is invariant. Take a context C1 such that [Sufficiency] is true in C1. In C1, suppose that S does not know P and is ignorant of P. Now shift to some other context C2 such that it is false that S is ignorant of the fact that P in C2. Since ‘know’ is contextually-invariant, it will still be true that S does not know P in C2, just as it was in C1. Thus, in C2, S does not know P and S is not ignorant of P—here we have a counterexample to [Sufficiency]. Now suppose ‘know’ is context sensitive, but ‘ignorant’ is invariant. Take a context C3 such that [Sufficiency] is true in C3. In C3, suppose that S knows that P and S is not ignorant of P. But now go to some other context C4 such that it is false that S knows that P in C4. Since ‘ignorant’ is contextually invariant, it will still be true that S is not ignorant of P in C4, just as it was in C3. Thus, in C4, S does not know that P and S is not ignorant of P—here, we have another counterexample to [Sufficiency]. Therefore, if one term is context-sensitive, while the other invariant, there will be counterexamples to [Sufficiency] in some contexts.
I have intentionally phrased these utterances in terms of ignorance of whether P, rather than ignorance of the fact that P. The latter presupposes that P is true, and it would be odd for Mary to presuppose that the plane stops in Chicago given that this very fact is being questioned in her context. However, I assume the context-sensitivity of the former is not substantially different from that of the latter. I also assume that, if P is true and S is not ignorant of whether P, then S is not ignorant of the fact that P.
Variations on attributor-contextualism can be dealt with similarly. For example, according to contrastivism (Schaffer 2004), knowledge ascriptions denote a three-place relation—S knows that P rather than Q—and the value for Q can vary depending on the attributor’s context. On this view, we must ask whether ignorance-ascriptions also denote a three-place relation and vary by context. If they don’t, then there will be counterexamples to [Sufficiency]. If they do, then their contextual variations do not dovetail with that of knowledge-ascriptions, which also allows for counterexamples to [Sufficiency].
Although there is much debate over whether ‘know’ is context-sensitive (e.g. Stanley 2004, 2005, chap. 2; Ludlow 2005; DeRose 2009, chap. 5), some of the main arguments against the context-sensitivity of ‘know’ do not apply with respect to ‘ignorant’. For example, it has been observed that ‘know’ lacks the key features exhibited by context-sensitive gradable expressions—expressions that can be combined with modifiers (e.g. ‘very’, ‘rather’, ‘really’) and are conceptually related to comparative constructions (e.g. ‘taller than’, ‘flatter than’) (Stanley 2004, p. 124). But ‘ignorant’ clearly has these features, as evinced by sentences like “Jill is rather ignorant of the fact that P” and “Jack is more ignorant of that fact than Jill is.” So, those who reject the context-sensitivity of ‘know’ on these grounds will have to find other reasons for resisting the claim that [Sufficiency] is false in some contexts.
For example, Levinson says that “not ignorant logically implies knows (because ignorance and knowledge are contradictories)...” (2000, p. 208). His parenthetical remark precludes the inference from being a (B)-type enthymeme.
Potential counterexamples will arise if we give a de dicto interpretation of P in one instance, but a de re interpretation in the other (e.g. Lois knows that superman can fly, but she’s ignorant of the fact that Clark Kent, who is in fact superman, can fly). To avoid this, we must insist that the same interpretation be given to each occurrence of P.
For ease of formulation, I occasionally speak as if sentences can conversationally implicate other sentences. But, technically speaking, it is the utterance of the sentence that conversationally implicates the proposition expressed by the other sentence.
There is an equivalent inference from ‘If P then Q’ to ‘If Q then P’, which Laurence Horn calls “Aristotle’s conversion” (2000, p. 298). Although I only appeal to conditional perfection in this paper, the explanation I propose can be easily framed in terms of Aristotle’s conversion, rather than conditional perfection, provided that we start with the contraposition of [Necessity]—For any truth P, if S is ignorant of the fact that P, then S does not know that P.
Geis and Zwicky (1971, p. 656) actually hold that the inference is an implicature, but not a conversational implicature. However, the pervasive trend, following their paper, has been to treat the inference as conversational.
Technically, Horn claims that we infer (12) from the contraposition of (11)—‘If S is unhappy, S isn’t happy’. This step is not an instance of conditional perfection, but is an equivalent inference known as Aristotle’s conversion. See Footnote 25 for explanation of Aristotle’s conversion.
An inference from ‘A’ to ‘B’ might be cancelable (and might be a conversational implicature), even if this inference cannot be canceled in all contexts where ‘A, but not B’ is uttered. It is enough if there are only some contexts where this inference is canceled. See Blome-Tillmann (2008) for discussion.
I also hold that equivalent sentences, like ‘S does not have knowledge’, ‘S fails to know’, and ‘S lacks knowledge’, will also have this implicature. This follows from the non-detachability of conversational implicature (i.e. truth-conditionally equivalent statements carry the same conversational implicatures).
This explanation can be stated more precisely if we distinguish between sentences and propositions. Let \({<}\hbox {Sufficiency}{>}\) and \({<}\hbox {Necessity}{>}\) stand for the propositions expressed by [Sufficiency] and [Necessity] respectively. The explanation has two parts. Part I: We intuit \({<}\hbox {Sufficiency}{>}\) because we accept the truth of [Necessity] and we mistakenly interpret [Necessity] as expressing the conjunction of \({<}\hbox {Necessity}{>}\) and \({<}\hbox {Sufficiency}{>}\). Part II: We mistakenly interpret [Necessity] as expressing this conjunction because [Necessity] conversationally implicates \({<}\hbox {Sufficiency}{>}\) via conditional perfection and negative strengthening. In Parts I and II, ‘we’ should technically refer only to English speakers, since [Necessity] is an English-language sentence. However, conversational implicatures are non-detachable, which means that ‘we’ could refer to non-English speakers whenever [Necessity] is replaced with its non-English equivalents. Moreover, the conversational implicatures in question are what Grice calls “generalized conversational implicature,” which can be detected even when the sentence is not uttered in context (Grice 1989, 37). According to Levinson, these implicatures are “hard to distinguish from the semantic content of linguistic expressions, because such implicatures will be routinely associated with the relevant expressions in all ordinary contexts” (1983, 127). It’s worth noting that Part II parallels the traditional Gricean explanation of why people interpret ‘P or Q’ as expressing the conjunction of \({<}\hbox {P}\) or \(\hbox {Q}{>}\) and \(<\)It’s not the case that both P and \(\hbox {Q}{>}\).
See Horn (1989, pp. 356–357) for discussion on of a similar pattern with regard to ‘not bad’.
An example of an understatement involving ‘not ignorant’ might be ‘Socrates is not ignorant of the fact that P—he’s no idiot!’ In this case, we clearly are licensed to infer that Socrates knows that P.
One explanation might be extracted from Heller (1999, p. 205ff) who rejects closure but admits that closure is true in some contexts. It could be claimed that closure’s truth in some contexts can make it seem as though closure is true in all contexts. However, the explanation is insufficient as it stands. There are some contexts in which ‘If x is tall, then x is taller than 7 feet’ is true, but its truth in some contexts doesn’t make this principle seem true in general. Another attempt at explaining away closure comes from Cohen (on behalf of Dretske and Nozick): “I suppose Dretske and Nozick could say that it is our failure to appreciate the deep truth about the nature of knowledge as revealed by their theory. We mistakenly believe in the closure principle because we fail to see how the tracking condition for knowledge falsifies it” (1999, p. 64). This proposal fails to explain the appeal of closure for reasons not mentioned by Cohen. The supposed fact that “we fail to see how the tracking condition... falsifies” closure only predicts that we will either believe in closure or suspend judgment on whether closure is true. But since the second disjunct is a possible outcome, the proposal thereby does not explain why we’re inclined to accept closure.
This inference assumes that knowledge is factive.
The no-ignorance principle may take on a different form depending on the closure principle from which it’s generated. For example, some closure principles have a weaker consequent. They replace ‘knows’ in the consequent with ‘is in a position to know’. In this case, the corresponding no-ignorance principle will say something about being in a position to lose one’s ignorance. But, just as before, this sort of no-ignorance principle would be entailed by its corresponding closure principle via [Necessity].
These claims will apply equally to the closure principles that Hawthorne relies on (2005, p. 31ff). Hawthorne provides an argument based on two closure principles, and aims to problematize the closure-denier’s view by showing that they are committed to denying one of these principles. The two principles are as follows:
Equivalence: If S knows a priori (with certainty) that P is equivalent to Q and knows that P, and competently deduces Q from P (retaining the knowledge that P), then S knows that Q.
Distribution: If S knows the conjunction of P and Q, then, as long as S is able to deduce Q, S is in a position to know that Q.
These two principles are intuitively plausible, and the closure-denier’s reasons for rejecting closure typically do not lead them to rejecting the first principle. Hawthorne then goes on to show that these two principles lead to the type of conclusion that the closure-denier wants to avoid—namely that one can know that one is not a BIV. The closure-denier is therefore committed to rejecting at least one of these principles, most likely Distribution. My response above applies equally to Hawthorne’s argument. Equivalence and Distribution each generate a no-ignorance principle that the closure-denier can accept. And this means that my general strategy for explaining away the intuitive appeal of [Closure] can be applied also to the intuitions upon which Distribution and Equivalence are based. If the closure-denier is committed to denying one of them, then there will be a suitable version of the Closure Hypothesis that can explain away its appeal.
To be sure, there are reasons for rejecting particular versions of knowledge-closure, such as [Closure], and these reasons might also license the rejection of the corresponding no-ignorance principle, like [NI]. (See David and Warfield 2008 for different problems for specific versions of closure). My claim is only that the reasons traditionally cited against the whole class of knowledge-closure principles are not reasons for rejecting the whole class of no-ignorance principles. Most arguments against knowledge-closure, such as those in Dretske (2005), are obviously irrelevant to no-ignorance principles. So I omit discussion of them. The only one that might seem to apply also to no-ignorance principles is the challenge discussed in this paragraph.
Some may have the intuition that Moore is ignorant of whether he’s a BIV. I don’t share this intuition, especially if we stipulate that Moore believes he’s not a BIV. But even so, there’s a distorting factor in the whether-formulation. Unlike [Ignorant], the whether-formulation doesn’t presuppose that Moore is not a BIV. As such, those who contemplate the whether-formulation could be leaving it open as to whether Moore is a BIV; and if he is a BIV, then he would be ignorant of whether he’s a BIV, since he would have the false belief that he’s not one. This distorting factor is absent from the Modified Puzzle as I’ve stated it, because [Ignorant] presupposes that Moore is not a BIV. The distorting factor is also absent from the original Old Ignorance Puzzle, because [Old-Not-Know] presupposes that Moore is not a BIV, given that factive verbs (e.g. ‘knows’) presuppose their embedded contents when the verb is negated (e.g. ‘S does not know that P’ presupposes P).
This is true according to Lewis’ rule of attention—“if in this context we are not in fact ignoring but attending to it, then for us now it is a relevant alternative” (1996, pp. 559 and 564). It’s also true according to DeRose’s variation, where the skeptical possibility becomes relevant when it occurs within the scope of an epistemic operator—“S does not know that...” (1995, p. 15, fn 22).
There are differing views about what determines the relevance of a possibility, but none would make this possibility irrelevant. The possibility of you having tonsillitis was explicitly mentioned by Ontoit, has practical significance for all parties involved, and is likely enough that Ontoit seeks further evidence in order to exclude it.
One might wonder how a person could distinguish between the high- and low-standards concepts of knowledge. Contextualists typically hold that the high-standards concept entails a concept such as sensitivity (DeRose 1995) or unrestricted infallibility (Lewis 1996). So, for the same reason mentioned with regard to Sosa’s hypothesis, if a subject reports that she’s not employing the concept of sensitivity/infallibility, then this report would be evidence against the view in question.
Greenberg has observed that certain African, Amerind, and Oceanic languages have an expression equivalent to our ‘good’ with no expression equivalent to our ‘bad’. But it turns out that competent speakers of these languages still have the concept of badness. According to Greenberg, such speakers convey that something is bad by negating their term for ‘good’ (1966, p. 52). According to Horn, this information is conveyed by conversational implicature (Horn 1989, chap. 5, p. 336, for discussion). But for these speakers to convey that something is bad, and to understand this when it is conveyed, they must possess the concept of badness, even if there’s no term for it in their language. These languages are closely analogous to language L. So, it’s far from clear that unilingual speakers of L would not lack the concept of ignorance.
Alternatively, without accepting a general closure principle, like [Simple-Closure] or [Closure], one might instead assume a specific instance of such a principle as background information. For instance, one may assume the following: If Moore knows that he has hands, then Moore knows that he’s not a handless-BIV. But the same problem arises for this approach—this specific instance of closure is only a contingent truth that must be assumed as background, before a contradiction can be derived from (22).
Even [Closure] is in need of much improvement before it can avoid counterexamples (see David and Warfield 2008, p. 143ff). Nonetheless, my basic point in this paragraph applies for all plausible versions of knowledge-closure. We must assume certain contingent truths, like (BG), before a contradiction can be derived from (22).
It cannot be claimed that (23) is awkward because the first conjunct entails the second conjunct (making the second one redundant). There is no such entailment—it’s possible to win without trying (e.g. the opponent may forfeit).
A further similarity is that the oddity of (22) and (23) persists even when their conjuncts are transposed.
To be clear, it’s possible that the awkwardness of (22) persists even when (BG) is excluded from the common ground, since there could be something else that causes the awkwardness of (22) whenever the common ground excludes (BG). But the same could also be said for the closure-denier’s explanation. It’s possible that all mechanisms that can cancel the implicature also create infelicity (e.g. see the discussion on redundancy in the next paragraph).
I have invoked conversational implicature to explain why we mistakenly believe or intuit \({<}\hbox {Sufficiency}{>}\), and that mistake is used to explain why we mistakenly think \({<}\hbox {NI}{>}\) and \({<}\hbox {Closure}{>}\) are equivalent. But, strictly speaking, the Closure Hypothesis could be true even if my way of explaining away \({<}\hbox {Sufficiency}{>}\) is false. So, an appeal to conversational implicature isn’t assumed by the Closure Hypothesis. Still, Hawthorne’s objection could be refocused on the question of how conversational implicatures can help explain our belief or intuition that \({<}\hbox {Sufficiency}{>}\) is true. In response, see my explanation in footnote 30 where I explain how such implicatures can play this role.
References
Antioch College. (1992). The Antioch College sexual offense policy. In L. Francis (Ed.), Date rape: Feminism philosophy, and the Law. University Park, PA: The Pennsylvania University Press.
Blome-Tillmann, M. (2008). Conversational implicature and the cancellability test. Analysis, 68, 156–160.
Blutner, R. (2004). Pragmatics and the lexicon. In L. Horn & G. Ward (Eds.), The handbook of pragmatics (pp. 488–514). Oxford: Blackwell Publishing.
Bonjour, L. (1987). Nozick, externalism, and skepticism. In L. Luper-Foy (Ed.), The possibility of knowledge (in ed.). Lanham, MD: Rowman and Littlefield.
Clark, H. (1996). Using language. Cambridge: Cambridge University Press.
Cohen, S. (1999). Contextualism, skepticism, and the structure of reasons. Nous Supplement: Philosophical Perspectives, 33, 57–89.
Cruse, A. (1986). Lexical semantics. Cambridge: Cambridge University Press.
David, M., & Warfield, T. (2008). Knowledge-closure and skepticism. In Q. Smith (Ed.), Epistemology: New essays (pp. 137–187). Oxford: Oxford University Press.
DeRose, K. (1995). Solving the skeptical puzzle. Philosophical Review, 104(7), 1–52.
DeRose, K. (2009). The Case for Contextualism: Knowledge, Skepticism, and Context, Vol. 1. Oxford: Oxford University Press.
Dretske, F. (2005). The case against closure. In M. Steup & E. Sosa (Eds.), Contemporary debates in epistemology (pp. 13–26). Oxford: Blackwell Publishing.
Driver, J. (1989). Virtues of ignorance. The Journal of Philosophy, 86, 373–384.
Engel, M. Jr. (2004). What’s wrong with contextualism, and a noncontextualist resolution of the skeptical paradox. Erkenntnis, 61, 203–231.
Feldman, R. (1999). Contextualism and skepticism. In J. Tomberlin (Ed.), Philosophical perspectives. Atascadero, CA: Ridgeview.
Flanagan, O. (1990). Virtue and ignorance. The Journal of Philosophy, 87, 420–428.
Geis, M., & Zwicky, A. (1971). On invited inferences. Linguistic Inquiry, 2, 561–566.
Goldman, A., & Olsson, E. (2009). Reliabilism and the value of knowledge. In A. Haddock, A. Millar, & D. Pritchard (Eds.), Epistemic value (pp. 19–41). Oxford: Oxford University Press.
Greenberg, J. (1966). Language universals. The Hague: Mouton and Co.
Grice, H. P. (1989). Studies in the way of words. Cambridge, MA: Harvard University Press.
Gulley, N. (1968). The philosophy of Socrates. New York: Macmillan.
Hawthorne, J. (2005). The case for closure. In M. Steup & E. Sosa (Eds.), Contemporary debates in epistemology (pp. 26–43). Oxford: Blackwell Publishing.
Hazlett, A. (2007). Grice’s Razor. Metaphilosophy, 38, 669–690.
Heller, M. (1999). Relevant alternatives and closure. Australasian Journal of Philosophy, 77, 196–208.
Horn, L. (1989). A natural history of negation. Chicago: University of Chicago Press.
Horn, L. (1991). Given as new: When redundant affirmation isn’t. Journal of Pragmatics, 15, 313–336.
Horn, L. (2000). From if to iff: Conditional perfection as pragmatic strengthening. Journal of Pragmatics, 32, 289–326.
Huang, Y. (2007). Pragmatics. Oxford: Oxford University Press.
Kittay, E. F. (1997). AH! My foolish heart: A reply to Alan Soble’s “Antioch’s ‘sexual offense policy’: A philosophical exploration”. Journal of Social Philosophy, 28, 153–159.
Kvanvig, J. (2006). Closure principles. Philosophy Compass, 1, 256–267.
LeMorvan, P. (2011). On ignorance: A reply to Peels. Philosophia, 39, 335–344.
LeMorvan, P. (2012). On ignorance: A vindication of the standard view. Philosophia, 40, 379–393.
Levinson, S. (1983). Pragmatics. Cambridge, UK: Cambridge University Press.
Levinson, S. (2000). Presumptive meanings. Cambridge, MA: The MIT Press.
Lewandowska-Tomaszczyk, B. (2007). Polysemy, prototypes, and radial categories. In D. Geeraerts & H. Cuyckens (Eds.), Oxford handbook of cognitive linguistics. Oxford: Oxford University Press.
Lewis, D. (1996). Elusive knowledge. Australasian Journal of Philosophy, 74, 549–567.
Ludlow, P. (2005). Contextualism and the new linguistic turn in epistemology. In G. Preyer & G. Peter (Eds.), Contextualism in philosophy. Oxford: Oxford University Press.
Nozick, R. (1981). Philosophical explanations. Cambridge, MA: Harvard University Press.
Peels, R. (2010). What Is ignorance? Philosophia, 38, 57–67.
Peels, R. (2011). Ignorance is lack of true belief: A rejoinder to LeMorvan. Philosophia, 39, 345–355.
Quine, W. V. O. (1960). Word and object. Cambridge, MA: The MIT Press.
Russell, B. (1948). Human knowledge: Its scope and its limits. New York: Simon and Schuster.
Schaffer, J. (2004). From contextualism to contrastivism. Philosophical Studies, 119, 73–103.
Schiffer, S. (1996). Contextualist Solutions to Scepticism. Proceedings of the Aristotelian Society, 96, 317–333.
Sosa, E. (1999). How to defeat opposition to Moore. Nous, Supplement: Philosophical Perspectives, 33, 141–153.
Sosa, E. (2000). Skepticism and contextualism. Philosophical Issues, 10, 1–18.
Stanley, J. (2004). On the linguistic basis for contextualism. Philosophical Studies, 119, 119–146.
Stanley, J. (2005). Knowledge and practical interests. Oxford: Clarendon Press.
Steup, M. (2005). Contextualism and conceptual disambiguation. Acta Analytica, 20, 3–15.
Unger, P. (1975). Ignorance: A case for skepticism. Oxford: Oxford University Press.
Vlastos, G. (1985). Socrates’ disavowal of knowledge. The Philosophical Quarterly, 35, 1–31.
Weiner, M. (2009). The (mostly harmless) inconsistency of knowledge ascriptions. Philosophers’ Imprint, 9, 1–25.
Williams, B. (1995/2006). Philosophy and the understanding of ignorance. In Diogene 169. (Reprinted in Philosophy as a humanistic discipline, pp. 169–179, by A. W. Moore, Ed. Princeton: Princeton University Press).
Williamson, T. (1997). Vagueness and ignorance. In R. Keefe & P. Smith (Eds.), Vagueness: A reader. Cambridge, MA: The MIT Press.
Zimmerman, M. (1988). An essay on moral responsibility. Totowa, NJ: Rowan and Littlefield.
Zwicky, A., & Sadock, J. (1975). Ambiguity tests and how to fail them. In J. Kimball (Ed.), Syntax and semantics (pp. 1–36). New York: Academic Press.
Acknowledgments
I would like to thank Matti Eklund, Nico Silins, Adam Pelser, Pierre LeMorvan, Rik Peels, Adam Bendorf and three anonymous reviewers for their very helpful comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kyle, B.G. The New and Old Ignorance Puzzles: How badly do we need closure?. Synthese 192, 1495–1525 (2015). https://doi.org/10.1007/s11229-014-0642-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-014-0642-8