In ' Unnatural Doubts' Michael Williams argues that Cartesian skepticism is not truly an "intuitive problem" (that is, one which we can state with little or no appeal to contentious theories) at all. According to Williams, the skeptic has rich theoretical commitments all his own, prominent among which is the epistemic priority thesis. I argue, however, that Williams's diagnostic critique of the epistemic priority thesis fails on his own conception of what is required for success. Furthermore, in a brief "Afterword" (...) I argue that the later Wittgenstein (to whom Williams sometimes appeals) would concur with my critique of Williams's antiskeptical efforts. (shrink)

The branch of philosophical logic which has become known as “belief change” has, in the course of its development, become alienated from its epistemological origins. However, as formal criteria do not suffice to defend a principled choice between competing systems for belief change, we do need to take their epistemological embedding into account. Here, on the basis of a detailed examination of Isaac Levi's epistemology, we argue for a new direction of belief change research and propose to construct systems for (...) belief change that can do without, but do not rule out, selection functions, in order to enable an *empirical* assessment of the relative merits of competing belief change systems. (shrink)

Christoph Jäger (2004) argues that Dretske’s information theory of knowledge raises a serious problem for his denial of closure of knowledge under known entailment: Information is closed under known entailment (even under entailment simpliciter); given that Dretske explains the concept of knowledge in terms of “information”, it is hard to stick with his denial of closure for knowledge. Thus, one of the two basic claims of Dretske would have to go. Since giving up the denial of closure would commit Dretske (...) to skepticism, it would most probably be better to rather give up the information-theoretic account of knowledge. But that means that one of the best externalist views of knowledge has to be given up. I argue here that Jäger is mistaken and that there is no problem for Dretske. There is a rather easy way out of Jäger’s problem. (shrink)

Stewart Cohen argues that several epistemological theories fall victim to the problem of easy knowledge: they allow us to know far too easily that certain sceptical hypotheses are false and that how things seem is a reliable indicator of how they are. This problem is a result of the theories' interaction with an epistemic closure principle. Cohen suggests that the theories should be modified. I argue that attempts to solve the problem should focus on closure instead; a new and plausible (...) epistemic closure principle can solve the problem of easy knowledge. My solution offers a uniform and more successful response to different versions of the problem of easy knowledge. (shrink)

The most prominent arguments for scepticism in modern epistemology employ closure principles of some kind. To begin my discussion of such arguments, consider Simple Knowledge Closure (SKC): (SKC) (Kxt[p] ∧ (p → q)) → Kxt[q].1 Assuming its truth for the time being, the sceptic can use (SKC) to reason from the two assumptions that, firstly, we don’t know ¬sh and that, secondly, op entails ¬sh to the conclusion that we don’t know op, where ‘op’ and ‘sh’ are shorthand for ‘ordinary (...) proposition’ and ‘sceptical hypothesis’ respectively. (SKC), however, fails for familiar reasons: since knowledge entails belief (KB), we can derive the falsity (F) from (SKC) by hypothetical syllogism, and thus reduce (SKC) to absurdity: (KB) Kxt[p] → Bxt[p]. (F) (Kxt[p] ∧ (p → q)) → Bxt[q]. (shrink)

JUSTIFICATION and knowledge are thought to be closed under known implication..1 This widely shared assumption is embodied in the following principles of epistemic closure.

Anthony Brueckner argues for a strong connection between the closure and the underdetermination argument for scepticism. Moreover, he claims that both arguments rest on infallibilism: In order to motivate the premises of the arguments, the sceptic has to refer to an infallibility principle. If this were true, fallibilists would be right in not taking the problems posed by these sceptical arguments seriously. As many epistemologists are sympathetic to fallibilism, this would be a very interesting result. However, in this paper I (...) will argue that Brueckner’s claims are wrong: The closure and the underdetermination argument are not as closely related as he assumes and neither rests on infallibilism. Thus even a fallibilist should take these arguments to raise serious problems that must be dealt with somehow. (shrink)

The Neo-Moorean response to the radical skeptical challenge boldly maintains that we can know we’re not the victims of radical skeptical hypotheses; accordingly, our everyday knowledge that would otherwise be threatened by our inability to rule out such hypotheses stands unthreatened. Given the leverage such an approach has against the skeptic from the very start, the Neo-Moorean line is an especially popular one; as we shall see, though, it faces several commonly overlooked problems. An initial problem is that this particular (...) brand of anti-skeptical strategy is available only to a theory of knowledge that will compromise itself to especially weak epistemic standards—indeed, standards as weak as our epistemic grounds are for accepting the denials of skeptical hypotheses. With this said, the aim here is to investigate whether the Neo-Moorean line could be advanced against the skeptic in a way that wouldn’t require wholesale lowering of epistemic standards. Unfortunately, as we’ll see, Sosa’s (2007; 2009) view as well as what I argue to be the other two most plausible contender-views for maintaining a Neo-Moorean line—Greco’s and Pritchard’s—run (for similar reasons) into dead ends. The way forward, I’ll argue, is to take on board a unique variety of robust virtue epistemology accord­ing to which knowledge is thought to be situated a certain way within a gradient balance between ability and luck. (shrink)

It is argued, on the basis of new counterexamples, that neither knowledge nor epistemic justification (or “epistemic rationality”) can reasonably be thought to be closed under logical implication. The argument includes an attempt to reconcile the fundamental intuitions of the opposing parties in the debate.

Peter Baumann and Nicholas Shackel defend me against a serious criticism by Christoph Jäger. They argue that my account of information is consistent with my denial of closure for knowledge. Information isn’t closed under known entailment either. I think that, technically speaking, they are right. But the way they are right doesn’t help me much in my effort to answer the skeptic. I describe a way in which information, like knowledge, fails to be closed in a way that makes an (...) information-based account of knowledge an effective tool in answering the skeptic. (shrink)

Kripke’s puzzle has puts pressure on the intuitive idea that one can believe that Superman can fly without believing that Clark Kent can fly. If this idea is wrong then many theories of belief and belief ascription are built from faulty data. I argue that part of the proper analysis of Kripke’s puzzle refutes the closure principles that show up in many important arguments in epistemology, e.g., if S is rational and knows that P and that P entails Q, then (...) if she considers these two beliefs and Q, then she is in a position to know that.. (shrink)

This paper evaluates a number of closure principles (for both knowledge and justification) that have appeared in the literature. Counterexamples are presented to all but one of these principles, which is conceded to be true but trivially so. It is argued that a consequence of the failure of these closure principles is that certain projects of doxastic logic are doomed, and that doxastic logic is of dubious merit for epistemologists interested in actual knowers in the actual world.

Trenton Merricks argues that on any reasonable account, warrant must entailtruth. I demonstrate three theses about the properties ofwarrant: (1) Warrant is not unique;there are many properties that satisfy the definition of warrant. (2) Warrant need not entail truth; there are some warrant properties that entailtruthand others that do not. (3) Warrant need not be closed under entailment, even if knowledge is. If knowledge satisfies closure, then some warrant properties satisfy closure while others do not;if knowledge violates closure, then allwarrant (...) properties violate closure. (shrink)

The standard contextualist solution to the skeptical paradox is intended to provide a way to retain epistemic closure while avoiding the excessive modesty of radical skepticism and the immodesty of Moorean dogmatism. However, contextualism’s opponents charge that its solution suffers from epistemic immodesty comparable to Moorean dogmatism. According to the standard contextualist solution, all contexts where an agent knows some ordinary proposition to be true are contexts where she also knows that the skeptical hypotheses are false. It has been hoped (...) that contrastivist theories of knowledge can mirror the contextualist solution while avoiding this epistemic immodesty. I review the main problems for contrastive closure and argue that none of the arguments currently in the literature pose an insurmountable problem for the contrastivist solution. However, I argue that contrastivist theories of knowledge, like their contextualist rivals, are indeed committed to epistemic immodesty. (shrink)

According to Fred Dretskes externalist theory of knowledge a subject knows that p if and only if she believes that p and this belief is caused or causally sustained by the information that p. Another famous feature of Dretskes epistemology is his denial that knowledge is closed under known logical entailment. I argue that, given Dretskes construal of information, he is in fact committed to the view that both information and knowledge are closed under known entailment. This has far-reaching consequences. (...) For if it is true that, as Dretske also believes, accepting closure leads to skepticism, he must either embrace skepticism or abandon his information theory of knowledge. The latter alternative would seem to be preferable. But taking this route would deprive one of the most powerfully developed externalist epistemologies of its foundation. (shrink)

This paper argues for a solution to a problem that contrastivism faces. The problem is that contrastivism cannot preserve closure, in spite of claims to the contrary by its defenders. The problem is explained and a response developed.

Nozick’s contribution to the epistemology of the last half of the twentieth century includes addressing the question of whether knowledge is closed under known implication. I argue that the question of closure provides a serious obstacle to Nozickian approaches to epistemology.

It is tempting to think that multi premise closure creates a special class of paradoxes having to do with the accumulation of risks, and that these paradoxes could be escaped by rejecting the principle, while still retaining single premise closure. I argue that single premise deduction is also susceptible to risks. I show that what I take to be the strongest argument for rejecting multi premise closure is also an argument for rejecting single premise closure. Because of the symmetry between (...) the principles, they come as a package: either both will have to be rejected or both will have to be revised. (shrink)

Epistemic closure, the idea that knowledge is closed under known implication, plays a central role in current discussions of skepticism and the semantics of knowledge reports. Contextualists in particular rely heavily on the truth of epistemic closure in staking out their distinctive response to the so-called "skeptical paradox." I argue that contextualists should re-think their commitment to closure. Closure principles strong enough to force the skeptical paradox on us are too strong, and closure principles weak enough to express unobjectionable epistemic (...) principles are too weak to generate the skeptical paradox. I briefly consider how the contextualist might live without (strong) closure. (shrink)

Most of us think we can always enlarge our knowledge base by accepting things that are entailed by (or logically implied by) things we know. The set of things we know is closed under entailment (or under deduction or logical implication), which means that we know that a given claim is true upon recognizing, and accepting thereby, that it follows from what we know. However, some theorists deny that knowledge is closed under entailment, and the issue remains controversial. The arguments (...) against closure include the following. (shrink)

In early essays and in more recent work, Fred Dretske argues against the closure of perception, perceptual knowledge, and knowledge itself. In this essay I review his case and suggest that, in a useful sense, perception is closed, and that, while perceptual knowledge is not closed under entailment, perceptually based knowledge is closed, and so is knowledge itself. On my approach, which emphasizes the safe indication account of knowledge, we can both perceive, and know, that sceptical scenarios (such as being (...) a brain in a vat) do not hold. (shrink)

Harman’s lottery paradox, generalized by Vogel to a number of other cases, involves a curious pattern of intuitive knowledge ascriptions: certain propositions seem easier to know than various higher-probability propositions that are recognized to follow from them. For example, it seems easier to judge that someone knows his car is now on Avenue A, where he parked it an hour ago, than to judge that he knows that it is not the case that his car has been stolen and driven (...) away in the last hour. Contextualists have taken this pattern of intuitions as evidence that ‘knows’ does not always denote the same relationship; subject-sensitive invariantists have taken this pattern of intuitions as evidence that non-traditional factors such as practical interests figure in knowledge; still others have argued that the Harman Vogel pattern gives us a reason to abandon the principle that knowledge is closed under known entailment. This paper argues that there is a psychological explanation of the strange pattern of intuitions, grounded in the manner in which we shift between an automatic or heuristic mode of judgment and a controlled or systematic mode. Understanding the psychology behind the pattern of intuitions enables us to see that the pattern gives us no reason to abandon traditional intellectualist invariantism. The psychological account of the paradox also yields new resources for clarifying and defending the single premise closure principle for knowledge ascriptions. (shrink)

How should the contrastivist formulate closure? That is, given that knowledge is a ternary contrastive state Kspq (s knows that p rather than q), how does this state extend under entailment? In what follows, I will identify adequacy conditions for closure, criticize the extant invariantist and contextualist closure schemas, and provide a contrastive schema based on the idea of extending answers. I will conclude that only the contrastivist can adequately formulate closure.

Closure for justification is the claim that thinkers are justified in believing the logical consequences of their justified beliefs, at least when those consequences are competently deduced. Many have found this principle to be very plausible. Even more attractive is the special case of Closure known as Single-Premise Closure. In this paper, I present a challenge to Single-Premise Closure. The challenge is based on the phenomenon of rational self-doubt – it can be rational to be less than fully confident in (...) one's beliefs and patterns of reasoning. In rough outline, the argument is as follows: Consider a thinker who deduces a conclusion from a justified initial premise via an incredibly long sequence of small competent deductions. Surely, such a thinker should suspect that he has made a mistake somewhere. And surely, given this, he should not believe the conclusion of the deduction even though he has a justified belief in the initial premise. (shrink)

Dretske proposes a theory of knowledge in terms of a theory of information, but wishes to deny that empirical knowledge settles the large question of scepticism. This leads him to deny the closure of knowledge under known entailment. In a recent paper Jäger argues that Dretske’s theory of information entails closure for knowledge, ‘at least for the kind of propositions here at issue’ (Jäger 2004:194). If Jäger is right, Dretske is seriously embarrassed and must give something up. In this paper (...) I show that there are two flaws in Jäger’s argument. The principle of informational closure considered by Jäger is incompatible with Dretske’s theory of information, and Jäger’s argument that Dretske is committed to a certain kind of substitution instance of that principle of informational closure is invalid. I propose adequacy conditions on signalled information and use them to motivate a formulation of a general closure principle for signalled information. I show that Dretske’s account of information satisfies the adequacy conditions, but in a way which commits him to an instance of the general closure principle. I argue that Dretske is consequently committed to closure for some cases of knowledge for which he wishes to deny closure. Finally, I sketch how, on the basis of the closure principle to which Dretske is committed, Jäger’s broader argument may yet go through. (shrink)

Harman and Lewis credit Kripke with having formulated a puzzle that seems to show that knowledge entails dogmatism. The puzzle is widely regarded as having been solved. In this paper we argue that this standard solution, in its various versions, addresses only a limited aspect of the puzzle and holds no promise of fully resolving it. Analyzing this failure and the proper rendering of the puzzle, it is suggested that it poses a significant challenge for the defense of epistemic closure.

Comments on Sherri Rousch’s Tracking Truth for the 2006 Philosophy of Science Association conference.

I argue against unqualified acceptance of the principle of deductive closure (DC): that, if p follows deductively from premises that are already known, we are in a position to know p. DC, I claim, is a sorites premise; it seems intuitively irresistible, but indiscriminate application of it leads to absurd conclusions. Furthermore, a theory on which the application of DC is restricted explains our practice of deriving new knowledge from old knowledge better than a theory on which our application of (...) DC is unrestricted. This restriction on the application of DC allows contextualists to meet an argument of Hawthorne’s that contextualism must lead either to absurd knowledge attributions or to constant shifting of the standards for knowledge. Even if the standard of knowledge remains constant, the absurd knowledge attribution is the conclusion of a sorites argument and should be rejected. (shrink)

A variation of Fitch’s Paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundness (while still requiring he be sound), Fitch’s Paradox is avoided. Provided one is willing to admit that sound knowers may be ignorant of their own soundness, this might offer a way out of the (...) paradox. (shrink)

Anthony Brueckner argues for a strong connection between the closure and the underdetermination argument for scepticism. Moreover, he claims that both arguments rest on infallibilism: In order to motivate the premises of the arguments, the sceptic has to refer to an infallibility principle. If this were true, fallibilists would be right in not taking the problems posed by these sceptical arguments seriously. As many epistemologists are sympathetic to fallibilism, this would be a very interesting result. However, in this paper I (...) will argue that Brueckner’s claims are wrong: The closure and the underdetermination argument are not as closely related as he assumes and neither rests on infallibilism. Thus even a fallibilist should take these arguments to raise serious problems that must be dealt with somehow. (shrink)

In this paper I argue for a doctrine I call ?infallibilism?, which I stipulate to mean that If S knows that p, then the epistemic probability of p for S is 1. Some fallibilists will claim that this doctrine should be rejected because it leads to scepticism. Though it's not obvious that infallibilism does lead to scepticism, I argue that we should be willing to accept it even if it does. Infallibilism should be preferred because it has greater explanatory power (...) than fallibilism. In particular, I argue that an infallibilist can easily explain why assertions of ?p, but possibly not-p? (where the ?possibly? is read as referring to epistemic possibility) is infelicitous in terms of the knowledge rule of assertion. But a fallibilist cannot. Furthermore, an infallibilist can explain the infelicity of utterances of ?p, but I don't know that p? and ?p might be true, but I'm not willing to say that for all I know, p is true?, and why when a speaker thinks p is epistemically possible for her, she will agree (if asked) that for all she knows, p is true. The simplest explanation of these facts entails infallibilism. Fallibilists have tried and failed to explain the infelicity of ?p, but I don't know that p?, but have not even attempted to explain the last two facts. I close by considering two facts that seem to pose a problem for infallibilism, and argue that they don't. (shrink)

Infallibilism is the claim that knowledge requires that one satisfies some infallibility condition. I spell out three distinct such conditions: epistemic, evidential and modal infallibility. Epistemic infallibility turns out to be simply a consequence of epistemic closure, and is not infallibilist in any relevant sense. Evidential infallibilism i s unwarranted but it is not an satisfactory characterization of the infallibilist intuition. Modal infallibility, by contrast, captures the core infallibilist intuition, and I argue that it is required to solve the Gettier (...) problem and account for lottery cases. Finally, I discuss whether modal infallibilism has sceptical consequences and argue that it is an open question whose answer depends on one’s account of alethic possibility. (shrink)

The present piece is a reply to G. Hoffmann on my (2007) infallibilist view of self-knowledge. Contra Hoffmann, it is argued that the view allows both (i) strictly a priori justification, and (ii) the Quinean revisability of any belief in light of new evidence.

A variation of Fitch’s Paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundness (while still requiring he be sound), Fitch’s Paradox is avoided. Provided one is willing to admit that sound knowers may be ignorant of their own soundness, this might offer a way out of the (...) paradox. (shrink)

I have argued that without an adequate solution to the knower paradox Fitch's Proof is- or at least ought to be-ineffective against verificationism. Of course, in order to follow my suggestion verificationists must maintain that there is currently no adequate solution to the knower paradox, and that the paradox continues to provide prima facie evidence of inconsistent knowledge. By my lights, any glimpse at the literature on paradoxes offers strong support for the first thesis, and any honest, non-dogmatic reflection on (...) the knower paradox provides strong support for the second. Whether verificationists want to go the route I've suggested is not for me todecide. As in the previous section my aim has been that of defending the mere viability of verificationism in the face of what many, many philosophers have taken to be its death-knell, namely Fitch's Proof. But, as the final objection makes clear, showing that verificationism can live in the face of Fitch's Proof is one thing; showing that it should live is another project. If nothing else, I hope that this papershows that verificationists still have a project to pursue; Fitch's Proof, contrary to popular opinion, need not bury verificationism.13. (shrink)

(T5) ϕ → ◊Kϕ |-- ϕ → Kϕ where ◊ is possibility, and ‘Kϕ’ is to be read as ϕ is known by someone at some time. Let us call the premise the knowability principle and the conclusion near-omniscience.2 Here is a way of formulating Fitch’s proof of (T5). Suppose the knowability principle is true. Then the following instance of it is true: (p & ~Kp) → ◊K(p & ~Kp). But the consequent is false, it is not possible to know (...) p & ~Kp. That is because the supposition that it is known is provably inconsistent.3 The inconsistency requires us to deny the possibility of the supposition, yielding ~◊K(p & ~Kp). This, together with the above instance of the knowability principle, entails ~(p & ~Kp), which is (classically) equivalent to p → Kp. Since p occurs in none of our undischarged assumptions, we may generalize to get near-omniscience, ϕ → Kϕ. QED. (shrink)

The paradox of knowability is a logical result suggesting that, necessarily, if all truths are knowable in principle then all truths are in fact known. The contrapositive of the result says, necessarily, if in fact there is an unknown truth, then there is a truth that couldn't possibly be known. More specifically, if p is a truth that is never known then it is unknowable that p is a truth that is never known. The proof has been used to argue (...) against versions of anti-realism committed to the thesis that all truths are knowable. For clearly there are unknown truths; individually and collectively we are non-omniscient. So, by the main result, it is false that all truths are knowable. The result has also been used to draw more general lessons about the limits of human knowledge. Still others have taken the proof to be fallacious, since it collapses an apparently moderate brand of anti-realism into an obviously implausible and naive idealism. (shrink)

Does a factive conception of knowability figure in ordinary use? There is some reason to think so. ‘Knowable’ and related terms such as ‘discoverable’, ‘observable’, and ‘verifiable’ all seem to operate factively in ordinary discourse. Consider the following example, a dialog between colleagues A and B: A: We could be discovered. B: Discovered doing what? A: Someone might discover that we're having an affair. B: But we are not having an affair! A: I didn’t say that we were. A’s remarks (...) sound contradictory. In this context the factivity of ‘someone might discover that’ explains this fact. So there is some reason to believe that knowability and related modalities are factive in ordinary use. For factive treatments of knowability in the context of epistemic theories of truth, compare Tennant (2000: 829) and Wright (2001: 59-60, n. 17). (shrink)

Tr(A) iff ‡K(A) To remedy the error, Dummett’s proposes the following inductive characterization of truth: (i) Tr(A) iff ‡K(A), if A is a basic statement; (ii) Tr(A and B) iff Tr(A) & Tr(B); (iii) Tr(A or B) iff Tr(A) v Tr(B); (iv) Tr(if A, then B) iff (Tr(A) Æ Tr(B)); (v) Tr(it is not the case that A) iff ¬Tr(A), where the logical constant on the right-hand side of each biconditional clause is understood as subject to the laws of intuitionistic (...) logic.2 The only other principle in play in Dummett’s discussion is (+) A iff Tr(A), which, as he notes, the anti-realist is likely to accept. (shrink)

This is a study of an alleged incompatibility (proposed by Sven Rosenkranz) between normal modal logic and factive conceptions of knowability.

The Knowability Paradox is a logical argument to the effect that, if there are truths not actually known, then there are unknowable truths. Recently, Alexander Paseau and Bernard Linsky have independently suggested a possible way to counter this argument by typing knowledge. In this article, we argue against their proposal that if one abstracts from other possible independent considerations supporting reasons for typing knowledge and considers the motivation for a type-theoretic approach with respect to the Knowability Paradox alone, there is (...) no substantive philosophical motivation to type knowledge, except that of solving the paradox. Every attempt to independently justify the typing of knowledge is doomed to failure. (shrink)

It is widely believed that for all p, or at least for all entertainable p, it is knowable a priori that (p iff actually p). It is even more widely believed that for all such p, it is knowable that (p iff actually p). There is a simple argument against these claims from four antecedently plausible premises.

The intuitionistic conception of truth defended by Dummett, Martin Löf and Prawitz, according to which the notion of proof is conceptually prior1 to the notion of truth, is a particular version of the epistemic conception of truth. The paradox of knowability (first published by Frederic Fitch in 1963) has been described by many authors2 as an argument which threatens the epistemic, and the intuitionistic, conception of truth. In order to establish whether this is really so, one has to understand what (...) the epistemic conception of truth really is. So I shall start inpart I with a description of the matter at issue between theepistemic conception of truth and the opposite position, therealistic conception of truth. Inpart II I shall very briefly describe the paradox. Inpart III I shall try to answer the question which appears in the title of this paper: What can we learn from the paradox of knowability?. My conclusion will be that the paradox of knowability is not a refutation of the epistemic conception of truth, but helps us to better formulate (and understand) such a view. (shrink)

The Knowability Paradox purports to show that the controversial but not patently absurd hypothesis that all truths are knowable entails the implausible conclusion that all truths are known. The notoriety of this argument owes to the negative light it appears to cast on the view that there can be no verification-transcendent truths. We argue that it is overly simplistic to formalize the views of contemporary verificationists like Dummett, Prawitz or Martin-Löf using the sort of propositional modal operators which are employed (...) in the original derivation of the Paradox. Instead we propose that the central tenet of verificationism is most accurately formulated as follows: if is true, then there exists a proof of . Building on the work of Artemov (Bull Symb Log 7(1): 1–36, 2001), a system of explicit modal logic with proof quantifiers is introduced to reason about such statements. When the original reasoning of the Paradox is developed in this setting, we reach not a contradiction, but rather the conclusion that there must exist non-constructed proofs. This outcome is evaluated relative to the controversy between Dummett and Prawitz about proof existence and bivalence. (shrink)

An interesting recent reply to the Paradox of Knowability is Neil Tennant's proposal: to restrict the anti-realist's knowability thesis to truths the knowing of which is logically consistent. However, this proposal is egregiously ad hoc unless motivated by something other than the wish to save anti-realism from embarrassment. We examine Tennant's argument that his restriction is motivated by parallel considerations in cases that are neutral with respect to debates about realism. We conclude that the cases are not neutral, nor the (...) considerations parallel. The failure of Tennant's argument provides an opportunity to reflect on, among other things, the nature of Moore's paradox, and the role of idealization in doxastic logic. (shrink)

Fitch’s paradox shows, from fairly innocent-looking assumptions, that if there are any unknown truths, then there are unknowable truths. This is generally thought to deliver a blow to antirealist positions that imply that all truths are knowable. The present paper argues that a probabilistic version of antirealism escapes Fitch’s result while still offering all that antirealists should care for.

To save antirealism from Fitchs Paradox, Tennant has proposed to restrict the scope of the antirealist principle that all truths are knowable to truths that can be consistently assumed to be known. Although the proposal solves the paradox, it has been accused of doing so in an ad hoc manner. This paper argues that, first, for all Tennant has shown, the accusation is just; second, a restriction of the antirealist principle apparently weaker than Tennants yields a non-ad hoc solution to (...) Fitchs Paradox; and third, the alternative is only apparently weaker than, and even provably equivalent to, Tennants. It is thereby shown that the latter is not ad hoc after all. (shrink)

This paper presents a generalized form of Fitch’s paradox of knowability, with the aim of showing that the questions it raises are not peculiar to the topics of knowledge, belief, or other epistemic notions. Drawing lessons from the generalization, the paper offers a solution to Fitch’s paradox that exploits an understanding of modal talk about what could be known in terms of capacities to know. It is argued that, in rare cases, one might have the capacity to know that p (...) even if it is metaphysically impossible for anyone to know that p , and that recognizing this fact provides the resources to solve Fitch’s paradox. (shrink)

A well-known proof by Alonzo Church, first published in 1963 by Frederic Fitch, purports to show that all truths are knowable only if all truths are known. This is the Paradox of Knowability. If we take it, quite plausibly, that we are not omniscient, the proof appears to undermine metaphysical doctrines committed to the knowability of truth, such as semantic anti-realism. Since its rediscovery by Hart and McGinn ( 1976), many solutions to the paradox have been offered. In this article, (...) we present a new proof to the effect that not all truths are knowable, which rests on different assumptions from those of the original argument published by Fitch. We highlight the general form of the knowability paradoxes, and argue that anti-realists who favour either an hierarchical or an intuitionistic approach to the Paradox of Knowability are confronted with a dilemma: they must either give up anti-realism or opt for a highly controversial interpretation of the principle that every truth is knowable. (shrink)

The paradox of knowability and the debate about it are shortly presented. Some assumptions which appear more or less tacitly involved in its discussion are made explicit. They are embedded and integrated in a Russellian framework, where a formal paradox, very similar to the Russell-Myhill paradox, is derived. Its solution is provided within a Russellian formal logic introduced by A. Church. It follows that knowledge should be typed. Some relevant aspects of the typing of knowledge are pointed out.

The so-called knowability paradox results from Fitch's argument that if there are any unknown truths, then there are unknowable truths. This threatens recent versions of semantical antirealism, the central thesis of which is that truth is epistemic. When this is taken to mean that all truths are knowable, antirealism is thus committed to the conclusion that no truths are unknown. The correct antirealistic response to the paradox should be to deny that the fundamental thesis of the epistemic nature of truth (...) entails the knowability of all truths. Correctly understood, the antirealistic conditions on a proposition's truth do not require that the proposition possess a verification-procedure which, when executed under the given conditions, issues in an agent's recognition of truth, but merely that there be a verification-procedure which, under these conditions, takes the value true . The knowability paradox and the related idealism problem (that antirealism seems, but is not, committed to the necessary existence of an epistemic agent) draw attention to the fact that certain propositions, those that are about verification-procedures themselves, may under certain conditions take the value true despite their unperformability under these circumstances. Thus these propositions' procedures can only be performed when the propositions are false, and they gain the appearance of antirealistic impossibility (e.g., that there is an unknown truth). This differs from the unperformability that antirealists object to, pertaining merely to matters of execution rather than to the logical structure of the procedures themselves. The force of antirealism's notion of epistemic truth is piecemeal, rather than consisting in a blanket characterization of truth as knowable. (shrink)

Truth’s universal knowability entails its discovery. This threatens antirealism, which is thought to require it. Fortunately, antirealism is not committed to it. Avoiding it requires adoption (and extension) of Dag Prawitz’s position in his long-term disagreement with Michael Dummett on the notion of provability involved in intuitionism’s identification of it with truth. Antirealism (intuitionism generalized) must accommodate a notion of lost-opportunity truth (a kind of recognition-transcendent truth), and even truth consisting in the presence of unperformable verifications. Dummett’s position cannot abide (...) this, while Prawitz’s can. Antirealism’s epistemic notion of truth derives from general features of its meaning theory, not from a universal knowability principle. (shrink)

This book provides a valuable look at the work of up and coming epistemologists. The topics covered range from the central issues of mainstream epistemology to the more formal issues in epistemic logic and confirmation theory. This book should be read by anyone interested in seeing where epistemology is currently focused and where it is heading. - Stewart Cohen , Arizona State University..

It is often claimed that anti-realists are compelled to reject the inference of the knowability paradox, that there are no unknown truths. I call those anti-realists who feel so compelled ‘faint-hearted’, and argue in turn that anti-realists should affirm this inference, if it is to be consistent. A major part of my strategy in defending anti-realism is to formulate an anti-realist definition of truth according to which a statement is true only if it is verified by someone, at some time. (...) I also liberalize what is meant by a verification to allow for indirect forms of verification. From this vantage point, I examine a key objection to anti-realism, that it is committed to the necessary existence of minds, and reject a response to this problem set forth by Michael Hand. In turn I provide a more successful anti-realist response to the necessary minds problem that incorporates what I call an ‘agential’ view of verification. I conclude by considering what intellectual cost there is to being an anti-realist in the sense I am advocating. (shrink)

(No abstract is available for this citation).

Addresses the question of why we find Fitch's knowability 'paradox' argument surprising.

I argue that Fitch’s ‘paradox of knowability’ presents no special problem for the epistemic anti-realist who believes that reality is epistemically accessible to us. For the claim which is the target of the argument (If p then it is possible to know p) is not a commitment of anti-realism. The epistemic anti-realist’s commitment is (or should be) to the recognizability of the states of affairs which render true propositions true, not to the knowability of the propositions themselves. A formal apparatus (...) for discussing the recognizability of states of affairs is offered, and other prima facie similar approaches to the paradox argument are reviewed. (shrink)

The best defense of the doctrine of the Incarnation implies that traditional Christianity has a special stake in the knowability paradox, a stake not shared by other theistic perspectives or by non-traditional accounts of the Incarnation. Perhaps, this stake is not even shared by antirealism, the view most obviously threatened by the paradox. I argue for these points, concluding that these results put traditional Christianity at a disadvantage compared to other viewpoints, and I close with some comments about the extent (...) of the burden incurred. (shrink)

The knowability paradox derives from a proof by Frederic Fitch in 1963. The proof purportedly shows that if all truths are knowable, it follows that all truths are known. Antirealists, wed as they are to the idea that truth is epistemic, feel threatened by the proof. For what better way to express the epistemic character of truth than to insist that all truths are knowable? Yet, if that insistence logically compels similar assent to some omniscience claim, antirealism is in jeopardy. (...) Response to the paradox has drifted toward a common theme, a theme I will argue is a non-starter in resolving the paradox. Seeing this point will also make clear the philosophical inadequacy of simply viewing the paradox as a refutation of a wide range of antirealisms. (shrink)

The knowability paradox threatens metaphysical or semantical antirealism, the view that truth is epistemic, by revealing an awful consequence of the claim [i] that all truths are knowable. Various attempts have been made to find a way out of the paradox.

This book thus provides a thorough investigation of the literature on the paradox, and also proposes a solution to the deeper of the two problems raised by ...

Verificationism is the doctrine stating that all truths are knowable. Fitch’s knowability paradox, however, demonstrates that the verificationist claim (all truths are knowable) leads to “epistemic collapse”, i.e., everything which is true is (actually) known. The aim of this article is to investigate whether or not verificationism can be saved from the effects of Fitch’s paradox. First, I will examine different strategies used to resolve Fitch’s paradox, such as Edgington’s and Kvanvig’s modal strategy, Dummett’s and Tennant’s restriction strategy, Beall’s paraconsistent (...) strategy, and Williamson’s intuitionistic strategy. After considering these strategies I will propose a solution that remains within the scope of classical logic. This solution is based on the introduction of a truth operator. Though this solution avoids the shortcomings of the non-standard (intuitionistic) solution, it has its own problems. Truth, on this approach, is not closed under the rule of conjunction-introduction. I will conclude that verificationism is defensible, though only at a rather great expense. (shrink)

In this paper, I focus on some intuitionistic solutions to the Paradox of Knowability. I first consider the relatively little discussed idea that, on an intuitionistic interpretation of the conditional, there is no paradox to start with. I show that this proposal only works if proofs are thought of as tokens, and suggest that anti-realists themselves have good reasons for thinking of proofs as types. In then turn to more standard intuitionistic treatments, as proposed by Timothy Williamson and, most recently, (...) Michael Dummett. Intuitionists can either point out the intuitionistc invalidity of the inference from the claim that all truths are knowable to the insane conclusion that all truths are known, or they can outright demur from asserting the existence of forever-unknown truths, perhaps questioning—as Dummett now suggests—the applicability of the Principle of Bivalence to a certain class of empirical statements. I argue that if intuitionists reject strict finitism—the view that all truths are knowable by beings just like us—the prospects for either proposal look bleak. (shrink)

Nozick analyzes fundamental issues, such as the identity of the self, knowledge and skepticism, free will, the foundations of ethics, and the meaning of life.

If proofs are nothing more than truth makers, then there is no force in the standard argument against classical logic (there is no guarantee that there is either a proof forA or a proof fornot A). The standard intuitionistic conception of a mathematical proof is stronger: there are epistemic constraints on proofs. But the idea that proofs must be recognizable as such by us, with our actual capacities, is incompatible with the standard intuitionistic explanations of the meanings of the logical (...) constants. Proofs are to be recognizable in principle, not necessarily in practice, as shown in section 1. Section 2 considers unknowable propositions of the kind involved in Fitch''s paradox:p and it will never be known thatp. It is argued that the intuitionist faces a dilemma: give up strongly entrenched common sense intuitions about such unknowable propositions, or give up verificationism. The third section considers one attempt to save intuitionism while partly giving up verificationism: keep the idea that a proposition is true iff there is a proof (verification) of it, and reject the idea that proofs must be recognizable in principle. It is argued that this move will have the effect that some standard reasons against classical semantics will be effective also against intuitionism. This is the case with Dummett''s meaning theoretical argument. At the same time the basic reason for regarding proofs as more than mere truth makers is lost. (shrink)

Recently predominant forms of anti-realism claim that all truths are knowable. We argue that in a logical explanation of the notion of knowability more attention should be paid to its epistemic part. Especially very useful in such explanation are notions of group knowledge. In this paper we examine mainly the notion of distributed knowability and show its effectiveness in the case of Fitch’s paradox. Proposed approach raised some philosophical questions to which we try to find responses. We also show how (...) we can combine our point of view on Fitch’s paradox with the others. Next we give an answer to the question: is distributed knowability factive? At the end, we present some details concerning a construction of anti-realist modal epistemic logic. (shrink)