Epistemicclosure has been a central issue in epistemology over the last forty years. According to versions of the relevant alternatives and subjunctivist theories of knowledge, epistemicclosure can fail: an agent who knows some propositions can fail to know a logical consequence of those propositions, even if the agent explicitly believes the consequence (having “competently deduced” it from the known propositions). In this sense, the claim that epistemicclosure can fail must be distinguished (...) from the fact that agents do not always believe, let alone know, the consequences of what they know—a fact that raises the “problem of logical omniscience” that has been central in epistemic logic. This paper, part I of II, is a study of epistemicclosure from the perspective of epistemic logic. First, I introduce models for epistemic logic, based on Lewis’s models for counterfactuals, that correspond closely to the pictures of the relevant alternatives and subjunctivist theories of knowledge in epistemology. Second, I give an exact characterization of the closure properties of knowledge according to these theories, as formalized. Finally, I consider the relation between closure and higher-order knowledge. The philosophical repercussions of these results and results from part II, which prompt a reassessment of the issue of closure in epistemology, are discussed further in companion papers. As a contribution to modal logic, this paper demonstrates an alternative approach to proving modal completeness theorems, without the standard canonical model construction. By “modal decomposition” I obtain completeness and other results for two non-normal modal logics with respect to new semantics. One of these logics, dubbed the logic of ranked relevant alternatives, appears not to have been previously identified in the modal logic literature. More broadly, the paper presents epistemology as a rich area for logical study. (shrink)
This paper considers two novel Bayesian responses to a well-known skeptical paradox. The paradox consists of three intuitions: first, given appropriate sense experience, we have justification for accepting the relevant proposition about the external world; second, we have justification for expanding the body of accepted propositions through known entailment; third, we do not have justification for accepting that we are not disembodied souls in an immaterial world deceived by an evil demon. The first response we consider rejects the third intuition (...) and proposes an explanation of why we have a faulty intuition. The second response, which we favor, accommodates all three intuitions; it reconciles the first and the third intuition by the dual component model of justification, and defends the second intuition by distinguishing two principles of epistemicclosure. (shrink)
According to the principle of epistemicclosure, knowledge is closed under known implication. The principle is intuitive but it is problematic in some cases. Suppose you know you have hands and you know that ‘I have hands’ implies ‘I am not a brain-in-a-vat’. Does it follow that you know you are not a brain-in-a-vat? It seems not; it should not be so easy to refute skepticism. In this and similar cases, we are confronted with a puzzle: epistemic (...)closure is an intuitive principle, but at times, it does not seem that we know by implication. In response to this puzzle, the literature has been mostly polarized between those who are willing to do away with epistemicclosure and those who think we cannot live without it. But there is a third way. Here I formulate a restricted version of the principle of epistemicclosure. In the standard version, the principle can range over any proposition; in the restricted version, it can only range over those propositions that are within the limits of a given epistemic inquiry and that do not constitute the underlying assumptions of the inquiry. If we adopt the restricted version, I argue, we can preserve the advantages associated with closure, while at the same time avoiding the puzzle I’ve described. My discussion also yields an insight into the nature of knowledge. I argue that knowledge is best understood as a topic-restricted notion, and that such a conception is a natural one given our limited cognitive resources. (shrink)
Those of us who have followed Fred Dretske's lead with regard to epistemicclosure and its impact on skepticism have been half-wrong for the last four decades. But those who have opposed our Dretskean stance, contextualists in particular, have been just wrong. We have been half-right. Dretske rightly claimed that epistemic status is not closed under logical implication. Unlike the Dretskean cases, the new counterexamples to closure offered here render every form of contextualist pro-closure maneuvering (...) useless. But there is a way of going wrong under Dretske's lead. As the paper argues, Cartesian skepticism thrives on closure failure in a way that is yet to be acknowledged in the literature. The skeptic can make do with principles which are weaker than the familiar closure principles. But I will further claim that this is only a momentary reprieve for the skeptic. As it turns out, one of the weaker principles on which a skeptical modus tollens must rest can be shown false. (shrink)
In spite of the intuitiveness of epistemicclosure, there has been a stubborn stalemate regarding whether it is true, largely because some of the “Moorean” things we seem to know easily seem clearly to entail “heavyweight” philosophical things that we apparently cannot know easily—or perhaps even at all. In this paper, I will show that two widely accepted facts about what we do and don’t know—facts with which any minimally acceptable understanding of knowledge must comport—are jointly inconsistent with (...) the truth of CLR. The proof works by supposing the truth of “Categorialism,” a thesis about the relation between basic categories and common nouns and predicates, which is itself a heavyweight claim that cannot be easily known to be either true or false. (shrink)
We report the results of four empirical studies designed to investigate the extent to which an epistemicclosure principle for knowledge is reflected in folk epistemology. Previous work by Turri (2015a) suggested that our shared epistemic practices may only include a source-relative closure principle—one that applies to perceptual beliefs but not to inferential beliefs. We argue that the results of our studies provide reason for thinking that individuals are making a performance error when their knowledge attributions (...) and denials conflict with the closure principle. When we used research materials that overcome what we think are difficulties with Turri’s original materials, we found that participants did not reject closure. Furthermore, when we presented Turri’s original materials to non-philosophers with expertise in deductive reasoning (viz., professional mathematicians), they endorsed closure for both perceptual and inferential beliefs. Our results suggest that an unrestricted closure principle—one that applies to all beliefs, regardless of their source—provides a better model of folk patterns of knowledge attribution than a source-relative closure principle. (shrink)
In this essay I present a new version of the Paradox of the Knower and show that this new paradox vitiates a certain argument against epistemicclosure. I then prove a theorem that relates the new paradox to epistemological scepticism. I conclude by assessing the use of the Knower in arguments against syntactical treatments of knowledge.
This essay corrects an error in the presentation of the Paradox of the Knowledge-Plus Knower, which is the variant of Kaplan and Montague’s Knower Paradox presented in C. Cross 2001: ‘The Paradox of the Knower without EpistemicClosure,’ MIND, 110, pp. 319–33. The correction adds a universally quantified transitivity principle for derivability as an additional assumption leading to paradox. This correction does not affect the status of the Knowledge-Plus paradox as a rebuttal to an argument against epistemic (...)closure, since the quantified transitivity principle is true in the standard model of arithmetic and therefore innocuous. (shrink)
Tracking accounts of knowledge were originally motivated by putative counter-examples to epistemicclosure. But, as is now well known, these early accounts have many highly counterintuitive consequences. In this note, I motivate a tracking-based account which respects closure but which resolves many of the familiar problems for earlier tracking account along the way.
In “The Paradox of the Knower without EpistemicClosure”, MIND 110:319-33, 2001, I develop a version of the Knower Paradox which does not assume epistemicclosure, and I use it to argue that the original Knower Paradox does not support an argument against epistemicclosure. In “The Paradox of the Knower without EpistemicClosure?”, MIND 113:95-107, 2004, Gabriel Uzquiano, using his own result, argues that my rebuttal to the anti-closure argument is (...) not successful. I respond here by arguing that in order to use Uzquiano’s result in an argument against closure, one must assume an implausible skepticism about arithmetic. (shrink)
_ Source: _Volume 7, Issue 4, pp 258 - 271 This contribution to the symposium on Annalisa Coliva’s _Extended Rationality_ is largely sympathetic with the moderate view of the structure of epistemic warrant which is defended in the book. However, it takes issue with some aspects of Coliva’s Wittgenstein-inspired ‘hinge epistemology’, focussing especially on her conception of propositional warrant, her treatment of epistemicclosure, her antirealist conception of truth, and the significance of her answer to so-called Humean (...) scepticism. (shrink)
Many people, such as Adam Smith, Milton Friedman, Irving Fisher, and William Sharpe, assume that free markets full of rational people automatically lead to ethical actions and outcomes. After all, at its equilibrium point, a perfectly competitive free market maximizes utility, respects autonomy, and fulfills justice’s dictates. Unfortunately, in some technology markets, there are a significant number of people who have undergone epistemicclosure. Epistemicclosure entails that all reliable evidence that would challenge deeply held beliefs (...) is dismissed as corrupted, whereas all supporting evidence, no matter how unreliable, is accepted as incontrovertible. Those who have the condition act irrationally within that domain. As a result, business decisions become much more difficult than they would be in a rational market. In this article, epistemicclosure’s ethical issues are developed. First, although they are acting irrationally within the closure’s domain, those with epistemicclosure can still be held accountable for their actions. Second, to deal ethically with epistemicclosure and its consequences, then it is vital to know what it is and its root causes, as well as to have a practical principle that can assist in making pragmatic decisions. Because some new technologies face epistemicclosure, then focusing on a particular representative case of it will help to illustrate the issue’s ethical dimensions. (shrink)
K-axiom-based epistemicclosure for explicit knowledge is rejected for even the most trivial cases of deductive inferential reasoning on account of the fact that the closure axiom does not extend beyond a raw consequence relation. The recognition that deductive inference concerns interaction as much as it concerns consequence allows for perspectives from logics of multi-agent information flow to be refocused onto mono-agent deductive reasoning. Instead of modeling the information flow between different agents in a communicative or announcement (...) setting, we model the information flow between different states of a single agent as that agent reasons deductively. The resource management of the database of agent states for the deductive reasoning fragment in question is covered by the residuated structure that encodes the nonassociative Lambek Calculus with permutation, bottom, and identity: NLP01. (shrink)
The idea that knowledge can be extended by inference from what is known seems highly plausible. Yet, as shown by familiar preface paradox and lottery-type cases, the possibility of aggregating uncertainty casts doubt on its tenability. We show that these considerations go much further than previously recognized and significantly restrict the kinds of closure ordinary theories of knowledge can endorse. Meeting the challenge of uncertainty aggregation requires either the restriction of knowledge-extending inferences to single premises, or eliminating epistemic (...) uncertainty in known premises. The first strategy, while effective, retains little of the original idea—conclusions even of modus ponens inferences from known premises are not always known. We then look at the second strategy, inspecting the most elaborate and promising attempt to secure the epistemic role of basic inferences, namely Timothy Williamson’s safety theory of knowledge. We argue that while it indeed has the merit of allowing basic inferences such as modus ponens to extend knowledge, Williamson’s theory faces formidable difficulties. These difficulties, moreover, arise from the very feature responsible for its virtue- the infallibilism of knowledge. (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)
Sharon Ryan (2000) argues against one epistemicclosure principle but defends another one. I argue that the phenomenon of blameless propositional recognition failure provides a counter-example to this closure principle. I suggest a revision to the closure principle to make it immune to this sort of counter-example.
The epistemicclosure principle says that knowledge is closed under known entailment. The closure principle is deeply implicated in numerous core debates in contemporary epistemology. Closure’s opponents claim that there are good theoretical reasons to abandon it. Closure’s proponents claim that it is a defining feature of ordinary thought and talk and, thus, abandoning it is radically revisionary. But evidence for these claims about ordinary practice has thus far been anecdotal. In this paper, I report (...) five studies on the status of epistemicclosure in ordinary practice. Despite decades of widespread assumptions to the contrary in philosophy, ordinary practice is ambivalent about closure. Ordinary practice does not endorse an unqualified version of the epistemicclosure principle, although it might endorse a source-relative version of the principle. In particular, whereas inferential knowledge is not viewed as closed under known entailment, perceptual knowledge might be. (shrink)
Ted A. Warfield reviews the history of epistemology and argues that epistemologists mistakenly take for granted the inference that the failure of closure of some necessary condition on knowledge is sufficient for the failure of epistemicclosure. So he concludes that epistemologists should avoid using this inference to explain the failure of epistemicclosure. However, I will defend the inference that epistemologists often employ in their discussions. My thesis is that although this inference is invalid, (...) one can still legitimately conclude the failure of epistemicclosure from the failure of closure of some necessary condition on knowledge. (shrink)
This paper contributes to the current debate about radical scepticism and the structure of warrant. After a presentation of the standard version of the radical sceptic’s challenge, both in its barest and its more refined form, three anti-sceptical responses, and their respective commitments, are being identified: the Dogmatist response, the Conservativist response and the Dretskean response. It is then argued that both the Dretskean and the Conservativist are right that the anti-sceptical hypothesis cannot inherit any perceptual warrants from ordinary propositions (...) about the environment—and so the Dogmatist response founders. However, if this is so EpistemicClosure lacks any clear rationale. There is therefore good reason to agree with both the Dretskean and the Dogmatist that perceptual warrants for ordinary propositions about the environment are enough in order for those propositions to enjoy a positive epistemic status—and so the Conservativist response founders. However, the Conservativist is nonetheless right that a warrant for the anti-sceptical hypothesis is needed. For contrary to what much of the recent literature suggests, the radical sceptic need not appeal to EpistemicClosure in order to cast doubt on the legitimacy of our beliefs in ordinary propositions about the environment: there is a Pyrrhonian version of scepticism that, though equally radical, is consistent with failure of EpistemicClosure. For this reason, the Dretskean response is insufficient to answer scepticism. (shrink)
The Knower Paradox has had a brief but eventful history, and principles of epistemicclosure (which say that a subject automatically knows any proposition she knows to be materially implied, or logically entailed, by a proposition she already knows) have been the subject of tremendous debate in epistemic logic and epistemology more generally, especially because the fate of standard arguments for and against skepticism seems to turn on the fate of closure. As far as I can (...) tell, however, no one working in either area has emphasized the result I emphasize in this paper: the Knower Paradox just falsifies even the most widely accepted general principles of epistemicclosure. After establishing that result, I discuss five of its more important consequences. (shrink)
This is an encyclopedia article about epistemicclosure principles. The article explains what they are, their various philosophical uses, how they are argued for or against, and provides an overview of the related literature.
The general principle of epistemicclosure stipulates that epistemic properties are transmissible through logical means. According to this principle, an epistemic operator, say ε, should satisfy any valid scheme of inference, such as: if ε(p entails q), then ε(p) entails ε(q). The principle of epistemicclosure under known entailment (ECKE), a particular instance of epistemicclosure, has received a good deal of attention since the last thirty years or so. ECKE states that: (...) if one knows that p entails q, and she knows that p, then she knows that q. It is widely accepted that ECKE constitutes an important piece of the skeptical argument, but the acceptance of an unrestricted version of ECKE is still a matter of debate. On the side of the defenders of ECKE, one finds Stine (1976), Brueckner (1985), Vogel (1990), and Feldman (1995). Others proposed a refutation or a limitation of the principle, like Dretske (1970), Nozick (1981), Hales (1995), Williams (1996), and Sosa (1999). As it turns out, the relevant alternatives view (RAV) elaborated by Dretske, which restricts the scope of ECKE, has been discussed extensively and acknowledged as one of the most important contributions. There is nonetheless a major unsolved difficulty pertaining to Dretske-RAV: the notion of relevant alternatives is defined in such a way that it is bounded by counterfactual possibilities. This ontological import leaves open the door to the skeptic. Some have tried to give more precision to this notion, like Stine (1976), who appealed to a Gricean approach to define relevant alternatives in conversational contexts. My proposal is in accordance with the gist of Dretske’s strategy, i.e. to restrict the validity of ECKE, and I claim that in order to escape the difficulties inherent to RAV one has to introduce a more robust notion, the notion of epistemic context. Epistemic contexts are a subclass of propositional contexts. In that perspective, the closure property is expressed in terms of a property of a relation between epistemic contexts. ECKE holds when and only when either the epistemic context of the premisses is the same as the epistemic context of the conclusion, or the epistemic context change between the premisses and the conclusion is permissible. Permissibility of epistemic context change is a function of consistency. By means of this epistemic context approach, I will show that: (1) epistemic contexts are defined by basic propositions (unchallenged justified beliefs), (2) ECKE holds only under very specific constraints, and (3) the skeptical argument involves a non-permissible change of epistemic context and, by the same token, cannot rely upon ECKE. (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)
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.
Closure is the epistemological thesis that if S knows that P and knows that P implies Q, then if S infers that Q, S knows that Q. Fred Dretske acknowledges that closure is plausible but contends that it should be rejected because it conflicts with the plausible thesis: Conclusive reasons : S knows that P only if S believes P on the basis of conclusive reasons, i.e., reasons S wouldn‘t have if it weren‘t the case that P. Dretske (...) develops an analysis of knowing that centers on CR, and argues that the requirement undermines skepticism by implying the falsity of closure. We develop a Dretske-style analysis of knowing that incorporates CR, and we argue that this analysis not only accords with closure, but also implies it. In addition, we argue that the analysis accounts for the prima facie plausibility of closure-invoking skeptical arguments, and nonetheless implies that they are fallacious. If our arguments turn out to be sound, the acceptability of Dretske‘s analysis of knowing will be significantly enhanced by the fact that, despite implying closure, it undermines closure-based skepticism. (shrink)
Anthony Brueckner has argued that claims about underdetermination of evidence are suppressed in closure-based scepticism (“The Structure of the Skeptical Argument”, Philosophy and Phenomenological Research 54:4, 1994). He also argues that these claims about underdetermination themselves lead to a paradoxical sceptical argument—the underdetermination argument—which is more fundamental than the closure argument. If Brueckner is right, the status quo focus of some predominant anti-sceptical strategies may be misguided. In this paper I focus specifically on the relationship between these two (...) arguments. I provide support for Brueckner’s claim that the underdetermination argument is the more fundamental sceptical argument. I do so by responding to a challenge to this claim put forward by Stewart Cohen (“Two Kinds of Skeptical Argument”, Philosophy and Phenomenological Research 58:1, 1998). Cohen invokes an alternative epistemic principle which he thinks can be used to challenge Brueckner. Cohen’s principle raises interesting questions about the relationship between evidential considerations and explanatory considerations in the context of scepticism about our knowledge of the external world. I explore these questions in my defence of Brueckner. (shrink)
Kripke’s puzzle has put 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, she is in a position to know that Q. (shrink)
According to a popular closure principle for epistemic justification, if one is justified in believing each of the premises in set Φ and one comes to believe that ψ on the basis of competently deducing ψ from Φ—while retaining justified beliefs in the premises—then one is justified in believing that ψ. This principle is prima facie compelling; it seems to capture the sense in which competent deduction is an epistemically secure means to extend belief. However, even the single-premise (...) version of this closure principle is in conflict with certain seemingly good inferences involving the epistemic possibility modal ♢. According to other compelling principles concerning competent deduction and epistemic justification, one can competently infer ¬♢φ from ¬φ in deliberation even though there are cases in which one can justifiably believe ¬φ but would be unjustified in believing ¬♢φ. Thus, as we argue, philosophers must choose between unrestricted closure for justification and the validity of these other principles. (shrink)
Single-premise epistemicclosure is the principle that: if one is in an evidential position to know that P where P entails Q, then one is in an evidential position to know that Q. In this paper, I defend the viability of opposition to closure. A key task for such an opponent is to precisely formulate a restricted closure principle that remains true to the motivations for abandoning unrestricted closure but does not endorse particularly egregious instances (...) of closure violation. I focus on two brands of epistemic theory that naturally incorporate closure restrictions. The first type holds that the truth value of a knowledge ascription is relative to a relevant question. The second holds that the truth value of a knowledge ascription is relative to a relevant topic. For each approach, I offer a formalization of a leading theory from the literature and use this formalization to evaluate the theory’s adequacy in terms of a precise set of desiderata. I conclude that neither theory succeeds in meeting these desiderata, casting doubt on the viability of the underlying approaches. Finally, I offer a novel variant of the topic-sensitive approach that fares better. (shrink)
In this article, I define and then defend the principle of information closure (pic) against a sceptical objection similar to the one discussed by Dretske in relation to the principle of epistemicclosure. If I am successful, given that pic is equivalent to the axiom of distribution and that the latter is one of the conditions that discriminate between normal and non-normal modal logics, a main result of such a defence is that one potentially good reason to (...) look for a formalization of the logic of “ $S$ is informed that $p$ ” among the non-normal modal logics, which reject the axiom, is also removed. This is not to argue that the logic of “ $S$ is informed that $p$ ” should be a normal modal logic, but that it could still be insofar as the objection that it could not be, based on the sceptical objection against pic, has been removed. In other word, I shall argue that the sceptical objection against pic fails, so such an objection provides no ground to abandon the normal modal logic B (also known as KTB) as a formalization of “ $S$ is informed that $p$ ”, which remains plausible insofar as this specific obstacle is concerned. (shrink)
This chapter provides a brief introduction to propositional epistemic logic and its applications to epistemology. No previous exposure to epistemic logic is assumed. Epistemic-logical topics discussed include the language and semantics of basic epistemic logic, multi-agent epistemic logic, combined epistemic-doxastic logic, and a glimpse of dynamic epistemic logic. Epistemological topics discussed include Moore-paradoxical phenomena, the surprise exam paradox, logical omniscience and epistemicclosure, formalized theories of knowledge, debates about higher-order knowledge, and (...) issues of knowability raised by Fitch’s paradox. The references and recommended readings provide gateways for further exploration. (shrink)
In this paper, I argue that the views of Robert Kane on the one hand and John Fischer and Mark Ravizza on the other both lead to the following conclusion: we should have very low confidence in our ability to judge that someone is acting freely or in a way for which they can be held responsible. This in turn means, I claim, that these views, in practice, collapse into a sort of hard incompatibilist position, or the position of a (...) free will denier. That would at least be an unintended consequence, and it might be regarded as a virtual reductio. Versions of the objection could likely be made against a number of other accounts of free will, but I will limit my focus to Kane and Fischer. Along the way, by way of response to some possible objections to my argument, I make some comments about epistemicclosure principles. (shrink)
This paper looks at an argument strategy for assessing the epistemicclosure principle. This is the principle that says knowledge is closed under known entailment; or (roughly) if S knows p and S knows that p entails q, then S knows that q. The strategy in question looks to the individual conditions on knowledge to see if they are closed. According to one conjecture, if all the individual conditions are closed, then so too is knowledge. I give a (...) deductive argument for this conjecture. According to a second conjecture, if one (or more) condition is not closed, then neither is knowledge. I give an inductive argument for this conjecture. In sum, I defend the strategy by defending the claim that knowledge is closed if, and only if, all the conditions on knowledge are closed. After making my case, I look at what this means for the debate over whether knowledge is closed. (shrink)
I argue that fallibilism, single-premise epistemicclosure, and one formulation of the “knowledge-action principle” are inconsistent. I will consider a possible way to avoid this incompatibility, by advocating a pragmatic constraint on belief in general, rather than just knowledge. But I will conclude that this is not a promising option for defusing the problem. I do not argue here for any one way of resolving the inconsistency.
The standard contextualist solution to the skeptical paradox is intended to provide a way to retain epistemicclosure 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)