Closure of Knowledge

As teorias epistemológicas do rastreamento sustentam que o conhecimento é uma relação real entre o agente cognitivo e seu ambiente. Os estados cognitivos de um agente epistêmico fazem o rastreamento da verdade das proposições que são objeto de conhecimento ao embasarem a crença em indicadores confiáveis da verdade (evidência, razões, ou métodos de formação de crença). A novidade nessa abordagem é que se dá pouca ênfase no tipo de justificação epistêmica voltada ao fornecimento de procedimentos de decisão doxástica ou regras (...) de responsabilidade epistêmica. Este artigo oferece um pouco da história das teorias de rastreamento e, então, defende-as contra muitas objeções que se pretendem (equivocadamente) refutadoras dessas teorias. PALAVRAS – CHAVE – Teorias de rastreamento. Nozick. Dretske. Conhecimento. ABSTRACT Tracking theories of knowledge maintain that knowledge is a real relation between cognitive agent and environment. Cognitive states of a knower track the truth of known propositions by basing belief on reliable indicators of truth (evidence, reasons, or belief forming methods). The novelty of this approach is that it places little emphasis on epistemic justification of a kind that aims at guiding epistemic agents by giving doxastic decision procedures or rules of epistemic responsibility. This paper gives some of the history of tracking theories, and then defends them against many of the objections most often judged (mistakenly) to refute tracking theories. KEY WORDS – Tracking theories. Nozick. Dretske. Knowledge. (shrink)

Tracking theories of knowledge are widely known to have the consequence that knowledge is not closed. Recent arguments by Vogel and Hawthorne claim both that there are no legitimate examples of knowledge without closure and that the costs of theories that deny closure are too great. This paper considers the tracking theories of Dretske and Nozick and the arguments by Vogel and Hawthorne. We reject the arguments of Vogel and Hawthorne and evaluate the costs of closure denial for tracking theories (...) of knowledge. (shrink)

In this paper I present a more refined analysis of the principles of deductive closure and positive introspection. This analysis uses the expressive resources of logics for different types of group knowledge, and discriminates between aspects of closure and computation that are often conflated. The resulting model also yields a more fine-grained distinction between implicit and explicit knowledge, and places Hintikka’s original argument for positive introspection in a new perspective.

Those of us who have followed Fred Dretske's lead with regard to epistemic closure 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)

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.

Knowledge closure is, roughly, the following claim: For every agent S and propositions P and Q, if S knows P, knows that P implies Q, and believes Q because it is so implied, then S knows Q. Almost every epistemologist believes that closure is true. Indeed, they often believe that it so obviously true that any theory implying its denial is thereby refuted. Some prominent epistemologists have nevertheless denied it, most famously Fred Dretske and Robert Nozick. There are closure advocates (...) who see other virtues in those accounts, however, and so who introduce revisions of one sort or another in order to preserve closure while maintaining their spirit. One popular approach is to replace the “sensitivity” constraint at the heart of both of those accounts with a “safety” constraint, as advocated by Timothy Williamson, Duncan Pritchard, Ernest Sosa, Stephen Luper, and others. The purpose of this essay is to show that this approach does not succeed: safety does not save closure. And neither does a popular variation on the safety theme, the safe-basis or safe-indicator account. (shrink)

Fred Dretske notoriously claimed that knowledge closure sometimes fails. Crispin Wright agrees that warrant does not transmit in the relevant cases, but only because the agent must already be warranted in believing the conclusion in order to acquire her warrant for the premise. So the agent ends up being warranted in believing, and so knowing, the conclusion in those cases too: closure is preserved. Wright's argument requires that the conclusion's having to be warranted beforehand explains transmission failure. I argue that (...) it doesn't, and that the correct explanation does not imply that the agent will end up warranted in believing the conclusion when transmission fails. Those who agree that transmission does fail in those cases, therefore, might as well follow Dretske in denying knowledge closure too. (shrink)

Here, I shall be examining the viability of a Moorean response to the Argument from Ignorance; i.e., one that tries to rebut the argument by denying its first premise that we cannot have knowledge that we are not BIVs. After first explicating the Argument from Ignorance in detail, I then go on to try and motivate this approach by critically examining two alternative approaches to dealing with radical scepticism: closure-denial, and attributer contextualism. Finding them wanting, I then turn to a (...) Moorean 'argument from knowledge', and diagnose why as it stands such an approach is ineffective, before going on to explore whether one can wed such an argument to an externalist framework in order to provide a more satisfying answer to the question of how one can know the denials of sceptical hypotheses, one that does not simply beg the question against the sceptic. Finding such a neo-Moorean approach to be initially promising, I then conclude by arguing that ultimately it winds up saving knowledge simpliciter only at the cost of losing rationally-grounded knowledge to the sceptic's grasp, and such a result is highly unpalatable. (shrink)

Contemporary discussions of skepticism often frame the skeptic’s argument around an instance of the closure principle. Roughly, the closure principle states that if a subject knows p, and knows that p entails q, then the subject knows q. The main contention of this paper is that the closure argument for skepticism is defective. We explore several possible classifications of the defect. The closure argument might plausibly be classified as begging the question, as exhibiting transmission failure, or as structurally inefficient. Interestingly, (...) perhaps, each of these has been proposed as the correct classification of Moore’s proof of an external world. (shrink)

Most solutions to the skeptical paradox about justified belief assume closure for justification, since the rejection of closure is widely regarded as a non-starter. I argue that the rejection of closure is not a non-starter, and that its problems are no greater than the problems associated with the more standard anti-skeptical strategies. I do this by sketching a simple version of the unpopular strategy and rebutting the three best objections to it. The general upshot for theories of justification is that (...) it is not a constraint on such theories that we must somehow have justification to believe that we are not massively deceived. (shrink)

This chapter focuses on the responses that proponents of virtue epistemology (VE) make to radical skepticism and particularly to two related forms of it, Pyrrhonian skepticism and the “underdetermination-based” argument, both of which have been receiving widening attention in recent debate. Section 1 of the chapter briefly articulates these two skeptical arguments and their interrelationship, while section 2 explains the close connection between a virtue-theoretic and a neo-Moorean response to them. In sections 3 and 4 I advance arguments for improving (...) the prospects of virtue-theoretic responses, sketching a particular version of VE that by recasting somewhat how we understand the “externalist turn in epistemology” also suggests ways of improving the adequacy of philosophical diagnoses and responses to skepticism. (shrink)

Certain puzzling cases have been discussed in the literature recently which appear to support the thought that knowledge can be obtained by way of deduction from a falsehood; moreover, these cases put pressure, prima facie, on the thesis of counter closure for knowledge. We argue that the cases do not involve knowledge from falsehood; despite appearances, the false beliefs in the cases in question are causally, and therefore epistemologically, incidental, and knowledge is achieved despite falsehood. We also show that the (...) principle of counter closure, and the concomitant denial of knowledge from falsehood, is well motivated by considerations in epistemological theory--in particular, by the view that knowledge is first in the epistemological order of things. (shrink)

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)

If the reliability of a source of testimony is open to question, it seems epistemically illegitimate to verify the source’s reliability by appealing to that source’s own testimony. Is this because it is illegitimate to trust a questionable source’s testimony on any matter whatsoever? Or is there a distinctive problem with appealing to the source’s testimony on the matter of that source’s own reliability? After distinguishing between two kinds of epistemically illegitimate circularity—bootstrapping and self-verification—I argue for a qualified version of (...) the claim that there is nothing especially illegitimate about using a questionable source to evaluate its own reliability. Instead, it is illegitimate to appeal to a questionable source’s testimony on any matter whatsoever, with the matter of the source’s own reliability serving only as a special case. (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)

This paper argues against common views that at least in many cases Robert Nozick is not forced to deny common closure principles. More importantly, Nozick does not – despite first (and second) appearances and despite his own words – deny closure. On the contrary, he is defending a more sophisticated and complex principle of closure. This principle does remarkably well though it is not without problems. It is surprising how rarely Nozick’s principle of closure has been discussed. He should be (...) seen not so much as a denier of closure than as someone who’s proposing an alternative, more complex principle of closure. (shrink)

This article gives an overview over different principles of epistemic closure, their attractions and their problems.

There are many ordinary propositions we think we know. Almost every ordinary proposition entails some "lottery proposition" which we think we do not know but to which we assign a high probability of being true (for instance: “I will never be a multi-millionaire” entails “I will not win this lottery”). How is this possible - given that some closure principle is true? This problem, also known as “the Lottery puzzle”, has recently provoked a lot of discussion. In this paper I (...) discuss one of the most promising answers to the problem: Stewart Cohen’s contextualist solution which is based on ideas about the salience of chances of error. After presenting some objections to it I sketch an alternative solution which is still contextualist in spirit. (shrink)

We report the results of four empirical studies designed to investigate the extent to which an epistemic closure 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)

It is undeniable that the skeptic's argument can grip you. How can you claim to know that you are not right now dreaming? And if you can't, how can you claim that you know anything about the external world? Some philosophers have argued that we may insist that the skeptic's inference from "You do not know that you are not now dreaming" to "You do not know you have hands" is illegitimate, because it relies on the false principle that knowledge (...) is closed under known entailment. I argue that this principle is true and, more importantly, that the force of the skeptic's argument does not rest on its truth. ;Responding to the skeptic can take either a direct or diagnostic route. The direct route tries to show that the skeptic's premises do not lead to the skeptic's conclusion. I do not believe this will meet with success. The diagnostic route locates the apparent force of the skeptic's argument in some part of it that is non-compulsory or a set of considerations that allow us to circumvent the argument altogether. This is the route I take. ;Skepticism, I claim, is not in essence a theoretical problem, i.e., a problem about the structure of our knowledge of the external world. This was G. E. Moore's insight into skepticism. Though rightfully criticized for not adequately explaining where he thought the skeptic goes wrong, Moore, I claim, was sensitive to where the force of the skeptic's argument lies---in the capacity to challenge a particular knowledge claim. ;Once we appreciate that a theoretical response won't address the skeptic's argument, we see our way to a set of considerations that might. I attempt to articulate a view I call "particularism", according to which our fundamental justificatory principles do not have underived authority, but rather an authority that is derived from particular cases of knowledge. Appreciating the nature of the authority these principles, I claim, explains the grip of the skeptic's argument, and provides a way of resistance. (shrink)

The lottery and preface paradoxes pose puzzles in epistemology concerning how to think about the norms of reasonable or permissible belief. Contextualists in epistemology have focused on knowledge ascriptions, attempting to capture a set of judgments about knowledge ascriptions and denials in a variety of contexts (including those involving lottery beliefs and the principles of closure). This article surveys some contextualist approaches to handling issues raised by the lottery and preface, while also considering some of the difficulties encountered by those (...) approaches. (shrink)

It is widely thought that if knowledge requires sensitivity, knowledge is not closed because sensitivity is not closed. This paper argues that there is no valid argument from sensitivity failure to non-closure of knowledge. Sensitivity does not imply non-closure of knowledge. Closure considerations cannot be used to adjudicate between safety and sensitivity accounts of knowledge.

Paul Boghossian has famously argued that semantic externalism is incompatible with authoritative self-knowledge. Boghossian also draws incompatibilist consequences from the slow switching thought experiment introduced by Tyler Burge. This paper develops three objections to Boghossian's incompatibilist argument.

There is reason to think that a familiar and frequently used epistemic closure principle is false. Given this, the relevant instance of that principle should be removed from a familiar skeptical argument, and replaced with an instance of a more plausible epistemic closure principle. Once this has been done, however, we see that even if the resulting skeptical argument is unsound, we need deny neither closure nor the claim that we know the things we ordinarily take ourselves to know. Nothing (...) that the skeptic can do, at least with an argument that makes use of an epistemic closure principle, can ever force us to relinquish closure or the utterly vast stretches of knowledge that we ordinarily take ourselves to have. (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)

So, C. I don’t know that T. Premises 1 and 2 are both plausible. However, C seems false—I do seem to know that there is a tree before me. AI presents a puzzle because its two plausible premises yield a conclusion whose negation is plausible. And no matter whether we accept or reject AI, we find that we must give up something plausible—either premise 1, premise 2, or the negation of C. But which of these should we give up? I (...) call this question the skeptical puzzle.1 Recently, Mark Heller2 has argued that we can solve the skeptical puzzle by giving up premise 2. I argue, however, that Heller does not adequately respond to an objection to his proposed solution. I go on to argue that we can solve the skeptical puzzle by giving up premise 1. (shrink)

The sensitivity condition on knowledge says that one knows that P only if one would not believe that P if P were false. Difficulties for this condition are now well documented. Keith DeRose has recently suggested a revised sensitivity condition that is designed to avoid some of these difficulties. We argue, however, that there are decisive objections to DeRose’s revised condition. Yet rather than simply abandoning his proposed condition, we uncover a rationale for its adoption, a rationale which suggests a (...) further revision that avoids our objections as well as others. The payoff is considerable: along the way to our revision, we learn lessons about the epistemic significance of certain explanatory relations, about how we ought to envisage epistemic closure principles, and about the epistemic significance of methods of belief formation. (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.

The notion of the rational closure of a positive knowledge base K of conditional assertions | (standing for if then normally ) was first introduced by Lehmann (1989) and developed by Lehmann and Magidor (1992). Following those authors we would also argue that the rational closure is, in a strong sense, the minimal information, or simplest, rational consequence relation satisfying K. In practice, however, one might expect a knowledge base to consist not just of positive conditional assertions, | , but (...) also negative conditional assertions, i (standing for not if then normally . Restricting ourselves to a finite language we show that the rational closure still exists for satisfiable knowledge bases containing both positive and negative conditional assertions and has similar properties to those exhibited in Lehmann and Magidor (1992). In particular an algorithm in Lehmann and Magidor (1992) which constructs the rational closure can be adapted to this case and yields, in turn, completeness theorems for the conditional assertions entailed by such a mixed knowledge base. (shrink)

Saul Kripke argued that the requirement that knowledge eliminate all possibilities of error leads to dogmatism . According to this view, the dogmatism puzzle arises because of a requirement on knowledge that is too strong. The paper argues that dogmatism can be avoided even if we hold on to the strong requirement on knowledge. I show how the argument for dogmatism can be blocked and I argue that the only other approach to the puzzle in the literature is mistaken.

The general principle of epistemic closure 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 epistemic closure under known entailment (ECKE), a particular instance of epistemic closure, 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)

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)

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)

E. J. Coffman defends Peter Klein’s work on epistemic closure against various objections that I raised in an earlier paper. In this paper, I respond to Coffman.

This paper argues that Epistemic Contextualism, Knowledge Closure, and the Knowledge Account of Assertion are inconsistent. The argument is developed by considering an objection to Contextualism that is unsuccessful. Some Contextualist responses are canvassed and rejected. Finally, it is argued that an analogue of the inconsistency arises for those who accept that justification is closed under known entailment.