I argue that we should solve the Lottery Paradox by denying that rational belief is closed under classical logic. To reach this conclusion, I build on my previous result that (a slight variant of) McGee’s election scenario is a lottery scenario (see Lissia 2019). Indeed, this result implies that the sensible ways to deal with McGee’s scenario are the same as the sensible ways to deal with the lottery scenario: we should either reject the Lockean Thesis or Belief (...) Closure. After recalling my argument to this conclusion, I demonstrate that a McGee-like example (which is just, in fact, Carroll’s barbershop paradox) can be provided in which the Lockean Thesis plays no role: this proves that denying Belief Closure is the right way to deal with both McGee’s scenario and the Lottery Paradox. A straightforward consequence of my approach is that Carroll’s puzzle is solved, too. (shrink)

Duncan Pritchard’s Epistemic Angst promises a novel solution to the closure-based sceptical problem that, unlike more traditional solutions, does not entail revising our fundamental epistemological commitments. In order to do this, it appeals to a Wittgensteinian account of rational evaluation, the overarching theme of which is that it neither makes sense to doubt nor to believe in our anti-sceptical hinge commitments. The purpose of this paper is to show that the argument for the claim that there can be no (...) rational basis to believe our anti-sceptical hinge commitments relies upon an implicit assumption about rational support that I label The Pritchensteinian Rational Grounds Principle. I argue that, insofar as this principle is intended to apply to closure-style inferences, it leads to irrational doxastic attitudes. I consider a seemingly plausible modification of the principle that would avoid this result but show that this modified principle faces serious problems of its own. -/- . (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)

Recent research has identified a tension between the Safety principle that knowledge is belief without risk of error, and the Closure principle that knowledge is preserved by competent deduction. Timothy Williamson reconciles Safety and Closure by proposing that when an agent deduces a conclusion from some premises, the agent’s method for believing the conclusion includes their method for believing each premise. We argue that this theory is untenable because it implies problematically easy epistemic access to one’s methods. (...) Several possible solutions are explored and rejected. (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)

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)

Duncan Pritchard recently proposed a Wittgensteinian solution to closure-based skepticism. According to Wittgenstein, all epistemic systems assume certain truths. The notions that we are not disembodied brains, that the Earth has existed for a long time and that one’s name is such-and-such all function as “hinge commitments.” Pritchard views a hinge commitment as a positive propositional attitude that is not a belief. Because closure principles concern only knowledge-apt beliefs, they do not apply to hinge commitments. Thus, from (...) the fact that a subject knows that he is sitting in a room, and the fact that the subject’s sitting in a room entails his bodily existence, it does not follow that the subject also knows that he is not an envatted brain. This paper rejects Pritchard’s non-belief reading of hinge commitments. I start by showing that the non-belief reading fails to solve the skeptical paradox because the reasons that Pritchard uses to support the non-belief reading do not exempt hinge propositions from closure principles. I then proceed to argue that the non-belief reading is false as it claims that hinge commitments, unlike ordinary beliefs, are rationally unresponsive—with the help of a scenario in which a subject’s experience is internally chaotic, we can safely conclude that the hinge commitment that one is not systematically mistaken about the world is equally responsive to one’s evidential situations. (shrink)

It has been argued that an advantage of the safety account over the sensitivity account is that the safety account preserves epistemic closure, while the sensitivity account implies epistemic closure failure. However, the argument fails to take the method-relativity of the modal conditions on knowledge, viz., sensitivity and safety, into account. In this paper, I argue that the sensitivity account and the safety account are on a par with respect to epistemic closure once the method-relativity of the (...) modal conditions is taken into account. Therefore, epistemic closure is no longer an arbiter in the debate. (shrink)

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)

The problem of closure for the traditional unstructured possible worlds model of attitudinal content is that it treats belief and other cognitive states as closed under entailment, despite apparent counterexamples showing that this is not a necessary property of such states. One solution to this problem, which has been proposed recently by several authors (Schaffer 2005; Yalcin 2018; Hoek forthcoming), is to restrict closure in an unstructured setting by treating propositional attitudes as question-sensitive. Here I argue that (...) this line of response is unsatisfying as it stands because the problem of closure is more general than is typically discussed. A version of the problem recurs for attitudes like wondering, entertaining, considering, and so on, which are directed at questions rather than propositions. For such questioning attitudes, the appeal to question-sensitivity is much less convincing as a solution to the problem of closure. (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)

Crispin Wright has articulated and defended the view that by incorporating non-evidential entitlements into our theory of knowledge, we can achieve a satisfactory reply to key skeptical challenges. Crucial to this view is the thesis that regions of thought are underpinned by ‘cornerstone’ propositions— propositions for which warrant is antecedently required in order for ordinary beliefs in that region to be supported by experiential evidence. Critics have noted that because cornerstone propositions are entailed by ordinary propositions, Closure delivers two (...) unwelcome results: (i) one can acquire evidential justification for cornerstones via deduction (alchemy); and (ii) the epistemic risk involved in accepting cornerstone propositions impugns the evidential justification we are supposed to have for ordinary propositions (leaching). It is argued here that leaching has been misdiagnosed by Wright and his critics as relying essentially on a Closure principle. Instead, it relies on a Counter-Closure-style principle. Once this point is recognized , Wright’s own solution to the leaching problem becomes unsatisfactory. However, a guiding maxim from the extant literature for demarcating true from false Counter-Closure-style principles can be usefully applied to identify a successful resolution to the leaching worry on Wright’s behalf. (shrink)

The present article illustrates a conflict between the claim that rational belief sets are closed under deductive consequences, and a very inclusive claim about the factors that are sufficient to determine whether it is rational to believe respective propositions. Inasmuch as it is implausible to hold that the factors listed here are insufficient to determine whether it is rational to believe respective propositions, we have good reason to deny that rational belief sets are closed under deductive consequences.

Generally, an epistemic fallibilist considers it reasonable to claim, “I know that P, but I may be wrong.” An epistemic infallibilist, on the other hand, would consider this claim absurd. I argue initially that infallibilism presents more advantages in its assertion of the claim’s absurdity than fallibilism does in making the claim. One, infallibilism is not faulted with the propensity for violations of epistemic closure that beleaguers some fallibilist accounts, due in part to the latter’s problematic shunting of fallible (...) epistemic standards across inferential chains. Two, infallibilism is more easily modelled doxastically than fallibilism, as the former’s understanding of certainty is more tractable than the latter’s idea of what counts as a viable standard of fallibility. A rectification of these fallibilist issues may then be called upon to motivate gradualist variants of fallibilism. For epistemic gradualism, the problematic modellability and shunting of standards is curtailed via an awareness that the standard for knowledge is just one out of many along a gradient that includes, at one extreme, the infallibilist standard of certainty. Specifically, first, gradualism, along with infallibilism, can be modelled doxastically through elucidating upon an obtaining relation between doubt and knowledge; next, the problem with violating closure, although not generally applicable to infallibilism, can be answered by gradualism with a reasonable denial of closure altogether that makes precise which epistemic standard is relevant for which part of an inferential chain; lastly, these modelling resources can be appropriated, by both gradualism and infallibilism, to successfully address a doxastically pertinent form of closure violation called rational self-doubt. (shrink)

Ernest Sosa and others have proposed a safety condition on knowledge: If S knows p, then in the nearest (non-actual) worlds in which S believes p, p is true.1 Colloquially, this is the idea that knowing requires not being easily mistaken. Here, I will argue that like another condition requiring a counterfactual relation between a subject’s belief and the world, viz. Robert Nozick’s sensitivity condition, safety leads, in certain cases, to the unacceptable result that knowledge is not closed under (...) known implication. (shrink)

A ‘lottery belief’ is a belief that a particular ticket has lost a large, fair lottery, based on nothing more than the odds against it winning. The lottery paradox brings out a tension between the idea that lottery beliefs are justified and the idea that that one can always justifiably believe the deductive consequences of things that one justifiably believes – what is sometimes called the principle of closure. Many philosophers have treated the lottery paradox as an (...) argument against the second idea – but I make a case here that it is the first idea that should be given up. As I shall show, there are a number of independent arguments for denying that lottery beliefs are justified. (shrink)

I present an intractable puzzle for the currently popular view that belief is weak—the view that expressions like ‘S believes p’ ascribe to S a doxastic attitude towards p that is rationally compatible with low credence that p. The puzzle concerns issues that arise on considering beliefs in conditionals. I show that proponents of weak belief either cannot consistently apply their preferred methodology when accommodating beliefs in conditionals, or they must deny that beliefs in conditionals can be used (...) in reasoning. (shrink)

In this essay I defend a solution to a skeptical paradox. The paradox I focus on concerns epistemic justification (rather than knowledge), and skeptical scenarios that entail that most of our ordinary beliefs about the external world are false. This familiar skeptical paradox hinges on a “closure” principle. The solution is to restrict closure, despite its first appearing as a fully general principle, so that it can no longer give rise to the paradox. This has some extra advantages. (...) First, it suggests a general strategy that provides solutions to other versions of the paradox, not just those that depend on closure. Second, it clarifies the relation between the paradox and other kinds of skeptical problem. (shrink)

The article proceeds upon the assumption that the beliefs and degrees of belief of rational agents satisfy a number of constraints, including: consistency and deductive closure for belief sets, conformity to the axioms of probability for degrees of belief, and the Lockean Thesis concerning the relationship between belief and degree of belief. Assuming that the beliefs and degrees of belief of both individuals and collectives satisfy the preceding three constraints, I discuss what further (...) constraints may be imposed on the aggregation of beliefs and degrees of belief. Some possibility and impossibility results are presented. The possibility results suggest that the three proposed rationality constraints are compatible with reasonable aggregation procedures for belief and degree of belief. (shrink)

This paper focuses on a potential problem with Sosa’s theory of default assumption, viz., the alleged incompatibility of this theory with the closure principle. Given the similarity between the notion of default assumption and Wittgenstein’s notion of hinge commitment, I suggest that two influential hinge epistemologies including Wright’s entitlement theory and Pritchard’s non-belief theory provide resources for possible solutions to the problem. I argue that default assumption should be classified as acceptance and hence as a non-doxastic propositional attitude. (...) Sosa’s theory can deal with the apparent incompatibility with the closure principle by adopting the solution of the non-belief theory, while also avoiding problems affecting the latter view. (shrink)

In this paper I defend the claim that justification is closed under conjunction, and confront its most alarming consequence — that one can have justification for believing propositions that are unlikely to be true, given one's evidence.

Agents are often assumed to have degrees of belief (“credences”) and also binary beliefs (“beliefs simpliciter”). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the “lottery paradox”: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed (...) that this problem generalizes: there exists no local function from degrees of belief to binary beliefs that satisfies some minimal conditions of rationality and non-triviality. “Locality” means that the binary belief in each proposition depends only on the degree of belief in that proposition, not on the degrees of belief in others. One might think that the impossibility can be avoided by dropping the assumption that binary beliefs are a function of degrees of belief. We prove that, even if we drop the “functionality” restriction, there still exists no local relation between degrees of belief and binary beliefs that satisfies some minimal conditions. Thus functionality is not the source of the impossibility; its source is the condition of locality. If there is any non-trivial relation between degrees of belief and binary beliefs at all, it must be a “holistic” one. We explore several concrete forms this “holistic” relation could take. (shrink)

The paper provides both a description of conspiracy beliefs and an insight into their cultural significance. On one side, it highlights their specific formal features, on the other, and this constitutes its peculiarity in the recent literature on the topic, it considers them within the broader genre of general conceptual beliefs, whose main characteristics are weak methodology and logical structure, strong affective and dispositional constraints, epistemic closure and mauvaise foi, and whose main function is practical and self-representative (not epistemic). (...) The paper also claims that political theory and social sciences had some influence in legitimizing certain ideas and stereotypes that are exacerbated in conspiracy beliefs, while other te(le)ological conceptions, such as finalism and providence, may be an important source of ideas that turn out to be widely spread in contemporary criticism towards those same beliefs. (shrink)

Recently, a number of cases have been proposed which seem to show that – contrary to widely held opinion – a subject can inferentially come to know some proposition p from an inference which relies on a false belief q which is essential. The standard response to these cases is to insist that there is really an additional true belief in the vicinity, making the false belief inessential. I present a new kind of case suggesting that a (...) subject can inferentially come to know a proposition from an essential false belief where no truth in the vicinity seems to be present. (shrink)

Two principles in epistemology are apparent examples of the close connection between rationality and truth. First, adding a disjunct to what it is rational to believe yields a proposition that’s also rational to believe. Second, what’s likely if believed is rational to believe. While these principles are accepted by many, it turns out that they clash. In light of this clash, we must relinquish the second principle. Reflecting on its rationale, though, reveals that there are two distinct ways to understand (...) the connection between rationality and truth. Rationality is fundamentally a guide to the belief-independent truth, rather than a guide to acquiring true beliefs. And this in turn has important implications for current discussions of permissivism, epistemic reasons, and epistemic consequentialism. (shrink)

Trent Dougherty argues (contra Jonathan Matheson) that when taking into consideration the probabilities involving skeptical theism (ST) and gratuitous evils, an agent may reasonably affirm both ST and that gratuitous evils exist. In other words, Dougherty thinks that assigning a greater than .5 probability to ST is insufficient to defeat the commonsense problem of evil. I argue that Dougherty’s response assumes, incorrectly, that ST functions solely as an evidential defeater, and that, when understood as a closure of inquiry defeater, (...) ST may still defeat reasonable belief in gratuitous evils, even in the face of strong evidence that gratuitous evils exist. (shrink)

Edmund Gettier (1963) argued that there can be justified true belief (JTB) that is not knowledge. I question the correctness of his argument by showing that Smith of Gettier’s famous examples does not earn justification for his incidentally true beliefs, while a doxastically more conscientious person S would come to hold justified but false beliefs. So, Gettier’s (and analogous) cases do not result in justified _and_ true belief. This is due to a tension between deductive closure of (...) justification and evidential support. For being justified, any believing, disbelieving, or withholding of deductively inferred propositions must be distributed proportionally to given evidential support. This proportionality principle has primacy over deductive closure in case of conflict. My argument does not save the JTB-account. But, instead of merely referring to an intuition, it explains why subjects in Gettier situations do not earn knowledge. (shrink)

ABSTRACT Drawing inspiration from Fred Dretske, L. S. Carrier, John A. Barker, and Robert Nozick, we develop a tracking analysis of knowing according to which a true belief constitutes knowledge if and only if it is based on reasons that are sensitive to the fact that makes it true, that is, reasons that wouldn’t obtain if the belief weren’t true. We show that our sensitivity analysis handles numerous Gettier-type cases and lottery problems, blocks pathways leading to skepticism, and (...) validates the epistemic closure thesis that correct inferences from known premises yield knowledge of the conclusions. We discuss the plausible views of Ted Warfield and Branden Fitelson regarding cases of knowledge acquired via inference from false premises, and we show how our sensitivity analysis can account for such cases. We present arguments designed to discredit putative counterexamples to sensitivity analyses recently proffered by Tristan Haze, John Williams and Neil Sinhababu, which involve true statements made by untrustworthy informants and strange clocks that sometimes display the correct time while running backwards. Finally, we show that in virtue of employing the paradox-free subjunctive conditionals codified by Relevance Logic theorists instead of the paradox-laden subjunctive conditionals codified by Robert Stalnaker and David Lewis. (shrink)

I show that the Lottery Paradox is just a version of the Sorites, and argue that this should modify our way of looking at the Paradox itself. In particular, I focus on what I call “the Cut-off Point Problem” and contend that this problem, well known by Sorites scholars, ought to play a key role in the debate on Kyburg’s puzzle. Very briefly, I show that, in the Lottery Paradox, the premises “ticket n°1 will lose”, “ticket n°2 will lose”… “ticket (...) n°1000 will lose” are equivalent to soritical premises of the form “~(the winning ticket is in {…, (tn)}) ⊃ ~(the winning ticket is in {…, tn, (tn + 1)})” (where “⊃” is the material conditional, “~” is the negation symbol, “tn” and “tn + 1” are “ticket n°n” and “ticket n°n + 1” respectively, and “{}” identify the elements of the lottery tickets’ set. The brackets in “(tn)” and “(tn + 1)” are meant to point out that in the antecedent of the conditional we do not always have a “tn” (and, as a result, a “tn + 1” in the consequent): consider the conditional “~(the winning ticket is in {}) ⊃ ~(the winning ticket is in {t1})”). As a result, failing to believe, for some ticket, that it will lose comes down to introducing a cut-off point in a chain of soritical premises. In this paper I explore the consequences of the different ways of blocking the Lottery Paradox with respect to the Cut-off Point Problem. A heap variant of the Lottery Paradox is especially relevant for evaluating the different solutions. One important result is that the most popular way out of the puzzle, i.e., denying the Lockean Thesis, becomes less attractive. Moreover, I show that, along with the debate on whether rational belief is closed under classical logic, the debate on the validity of modus ponens should play an important role in discussions on the Lottery Paradox. -/- . (shrink)

Vann McGee has presented a putative counterexample to modus ponens. I show that (a slightly modified version of) McGee’s election scenario has the same structure as a famous lottery scenario by Kyburg. More specifically, McGee’s election story can be taken to show that, if the Lockean Thesis holds, rational belief is not closed under classical logic, including classical-logic modus ponens. This conclusion defies the existing accounts of McGee’s puzzle.

Choices confront us with questions. How we act depends on our answers to those questions. So the way our beliefs guide our choices is not just a function of their informational content, but also depends systematically on the questions those beliefs address. This paper gives a precise account of the interplay between choices, questions and beliefs, and harnesses this account to obtain a principled approach to the problem of deduction. The result is a novel theory of belief-guided action that (...) explains and predicts the decisions of agents who, like ourselves, fail to be logically omniscient: that is, of agents whose beliefs may not be deductively closed, or even consistent. (Winner of the 2021 Isaac Levi Prize.). (shrink)

In light of the problem of logical omniscience, some scholars have argued that belief is question-sensitive: agents don't simply believe propositions but rather believe answers to questions. Hoek (2022) has recently developed a version of this approach on which a belief state is a "web" of questions and answers. Here, we present several challenges to Hoek's question-sensitive account of belief. First, Hoek's account is prone to very similar logical omniscience problems as those he claims to address. Second, (...) the link between belief and action he proposes is too rigid. We close by sketching a generalization of the account that can meet these challenges. (shrink)

Epistemologists have recently proposed a number of norms governing rational inquiry. My aim in this paper is to unify and explain recently proposed norms of inquiry by developing a general account of the conditions under which inquiries are rational, analogous to theories such as evidentialism and reliabilism for rational belief. I begin with a reason-responsiveness conception of rationality as responding correctly to possessed normative reasons. I extend this account with a series of claims about the normative reasons for inquiry (...) that we possess. I apply the account to shed light on two classes of norms that have featured prominently in recent discussions: norms of clutter avoidance forbidding agents from engaging in trivial inquiries, and norms of logical non-omniscience governing properties such as the deductive closure and consistency of an agent's belief state. I conclude with a discussion of the sense in which norms of inquiry should be regarded as epistemic norms. (shrink)

What epistemic defect needs to show up in a skeptical scenario if it is to effectively target some belief? According to the false belief account, the targeted belief must be false in the skeptical scenario. According to the competing ignorance account, the targeted belief must fall short of being knowledge in the skeptical scenario. This paper argues for two claims. The first is that, contrary to what is often assumed, the ignorance account is superior to the (...) false belief account. The second is that the ignorance account ultimately hobbles the skeptic. It does so for two reasons. First, when this account is joined with either a closure-based skeptical argument or a skeptical underdetermination argument, the best the skeptic can do is show that we don’t know that we know. And second, the ignorance account directly implies the maligned KK principle. (shrink)

The paper is concerned with the rational requirements for suspended judgment, or what suspending judgment about a question rationally commits one to. It shows that two purported rational requirements for suspended judgment cannot both be true at the same time, at least when the entailment relation between questions is understood a certain way. The first one says that one is rationally required to suspend judgment about those questions that are entailed by the questions that one already suspends judgment about. The (...) second one says that one is rationally required to believe the presuppositions of the questions one suspends judgment about. Two plausible solutions to the problem are discussed. One of them explicates the relation of entailment between questions in an alternative manner, and the other one rejects the presupposition requirement. Either way, a closure requirement for suspended judgment can be maintained which is analogous to the closure requirement for belief. Whereas belief is ideally closed under entailment between propositions, suspended judgment is ideally closed under entailment between questions. (shrink)

Paradoxes have played an important role both in philosophy and in mathematics and paradox resolution is an important topic in both fields. Paradox resolution is deeply important because if such resolution cannot be achieved, we are threatened with the charge of debilitating irrationality. This is supposed to be the case for the following reason. Paradoxes consist of jointly contradictory sets of statements that are individually plausible or believable. These facts about paradoxes then give rise to a deeply troubling epistemic problem. (...) Specifically, if one believes all of the constitutive propositions that make up a paradox, then one is apparently committed to belief in every proposition. This is the result of the principle of classical logical known as ex contradictione (sequitur) quodlibetthat anything and everything follows from a contradiction, and the plausible idea that belief is closed under logical or material implication (i.e. the epistemic closure principle). But, it is manifestly and profoundly irrational to believe every proposition and so the presence of even one contradiction in one’s doxa appears to result in what seems to be total irrationality. This problem is the problem of paradox-induced explosion. In this paper it will be argued that in many cases this problem can plausibly be avoided in a purely epistemic manner, without having either to resort to non-classical logics for belief (e.g. paraconsistent logics) or to the denial of the standard closure principle for beliefs. The manner in which this result can be achieved depends on drawing an important distinction between the propositional attitude of belief and the weaker attitude of acceptance such that paradox constituting propositions are accepted but not believed. Paradox-induced explosion is then avoided by noting that while belief may well be closed under material implication or even under logical implication, these sorts of weaker commitments are not subject to closure principles of those sorts. So, this possibility provides us with a less radical way to deal with the existence of paradoxes and it preserves the idea that intelligent agents can actually entertain paradoxes. (shrink)

I defend the thesis that friendship can constitutively require epistemic irrationality against a recent, forceful challenge, raised by proponents of moral and pragmatic encroachment. Defenders of the “encroachment strategy” argue that exemplary friends who are especially slow to believe that their friends have acted wrongly are simply sensitive to the high prudential or moral costs of falsely believing in their friends’ guilt. Drawing on psychological work on epistemic motivation (and in particular on the notion of “need for closure”), I (...) propose a different picture of what friendship requires in the doxastic realm. I argue that contrary to what the encroachment strategy suggests, exemplary friends’ belief formation ought not be guided by a concern with accuracy or error avoidance, but instead by a need to avoid a “specific closure” – namely, a need to avoid concluding in their friends’ guilt. I propose that exemplary friendship often generates a defeasible, doxastic obligation to exemplify such a need, despite its inherent corrupting effects on exemplary friends’ epistemic faculties. (shrink)

In an earlier paper, I presented a novel objection to closure-based skeptical arguments. There I argued that the best account of what makes skeptical scenarios effective cripples the closure-based skeptical arguments that use those scenarios. On behalf of the skeptic, Christopher Buford and Anthony Brueckner have replied to my objection. Here I review my original argument, criticize their replies, and highlight two important issues for further investigation.

Mental causation, idea that it is us – via our minds – who cause bodily actions is as commonsensical as it is indispensable for our understanding of ourselves as rational agents. Somewhat less uncontroversial, but nonetheless widespread (at least among ordinary people) is the idea that the mind is non-physical, following the intuition that what is physical can neither act nor think nor judge morally. Taken together, and cast into a metaphysical thesis, the two intuitions yield interactive dualism: the view (...) that human persons and their minds are non-physical but can nonetheless interact with their bodies, most notably through their brains. This thesis has two main objectives: first, to defend interactive dualism against objections, and second, to show how it can blend in with a physical world in which laws of nature hold. The first part (chapter 1) consists in a brief motivation of interactive dualism as opposed to non-interactive dualism. I argue that non-interactive, epiphenomenalist dualism sacrifices so many crucial aspects of our human existence that interactive dualism is highly to be preferred to it, barring even stronger counterarguments against the latter. It is those putative counterarguments I address in parts II and III. Part II takes on the philosophical objections from the causal closure of the physical and from causal heterogeneity. The former takes the success of physics and physiology as basis for the doctrine of the causal closure of the physical (CCP). I argue against this that there is not only no convincing argument for CCP, but also that any science-based belief in CCP cannot be epistemically justified. As regards the causal heterogeneity objection, it is ‘weighed and found wanting’, because it relies on unwarranted assumptions about causation. In part III, I examine the objection from energy conservation. It roughly says that if interactive dualism were true, then energy would not be conserved, which physics taught us cannot be the case. My reply is that the underlying conception of energy (and momentum) conservation is wrong-headed and not the one that actual physicists use. Instead of being categorical and global, conservation laws are conditional and local, thereby making natural room for mental interaction. Some dualists, however, have sought to make interactive dualism conservation-friendly, notably by invoking quantum physics; I show that these attempts are unnecessary and create more problems than they solve. Finally, in chapter 9, I turn the tables on non-interactionists by investigating current neurophysiological literature on volitional actions, which, though not addressing the question directly, still encourages the interactive dualist picture more than a non-interactionist one. Part IV is about the interplay between interactive dualism and the laws of nature. The ultimate goal is, if possible, to come up with a theory of the laws of nature that explains the lawlike behavior of nature and at the same time makes room for interaction. I begin by pointing out that the laws of nature are or at least should be what physicalists worry about (chapter 10). I then proceed with a historical survey on the development of the notion of laws of nature (chapter 11) that sheds light on its theistic origin. This is followed by an inquiry into the question how a law of nature could possibly be broken (chapter 12) and a survey of the extant metaphysical theories of the laws of nature with special regard to their receptivity to interaction (chapter 13). Finally, in chapter 14 I develop a theory of the laws of nature both faithful to their divine origin and the possibility of mental interaction: dispositionalist divine decretalism, a synthesis of dispositionalism and Jeffrey Koperski’s divine decretalism. (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)

Epistemologists have proposed various norms of assertion to explain when a speaker is in an epistemic position to assert a proposition. In this article I propose a distinct necessary condition on assertibility: that a speaker should assert only what she sensitively believes, where a subject's belief is sensitive just in case the subject would not hold it if it were false. I argue that the Sensitivity Rule underwrites simple explanations for three key features of assertibility that pose explanatory challenges (...) to other prominent proposals: the fact that assertibility is open under known entailment, the general impropriety of assertions that a lottery ticket has lost made purely on the basis of the speaker's knowledge of the odds, and the fact that assertibility varies widely with features of the conversational context. I close by considering three distinct roles the Sensitivity Rule might play in the overall theory of assertibility. (shrink)

Deductive Cogency holds that the set of propositions towards which one has, or is prepared to have, a given type of propositional attitude should be consistent and closed under logical consequence. While there are many propositional attitudes that are not subject to this requirement, e.g. hoping and imagining, it is at least prima facie plausible that Deductive Cogency applies to the doxastic attitude involved in propositional knowledge, viz. belief. However, this thought is undermined by the well-known preface paradox, leading (...) a number of philosophers to conclude that Deductive Cogency has at best a very limited role to play in our epistemic lives. I argue here that Deductive Cogency is still an important epistemic requirement, albeit not as a requirement on belief. Instead, building on a distinction between belief and acceptance introduced by Jonathan Cohen and recent developments in the epistemology of understanding, I propose that Deductive Cogency applies to the attitude of treating propositions as given in the context of attempting to understand a given phenomenon. I then argue that this simultaneously accounts for the plausibility of the considerations in favor of Deductive Cogency and avoids the problematic consequences of the preface paradox. (shrink)

I present an approach to our conceiving absolute impossibilities—things which obtain at no possible world—in terms of ceteris paribus intentional operators: variably restricted quantifiers on possible and impossible worlds based on world similarity. The explicit content of a representation plays a role similar in some respects to the one of a ceteris paribus conditional antecedent. I discuss how such operators invalidate logical closure for conceivability, and how similarity works when impossible worlds are around. Unlike what happens with ceteris paribus (...) counterfactual conditionals, the closest worlds are relevantly closest belief-worlds: closest to how things are believed to be, rather than to how they are. Also, closeness takes into account apriority and the opacity of intentional contexts. (shrink)

The Preface Paradox is often discussed for its implications for rational belief. Much less discussed is a variant of the Preface Paradox for knowledge. In this paper, I argue that the most plausible closure-friendly resolution to the Preface Paradox for Knowledge is to say that in any given context, we do not know much. I call this view “Socraticism”. I argue that Socraticism is the most plausible view on two accounts—(1) this view is compatible with the claim that (...) most of our knowledge ascriptions are true, and (2) provided that (1) is true, the costs of accepting Socraticism are much less than the costs of accepting any other resolution to the Paradox. I argue for (1) in Section 2 by developing a question-sensitive contextualist model for knowledge that shows how Socraticism is compatible with the claim that most of our knowledge ascriptions are true. I also argue how this contextualist model can achieve this result where other contextualist models fail. I then consider other closure-friendly solutions to the paradox in Section 3 and show how accepting those solutions forces us to give up a number of plausible epistemic principles. (shrink)

What can we learn from cases of knowledge from falsehood? Critics of knowledge-first epistemology have argued that these cases provide us with good reason for rejecting the knowledge accounts of evidence, justification, and the norm of belief. I shall offer a limited defense of the knowledge-first approach to these matters. Knowledge from falsehood cases should undermine our confidence in like-from-like reasoning in epistemology. Just as we should be open to the idea that knowledge can come from non-knowledge, we should (...) be open to the idea that justified beliefs can come from unjustified beliefs. (shrink)

I want to model a finite, fallible cognitive agent who imagines that p in the sense of mentally representing a scenario—a configuration of objects and properties—correctly described by p. I propose to capture imagination, so understood, via variably strict world quantifiers, in a modal framework including both possible and so-called impossible worlds. The latter secure lack of classical logical closure for the relevant mental states, while the variability of strictness captures how the agent imports information from actuality in the (...) imagined non-actual scenarios. Imagination turns out to be highly hyperintensional, but not logically anarchic. Section 1 sets the stage and impossible worlds are quickly introduced in Sect. 2. Section 3 proposes to model imagination via variably strict world quantifiers. Section 4 introduces the formal semantics. Section 5 argues that imagination has a minimal mereological structure validating some logical inferences. Section 6 deals with how imagination under-determines the represented contents. Section 7 proposes additional constraints on the semantics, validating further inferences. Section 8 describes some welcome invalidities. Section 9 examines the effects of importing false beliefs into the imagined scenarios. Finally, Sect. 10 hints at possible developments of the theory in the direction of two-dimensional semantics. (shrink)

Why do our intuitive knowledge ascriptions shift when a subject's practical interests are mentioned? Many efforts to answer this question have focused on empirical linguistic evidence for context sensitivity in knowledge claims, but the empirical psychology of belief formation and attribution also merits attention. The present paper examines a major psychological factor (called ?need-for-closure?) relevant to ascriptions involving practical interests. Need-for-closure plays an important role in determining whether one has a settled belief; it also influences the (...) accuracy of one's cognition. Given these effects, it is a mistake to assume that high- and low-stakes subjects provided with the same initial evidence are perceived to enjoy belief formation that is the same as far as truth-conducive factors are concerned. This mistaken assumption has underpinned contextualist and interest-relative invariantist treatments of cases in which contrasting knowledge ascriptions are elicited by descriptions of subjects with the same initial information and different stakes. The paper argues that intellectualist invariantism can easily accommodate such cases. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, (...) undecidable propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for epistemic (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

Even if our justified beliefs are closed under known entailment, there may still be instances of transmission failure. Transmission failure occurs when P entails Q, but a subject cannot acquire a justified belief that Q by deducing it from P. Paradigm cases of transmission failure involve inferences from mundane beliefs (e.g., that the wall in front of you is red) to the denials of skeptical hypotheses relative to those beliefs (e.g., that the wall in front of you is not (...) white and lit by red lights). According to the Bayesian explanation, transmission failure occurs when (i) the subject’s belief that P is based on E, and (ii) P(Q|E) P(Q). No modifications of the Bayesian explanation are capable of accommodating such cases, so the explanation must be rejected as inadequate. Alternative explanations employing simple subjunctive conditionals are fully capable of capturing all of the paradigm cases, as well as those missed by the Bayesian explanation. (shrink)