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.

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)

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)

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)

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 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)

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)

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)

Deduction is important to scientific inquiry because it can extend knowledge efficiently, bypassing the need to investigate everything directly. The existence of closure failure—where one knows the premises and that the premises imply the conclusion but nevertheless does not know the conclusion—is a problem because it threatens this usage. It means that we cannot trust deduction for gaining new knowledge unless we can identify such cases ahead of time so as to avoid them. For philosophically engineered examples we have (...) “inner alarm bells” to detect closure failure, but in scientific investigation we would want to use deduction for extension of our knowledge to matters we don’t already know that we couldn’t know. Through a quantitative treatment of how fast probabilistic sensitivity is lost over steps of deduction, I identify a condition that guarantees that the growth of potential error will be gradual; thus, dramatic closure failure is avoided. Whether the condition is fulfilled is often obvious, but sometimes it requires substantive investigation. I illustrate that not only safe deduction but the discovery of dramatic closure failures can lead to scientific advances. (shrink)

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

In response to the claim that certain epistemically defective inferences such as Moore’s argument lead us to the conclusion that we ought to abandon closure, Crispin Wright suggests that we can avoid doing so by distinguishing it from a stronger principle, namely transmission. Where closure says that knowledge of a proposition is a necessary condition on knowledge of anything one knows to entail it, transmission makes a stronger claim, saying that by reasoning deductively from known premises one can (...) thereby acquire knowledge of or justification for the conclusion. Wright’s thought is that in cases such as Moore what is really going on is a failure of transmission, not a failure of closure. The problem with this claim is that it relies on an outdated formulation of closure which few nowadays would find plausible. Once we stipulate that it is the intuitive closure principle that deserves our attention, it becomes far less obvious that the project of diagnosing what is wrong with arguments such as Moore in terms of transmission failure but not closure failure can be vindicated. In order to demonstrate this claim, I consider intuitive closure of propositional justification vs. transmission of propositional justification and concede that perhaps these can come apart in the way that Wright suggests. I then argue that despite this concession, we also need an answer to the question of whether intuitive closure for doxastic justification and transmission for doxastic justification can come apart. We need an answer to this question because our ultimate interest in these issues stems from our interest in whether knowledge obeys closure, not merely whether propositional justification does. I argue that, even on the assumption that there is transmission failure of propositional justification, there is no transmission failure of doxastic justification. And if this is true, then there is no transmission failure of knowledge either. The transmission failure diagnosis of Moore’s argument and its ilk is thus in trouble. (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)

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)

This article aims to provide a structural analysis of the problems related to the easy knowledge problem. The easy knowledge problem is well known. If we accept that we can have basic knowledge via a source without having any prior knowledge about the reliability or accuracy of this source, then we can acquire knowledge about the reliability or accuracy of this source too easily via information delivered by the source. Rejecting any kind of basic knowledge, however, leads into an infinite (...) regress and, plausibly, to skepticism. The article argues that the third alternative, accepting basic knowledge but rejecting easy knowledge, entails closure failure. This is obviously the case for deductive bootstrapping, but, notably, the problem also arises for inductive bootstrapping. Hence, the set of problems related to the easy knowledge problem has the structure of a trilemma. We are forced to accept easy knowledge, closure failure, or skepticism. (shrink)

Carter and Pritchard (2016) and Pritchard (2010, 2012, 2016) have tried to reconcile the intuition that perceptual knowledge requires only limited discriminatory abilities with the closure principle. To this end, they have introduced two theoretical innovations: a contrast between two ways of introducing error-possibilities and a distinction between discriminating and favoring evidence. I argue that their solution faces the “sufficiency problem”: it is unclear whether the evidence that is normally available to adult humans is sufficient to retain knowledge of (...) the entailing proposition and come to know the entailed proposition. I submit that, on either infallibilist or fallibilist views of evidence, Carter and Pritchard have set the bar for deductive knowledge too low. At the end, I offer an alternative solution. I suggest that the knowledge-retention condition of the closure principle is not satisfied in zebra-like scenarios. (shrink)

This paper looks at an argument strategy for assessing the epistemic closure 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 (...) class='Hi'>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)

It’s often thought that the phenomenon of risk aggregation poses a problem for multi-premise closure but not for single-premise closure. But recently, Lasonen-Aarnio and Schechter have challenged this thought. Lasonen-Aarnio argues that, insofar as risk aggregation poses a problem for multi-premise closure, it poses a similar problem for single-premise closure. For she thinks that, there being such a thing as deductive risk, risk may aggregate over a single premise and the deduction itself. Schechter argues that (...) single-premise closure succumbs to risk aggregation outright. For he thinks that there could be a long sequence of competent single-premise deductions such that, even though we are justified in believing the initial premise of the sequence, intutively, we are not justified in believing the final conclusion. This intuition, Schechter thinks, vitiates single-premise closure. In this paper, I defend single-premise closure against the arguments offered by Lasonen-Aarnio and Schechter. (shrink)

Dogmatism holds that an experience or seeming that p can provide prima facie immediate justification for believing p in virtue of its phenomenology. Dogmatism about perceptual justification has appealed primarily to proponents of representational theories of perceptual experience. Call dogmatism that takes perceptual experience to be representational "representational phenomenal dogmatism." As we show, phenomenal seemings play a crucial role in dogmatism of this kind. Despite its conventional appeal to representational theorists, dogmatism is not by definition committed to any particular view (...) of perceptual experience. Naive realists and disjunctivists who hold that perceptual experience is a perceptual relation of direct acquaintance can also endorse dogmatism. Indeed, we argue that they ought to do so. Otherwise, they cannot maintain that relationalism about perceptual experience has an epistemic advantage compared to the representational view. We then show that even if we grant that relationalism has this advantage, only dogmatism that takes perceptual experience to be representational can be extended to account for non-deductive inferential justification. As an account of the latter is required to avoid succumbing to skepticism, relationalism, we argue, does not have the epistemic advantage its defenders claim it has. (shrink)

Many common arguments for physicalism begin with the principle that the cosmos is “causally closed.” But how good are the arguments for causal closure itself? I argue that the deductive, a priori arguments on behalf of causal closure tend to beg the question. The extant inductive arguments fare no better. They commit a sampling error or a non-sequitur, or else offer conclusions that remain compatible with causal openness. In short, we have no good arguments that the physical (...) world is causally closed. (shrink)

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)

In my 1991 paper, AAnti-Individualism and Privileged Access,@ I argued that externalism in the philosophy of mind is incompatible with the thesis that we have privileged , nonempirical access to the contents of our own thoughts.¹ One of the most interesting responses to my argument has been that of Martin Davies (1998, 2000, and Chapter _ above) and Crispin Wright (2000 and Chapter _ above), who describe several types of cases to show that warrant for a premise does not always (...) transmit to a known deductive consequence of that premise, and who contend that this fact under-mines my argument for incompatibilism. I will try to show here that the Davies/Wright point about transmission of warrant does not adversely affect my argument. (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)

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)

Several recent results on the aggregation of judgments over logically connected propositions show that, under certain conditions, dictatorships are the only propositionwise aggregation functions generating fully rational (i.e., complete and consistent) collective judgments. A frequently mentioned route to avoid dictatorships is to allow incomplete collective judgments. We show that this route does not lead very far: we obtain oligarchies rather than dictatorships if instead of full rationality we merely require that collective judgments be deductively closed, arguably a minimal condition of (...) rationality, compatible even with empty judgment sets. We derive several characterizations of oligarchies and provide illustrative applications to Arrowian preference aggregation and Kasher and Rubinsteinís group identification problem. (shrink)

A framing effect occurs when an agent's choices are not invariant under changes in the way a decision problem is presented, e.g. changes in the way options are described (violation of description invariance) or preferences are elicited (violation of procedure invariance). Here we identify those rationality violations that underlie framing effects. We attribute to the agent a sequential decision process in which a “target” proposition and several “background” propositions are considered. We suggest that the agent exhibits a framing effect if (...) and only if two conditions are met. First, different presentations of the decision problem lead the agent to consider the propositions in a different order (the empirical condition). Second, different such “decision paths” lead to different decisions on the target proposition (the logical condition). The second condition holds when the agent's initial dispositions on the propositions are “implicitly inconsistent,” which may be caused by violations of “deductive closure.” Our account is consistent with some observations made by psychologists and provides a unified framework for explaining violations of description and procedure invariance. (shrink)

Critical examination of Alchourrón and Bulygin’s set-theoretic definition of normative system shows that deductive closure is not an inevitable property. Following von Wright’s conjecture that axioms of standard deontic logic describe perfection-properties of a norm-set, a translation algorithm from the modal to the set-theoretic language is introduced. The translations reveal that the plausibility of metanormative principles rests on different grounds. Using a methodological approach that distinguishes the actor roles in a norm governed interaction, it has been shown that (...) metanormative principles are directed second-order obligations and, in particular, that the requirement related to deductive closure is directed to the norm-applier role rather than to the norm-giver role. The approach has been applied to the case of pure derogation yielding a new result, namely, that an independence property is a perfection-property of a norm-set in view of possible derogation. This paper in a polemical way touches upon several points raised by Kristan in his recent paper. (shrink)

Judgment-aggregation theory has always focused on the attainment of rational collective judgments. But so far, rationality has been understood in static terms: as coherence of judgments at a given time, defined as consistency, completeness, and/or deductive closure. This paper asks whether collective judgments can be dynamically rational, so that they change rationally in response to new information. Formally, a judgment aggregation rule is dynamically rational with respect to a given revision operator if, whenever all individuals revise their judgments (...) in light of some information (a learnt proposition), then the new aggregate judgments are the old ones revised in light of this information, i.e., aggregation and revision commute. We prove an impossibility theorem: if the propositions on the agenda are non-trivially connected, no judgment aggregation rule with standard properties is dynamically rational with respect to any revision operator satisfying some basic conditions on revision. Our theorem is the dynamic-rationality counterpart of some well-known impossibility theorems for static rationality. We also explore how dynamic rationality might be achieved by relaxing some of the conditions on the aggregation rule and/or the revision operator. Notably, premise-based aggregation rules are dynamically rational with respect to so-called premise-based revision operators. (shrink)

In solving judgment aggregation problems, groups often face constraints. Many decision problems can be modelled in terms the acceptance or rejection of certain propositions in a language, and constraints as propositions that the decisions should be consistent with. For example, court judgments in breach-of-contract cases should be consistent with the constraint that action and obligation are necessary and sufficient for liability; judgments on how to rank several options in an order of preference with the constraint of transitivity; and judgments on (...) budget items with budgetary constraints. Often more or less demanding constraints on decisions are imaginable. For instance, in preference ranking problems, the transitivity constraint is often contrasted with the weaker acyclicity constraint. In this paper, we make constraints explicit in judgment aggregation by relativizing the rationality conditions of consistency and deductive closure to a constraint set, whose variation yields more or less strong notions of rationality. We review several general results on judgment aggregation in light of such constraints. (shrink)

One of the central tasks of a theory of argumentation is to supply a theory of appraisal: a set of standards and norms according to which argumentation, and the reasoning involved in it, is properly evaluated. In their most general form, these can be understood as rational norms, where the core idea of rationality is that we rightly respond to reasons by according the credence we attach to our doxastic and conversational commitments with the probative strength of the reasons we (...) have for them. Certain kinds of rational failings are so because they are manifestly illogical – for example, maintaining overtly contradictory commitments, violating deductive closure by refusing to accept the logical consequences of one’s present commitments, or failing to track basing relations by not updating one’s commitments in view of new, defeating information. Yet, according to the internal and empirical critiques, logic and probability theory fail to supply a fit set of norms for human reasoning and argument. Particularly, theories of bounded rationality have put pressure on argumentation theory to lower the normative standards of rationality for reasoners and arguers on the grounds that we are bounded, finite, and fallible agents incapable of meeting idealized standards. This paper explores the idea that argumentation, as a set of practices, together with the procedures and technologies of argumentation theory, is able to extend cognition such that we are better able to meet these idealized logical standards, thereby extending our responsibilities to adhere to idealized rational norms. (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)

Group decisions must often obey exogenous constraints. While in a preference aggregation problem constraints are modelled by restricting the set of feasible alternatives, this paper discusses the modelling of constraints when aggregating individual yes/no judgments on interconnected propositions. For example, court judgments in breach-of-contract cases should respect the constraint that action and obligation are necessary and sufficient for liability, and judgments on budget items should respect budgetary constraints. In this paper, we make constraints in judgment aggregation explicit by relativizing the (...) rationality conditions of consistency and deductive closure to a constraint set, whose variation yields more or less strong notions of rationality. This approach of modelling constraints explicitly contrasts with that of building constraints as axioms into the logic, which turns compliance with constraints into a matter of logical consistency and thereby conflates requirements of ordinary logical consistency and requirements dictated by the environment . We present some general impossibility results on constrained judgment aggregation; they are immediate corollaries of known results on judgment aggregation. (shrink)

The paper argues that knowledge is not closed under logical inference. The argument proceeds from the openness of evidential support and the dependence of empirical knowledge on evidence, to the conclusion that knowledge is open. Without attempting to provide a full-fledged theory of evidence, we show that on the modest assumption that evidence cannot support both a proposition and its negation, or, alternatively, that information that reduces the probability of a proposition cannot constitute evidence for its truth, the relation of (...) evidential support is not closed under known entailment. Therefore the evidence-for relation is deductively open regardless of whether evidence is probabilistic or not. Given even a weak dependence of empirical knowledge on evidence, we argue that empirical knowledge is also open. On this basis, we also respond to the strongest argument in support of knowledge closure. Finally, we present a number of significant benefits of our position, namely, offering a unified explanation for a range of epistemological puzzles. (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)

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)

The primary aim of this paper is to critically evaluate the deductive model of ethical applications, which is based on normative ethical theories like deontology and consequentialism, and to show why a number of models have failed to furnish appropriate resolutions to practical moral problems. Here, for the deductive model, I want to call it a “Linear Mechanical Model” because the basic assumption of this model is that if a normative theory is sacrosanct, then the case is as (...) it is. The conclusion derived from the case will also be correct, true and acceptable. However, traditional ethicists used to apply their ethical theories, but they did not know which moral theory was effective on the ground level of reality. The study will show readers how ethical theories are in conflict with each other in the case of euthanasia. In more precise words, “which ethical theories are said to be applied, meta-ethical or normative, or both for the resolution of ethical problems? If normative theories are said to be applied, how the application can take place when it is contrary to our experience, that (then) in a situation of moral crises, no one really applies a theory?” For that, my argument is the linear model has failed because it is rigid, often ignores the agents’ intrinsic values, and has no space to amend it, no matter how bizarre the consequence is. Its alternative is the Inductive model. For that, the paper will take three moral principles (autonomy, beneficence including maleficence, and justice) of Beauchamp & Childress. This suggests us for resolving value-laden moral problems, we should consider some steps such as a) recognising moral issues to start with; b) developing the moral imagination; c) sharpening analytical/critical skills; d) testing out disagreements; e) effecting decisions and behavior; and f) implementation, closure, and process are of vital importance, in other words, it starts with the free and informed consensus of all interested parties, but this model also has been failed because the model could not give a systematic organization to their way of resolution. Here, my argument is that the inductive model provides resolution of the practical problem but ignores what is ethically obligatory, permissible, or wrong in that situation, and there are no appropriate suggestions in the case of a moral crisis. (shrink)

This paper argues that a necessary condition on inferential knowledge is that one knows all the propositions that knowledge depends on. That is, I will argue in support of a principle I call the Knowledge from Knowledge principle: (KFK) S knows that p via inference or reasoning only if S knows all the propositions on which p depends. KFK meshes well with the natural idea that (at least with respect to deductively valid or induc- tively strong arguments) the epistemic status (...) of one’s belief in the conclusion of an argument is a function of the epistemic status of the attitudes one has to the premises of that argument. One gets what one puts in: S’s belief in the conclusion C of an argument A has epistemic status E for S only if S’s belief in each of the premises C depends on also has epistemic status E.1 This is compatible, of course, with the epistemic status of S’s conclusion being greater than the epistemic status of the premises on which the conclusion of her reasoning depends. Furthermore, even though KFK applies more straightforwardly to non-suppositional inferences, we can also plausibly apply the principle to sup- positional reasoning if we treat S’s assuming for the sake of argument that p,2 as S assuming for the sake of argument that she knows that p.3 Although extremely plausible, philosophers have failed to present a concerted case in support of KFK. Most of their energy goes to articulating and/or defending some form of closure principle for knowledge.4 What is more, recently versions of this principle have been dismissed as problematic but I think without the reasons in its support been fully appreciated. This paper is an e fort to change the current state of affairs. Its focus is positive, however: my goal is to make the best case I can in support of KFK.5 To that end, the paper presents the reasons we have to accept KFK (§1), consid- ers an objection to the principle (§2), and situates the principle in the broader normative context of knowledge norms (§3). (shrink)

The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory (...) validating all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker-than-classical K3 logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to--whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non-classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities. (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)

The aim of this paper is that of underlining the actuality and complexity of Murray Bookchin’s production through a brief analysis of the central concepts of his philosophy: social ecology and dialectical naturalism. We argue that, starting from the perspective of a necessary unity of praxis and theory – respectively expressed by the concepts above -, Bookchin fails to take into account the theoretical implication of the interplay of first and second nature, the outcome being a closure of human (...) praxis into a logical and a-historical dimension. Albeit it is philosophically necessary to consider humankind as always already located within an environment whose crisis reflect societal contradictions and viceversa, Bookchin’s naturalism can display the misleading scope of deducting ethics from a natural state, renewing the inherent philosophical fallacies of the Enlightenment era. (shrink)

This paper proposes the feasibility of a second-order approach in cosmology. It is intended to encourage cosmologists to rethink standard ideas in their field, leading to a broader concept of self-organization and of science itself. It is argued, from a cognitive epistemology perspective, that a first-order approach is inadequate for cosmology; study of the universe as a whole must include study of the scientific observer and the process of theorizing. Otherwise, concepts of self-organization at the cosmological scale remain constrained by (...) unacknowledged assumptions and biases. Examples of limiting notions are discussed in the context of alternatives. To include the role of the theorist does not mean reducing science to subjective or sociological terms. On the contrary, second-order science would provide a more complete portrait of nature. The work of cosmologist Lee Smolin is discussed as a candidate example of second-order cosmology. (shrink)

Causal closure arguments against interactionist dualism are currently popular amongst physicalists. Such an argument appeals to some principles of the causal closure of the physical, together with certain other premises, to conclude that at least some mental events are identical with physical events. However, it is crucial to the success of any such argument that the physical causal closure principle to which it appeals is neither too strong nor too weak by certain standards. In this paper, it (...) is argued that various forms of naturalistic dualism, of an emergentist character, are consistent with the strongest physical causal closure principles that can plausibly be advocated. (shrink)

According to some philosophers, we are “cognitively closed” to the answers to certain problems. McGinn has taken the next step and offered a list of examples: the mind/body problem, the problem of the self and the problem of free will. There are naturalistic, scientific answers to these problems, he argues, but we cannot reach them because of our cognitive limitations. In this paper, we take issue with McGinn's thesis as the most well-developed and systematic one among the so-called “new mysterians”. (...) McGinn aims to establish a strong, representational notion of cognitive closure: a principled inaccessibility of a true theory of certain properties of the world, but he offers arguments that only bear on difficulties with psychologically grasping the correct answers. The latter we label psychological closure. We argue that representational closure does not follow from psychological closure, and that McGinn's case therefore falters. We could very well be able to represent the correct answer to some question, even without being able to grasp that answer psychologically. McGinn's mistake in deriving representational closure from psychological closure rests on a fallacy of equivocation relating to the concept of ‘understanding’. By making this distinction explicit, we hope to improve our thinking about the limits of science in particular and human knowledge in general. (shrink)

The acceptance of causal closure has had a profoundly limiting effect on the philosophical treatment of sui generis mental causation in recent decades. Philosophical treatments of special divine action have been likewise hampered by a widespread commitment to closure. If fundamental reality is as closure tells us it is, then nonphysical minds—human and divine— are either causally impotent or redundant. In this paper, I reject this limitation as baseless. Specifically, I will show how Hempel’s dilemma poses a (...) far greater challenge when applied to a causal closure principle than it did to the task of defining physicalism. Reponses to the dilemma can be used to disambiguate closure, but not without significant cost. In light of Hempel’s dilemma, there is no conception of closure that can do all of the following: rule out sui generis mental causation, have a reasonable chance of being true, and avoid problematic circularity. At the end of the day, I maintain that closure, properly understood, is, or ought to be, just one methodological stance among many. If this is correct, it is a stance that a theist can freely reject. (shrink)

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

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)

Epistemologists understand radical skepticism as arising from two principles: Closure and Underdetermination. Both possess intuitive prima facie support for their endorsement. Understanding how they engender skepticism is crucial for any reasonable anti-skeptical attempt. The contemporary discussion has focused on elucidating the relationship between them to ascertain whether they establish distinct skeptical questions and which of the two constitutes the ultimately fundamental threat. Major contributions to this debate are due to Brueckner, Cohen, and Pritchard. This contribution aims at defending Brueckner’s (...) contention that underdetermination expresses the fundamental skeptical threat and that the closure-based argument can ultimately be reduced to it, at least concerning skeptical contexts. This will be achieved by undermining Cohen’s objections to Brueckner on both counts. Cohen’s argument endorses a picture of evidential underdetermination, which, while apt for non-skeptical contexts, cannot be applied to radical skepticism. A comparison with a case of scientific underdetermination is developed to argue for this idea. Our argument is then applied to the principle equivalence issue and to objections against it. It is then shown how this analysis possesses a distinctive effect on our understanding of the skeptical threat and the assessment of successful anti-skeptical strategies. (shrink)

Knowledge representation (KR) is actually more than representation: It involves also inference, namely inference of “new” knowledge, i.e. new facts. Logic programming is a suitable KR medium, but more often than not discussions on this programming paradigm focus on aspects other than KR. In this paper, I elaborate on the general theory of logic programming and give the essentials of two of its main implementations, to wit, Prolog and Datalog, from the viewpoint of deductive computing over knowledge bases, which (...) includes deductive programming. (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 epistemic closure. 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)

The principle of epistemic closure is the claim that what is known to follow from knowledge is known to be true. This intuitively plausible idea is endorsed by a vast majority of knowledge theorists. There are significant problems, however, that have to be addressed if epistemic closure – closed knowledge – is endorsed. The present essay locates the problem for closed knowledge in the separation it imposes between knowledge and evidence. Although it might appear that all that stands (...) between knowing the truth of the premises of a valid inference and knowledge of its conclusion is inferring it from the premises, the evidence for each of the premises may jointly count against the conclusion. The intuitive view regarding inferred knowledge says one thing, the evidence says another. One epistemological framework that seems to have the resources to resolve this tension endorses the view that knowledge always requires conclusive evidence. A second framework resolves the tension by limiting the scope of the closure principle. Only inferences drawn directly from propositions contained in the scope of a single knowledge operator are considered closed. The aim of the present essay is to revive the unpopular third option, the idea that knowledge is open. The essay proceeds by arguing that in different ways the two former frameworks only succeed in relocating the problem, not in resolving it. The first framework, the infallibilist view, relocates the problem to a sharp separation between knowledge of the occurrences of events from knowledge of their chance of occurring, a separation leading to several significant additional problems. The fallibilist view, the second framework, in endorsing closure neglects to take into full account the ways in which evidence fails to be transitive. For instance, evidence can count in favor of a conjunction while counting against each of its conjuncts. This fact, which is argued for in the essay on probabilistic as well as non-probabilistic grounds, is used as the foundation of an argument against closed knowledge that can be used as a way to understand several of the most fundamental challenges of epistemology. Not only can an open knowledge view that is based on open evidence resolve all these problems in a simple and natural way, it can also respond to formidable challenges that significantly hinder other open knowledge views. There are good reasons, then, to view both knowledge and evidence as open. (shrink)

According to the principle of Conjunction Closure, if one has justification for believing each of a set of propositions, one has justification for believing their conjunction. The lottery and preface paradoxes can both be seen as posing challenges for Closure, but leave open familiar strategies for preserving the principle. While this is all relatively well-trodden ground, a new Closure-challenging paradox has recently emerged, in two somewhat different forms, due to Backes :3773–3787, 2019a) and Praolini :715–726, 2019). This (...) paradox synthesises elements of the lottery and the preface and is designed to close off the familiar Closure-preserving strategies. By appealing to a normic theory of justification, I will defend Closure in the face of this new paradox. Along the way I will draw more general conclusions about justification, normalcy and defeat, which bear upon what Backes :2877–2895, 2019b) has dubbed the ‘easy defeat’ problem for the normic theory. (shrink)