In this paper I argue first, that a contrastive account of self-knowledge and the propositional attitudes entails an anti-individualist account of propositional attitude concepts, second, that the final account provides a solution to the McKinsey paradox, and third, that the account has the resources to explain why certain anti-skeptical arguments fail.

In this paper, I focus on the Armchair Access Problem for E=K as presented by Nicholas Silins (2005), and I argue, contra Silins, that it does not represent a real threat to E=K. More precisely, I put forward two lines of response, both of which put pressure on the main assumption of the argument, namely, the Armchair Access thesis. The first line of response focuses on its scope, while the second line of response focuses on its nature. The second line (...) of response is the most interesting one, for it represents the framework within which I develop a novel account of second-order knowledge, one that involves evaluation of counterfactual conditionals and the employment of our imaginative capacities, i.e., an imagination-based account of second-order knowledge. The two lines of response are shown to be jointly compatible and mutually supportive. I then conclude that the Armchair Access Problem is not a challenge for E=K, yet it relies on the ambiguity of the notion of armchair knowledge underpinning the Armchair Access thesis. (shrink)

In this paper, I consider the so-called Access Problem for Duncan Pritchard’s Epistemological Disjunctivism (2012). After reconstructing Pritchard’s own response to the Access Problem, I argue that in order to assess whether Pritchard’s response is a satisfying one, we first need an account of the notion of ‘Reflective Access’ that underpins Pritchard’s Epistemological Disjunctivism. I provide three interpretations of the notion of Reflective Access: a metaphysical interpretation, a folk interpretation, and an epistemic interpretation. I argue that none of these three (...) interpretations comes without problems. I conclude that, until we have a clear and unproblematic account of Reflective Access, the Access Problem remains a challenge for Pritchard’s Epistemological Disjunctivism. (shrink)

Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with (...) the so-called paradoxes of higher-order vagueness. We offer a proposal that makes strides on both issues. We argue that the intuitionist’s characteristic rejection of any third alethic value alongside true and false is best elaborated by taking the normal modal system S4M to be the sentential logic of the operator ‘it is clearly the case that’. S4M opens the way to an account of higher-order vagueness which avoids the paradoxes that have been thought to infect the notion. S4M is one of the modal counterparts of the intuitionistic sentential calculus and we use this fact to explain why IPC is the correct sentential logic to use when reasoning with vague statements. We also show that our key results go through in an intuitionistic version of S4M. Finally, we deploy our analysis to reply to Timothy Williamson’s objections to intuitionistic treatments of vagueness. (shrink)

This paper intends to further the understanding of the formal properties of (higher-order) vagueness by connecting theories of (higher-order) vagueness with more recent work in topology. First, we provide a “translation” of Bobzien's account of columnar higher-order vagueness into the logic of topological spaces. Since columnar vagueness is an essential ingredient of her solution to the Sorites paradox, a central problem of any theory of vagueness comes into contact with the modern mathematical theory of topology. Second, Rumfitt’s recent topological (...) reconstruction of Sainsbury’s theory of prototypically defined concepts is shown to lead to the same class of spaces that characterize Bobzien’s account of columnar vagueness, namely, weakly scattered spaces. Rumfitt calls these spaces polar spaces. They turn out to be closely related to Gärdenfors’ conceptual spaces, which have come to play an ever more important role in cognitive science and related disciplines. Finally, Williamson’s “logic of clarity” is explicated in terms of a generalized topology (“locology”) that can be considered an alternative to standard topology. Arguably, locology has some conceptual advantages over topology with respect to the conceptualization of a boundary and a borderline. Moreover, in Williamson’s logic of clarity, vague concepts with respect to a notion of a locologically inspired notion of a “slim boundary” are (stably) columnar. Thus, Williamson’s logic of clarity also exhibits a certain affinity for columnar vagueness. In sum, a topological perspective is useful for a conceptual elucidation and unification of central aspects of a variety of contemporary accounts of vagueness. (shrink)

Abstract. The aim of this paper is to present a topological method for constructing discretizations (tessellations) of conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. Alexandroff spaces, as they are called today, have many interesting properties that distinguish them from other topological spaces. In particular, they exhibit a 1-1 correspondence between their specialization orders and their topological structures. Recently, a special type of Alexandroff spaces was (...) used by Ian Rumfitt to elucidate the logic of vague concepts in a new way. According to his approach, conceptual spaces such as the color spectrum give rise to classical systems of concepts that have the structure of atomic Boolean algebras. More precisely, concepts are represented as regular open regions of an underlying conceptual space endowed with a topological structure. Something is subsumed under a concept iff it is represented by an element of the conceptual space that is maximally close to the prototypical element p that defines that concept. This topological representation of concepts comes along with a representation of the familiar logical connectives of Aristotelian syllogistics in terms of natural settheoretical operations that characterize regular open interpretations of classical Boolean propositional logic. In the last 20 years, conceptual spaces have become a popular tool of dealing with a variety of problems in the fields of cognitive psychology, artificial intelligence, linguistics and philosophy, mainly due to the work of Peter Gärdenfors and his collaborators. By using prototypes and metrics of similarity spaces, one obtains geometrical discretizations of conceptual spaces by so-called Voronoi tessellations. These tessellations are extensionally equivalent to topological tessellations that can be constructed for Alexandroff spaces. Thereby, Rumfitt’s and Gärdenfors’s constructions turn out to be special cases of an approach that works for a more general class of spaces, namely, for weakly scattered Alexandroff spaces. This class of spaces provides a convenient framework for conceptual spaces as used in epistemology and related disciplines in general. Alexandroff spaces are useful for elucidating problems related to the logic of vague concepts, in particular they offer a solution of the Sorites paradox (Rumfitt). Further, they provide a semantics for the logic of clearness (Bobzien) that overcomes certain problems of the concept of higher2 order vagueness. Moreover, these spaces help find a natural place for classical syllogistics in the framework of conceptual spaces. The crucial role of order theory for Alexandroff spaces can be used to refine the all-or-nothing distinction between prototypical and nonprototypical stimuli in favor of a more fine-grained gradual distinction between more-orless prototypical elements of conceptual spaces. The greater conceptual flexibility of the topological approach helps avoid some inherent inadequacies of the geometrical approach, for instance, the so-called “thickness problem” (Douven et al.) and problems of selecting a unique metric for similarity spaces. Finally, it is shown that only the Alexandroff account can deal with an issue that is gaining more and more importance for the theory of conceptual spaces, namely, the role that digital conceptual spaces play in the area of artificial intelligence, computer science and related disciplines. Keywords: Conceptual Spaces, Polar Spaces, Alexandroff Spaces, Prototypes, Topological Tessellations, Voronoi Tessellations, Digital Topology. (shrink)

Dretske is a “conciliatory skeptic” on self-knowledge. Take some subject S such that S thinks that P and S knows that she has thoughts. Dretske’s theory can be put as follows: S has a privileged way of knowing what she thinks, but she has no privileged way of knowing that she thinks it. There is much to be said on behalf of conciliatory skepticism and Dretske’s defense of it. We aim to show, however, that Dretske’s defense fails, in that if (...) his defense of CS’s skeptical half succeeds, then his defense of CS’s conciliatory half fails. We then suggest a potential way forward. We suggest in particular that the correct way of being a Dretskean conciliatory skeptic is to deny that S has a privileged way of knowing about her thoughts, but to grant that she is nonetheless an authority on her thoughts. (shrink)

The aim of this paper is to show that every topological space gives rise to a wealth of topological models of the modal logic S4.1. The construction of these models is based on the fact that every space defines a Boolean closure algebra (to be called a McKinsey algebra) that neatly reflects the structure of the modal system S4.1. It is shown that the class of topological models based on McKinsey algebras contains a canonical model that can be (...) used to prove a completeness theorem for S4.1. Further, it is shown that the McKinsey algebra MKX of a space X endoewed with an alpha-topologiy satisfies Esakia's GRZ axiom. (shrink)

The paradox of pain refers to the idea that the folk concept of pain is paradoxical, treating pains as simultaneously mental states and bodily states. By taking a close look at our pain terms, this paper argues that there is no paradox of pain. The air of paradox dissolves once we recognize that pain terms are polysemous and that there are two separate but related concepts of pain rather than one.

nated discussion of the semantics of such verbs. I will call this view.

Supererogatory acts—good deeds “beyond the call of duty”—are a part of moral common sense, but conceptually puzzling. I propose a unified solution to three of the most infamous puzzles: the classic Paradox of Supererogation (if it’s so good, why isn’t it just obligatory?), Horton’s All or Nothing Problem, and Kamm’s Intransitivity Paradox. I conclude that supererogation makes sense if, and only if, the grounds of rightness are multi-dimensional and comparative.

I distinguish paradoxes and hypodoxes among the conundrums of time travel. I introduce ‘hypodoxes’ as a term for seemingly consistent conundrums that seem to be related to various paradoxes, as the Truth-teller is related to the Liar. In this article, I briefly compare paradoxes and hypodoxes of time travel with Liar paradoxes and Truth-teller hypodoxes. I also discuss Lewis’ treatment of time travel paradoxes, which I characterise as a Laissez Faire theory of time travel. Time travel paradoxes are impossible according (...) to Laissez Faire theories, while it seems hypodoxes are possible. (shrink)

This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning---one which takes meaning to be constituted by assertibility and deniability conditions---and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system---ST---that conservatively extends (...) classical logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered. (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)

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)

It is widely accepted that there is what has been called a non-hypocrisy norm on the appropriateness of moral blame; roughly, one has standing to blame only if one is not guilty of the very offence one seeks to criticize. Our acceptance of this norm is embodied in the common retort to criticism, “Who are you to blame me?”. But there is a paradox lurking behind this commonplace norm. If it is always inappropriate for x to blame y for (...) a wrong that x has committed, then all cases in which x blames x (i.e. cases of self-blame) are rendered inappropriate. But it seems to be ethical common-sense that we are often, sadly, in position (indeed, excellent, privileged position) to blame ourselves for our own moral failings. And thus we have a paradox: a conflict between the inappropriateness of hypocritical blame, and the appropriateness of self-blame. We consider several ways of resolving the paradox, and contend none is as defensible as a position that simply accepts it: we should never blame ourselves. In defending this startling position, we defend a crucial distinction between self-blame and guilt. (shrink)

We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. _Reckless_ theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; _timid_ theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; _non-transitive_ theories deny the principle that, if A is better than B and B is better than C, then A must be better than (...) C. Having set up this trilemma, we study its horns. Non-transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty. (shrink)

There is a fairly general consensus that names are Millian (or Russellian) genuine terms, that is, are singular terms whose sole semantic function is to introduce a referent into the propositions expressed by sentences containing the term. This answers the question as to what sort of proposition is expressed by use of sentences containing names. But there is a second serious semantic problem about proper names, that of how the referents of proper names are determined. This is the question that (...) I will discuss in this paper. Various views consistent with Millianism have been proposed as to how the semantic referents of proper names are determined. These views can be classified into (1) description theories and (2) causal theories, but they can also be classified into (3) social practice theories, on which a name’s referent is determined by a social practice involving the referent, and (4) individualistic theories, on which the referent of the use of a name is determined by the speaker’s state of mind. Here I argue against social practice theories of the sorts proposed by Kripke and Evans and in favor of an individualistic approach to name reference. I argue that social practice is irrelevant to determining name reference and that, as a consequence, names have no meanings in natural languages. In the second part of the paper I motivate and propose a new form of individualistic theory which incorporates features of both description theories and Evans’s social practice theory. (shrink)

Counterfactuals are somewhat tolerant. Had Socrates been at least six feet tall, he need not have been exactly six feet tall. He might have been a little taller—he might have been six one or six two. But while he might have been a little taller, there are limits to how tall he would have been. Had he been at least six feet tall, he would not have been more than a hundred feet tall, for example. Counterfactuals are not just tolerant, (...) then, but bounded. This paper presents a surprising paradox: If counterfactuals are tolerant and bounded, then we can prove a flat contradiction using natural rules of inference. Something has to go then. But what? (shrink)

This paper gives a definition of self-reference on the basis of the dependence relation given by Leitgeb (2005), and the dependence digraph by Beringer & Schindler (2015). Unlike the usual discussion about self-reference of paradoxes centering around Yablo's paradox and its variants, I focus on the paradoxes of finitary characteristic, which are given again by use of Leitgeb's dependence relation. They are called 'locally finite paradoxes', satisfying that any sentence in these paradoxes can depend on finitely many sentences. I (...) prove that all locally finite paradoxes are self-referential in the sense that there is a directed cycle in their dependence digraphs. This paper also studies the 'circularity dependence' of paradoxes, which was introduced by Hsiung (2014). I prove that the locally finite paradoxes have circularity dependence in the sense that they are paradoxical only in the digraph containing a proper cycle. The proofs of the two results are based directly on König's infinity lemma. In contrast, this paper also shows that Yablo's paradox and its nested variant are non-self-referential, and neither McGee's paradox nor the omega-cycle liar paradox has circularity dependence. (shrink)

In “Naming and Necessity” Saul Kripke describes some cases which, he claims, provide counterexamples both to cluster theories and, more generally, to description theories of proper names. My view of these cases is that while they do not provide counterexamples to cluster theories, they can be used to provide evidence against single-description theories. In this paper I shall defend both of the claims involved in my view.

This is an anthology of ?fteen papers concerning various philosophical problems related to the topic of self-knowledge. All but one of the papers were previously unpublished, and all but two are descendants of presentations at a conference on self-knowledge held at the University of St Andrews in 1995. The collection.

What José Luis Bermúdez calls the paradox of self-consciousness is essentially the conflict between two claims: (1) The capacity to use first-personal referential devices like “I” must be explained in terms of the capacity to think first-person thoughts. (2) The only way to explain the capacity for having a certain kind of thought is by explaining the capacity for the canonical linguistic expression of thoughts of that kind. (Bermúdez calls this the “Thought-Language Principle”.) The conflict between (1) and (2) (...) is obvious enough. However, if a paradox is an unacceptable conclusion drawn from apparently valid reasoning from apparently true premises, then Bermúdez’s conflict is no paradox. It is rather a conflict between the view that thought must be explained in terms of language, and the view that first person linguistic reference must be explained in terms of first-person thought. Neither view is immediately obvious, and nor is it obvious that the arguments for either are equally compelling. What we have here is a difference of philosophical opinion, not a paradox. (shrink)

I offer a new, limited solution to divine hiddenness based on a particular epistemic paradox: sometimes, knowing about a desired outcome or relevant features of that desired outcome would prevent the outcome in question from occurring. I call these cases epistemically self-defeating situations. This solution, in essence, says that divine hiddenness or silence is a necessary feature of at least some morally excellent or desirable states of affairs. Given the nature of the paradox, an omniscient being cannot completely (...) eliminate hiddenness, just as an omnipotent being cannot create a rock so heavy that they cannot lift it. Epistemically self-defeating situations provide an undercutting defeater for the assumption that any nonresistant nonbeliever could always, at any time, be in conscious relationship with a perfectly loving God. Thankfully, silence is a temporary feature of epistemically self-defeating situations: once the outcome is achieved, agents can know in full. (shrink)

I present a paradoxical combination of desires. I show why it's paradoxical, and consider ways of responding. The paradox saddles us with an unappealing trilemma: either we reject the possibility of the case by placing surprising restrictions on what we can desire, or we deny plausibly constitutive principles linking desires to the conditions under which they are satisfied, or we revise some bit of classical logic. I argue that denying the possibility of the case is unmotivated on any reasonable (...) way of thinking about mental content, and rejecting those desire-satisfaction principles leads to revenge paradoxes. So the best response is a non-classical one, according to which certain desires are neither determinately satisfied nor determinately not satisfied. Thus, theorizing about paradoxical propositional attitudes helps constrain the space of possibilities for adequate solutions to semantic paradoxes more generally. (shrink)

This paper brings two fresh perspectives on Lewis’s theory of time travel. First: many key aspects and theoretical desiderata of Lewis’s theory can be captured in a framework that does not commit to eternalism about time. Second: implementing aspects of Lewisian time travel in a non-eternalist framework provides theoretical resources for a better treatment of time travel to the future. While time travel to the past has been extensively analyzed, time travel to the future has been comparatively underexplored. I make (...) progress on this topic. Along the way, I discuss Lewis’s lesser-known time travel oeuvre, especially his volume of correspondence and lectures on the topic collected in Beebee and Fisher (2020) and Janssen-Lauret & MacBride (forthcoming). Lewis’s body of unpublished work on time travel yields fruitful insights into his broader thinking on the subject. (shrink)

Philosophers have long argued that duties to oneself are paradoxical, as they seem to entail an incoherent power to release oneself from obligations. I argue that self-release is possible, both as a matter of deontic logic and of metaethics.

The present work outlines a logical and philosophical conception of propositions in relation to a group of puzzles that arise by quantifying over them: the Russell-Myhill paradox, the Prior-Kaplan paradox, and Prior's Theorem. I begin by motivating an interpretation of Russell-Myhill as depending on aboutness, which constrains the notion of propositional identity. I discuss two formalizations of of the paradox, showing that it does not depend on the syntax of propositional variables. I then extend to propositions a (...) modal predicative response to the paradoxes articulated by an abstraction principle for propositions. On this conception, propositions are “shadows” of the sentences that express them. Modal operators are used to uncover the implicit relation of dependence that characterizes propositions that are about propositions. The benefits of this approach are shown by application to other intensional puzzles. The resulting view is an alternative to the plenitudinous metaphysics of impredicative comprehension principles. (shrink)

En décadas recientes se ha considerado que una formulación adecuada del autoconocimiento (AC) debería ser consistente con la tesis del externalismo (E). Michael McKinsey es uno de los personajes que ha enfatizado con mayor ahínco que la conjunción de ambas posturas es inconsistente. En este trabajo defiendo la idea de que las objeciones presentadas por McKinsey no afectan de manera importante la formulación davidsoniana de la autoridad de la primera persona (AC3) en conjunción con (E); señalo, además, que (...) si no pudiera hacerse una reconstrucción à la Davidson de (AC3) desde la postura de McKinsey sería en virtud de las diferencias metodológicas, semánticas, epistemológicas y ontológicas entre ambos autores, y no debido a que esta reconstrucción en sí misma sea incompatible con el externalismo. (shrink)

Our evidence can be about different subject matters. In fact, necessarily equivalent pieces of evidence can be about different subject matters. Does the hyperintensionality of ‘aboutness’ engender any hyperintensionality at the level of rational credence? In this paper, I present a case which seems to suggest that the answer is ‘yes’. In particular, I argue that our intuitive notions of independent evidence and inadmissible evidence are sensitive to aboutness in a hyperintensional way. We are thus left with a paradox. (...) While there is strong reason to think that rational credence cannot make such hyperintensional distinctions, our intuitive judgements about certain cases seem to demand that it does. (shrink)

This paper is concerned with the paradox of decrease. Its aim is to defend the answer to this puzzle that was propounded by its originator, namely, the Stoic philosopher Chrysippus. The main trouble with this answer to the paradox is that it has the seemingly problematic implication that a material thing could perish due merely to extrinsic change. It follows that in order to defend Chrysippus’ answer to the paradox, one has to explain how it could be (...) that Theon is destroyed by the amputation without changing intrinsically. In this paper, I shall answer this challenge by appealing to the broadly Aristotelian idea that at least some of the proper parts of a material substance are ontologically dependent on that substance. I will also appeal to this idea in order to offer a new solution to the structurally similar paradox of increase. In this way, we will end up with a unified solution to two structurally similar paradoxes. (shrink)

Given any proposition, is it possible to have rationally acceptable attitudes towards it? Absent reasons to the contrary, one would probably think that this should be possible. In this paper I provide a reason to the contrary. There is a proposition such that, if one has any opinions about it at all, one will have a rationally unacceptable set of propositional attitudes—or if one doesn’t, one will end up being cognitively imperfect in some other manner. The proposition I am concerned (...) with is a self-referential propositional attitude ascription involving the propositional attitude of rejection. Given a basic assumption about what constitutes irrationality, and a few assumptions about the nature of cognitively ideal agents, a paradox results. This paradox is superficially like the Liar, but it is importantly different in that no alethic notions are involved at all. As such, it stands independent of the Liar and is not a ‘revenge’ version of it. After setting out the paradox I discuss possible responses. After considering several I argue that one is best off simply accepting that the paradox shows us something surprising and interesting about rationality: that some cognitive shortfall is unavoidable even for ideal agents. I argue that nothing disastrous follows from accepting this conclusion. (shrink)