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)

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.

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)

Prior to Kripke's seminal work on the semantics of modal logic, McKinsey offered an alternative interpretation of the necessity operator, inspired by the Bolzano-Tarski notion of logical truth. According to this interpretation, `it is necessary that A' is true just in case every sentence with the same logical form as A is true. In our paper, we investigate this interpretation of the modal operator, resolving some technical questions, and relating it to the logical interpretation of modality and some views (...) in modal metaphysics. In particular, we present an hitherto unpublished solution to problems 41 and 42 from Friedman's 102 problems, which uses a different method of proof from the solution presented in the paper of Tadeusz Prucnal. (shrink)

There has been much discussion recently of what has been labeled the “Brown-Boghossian-McKinsey”, “Brown-McKinsey” or sometimes just “McKinsey” arguments for the incompatibility of externalism and self-knowledge. However, while the three author's arguments have been treated as interchangeable, they are not identical. In particular, Brown’s and Boghossian’s arguments have a fairly serious flaw that cannot so easily be attributed to McKinsey. In what follows, I’ll (1) present a version of the ‘received’ “Brown-Boghossian-McKinsey” argument, (2) outline what (...) I take to be the most serious objection to it, (3) explain why this sort of objection does not seem, or do not seem immediately, to tell against McKinsey’s argument, and (4) suggest a number of alternative responses that might apply to McKinsey as well. (shrink)

I look at incompatibilist arguments aimed at showing that the conjunction of the thesis that a subject has privileged, a priori access to the contents of her own thoughts, on the one hand, and of semantic externalism, on the other, lead to a putatively absurd conclusion, namely, a priori knowledge of the external world. I focus on arguments involving a variety of externalism resulting from the singularity or object-dependence of certain terms such as the demonstrative ‘that’. McKinsey argues that (...) incompatibilist arguments employing such externalist theses are at their strongest, and conclusively show that privileged access must be rejected. While I agree on the truth of the relevant externalist theses, I show that all plausible versions of the incompatibilist reductio argument as applied to such theses are fundamentally flawed, for these versions of the argument must make assumptions that lead to putatively absurd knowledge of the external world independently of the thesis of privileged access. (shrink)

I look at incompatibilist arguments aimed at showing that the conjunction of the thesis that a subject has privileged, a priori access to the contents of her own thoughts, on the one hand, and of semantic externalism, on the other, lead to a putatively absurd conclusion, namely, a priori knowledge of the external world. I focus on arguments involving a variety of externalism resulting from the singularity or object‐dependence of certain terms such as the demonstrative ‘that’. McKinsey argues that (...) incompatibilist arguments employing such externalist theses are at their strongest, and conclusively show that privileged access must be rejected. While I agree on the truth of the relevant externalist theses, I show that all plausible versions of the incompatibilist reductio argument as applied to such theses are fundamentally flawed, for these versions of the argument must make assumptions that lead to putatively absurd knowledge of the external world independently of the thesis of privileged access. (shrink)

When you think about a particular object, what makes your thought about that object? Roderick Chisholm, Ernest Sosa and Michael McKinsey have defended 'latitudinarian', 'descriptivist', or what I call 'liberal' answers to that question. In this paper I carefully consider the motivation for these liberal views and show how it extends in unanticipated ways to motivate views that are considerably more liberal.

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)

Note first that knowledge of one's own thought-contents would not count as a priori according to the usual criteria for knowledge of this kind. Surely, then, incompatibilists are using this term to refer to some other, stipulatively defined, epistemic property. But could this be, as suggested by McKinsey { 1 99 1: 9), the property of being knowable 'just by thinking' or 'from the armchair'? Certainly not if these were metaphors for knowledge attainable on the basis of reason alone, (...) since self-knowledge would fail to come out a priori in this sense. And exactly the same would happen if the property were that of being knowable by inference, since, according to a common intuition, self-knowledge is noninferential. (shrink)

This is an encyclopedia article about epistemic closure principles. The article explains what they are, their various philosophical uses, how they are argued for or against, and provides an overview of the related literature.

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)

The content of the externalist thesis about the mind depends crucially on how we define the distinction between the internal and the external. According to the usual understanding, the boundary between the internal and the external is the skull or the skin of the subject. In this paper I argue that the usual understanding is inadequate, and that only the new understanding of the external/internal distinction I suggest helps us to understand the issue of the compatibility of externalism and privileged (...) access. (shrink)

In “The Irrelevance of the Diachronic Money-Pump Argument for Acyclicity,” The Journal of Philosophy CX, 8 (August 2013), 460-464, Johan E. Gustafsson contends that if Davidson, McKinsey and Suppes’ diachronic money-pump argument in their "Outlines of a Formal Theory of Value, I," Philosophy of Science 22 (1955), 140-160 is valid, so is the synchronic argument Gustafsson himself offers. He concludes that the latter renders irrelevant diachronic choice considerations in general, and the two best-known diachronic solutions to the money pump (...) problem in particular. I argue here that this reasoning is incorrect, and that Gustafsson’s synchronic argument is faulty on independent grounds. Specifically, it is based on a false analogy between the derivation of a synchronic ordinal ranking from a transitive series of pairwise comparisons, and the putative derivation of such a ranking from an intransitive series. The latter is not possible under the assumption of revealed preference theory, and is highly improbable even if that assumption is rejected. Moreover, Gustafsson’s argument raises issues of fidelity to the historical texts that must be addressed. I conclude that the money pump, and cyclical choice more generally, are necessarily diachronic; and therefore that the two best-known diachronic solutions to the money pump problem remain relevant. (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)

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)

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)