This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine 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 cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic two-dimensional semantics. 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} are 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 my 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. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that 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 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 the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent 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 while bypassing the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. 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 identity and diversity of individual objects may be grounded or ungrounded, and intrinsic or contextual. Intrinsic individuation can be grounded in haecceities, or absolute discernibility. Contextual individuation can be grounded in relations, but this is compatible with absolute, relative or weak discernibility. Contextual individuation is compatible with the denial of haecceitism, and this is more harmonious with science. Structuralism implies contextual individuation. In mathematics contextual individuation is in general primitive. In physics contextual individuation may be grounded in relations via (...) weak discernibility. (shrink)

According to actualism about possible worlds everything that exists is actual. Possible worlds and individuals are actually existing abstract parts of the actual world. Aristotelian actualism is a view that there are only actual individuals but no possible ones, nor their individual abstract representatives. Because of that, our actualist account of modality should differ depending on whether it concerns actual individuals or possible ones. The main goal of the dissertation is to develop a metaphysical framework for Aristotelian actualism. Chapter 1 (...) explains basic issues associated with the possible world approach to modality. I overview modal realist and actualist views on possible worlds and explain why I support the actualist approach. Subsequently, I introduce a distinction between Platonic and Aristotelian actualism, and discuss some semantic issues associated with actualism as such. In Chapter 2 I argue that Aristotelian actualism, modeled on linguistic ersatzism, is preferable over its Platonic counterpart. Subsequently, I propose a metaphysical framework for Aristotelian ersatzism which is based on a claim that our modal concepts work differently for actual and possible individuals. In order to explain that claim I introduce three specific differences concerning modal features of actual and possible individuals: (a) Representational Difference, according to which actual and possible individuals are represented differently by possible worlds; (b) Metaphysical Difference, according to which actual and possible individuals are represented by possible worlds as having different metaphysical nature; (c) Modal Difference, which says while there are singular and contingent possibilities involving actual individuals, all possibilities about possible individuals are general and necessary. I propose to interpret those differences in terms of the doctrines of haecceitism, antihaecceitism and existentialism. There is however no consensus on how those views should be characterized. Chapters 3, 4, and 5 focus on providing a precise characterization of those doctrines. Chapter 3 focuses on the doctrines of modal haecceitism and antihaecceitism, which I view as opposite accounts of how possible worlds represent possibilities. According to modal haecceitism what possible worlds say about particular individuals does not supervene on what they say qualitatively. Modal antihaecceitism is a denial of such a claim. Chapter 4 concerns metaphysical haecceitism and antihaecceitism, which I take to be alternative accounts of the fundamental structure of reality. For the metaphysical haecceitist reality contains irreducible singular facts, while for the metaphysical antihaecceitist reality is purely qualitative and general. Chapter 5 focuses on an argument between existentialists and antiexistentialists. Existentialists claim that there are contingent singular propositions, while antiexistentialists deny that. I defend existentialism against antiexistentialist counterarguments, as well as criticize some of the antiexistentialist accounts of singular propositions modeled on the notion of individual essence. In Chapter 6, by appealing to the results of investigations conducted in Chapters 3, 4 and 5, I reconsider Representational, Metaphysical and Modal Differences. According to a view that I propose: (a) Representational Difference entails (extreme) modal haecceitism for actual individuals but (extreme) modal antihaecceitism for possible individuals; (b) Metaphysical Difference entails metaphysical haecceitism (individualism) for actual individuals, but metaphysical antihaecceitism (generalism) for possible individuals; finally (c) Modal Difference entails existentialism: while there are singular and contingent possibilities involving actual individuals, all possibilities about possible individuals are general and necessary. In Chapter 6, I also explain the implications of those views for the various issues, including transworld identity, essentialism, or the modal status of modal space. Lastly, Chapter 7 overviews some semantic and metaphysical applications of Aristotelian ersatzism. I explain how it manages to accommodate Kripkean semantics and how it is able to account for the possibilities of indiscernibles, alien individuals and iterated modalities. I also address some possible objections to my proposal, including an issue of implicit representation and the Humphrey objection. (shrink)

In this paper I show that a novel ontic reading of explanation, intending to capture the de re essential features of individuals, can support the qualitative view of individual essences. It is argued further that the putative harmful consequences of the Leibniz Principle and its converse for the qualitative view can be avoided, provided that individual essences are not construed in the style of the naïve bundle theory with set-theoretical identity- conditions. Adopting either the more sophisticated two-tier BT or, alternatively, (...) the neo-Aristotelian position of taking essences as natures in the Aristotelian sense, can help to evade these main charges against the qualitative view. The functional parallels with the alternative haecceitistic view of individuation and individual essence will also be considered. (shrink)

This paper aims to demonstrate that the ontology of consciousness is consistent with both the modal and the metaphysical versions of Haecceitism. I examine the varieties of Haecceitism, and I specify the intended versions that the arguments will vindicate. I define the property of 'being purely qualitative', and examine its relation to the properties of phenomenal consciousness. I draw, inter alia, on Bayesian perceptual psychology, in order to specify the identity-conditions of phenomenal properties in detail. I provide two, abductive arguments (...) for the claim that the identity-conditions on some individuals are metaphysically haecceitistic, in virtue of the relations that hold between those individuals and the phenomenal properties that they instantiate. The first argument is corroborated by empirical results concerning the phenomenological effects of attention. The second argument is corroborated by empirical results from the study of color in vision science. The arguments vindicate a version of Metaphysical Haecceitism, because the individuals are shown to be typed by the phenomenal properties that they instantiate, although quantification over the individuals is an ineliminable condition on their identity and distinctness. I provide, then, a regimentation of the extant proposals in the ontology of consciousness, using the logic of hyperintensional ground, as augmented by the Bayesian probability calculus. The hyperintensional regimentation vindicates a version of Modal Haecceitism, because the probabilistic ontological dependence of the parts of worlds on other parts thereof provides an ineliminable condition on the identity and distinctness of worlds. (shrink)

This book aims to develop certain aspects of Gottlob Frege’s theory of meaning, especially those relevant to intensional logic. It offers a new interpretation of the nature of senses, and attempts to devise a logical calculus for the theory of sense and reference that captures as closely as possible the views of the historical Frege. (The approach is contrasted with the less historically-minded Logic of Sense and Denotation of Alonzo Church.) Comparisons of Frege’s theory with those of Russell and others (...) are given. It is in the end shown that developing Frege’s theory in these ways reveals serious problems hitherto largely unnoticed, including those possibly rendering a Fregean intensional logic inconsistent even if his naïve class theory is excluded. (shrink)

This paper discusses certain problems arising within the treatment of the senses of functions in Alonzo Church's Logic of Sense and Denotation. Church understands such senses themselves to be "sense-functions," functions from sense to sense. However, the conditions he lays out under which a sense-function is to be regarded as a sense presenting another function as denotation allow for certain undesirable results given certain unusual or "deviant" sense-functions. Certain absurdities result, e.g., an argument can be found for equating any two (...) senses of the same type. An alternative treatment of the senses of functions is discussed, and is thought to do better justice to Frege's original theory. (shrink)

This paper presents a model-theoretic semantics for discourse "about" natural numbers, one that captures what I call "the mathematical-object picture", but avoids what I can "the mathematical-object theory".

The infamous Hole Argument has led philosophers to develop various versions of substantivalism, of which metric essentialism and sophisticated substantivalism are the most popular. In this journal, Trevor Teitel has recently advanced novel arguments against both positions. However, Teitel does not discuss the position of Jeremy Butterfield, which appeals to Lewisian counterpart theory in order to avoid the Hole Argument. In this note I show that the Lewis-Butterfield view is immune to Teitel’s challenges.

This paper reviews the hole argument as an argument against spacetime substantivalism. After a careful presentation of the argument itself, I critically review possible responses.

semantic minimalism and moderte contextualism.

David Lewis argues at length against haecceitism and goes as far as claiming that, on a certain counterpart-theoretic construal, the doctrine is unintelligible or inconsistent. I argue, contra Lewis, that both qualitative and non-qualitative counterpart theory are in fact committed to haecceitism, but that this commitment is harmless since what is really at stake for a counterpart theorist such as Lewis are more general supervenience claims that are independent of haecceitism. I further argue that Lewis's formulation of the doctrine suffers (...) from two important defects that, once remedied, free counterpart theory of its haecceitistic commitments. Along the way I discuss an objection to the effect that the cheap substitute is inconsistent in the presence of an 'actually' operator. This paper therefore brings together important critical discussion on haecceitism and counterpart theory. (shrink)

Oferecendo uma visão histórica do problema dos universais, focando-se nas contribuições do filósofo medieval John Duns Scoto e do fundador do Pragmatismo Americano, Charles Pierce, este artigo apresenta a concepção de Pierce sobre o problema. Tal visão é rastreada explicando a conexão entre Aristóteles, Duns Scoto e Pierce. As considerações de Pierce foram chamadas por ele mesmo de “Realismo Escolástico” e tal Realismo dos universais tem com objetivo fornecer considerações factíveis para o Realismo Científico contemporâneo. O problema dos universais, depois (...) de tal leitura, aparece como um tema permanente e vibrante que define os problemas filosóficos tradicionais e contemporâneos. (shrink)

Using the Hilbert-Bernays account as a spring-board, we first define four ways in which two objects can be discerned from one another, using the non-logical vocabulary of the language concerned. Because of our use of the Hilbert-Bernays account, these definitions are in terms of the syntax of the language. But we also relate our definitions to the idea of permutations on the domain of quantification, and their being symmetries. These relations turn out to be subtle---some natural conjectures about them are (...) false. We will see in particular that the idea of symmetry meshes with a species of indiscernibility that we will call `absolute indiscernibility'. We then report all the logical implications between our four kinds of discernibility. We use these four kinds as a resource for stating four metaphysical theses about identity. Three of these theses articulate two traditional philosophical themes: viz. the principle of the identity of indiscernibles, and haecceitism. The fourth is recent. Its most notable feature is that it makes diversity weaker than what we will call individuality : two objects can be distinct but not individuals. For this reason, it has been advocated both for quantum particles and for spacetime points. Finally, we locate this fourth metaphysical thesis in a broader position, which we call structuralism. We conclude with a discussion of the semantics suitable for a structuralist, with particular reference to physical theories as well as elementary model theory. (shrink)

Often Bertrand Russell defends his view that names differ from descriptions in that names have meaning but descriptions do not by using a “proof.” Recently in this journal it has been debated whether Russell's “proof” fails or not. The familiar objection to Russell's argument is that it is circular or it involves a sense/reference equivocation. Avrum Stroll suggests a novel criticism by making use of a “mirror argument“ which attempts to show that Russell's argument can be used to conclude that (...) "Scott" has no meaning, and that thus the argument proves too much or nothing. Robert Fahrnkopf defends Russell's argument, but, I believe, he does not go far enough in his defense. So it will be useful to carry this debate a few steps further. (shrink)

Often Bertrand Russell defends his view that names differ from descriptions in that names have meaning but descriptions do not by using a “proof.” Recently in this journal it has been debated whether Russell's “proof” fails or not. The familiar objection to Russell's argument is that it is circular or it involves a sense/reference equivocation. Avrum Stroll suggests a novel criticism by making use of a “mirror argument“ which attempts to show that Russell's argument can be used to conclude that (...) "Scott" has no meaning, and that thus the argument proves too much or nothing. Robert Fahrnkopf defends Russell's argument, but, I believe, he does not go far enough in his defense. So it will be useful to carry this debate a few steps further. (shrink)

The most commonly heard proposals for reducing possible worlds to language succumb to a simple cardinality argument: it can be shown that there are more possible worlds than there are linguistic entities provided by the proposal. In this paper, I show how the standard proposals can be generalized in a natural way so as to make better use of the resources available to them, and thereby circumvent the cardinality argument. Once it is seen just what the limitations are on these (...) more general proposals, it can be clearly seen where the real difficulty lies with any attempt to reduce possible worlds to language. Roughly, the difficulty is this: no actual language could have the descriptive resources needed to represent all the ways things might have been. I conclude by arguing that this same difficulty spells doom for any nominalist or conceptualist proposal for reducing possible worlds. (shrink)

Existentialism concerning singular propositions is the thesis that singular propositions ontologically depend on the individuals they are directly about in such a way that necessarily, those propositions exist only if the individuals they are directly about exist. Haecceitism is the thesis that what non-qualitative facts there are fails to supervene on what purely qualitative facts there are. I argue that existentialism concerning singular propositions entails the denial of haecceitism and that this entailment has interesting implications for debates concerning the philosophy (...) of language, the nature of propositions, and the metaphysics of modality. (shrink)

Ontological functionalism's defining tenet is that mental properties can be defined wholly in terms of the general pattern of interaction of ontologically prior realizations. Ideological functionalism's defining tenet is that mental properties can only be defined nonreductively, in terms of the general pattern of their interaction with one another. My Self-consciousness Argument establishes: ontological functionalism is mistaken because its proposed definitions wrongly admit realizations into the contents of self-consciousness; ideological functionalism is the only viable alternative for functionalists. Michael Tooley's critique (...) misses the target: he offers no criticism of - except for an incidental, and incorrect, attack on certain self-intimation principles - and, since he himself proposes a certain form of nonreductive definition, he tacitly accepts. Finally, as with all other nonreductive definitions, Tooley's proposal can be shown to undermine functionalism's ultimate goal: its celebrated materialist solution to the Mind-Body Problem. The explanation of these points will require a discussion of: Frege-Russell disagreements regarding intensional contexts; the relationship between self-consciousness and the traditional doctrine of acquaintance; the role of self-intimation principles in functionalist psychology; and the Kripke-Lewis controversy over the nature of theoretical terms. (shrink)

Possible-worlds talk obscures, rather than clarifies, the debate about haecceitism. In this paper I distinguish haecceitism and anti-haecceitism from other doctrines that sometimes go under those names. Then I defend the claim that there are no non-tendentious definitions of ‘haecceitism’ and ‘anti-haecceitism’ using possible-worlds talk. That is, any definition of ‘haecceitism’ using possible-worlds talk depends, for its correctness, on a substantive theory of the nature of possible worlds. This explains why using possible-worlds talk when discussing haecceitism causes confusion: if the (...) parties to the discussion presuppose different theories of the nature of possible worlds, then they will mean different things by ‘haecceitism’. (shrink)

§0. Alonzo Church's contributions to philosophy and to that most philosophical part of logic, intensional logic, are impressive indeed. He wrote relatively few papers actually devoted to specifically philosophical issues, as distinguished from related technical work in logic. Many of his contributions appear in reviews for The Journal of Symbolic Logic, and it can hardly be maintained that one finds there a “philosophical system”. But there occur a clearly articulated and powerful methodology, terse arguments, often of “crushing cogency”, and philosophical (...) observations of the first importance.Many of the less formal philosophical contributions center around questions concerning meaning, but there are important clarifications and insights into matters of the epistemology and ontology of the sciences, especially the formal sciences.1.1. The logistic method. Church's writings on philosophical matters exhibit an unwavering commitment to what he called the “logistic method”. The term did not catch on and now one would just speak of “formalization”. The use of these ideas is now so common and familiar among logicians and logically-oriented philosophers that they are simply taken for granted. But they deserve to be celebrated and re-emphasized, for there are philosophers who seriously underestimate and even consciously reject these techniques. (shrink)

I present an argument for an interpretation ofKant's views on the nature of the ‘content [Inhalt]’ of ‘cognition [Erkenntnis]’. In contrast to one of the longest standing interpretations ofKant's views on cognitive content, which ascribes toKant a straightforwardly psychologistic understanding of content, and in contrast as well to the more recently influential reading ofKant put forward byMcDowell and others, according to whichKant embraces a version ofRussellianism, I argue thatKant's views on this topic are of a much moreFregean bent than has (...) traditionally been admitted or appreciated. I conclude by providing a sketch of how a better grasp ofKant's views on cognitive content in general can help bring into sharper relief what is, and what is not, at stake in the recent debates over whether Kant accepts a particular kind of cognitive content—namely, non‐conceptual content. (shrink)

The dogma that the propositional logic of metaphysical modality is S5 is rebutted in related installments (previously published and unpublished essays).

Sądzimy, że świat mógłby być zupełnie inny, niż jest, nie tylko ze względu na to jak się rzeczy mają, lecz także ze względu na to, co istnieje. Nasze potoczne intuicje dopuszczają, że mogłoby istnieć coś innego niż to, co faktycznie istnieje. Pewne konkretne indywiduum, które istnieje, mogłoby nie istnieć, mógłby też istnieć ktoś inny. Wydaje się, że możemy wypowiadać prawdziwe sądy dotyczące czysto możliwych indywiduów, np. to, że mogłabym mieć siostrę, która mogłaby być baletnicą, ale została bokserką. Przygodne istnienie indywiduów (...) stanowi problem dla zwolennika aktualizmu, który uważa, że istnieje tylko świat rzeczywisty oraz indywidua go zamieszkujące. W książce Mere Possibilities Stalnaker chce pogodzić intuicję, że indywidua istnieją w sposób przygodny z aktualizmem i pokazać, jak reprezentować warunki prawdziwości zdań o czystych możliwościach na gruncie realistycznie interpretowanej semantyki światów możliwych. (shrink)

The book is about logical analysis of natural language. Since we humans communicate by means of natural language, we need a tool that helps us to understand in a precise manner how the logical and formal mechanisms of natural language work. Moreover, in the age of computers, we need to communicate both with and through computers as well. Transparent Intensional Logic is a tool that is helpful in making our communication and reasoning smooth and precise. It deals with all kinds (...) of linguistic context in a fully compositional and anti-contextual way. (shrink)

In this dissertation, I investigate a conception of thoughts figuring in ordinary discourse, and argue that this conception is an improvement over a certain standard conception employed in current philosophical and linguistic endeavors. ;In Chapter 2, I discuss the leading principles of the standard conception, a conception according to which thoughts in general are to be identified with propositions. I also briefly preview some of the main features that distinguish the conception developed in the course of this study from the (...) standard conception. ;Chapter 4 is the heart of the thesis. I isolate a reading of the verb 'think' that I contend is both familiar from and central to our ordinary discourse about thoughts and thinking--the "generic reading", I call it. An investigation of the relation expressed by the verb, 'think', on this generic reading, and of the correlative conception of thoughts, occupies the remainder of the study. ;If this ordinary conception of thoughts is to serve the principal functions to which thoughts have standardly been assigned, in philosophical and linguistic endeavors, then there should be a discernible sense in which it is correct to say that thoughts, so conceived, are things that sentences express. In Chapter 5, I discuss the relevant notion of sentential expression. Accounts of this notion have commonly faced a stumbling block in the case of non-declarative sentences. What sort of thoughts, for example, can imperatives or interrogatives be said to express? In Chapter 6, I explain how, on the present conception, there is a clear sense in which sentences of a variety of grammatical moods--imperatives and interrogatives as well as declaratives--may be said, with equal propriety, to express thoughts. ;In Chapter 7, I discuss a fundamental thesis of the standard conception, and argue, in Chapter 8, that any account of the nature of thoughts accommodating this thesis is incompatible with the conception of thoughts arrived at in Chapter 4. Then, in order to retain this familiar conception and its benefits, a new account of the nature of thoughts must be provided. Such an account is described in Chapter 9. (shrink)

The paper is about the interpretation of opaque verbs like “seek”, “owe”, and “resemble” which allow for unspecific readings of their (indefinite) objects. It is shown that the following two observations create a problem for semantic analysis: (a) The opaque position is upward monotone: “John seeks a unicorn” implies “John seeks an animal”, given that “unicorn” is more specific than “animal”. (b) Indefinite objects of opaque verbs allow for higher-order, or “underspecific”, readings: “Jones is looking for something Smith is looking (...) for” can express that there is something unspecific that both Jones and Smith are looking for. Given (a) and (b), it would seem that the following inference is hard to escape, if the premisses are construed unspecifically and the conclusion is taken on its under- specific reading: Jones is looking for a sweater. Smith is looking for a pen. Smith is looking for something Jones is looking for. (shrink)

This paper investigates the prospects of developing a branching modal framework while keeping with the spirit of Humean Supervenience. It is argued that such an approach is bound to face hard problems regarding haecceitism and the notion of recombination. Possible directions for future philosophical developments of branching frameworks are suggested.

A distinction is developed between two uses of definite descriptions, the "attributive" and the "referential." the distinction exists even in the same sentence. several criteria are given for making the distinction. it is suggested that both russell's and strawson's theories fail to deal with this distinction, although some of the things russell says about genuine proper names can be said about the referential use of definite descriptions. it is argued that the presupposition or implication that something fits the description, present (...) in both uses, has a different genesis depending upon whether the description is used referentially or attributively. this distinction in use seems not to depend upon any syntactic or semantic ambiguity. it is also suggested that there is a distinction between what is here called "referring" and what russell defines as denoting. definite descriptions may denote something, according to his definition, whether used attributively or referentially. (shrink)

This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model other axioms (...) of Church’s intensional logic that have been criticized by Parsons and Klement: this, it turns out, is due to resources which also permit an interpretation of a fragment of Gallin’s intensional logic. Finally, the relation between the predicative response to the Russell-Myhill paradox of propositions and the Russell paradox of sets is discussed, and it is shown that the predicative conception of set induced by this predicative intensional logic allows one to respond to the Wehmeier problem of many non-extensions. (shrink)

I introduce and defend the semantic notion of counterfactual identity, distinguishing it from the metaphysical notion of transworld identity. After showing that Lewis's counterpart theory misconstrues counterfactual identity facts, I outline and motivate a ‘Leibnizian counterpart theory’ where the notion of counterfactual identity is adequately modelled. Finally, I show that counterfactual identity can be characterized without relying on some implausible features of Lewis's theory of conditionals.

I present an argument for an interpretation of Kant's views on the nature of the ‘content [Inhalt]’ of ‘cognition [Erkenntnis]’. In contrast to one of the longest standing interpretations of Kant's views on cognitive content, which ascribes to Kant a straightforwardly psychologistic understanding of content, and in contrast as well to the more recently influential reading of Kant put forward by McDowell and others, according to which Kant embraces a version of Russellianism, I argue that Kant's views on this topic (...) are of a much more Fregean bent than has traditionally been admitted or appreciated. I conclude by providing a sketch of how a better grasp of Kant's views on cognitive content in general can help bring into sharper relief what is, and what is not, at stake in the recent debates over whether Kant accepts a particular kind of cognitive content—namely, non-conceptual content. (shrink)

Background independence begins life as an informal property that a physical theory might have, often glossed as 'doesn't posit a fixed spacetime background'. Interest in trying to offer a precise account of background independence has been sparked by the pronouncements of several theorists working on quantum gravity that background independence embodies in some sense an essential discovery of the General Theory of Relativity, and a feature we should strive to carry forward to future physical theories. This paper has two goals. (...) The first is to investigate what a world must be like in order to be truly described by a background independent theory given extant accounts of background independence. The second is to argue that there are no non-empirical reasons to be more confident in theories that satisfy extant accounts of background independence than in theories that don't. The paper concludes by drawing a general moral about a way in which focussing primarily on mathematical formulations of our physical theories can adversely affect debates in the metaphysics of physics. (shrink)

In this paper I argue that questions about the semantics of rigid designation are commonly and illicitly run together with distinct issues, such as questions about the metaphysics of essence and questions about the theoretical legitimacy of the possible-worlds framework. I discuss in depth two case studies of this phenomenon – the first concerns the relation between rigid designation and reference, the second concerns the application of the notion of rigidity to general terms. I end by drawing out some conclusions (...) about the relations between rigid designation, semantic frameworks, reference, and essence. (shrink)

I discuss Stalnaker’s views on modality. In particular, his views on actualism, anti-essentialism, counterpart theory, and the Barcan formulas.