It is often assumed that pluralities are rigid, in the sense of having all and only their actual members necessarily. This assumption is operative in standard approaches to modal plural logic. I argue that a sceptical approach towards the assumption is warranted.

The recent focus of Philip Kitcher’s research has been, somewhat surprisingly in the light of his earlier work, the philosophical analyses of literary works and operas. The aim of this paper is to show that there is no discontinuity between this new direction and Kitcher's earlier work in the philosophy of science: Kitcher’s contributions to the philosophy of science and his more recent endeavors into the philosophy of literature and of music are grounded in the same big picture attitude towards (...) the human mind – and attitude that he would undoubtedly call ‘pragmatic’: one that emphasizes the importance of those mental processes that are not rational. (shrink)

This paper aims to provide hyperintensional foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by (...) Hale and Wright and examined in Hale (2013), and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest that observational type theory can be applied to first-order abstraction principles in order to make abstraction principles recursively enumerable. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics. (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 two-dimensional (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)

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 two-dimensional (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)

To several critics of the philosophical method of cases—Robert Cummins, Jonathan Weinberg and his colleagues, and Avner Baz—the fact that philosophical intuitions cannot be calibrated means that we cannot rule out the skeptical hypothesis that the outcome of our theorizing based on these intuitions is deeply distorted by our cognitive artifacts. Moreover, they take this hypothesis to license the negative conclusion that we are unable to have much of the armchair knowledge we typically attribute to ourselves when philosophizing based on (...) appeal to philosophical intuitions. This paper addresses this skeptical argument and shows how this negative conclusion can be resisted. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:James and Waismann on Temperament in PhilosophyJohn Cappsfor william james, philosophyis inextricably linked to what he calls temperament. In the first of his Pragmatismlectures, he claims that "the history of philosophy is to a great extent that of a certain clash of human temperaments" ( Pragmatism11), while conceding that this will strike many philosophers as "undignified." In a similar vein, he elsewhere writes that philosophy seeks "by hard reasoning (...) for results emotionally valuable" ( Some Problems of Philosophy11). It's not hard to see a connection between these two claims: whether a philosophical conclusion is "emotionally valuable" will presumably depend, at least in part, on the reader's temperament. A philosophical work will leave some readers cold while resonating with others; some philosophy will engage one's interest and energy, while other philosophy will seem not so much mistaken as alien, remote from what one might ever find useful, interesting, or enlightening.James's meta-philosophical claim—his philosophy of philosophy—has received surprisingly little attention. Much of the literature has focused instead on what he meant by "temperament" in the context of nineteenth- and early twentieth-century theories of psychology and brain science. Much less attention has been paid to whether he is right and what the consequences would be if he is right. 1I aim to address this gap by first raising some fundamental issues with James's position. To see better what he should have said, I will then turn to some later but surprisingly similar remarks by the Anglo-Austrian philosopher and mathematician Friedrich Waismann, before turning to a more recent account of philosophical methodology defended by Timothy Williamson.1. James on Philosophy and TemperamentHilary and Ruth Anna Putnam have written that "perhaps the most shocking claim that James makes—the claim that is the centerpiece of the very first of the Lectures on Pragmatism—is that the decision we make on any metaphysical [End Page 46]question … is and ought to be a matter of 'temperament'" (227). While the Putnams do not explain what makes this his "most shocking" claim, it is likely because James accuses philosophers of being either systematically dishonest or self-deluded. Here is what James writes:Of whatever temperament a professional philosopher is, he tries when philosophizing to sink the fact of his temperament. Temperament is no conventionally recognized reason, so he urges impersonal reasons only for his conclusions. Yet his temperament really gives him a stronger bias than any of his more strictly objective premises. It loads the evidence for him one way or the other, making for a more sentimental or a more hard-hearted view of the universe, just as this fact or that principle would. He trustshis temperament…. Yet in the forum he can make no claim, on the bare ground of his temperament, to superior discernment or authority. There arises thus a certain insincerity in our philosophic discussions: the potentest of all our premises is never mentioned.( Pragmatism11)According to James, then, one's "temperament" plays an important role in determining the sorts of philosophical positions one finds congenial—and yet professional philosophers are either in denial that temperament plays this role or are actively committed to concealing this fact. Nor does James limit his claim, as the Putnams suggest, to only metaphysical questions: while he tends to focus on more large-scale alternatives (empiricism vs. rationalism, atheism vs. theism—perhaps because the lectures were delivered before a popular audience), the same point should hold across the board. So whether it is the choice between consequentialism vs. deontological ethical theories, or procedural vs. substantive accounts of justice, or functionalist vs. behaviorist philosophies of mind, James would argue that temperament plays a crucial role. 2I will refer to this as his "temperament thesis" (TT): TT: One's philosophical commitments are, in part, a function of one's temperament. A few points of clarification are in order. First, while James describes temperament as providing the "potentest" support for philosophical claims, he does not claim that it is decisive or that it swamps all other considerations. Temperament "loads the evidence" but can apparently be overridden when sufficient evidence or compelling... (shrink)

The question “What is philosophy?” is difficult to answer because it seems to presuppose answers to long‐standing and controversial philosophical questions. As answers to these questions affect one’s metaphilosophy, apparently irresolvable philosophical disagreements are then converted into deadlock concerning the nature of the discipline. As this problem is unique to philosophy, however, this difficulty itself reveals something of philosophy’s essential nature. As, under analysis, it turns out to arise from a definite way of posing problems, philosophy can initially be defined (...) by a particular mode of problematisation. This essay establishes this argument and proposes a method for developing this insight into a fully realised, socio‐historical metaphilosophy. This involves stages of (a) hermeneutical analysis and (b) historical contextualisation, both of which increase the account’s empirical adequacy. A conclusion discusses the extent to which philosophy is on trial here and argues that questioning the future of philosophy is not inherently philistine. (shrink)

Widespread and lasting consensus has not been philosophy's fate. Indeed, one of philosophy's most striking features is its ability to accommodate “not only different answers to philosophical questions” but also “total disagreement on what questions are philosophical” (Rorty 1995, 58). It is therefore hardly surprising that philosophers' responses to this metaphilosophical predicament have been similarly varied. This article considers two recent diagnoses of philosophical diversity: Kornblith and Rescher (respectively) claim that taking philosophical disagreement seriously does not lead to metaphilosophical scepticism. (...) The article argues that their confidence is misplaced in so far as both wrongly assume that ordinary, first-order philosophical practice and second-order metaphilosophical reflection are separate enterprises. We can say that the universe consists of a substance, and this substance we will call “atoms,” or else we will call it “monads.” Democritus called it atoms. Leibniz called it monads. Fortunately, the two men never met, or there would have been a very dull argument. (Allen 1997, 171) When will philosophers learn to be less pretentious and arrogant in their claims? One would imagine that the philosophic experiences of twenty-five centuries would have taught them the fallacy of self-esteem! (Schilpp 1935, 233). (shrink)