Divine Action in the Eucharist

Thomas Aquinas has long been the gold standard for theology of divine action in the Eucharist. Yet his account raises a number of difficulties. His position rests on a literal reading of scripture, a network of concomitant miracles that are dubious, and the danger of multiple incarnations, and a metaphysical apparatus that lacks credibility. This chapter argues that we should look for a better way to think about the Eucharist. First, it engages the proposal of Michael Dummett, a Roman Catholic philosopher, and second, it offers its own alternative sketch of divine action in the Eucharist which avoids the problems associated with Aquinas’s account.

A Two-Part Defense of Intuitionistic Mathematics

The classical interpretation of mathematical statements can be seen as comprising two separate but related aspects: a domain and a truth-schema. L. E. J. Brouwer’s intuitionistic project lays the groundwork for an alternative conception of the objects in this domain, as well as an accompanying intuitionistic truth-schema. Drawing on the work of Arend Heyting and Michael Dummett, I present two objections to classical mathematical semantics, with the aim of creating an opening for an alternative interpretation. With this accomplished, I then make the case for intuitionism as a suitable candidate to fill this void.

Philosophy and Me

This chapter is an autobiographical piece, confined, largely, to the role of philosophy in Dorothy Edgington’s life. It sketches Edgington’s rather tortuous route into the subject, her time as a student, her subsequent career in London and Oxford, and also some of the visiting positions in other parts of the world that turned out to be significant for her. On some of her favourite topics—conditionals, probability, vagueness, knowability—she writes of how her interest in them arose, how it developed, and of some of the philosophers who have influenced her most, especially Ernest Adams, Jonathan Bennett, and Michael Dummett.

Arithmetic, Logicism, and Frege’s Definitions

This paper describes an exegetical puzzle that lies at the heart of Frege’s writings—how to reconcile his logicism with his definitions and claims about his definitions. It also reviews two interpretations that try to resolve this puzzle: the “explicative interpretation” and the “analysis interpretation.” This paper defends the explicative interpretation and critiques the careful and sophisticated defenses of the analysis interpretation given by Michael Dummett and Patricia Blanchette. Specifically, I argue that Frege’s texts either are inconsistent with the analysis interpretation or do not support it. I also defend the explicative interpretation from the recent charge that it cannot make sense of Frege’s logicism. While I do not provide the explicative interpretation’s full solution to the puzzle, I show that its main competitor is seriously problematic.

A Two-Part Defense of Intuitionistic Mathematics

The classical interpretation of mathematical statements can be seen as comprising two separate but related aspects: a domain and a truth-schema. L. E. J. Brouwer’s intuitionistic project lays the groundwork for an alternative conception of the objects in this domain, as well as an accompanying intuitionistic truth-schema. Drawing on the work of Arend Heyting and Michael Dummett, I present two objections to classical mathematical semantics, with the aim of creating an opening for an alternative interpretation. With this accomplished, I then make the case for intuitionism as a suitable candidate to fill this void.

A semântica do passado

Este artigo apresenta a linguagem do passado, no contexto do antirrealismo de Michael Dummett. Ao final, de modo breve, o papel dos condicionais contrafáticos é enfatizado.

Semantic Realism, Actually

Michael Dummett offered a semantic characterisation of a variety of realism-antirealism debates. This approach has fallen out of fashion. This has been to the detriment of metaphysics. This paper offers an accurate characterisation of Dummett’s view, often lacking in the literature, and then defends it against a range of attacks (from Devitt, Miller and Williamson). This understanding of realism debates is resilient, and if we take it seriously the philosophical terrain looks importantly different. In particular, the philosophy of language has a foundational role with respect to metaphysics.

S5 as the Logic of Metaphysical Modality: Two Arguments for and Two Arguments against

Two arguments for S5 being the logic of metaphysical modality are favourably discussed: one from the logic of absolute necessity, one from Timothy Williamson. Two arguments against S5 being the logic of metaphysical modality are discussed and rebuffed: one from Nathan Salmon against S4, and thereby S5, being the logical of metaphysical modality; and one from Michael Dummett against the B principle for metaphysical modality. In the Appendix, some comments are offered on the logics of ‘true in virtue of the nature of’, and its relation to logical necessity. It is argued that the logic both of ‘true in virtue of the nature of x’ and of essentialist logical necessity is S5.

Wright and Revisionism

Do considerations in the theory of meaning pose a challenge to classical logic, and in particular to the law of excluded middle? Michael Dummett suggested an affirmative answer to this question, and advocated a form of logical revisionism. In his 1981 study “Anti-Realism and Revisionism,” Crispin Wright developed a critique of Dummett’s case for logical revisionism, but in more recent work (e.g., his 1992 book Truth and Objectivity), Wright has advanced an argument in favour of logical revisionism. This chapter investigates the nature and limitations of anti-realist revisionism, and offers a critique of Wright’s arguments in favour of logical revisionism. It also develops an alternative proposal about how revisionism might proceed.