Jc Beall

This paper comprises replies to three symposium papers that approach my work from broadly Hegelian or so-called continental perspectives: Estrada-González (2024), Ficara (2024), and Shores (2023). The goal is not to settle exegetical questions about Hegel but to clarify how a subclassical—in particular, glut-theoretic (and, if relevant, gap-theoretic)—framework interacts with speculative and continental treatments of contradiction and negation. Each main section may be read independently, though together they emphasize the same theme: Logic, as the sparse and topic-neutral closure relation (here taken to be FDE) on all true theories, remains distinct from the richer, extralogical theorizing that particular programs—including Hegelian and continental ones—may require. I am deeply honored by the work of each author and grateful for the engagement.

This paper comprises replies to six symposium papers that approach my work from within the philosophy of religion and, in particular, the philosophy of Christian theology: d’Agostini (2024), Casati and Fujikawa (2024), DeVito (2023), Gómez Gutiérrez (2023), Joaquin and DeVito (2023), and Reese (2023). Each paper raises questions concerning the role of a subclassical — in particular, glut-theoretic (and, in some cases, gap-theoretic) — account of consequence in modelling the apparent contradictions at the heart of orthodox Christian theology. The aim in what follows is not to settle broader debates about divine attributes, free will, or conciliar authority, but to clarify how a modest logical base (here taken to be FDE), together with theory-specific vocabulary as needed, interacts with and supports a contradictory theology. Each section may be read independently; together they emphasise a common theme: the logic of theology is sparse and topic-neutral, while the theology itself may be rich, extralogical, and in some cases genuinely contradictory. I am deeply grateful to each author for their insightful contributions.

This paper comprises responses to (in alphabetical order) Calasso and Logan (2023), Caret (2024), Omori and Arenhart (2023), and Standefer, Shear, and French (2023). Given space limitations, responses are not exhaustive; future work will engage the work further. The target papers divide roughly into philosophy of logic and strictly philosophical logic (some formal logic fueled by some philosophical issue). The former, being largely dialectical, requires more ink; the latter, except to the extent that it dips a toe into philosophy of logic, stands on its own promise and results. I am deeply honored by the contributions of each paper, and hereby thank all involved.

This chapter presents what is called ’deflated truth pluralism.’ The aim is not to argue for a particular version of deflated truth pluralism, but rather only to illustrate the sort of view involved. This sort of truth pluralism is deflated in at least two senses: it essentially revolves around a deflationary conception of truth; and it acknowledges only deflationarily respectable truth-predicates in the plurality. After presenting the view and motivation for it, the chapter closes by briefly responding to a few objections and/or questions about deflated truth pluralism.

This chapter focuses on two leading alternatives to the book's (paraconsistent, non-paracomplete) theory, namely, Kripke's and Field's. It sketches Kripke's account, focusing on the ‘formal picture’ which is presupposed in Field's account, and then sketches Field's account. By way of framing the discussion, the chapter begins with a brief background note on general, guiding projects. It concludes by discussing points of agreement and disagreement between Field's account and the book's, and briefly discusses how one might adjudicate between the two approaches.

This chapter sketches the basic idea of transparent truth qua constructed device and the basic ‘merely semantic’ view of resulting paradoxes. The chapter is structured as follows. Section 1.1 sketches the target conception of truth. Section 1.2 discusses relevant features of our base language, particularly negation. Section 1.3 mentions the target phenomenon (paradox). Section 1.4 sketches the basic logical framework. Drawing on the canvassed ideas in preceding sections, Section 1.5 presents the overall basic position.

On one hand, vague predicates seem to be useful; on the other, they appear to be fully tolerant (and thereby useless). Utility demands cutoffs; tolerance forbids them. This tension has fueled much work on vagueness. This chapter gives a very modest proposal on how to escape this apparent tension. The proposal is not profound, but it may be liberating. Genuinely vague predicates are without cutoffs, but they are useful in providing us the ingredients for sharp look-alikes of the vague. If this is right, the existence of cutoffs is neither a worry nor surprising.

Deflationist accounts of truth are widely held in contemporary philosophy: they seek to show that truth is a dispensable concept with no metaphysical depth. However, logical paradoxes present problems for deflationists, which their work has struggled to overcome. In this volume of fourteen original essays, a distinguished team of contributors explore the extent to which, if at all, deflationism can accommodate paradox. The volume will be of interest to philosophers of logic, philosophers of language, and anyone working on truth. Contributors Bradley Armour-Garb, Jody Azzouni, JC Beall, Hartry Field, Christopher Gauker, Michael Glanzberg, Dorothy Grover, Anil Gupta, Volker Halbach, Leon Horsten, Paul Horwich, Graham Priest, Greg Restall, Alan Weir.