Jc Beall

_Logic: The Basics_ is a hands-on introduction to the philosophically alive field of logical inquiry. Covering both classical and non-classical theories, it presents some of the core notions of logic such as validity, basic connectives, identity, ‘free logic’ and more. This book: introduces some basic ideas of logic from a semantic and philosophical perspective uses logical consequence as the focal concept throughout considers some of the controversies and rival logics that make for such a lively field This accessible guide includes chapter summaries and suggestions for further reading as well as exercises and sample answers throughout. It is an ideal introduction for those new to the study of logic as well as those seeking to gain the competence and skills needed to move to more advanced work in logic.

Semantic and soritical paradoxes challenge entrenched, fundamental principles about language - principles about truth, denotation, quantification, and, among others, 'tolerance'. Study of the paradoxes helps us determine which logical principles are correct. So it is that they serve not only as a topic of philosophical inquiry but also as a constraint on such inquiry: they often dictate the semantic and logical limits of discourse in general. Sixteen specially written essays by leading figures in the field offer new thoughts and arguments about the paradoxes.

One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley–Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing a general conception of conditionality that may unify the three given conceptions.

The principal aim of this paper is to very briefly discuss one way in which FDE may be ‘the one true logic’ – an idea which neither Belnap nor Dunn have ever been keen to promote, but an idea which, properly understood, is worth having plainly on the table. After presenting the simple sense in which FDE may be plausibly thought of as the one true logic, I briefly rehearse a simple argument for thinking as much. (The argument is one I have advanced elsewhere (Beall, The simple argument for subclassical logic. In Juhl and Schechter (eds) Philosophical issues: philosophy of logic and inference (Annual Supplement to Noûs). Wiley, 2018, Forthcoming) but it seems especially appropriate to repeat in this volume.) There are two other aims of this paper, one of which is to keep the paper very short. The last but not least aim is to honor the pioneering work of Belnap and Dunn on FDE and its philosophical applications. Let me say from the start that the paper necessarily fails to achieve its last aim, not for lack of aiming or even for poorly aiming; rather, the honor that both Belnap and Dunn deserve for their work is not something that this paper – perhaps any paper – can reflect. By my lights, their work on the topic (both mathematical and philosophical) is what we should all aspire to do. Both logic and its philosophy are vastly better for their efforts. (I also want to explicitly record a small personal note to both Professor Belnap and Professor Dunn. Some people make a lot of their ‘intellectual heritage’ or ‘family line’ in PhDs and so forth. I’m not one of those people. Still, if one looks carefully beyond the exact letters of my ‘lineage’, one sees that I learned a lot of my logical background – though perhaps not logical proclivities – from Gary Hardegree, who gained much of his own logical background from Professor Dunn, who in turn gained valuable logical background from Professor Belnap. As a personal note to Nuel and Mike: thank you both. You remain, in so many ways, key sources in my intellectual development. (I’m sorry for the deviant turn that my own views have taken!))

Recent works in theology—including Beall (The Contradictory Christ and Divine Contradiction) and essays in Rutledge (Paradox and Contradiction in Theology)—have articulated or defended contradictory or contradictory-like theologies. Given the use of contemporary formal logic in setting out these theologies, a natural question concerning the existence of historical precedents to contradictory or contradictory-like theologies has arisen. In this article we present a short, accessible overview of contradictory and contradictory-like theologies alongside an attempt to address the question of historical precedents for such views.

Logic: the Basics is an accessible introduction to several core areas of logic. This thoroughly revised second edition not only comprehensively covers the standard topics in logic at an introductory level but also gives the reader an idea of how they can take their knowledge further. With its wealth of exercises (many of which have solutions in the encyclopedic online supplement) Logic: the Basics will be useful as a textbook in courses ranging from the introductory level to the early graduate level and also as a reference for students and researchers in philosophical logic.

A longstanding problem confronting Christian theology and its doctrine of incarnation is the apparent contradiction that it faces. For example, to be divine, in the relevant sense, is to have the limitlessness of God. To be human, in the relevant sense, is to have the limitations of humans. The incarnation (in the person of Jesus per Christian doctrine) is to be both divine and human. Many theologians and sympathetic philosophers have attempted to ‘consistentize’ (i.e., make consistent) incarnation. Timothy Pawl has been one of the latest to do so. In this paper, I concisely note a dilemma for Pawl’s approach.