Truth: The Basics is a concise and engaging introduction to philosophical theories about the nature of truth. The two authors – leading philosophers in this field – build the book around a single question: what, if anything, is common to all truths, which makes them true? The book explores five important answers (‘theories’) to the given question: correspondence, semantic, verifiability, transparency, and plurality. For each given theory, the following questions are addressed:...

Building on his paradigm-shifting work on the incarnation in The Contradictory Christ (OUP, 2021), Jc Beall extends a robust contradictory theology with an account of the trinity. Throughout the history of the Christian church, heretics, apophatics, mystics, atheists, and many others have long proclaimed that the doctrine of the trinity - one of the central doctrines of the Christian faith - is contradictory. In this work, Beall agrees; however, as Beall convincingly argues, one n...

Apparent contradiction is common in traditional monotheism, and perhaps especially so in standard Christian theology given central doctrines such as the incarnation and trinity. This Element aims to chart out a very elementary but abstract framework through which such contradictions may be approached. This Element does not attempt to address the many options for thinking about contradictions in the face of logical entailment; it charts only a few salient abstract options.

In this ground-breaking study, Jc Beall shows that the fundamental "problem" of Christology is simple to see from the role that Christ occupies: the Christ figure is to have the divine and essentially limitless properties of the one and only God but Christ is equally to have the human, essentially limit-imposing properties involved in human nature, limits essentially involved in being human. The role that Christ occupies thereby appears to demand a contradiction: all of the limitlessness o...

Logic: The Basics is an accessible introduction to several core areas of logic. The first part of the book features a self-contained introduction to the standard topics in classical logic, such as:· mathematical preliminaries· propositional logic· quantified logic (first monadic, then polyadic)· English and standard ‘symbolic translations’· tableau procedures.Alongside comprehensive coverage of the standard topics, this thoroughly re...

Among the various conceptions of truth is one according to which 'is true' is a transparent, entirely see-through device introduced for only practical (expressive) reasons. This device, when introduced into the language, brings about truth-theoretic paradoxes (particularly, the notorious Liar and Curry paradoxes). The options for dealing with the paradoxes while preserving the full transparency of 'true' are limited. In Spandrels of Truth, Beall concisely presents and defends a mo...

An accessible explanation of Kurt Gödel's groundbreaking work in mathematical logic: " An excellent nontechnical account." — Bulletin of the American Mathematical SocietyIn 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public r...

This revised and considerably expanded 2nd edition, published in 2008, brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are exp...

Logic is essential to correct reasoning and also has important theoretical applications in philosophy, computer science, linguistics, and mathematics. This book provides an exceptionally clear introduction to classical logic, with a unique approach that emphasizes both the hows and whys of logic. Here Nicholas Smith thoroughly covers the formal tools and techniques of logic while also imparting a deeper understanding of their underlying rationales and broader philosophical significance. In...

A brief account of philosophical logic from one of the world's leading authoritiesPhilosophical Logic is a clear and concise critical survey of nonclassical logics of philosophical interest written by one of the world's leading authorities on the subject. After giving an overview of classical logic, John Burgess introduces five central branches of nonclassical logic (temporal, modal, conditional, relevantistic, and intuitionistic), focusing on the sometime...

It seems reasonable to believe that there might have existed things other than those that in fact exist, or have existed. But how should we understand such claims? Standard semantic theories exploit the Leibnizian metaphor of a set of all possible worlds: a proposition might or must be true if it is true in some or all possible worlds. The actualist, who believes that nothing exists except what actually exists, prefers to talk of possible states of the world, or of ways that a world might ...

The main purpose of this book is the development of a new method for the semantical analysis of meaning, that is, a new method for analyzing and describing the meanings of linguistic expressions. This method, called the method of extension and intension, is developed by modifying and extending certain customary concepts, especially those of class and property. The method will be contrasted with various other semantical methods used in traditional philosophy or by contemporary authors. Thes...