What is the proper role of logic in analytic theology? This question is thrown into sharp relief when a basic logical principle is questioned, as in Beall’s ‘Christ – A Contradiction.’ Analytic philosophers of logic have debated between exceptionalism and anti-exceptionalism, with the tide shifting towards anti-exceptionalism in recent years. By contrast, analytic theologians have largely been exceptionalists. The aim of this paper is to argue for an anti-exceptionalist view, specifically treating logic as a modelling tool. Along the way I (...) critically engage with Beall on the role of logic in theology, maintaining that theological inquiry is in some ways disanalogous with other theoretical enterprises. (shrink)

The divine attributes of omniscience and omnipotence have faced objections to their very consistency. Such objections rely on reasoning parallel to semantic paradoxes such as the Liar or to set-theoretic paradoxes like Russell's paradox. With the advent of paraconsistent logics, dialetheism—the view that some contradictions are true—became a major player in the search for a solution to such paradoxes. This paper explores whether dialetheism, armed with the tools of paraconsistent logics, has the resources to respond to the objections levelled against (...) the divine attributes. (shrink)

Those who accept the necessity of mereological universalism face what has come to be known as the ‘junk argument’ due to Bohn [2009], which proceeds from the incompatibility of junk with universalism and the possibility of junk, to conclude that mereological universalism isn't metaphysically necessary. Most attention has focused on ; however, recent authors have cast doubt on . This paper undertakes a defence of premise against three main objections. The first is a new objection to the effect that Bohn's (...) defence of that premise presupposes far too much. I show that one can defend premise from a much weaker set of assumptions. The second objection, due to Contessa [2012], is that those who accept unrestricted composition should only accept the existence of binary sums rather than infinitary fusions. I argue that this conception of unrestricted composition is problematic: it is in conflict with an intuitive remainder principle. The final objection is .. (shrink)

Mereological principles are often controversial; perhaps the most stark contrast is between those who claim that Weak Supplementation is analytic—constitutive of our notion of proper parthood—and those who argue that the principle is simply false, and subject to many counterexamples. The aim of this paper is to diagnose the source of this dispute. I’ll suggest that the dispute has arisen by participants failing to be sensitive to two different conceptions of proper parthood: the outstripping conception and the non-identity conception. I’ll (...) argue that the outstripping conception (together with a specific set of definitions for other mereological notions), can deliver the analyticity of Weak Supplementation on at least one sense of ‘analyticity’. I’ll also suggest that the non-identity conception cannot do so independently of considerations to do with mereological extensionality. (shrink)

Traditional monotheism has long faced logical puzzles. We argue that such puzzles rest on the assumed logical truth of the Law of Excluded Middle, which we suggest there is little theological reason to accept. By way of illustration we focus on God's alleged stone problem, and present a simple but plausible ‘gappy’ framework for addressing this puzzle. We assume familiarity with the proposed logic but an appendix is offered as a brief review.

Is a whole something more than the sum of its parts? Are there things composed of the same parts? If you divide an object into parts, and divide those parts into smaller parts, will this process ever come to an end? Can something lose parts or gain new ones without ceasing to be the thing it is? Does any multitude of things (including disparate things such as you, this book, and the tail of a cat) compose a whole of some (...) sort? Questions such as these have occupied us for at least as long as philosophy has existed. They define the field that has come to be known as mereology-the study of all relations of part to whole and of part to part within a whole-and have deep and far-reaching ramifications in metaphysics as well as in logic, the foundations of mathematics, the philosophy of language, the philosophy of science, and beyond. In Mereology, A. J. Cotnoir and Achille C. Varzi have compiled decades of advanced research into a comprehensive, up-to-date, and formally rigorous picture. The early chapters cover the more classical aspects of mereology; the rest of the book deals with variants and extensions. Whether you are an established professional philosopher, an interested student, or a newcomer, inside you will find all the tools you need to join this ever-evolving field of inquiry and theorize about all things mereological. (shrink)

Priest’s 2014 theory of unity and identity, based on a paraconsistent logic, has a wide range of applications. In this paper, I apply his theory to some puzzles concerning mereology and topology. These puzzles suggest that the classical mereotopology needs to be revised. I compare and contrast the Priest-inspired solution with another, based on classical logic, that requires the co-location of boundaries. I suggest that the co-location view should be preferred on abductive grounds.

Mereotopology is a theory of connected parts. The existence of boundaries, as parts of everyday objects, is basic to any such theory; but in classical mereotopology, there is a problem: if boundaries exist, then either distinct entities cannot be in contact, or else space is not topologically connected . In this paper we urge that this problem can be met with a paraconsistent mereotopology, and sketch the details of one such approach. The resulting theory focuses attention on the role of (...) empty parts, in delivering a balanced and bounded metaphysics of naive space. (shrink)

The fundamental problem of Christology is the apparent contradiction of Christ as recorded at Chalcedon. Christ is human and Christ is divine. Being divine entails being immutable. Being human entails being mutable. Were Christ two different persons there’d be no apparent contradiction. But Chalcedon rules as much out. Were Christ only partly human or only partly divine there’d be no apparent contradiction. But Chalcedon rules as much out. Were the very meaning of ‘mutable’ and/or ‘immutable’ other than what they are, (...) there’d be no apparent contradiction. But the meaning is what it is, and changing the meaning of our terms to avoid the apparent contradiction of Christ is an apparent flight from reality. What, in the end, is the explanation of the apparent contradiction of Christ? Theologians and philosophers have long advanced many consistency-seeking answers, all of which increase the metaphysical or semantical complexity of the otherwise strikingly simple but radical core of Christianity’s GodMan. In this paper, I put the simplest explanation on the theological table: namely, Christ appears to be contradictory because Christ is contradictory. This explanation may sound complicated to the many who are steeped in the mainstream account of logic according to which logic precludes the possibility of true contradictions. But the mainstream account of logic can and should be rejected. Ridding theology of the dogma of mainstream logic illuminates the simple though striking explanation of the apparent contradiction of Christ — namely, that Christ is a contradictory being. Just as the simplest explanation to the apparent roundness of the earth has earned due acceptance, so too should the simplest explanation of the apparent contradiction of Christ. (shrink)

This paper is a systematic exploration of non-wellfounded mereology. Motivations and applications suggested in the literature are considered. Some are exotic like Borges’ Aleph, and the Trinity; other examples are less so, like time traveling bricks, and even Geach’s Tibbles the Cat. The authors point out that the transitivity of non-wellfounded parthood is inconsistent with extensionality. A non-wellfounded mereology is developed with careful consideration paid to rival notions of supplementation and fusion. Two equivalent axiomatizations are given, and are compared to (...) classical mereology. We provide a class of models with respect to which the non-wellfounded mereology is sound and complete. (shrink)

First published in 1952, British Empirical Philosophers is a comprehensive picture of one of the most important movements in the history of philosophic thought. In his introduction, Professor A. J. Ayer distinguishes the main problems of empiricism and gives a critical account of the ways in which the philosophers whose writings are included in this volume attempted to solve them. Editors Ayer and Raymond Winch bring together an authoritative abridgement of John Locke’s Essay Concerning Human Understanding ; Bishop George Berkeley’s (...) Principles of Human Knowledge ; almost the entire first book of David Hume’s Treatise Concerning Human Nature ; and extracts from Thomas Reid’s Essay on the Intellectual Powers of Man and John Stuart Mill’s Examination of Sir William Hamilton’s Philosophy. (shrink)

First published in 1952, British Empirical Philosophers is a comprehensive picture of one of the most important movements in the history of philosophic thought. In his introduction, Professor A. J. Ayer distinguishes the main problems of empiricism and gives a critical account of the ways in which the philosophers whose writings are included in this volume attempted to solve them. Editors Ayer and Raymond Winch bring together an authoritative abridgement of John Locke’s Essay Concerning Human Understanding ; Bishop George Berkeley’s (...) Principles of Human Knowledge ; almost the entire first book of David Hume’s Treatise Concerning Human Nature ; and extracts from Thomas Reid’s Essay on the Intellectual Powers of Man and John Stuart Mill’s Examination of Sir William Hamilton’s Philosophy. (shrink)

One of the primary burdens of the mereological nihilist is accounting for our ordinary intuitions about material objects. It certainly *seems* as if I am typing on a keyboard, which has particular keys and buttons as parts. But such intuitions are mistaken if mereological nihilism is right, leading to widespread error. So nihilists often propose paraphrases of our everyday utterances as compensation. Cotnoir aims to deliver a new paraphrase strategy on behalf of the nihilist: one that interprets parthood and (...) composition modally, and interprets (spatial) parts as (modal) counterparts. He advertises this view as the spatial analog of Sider’s stage-theoretic view. Unfortunately, I argue, it isn't. The spatial analog to the above views would be something like the following: individuals are region-bound spatial bits. Certain spatial claims about these objects may be true if the relevant spatial bits have the appropriate spatial counterparts. The table is flat iff the table (a spatial bit) has a spatial counterpart that is flat. That is, spatial *counterparts* make certain spatial claims true. Call this the *bit-theoretic* view. In this paper, I use the bit-theoretic view as a foil for highlighting certain aspects of Cotnoir’s proposal, as well as to show that the very ways in which Cotnoir’s view differs from the bit-theoretic view are ways in which it undermines advantages of nihilism. (shrink)

This book outlines the realist and pluralist philosophy of John Anderson, Australia's most original thinker. His teaching at Sydney University and his arti6es have deeply influenced Australian intellectual life. Several main themes run through his work, but Anderson never gave an overall account of his views. This is remedied here: exhibiting the range of Anderson's thought from logic, epistemology and theory of mind, to language and social theory, this volume sketches realism as a systematic philosophical position, while showing something of (...) the history of ideas in Australia. (shrink)

The dictionary shows philosophers at their best (and their worst), at their most perverse and their most elegant. Organised by philosopher, and indexed by thought, concept and phrase, it enables readers to discover who said what, and what was said by whom. Over 300 philosophers are represented, from Aristotle to Zeno, including Einstein, Aquinas, Sartre and De Beauvoir, and the quotations range from short cryptic phrases to longer statements. This Dictionary of Philosophical Quotations d will not change your life. It (...) will change your mind. (shrink)

The criterion of truth is the measure of the truthfulness and reliability of our knowledge. It is also the basis for determining the correctness of our concepts and how much our perceptions, ideas, and concepts accord with objective reality. Idealism holds to the idea that the criterion of truth does not involve the integration between theory as created by human intelligence and objective reality, but rather that the criterion of truth involves the "clarity and correctness" of perception, viewpoints, and concepts (...) by the subject. For instance, the Machists 1 think that the criterion of truth is experience, however, they neither interpret experience from a materialistic viewpoint, nor view experience as the result of humans interacting with nature as they reform it. The Machists view experience as a summary of perceptions and as the subjective experience of humans. In this sense, perception must be tested by perception itself. In attempting to escape the trap of solipsism , they proposed "collective experience" as the criterion of truth. According to such a view, anything that involves "common significance," that is, anything acknowledged by everyone, is the truth. Lenin exposed the absurdity of idealist theory by pointing out that by following the view of "socially formed experience" it is very easy to consider as normal the most absurd and farcical notions, such as ghosts, for such beliefs are also a form of human "experience." Religion also possesses a "common significance," for innumerable people believe in ghosts and miracles, etc. Nevertheless, religion does not become the truth because of this. The concept of the "criterion of truth" held by the Machists played a dominant role in modern bourgeois philosophy. Jean Jacques Rousseau and John Dewey, along with other reactionaries in philosophy all denied scientific criteria. They would rather that the masses remain ignorant of how to understand and determine the truth. (shrink)

A. J. Ayer was one of the foremost analytical philosophers of the twentieth century, and was known as a brilliant and engaging speaker. In essays based on his influential Dewey Lectures, Ayer addresses some of the most critical and controversial questions in epistemology and the philosophy of science, examining the nature of inductive reasoning and grappling with the issues that most concerned him as a philosopher. This edition contains revised and expanded versions of the lectures and two additional essays. Ayer (...) begins by considering Hume's formulation of the problem of induction and then explores the inferences on which we base our beliefs in factual matters. In other essays, he defines the three kinds of probability that inform inductive reasoning and examines the various criteria for verifiability and falsifiability. In his extensive introduction, Graham Macdonald discusses the arguments in _Probability and Evidence_, how they relate to Ayer's other works, and their influence in contemporary philosophy. He also provides a brief biographical sketch of Ayer, and includes a bibliography of works about and in response to _Probability and Evidence_. (shrink)

"The philosophical works of A. J. Ayer": p. [334]-341. Bibliography: p. [343]-346. Includes indexes.

I want to discuss a view of punishment which stresses its ‘expressive’ character and seeks in that its justification. While I shall label this view ‘expressionism’, I should warn that most theorists who express an ‘expressionist’ view do not present it as an exhaustive account, but rather claim to be highlighting an aspect that tends to be neglected within the rationalist framework common to retributivism and utilitarianism. Among contemporary writings I shall focus on Joel Feinberg's article, ‘The Expressive Function of (...) Punishment’ in The Monist 49, No. 4 . While I accept that ‘expression’ usefully sums up much of what underlies punitive practices, I shall urge that the term conceals a variety of more or less amalgamated ingredients which need to be disentangled for critical inspection. I shall argue that under those aspects, punishment's justification continues to be elusive. I do not imagine that these arguments will deter my more punitive colleagues from continuing to seek such justification, but I hope they will search elsewhere. Feinberg writes: Punishment is a conventional device for the expression of attitudes of resentment and indignation, and of judgments of disapproval and reprobation, either on the part of the punishing authority himself or of those ‘in whose name’ the punishment is inflicted. Punishment, in short, has a symbolic significance largely missing from other kinds of penalties. (shrink)