Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. This book cuts through a host of technicalities that have obscured previous (...) discussions of these projects, and presents clear, concise accounts of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluate each and to compare different ones. The authors also offer critical discussion, rare in the literature, of the aims and claims of nominalistic interpretation, suggesting that it is significant in a very different way from that usually assumed. (shrink)

Introduction A brief look at the competing present-day interpretations of Hume's philosophy will leave the uninitiated reader completely baffled. On the one hand , Hume is seen as a philosopher who attempted to analyse concepts with ...

While we are commonly told that the distinctive method of mathematics is rigorous proof, and that the special topic of mathematics is abstract structure, there has been no agreement among mathematicians, logicians, or philosophers as to just what either of these assertions means. John P. Burgess clarifies the nature of mathematical rigor and of mathematical structure, and above all of the relation between the two, taking into account some of the latest developments in mathematics, including the rise of experimental (...) mathematics on the one hand and computerized formal proofs on the other hand. Along the way, a great many historical developments in mathematics, philosophy, and logic are surveyed. Yet very little in the way of background knowledge on the part of the reader is presupposed. (shrink)

In this paper Sullins argues that in certain circumstances robots can be seen as real moral agents. A distinction is made between persons and moral agents such that, it is not necessary for a robot to have personhood in order to be a moral agent. I detail three requirements for a robot to be seen as a moral agent. The first is achieved when the robot is significantly autonomous from any programmers or operators of the machine. The second is when (...) one can analyze or explain the robot's behavior only by ascribing to it some predisposition or 'intention' to do good or harm. And finally, robot moral agency requires the robot to behave in a way that shows and understanding of responsibility to some other moral agent. Robots with all of these criteria will have moral rights as well as responsibilities regardless of their status as persons. (shrink)

Mathematics tells us there exist infinitely many prime numbers. Nominalist philosophy, introduced by Goodman and Quine, tells us there exist no numbers at all, and so no prime numbers. Nominalists are aware that the assertion of the existence of prime numbers is warranted by the standards of mathematical science; they simply reject scientific standards of warrant.

This volume reprints a dozen of the author’s papers, most with substantial postscripts, and adds one new one. The bulk of the material is on topics in philosophy of language, but there are also two papers on philosophy of mathematics written after the appearance of the author’s collected papers on that subject, and one on epistemology. As to the substance of Field’s contributions, limitations of space preclude doing much more below than indicating the range of issues addressed, and the general (...) orientation taken towards them. As to the style of his writing, it well exhibits the first of the two virtues, clarity and conciseness, that one looks for in philosophical prose. (shrink)

David Hume's A Treatise of Human Nature presents the most important account of skepticism in the history of modern philosophy. In this lucid and thorough introduction to the work, John P. Wright examines the development of Hume's ideas in the Treatise, their relation to eighteenth-century theories of the imagination and passions, and the reception they received when Hume published the Treatise. He explains Hume's arguments concerning the inability of reason to establish the basic beliefs which underlie science and morals, (...) as well as his arguments showing why we are nevertheless psychologically compelled to accept such beliefs. The book will be a valuable guide for those seeking to understand the nature of modern skepticism and its connection with the founding of the human sciences during the Enlightenment. (shrink)

This book surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in ...

Philosophical 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, focusing on the sometimes problematic relationship between formal apparatus and intuitive motivation. Requiring minimal background and arranged to make the more technical material optional, the book offers a choice between an overview and in-depth study, and it balances (...) the philosophical and technical aspects of the subject.The book emphasizes the relationship between models and the traditional goal of logic, the evaluation of arguments, and critically examines apparatus and assumptions that often are taken for granted. Philosophical Logic provides an unusually thorough treatment of conditional logic, unifying probabilistic and model-theoretic approaches. It underscores the variety of approaches that have been taken to relevantistic and related logics, and it stresses the problem of connecting formal systems to the motivating ideas behind intuitionistic mathematics. Each chapter ends with a brief guide to further reading.Philosophical Logic addresses students new to logic, philosophers working in other areas, and specialists in logic, providing both a sophisticated introduction and a new synthesis. (shrink)

Telerobotically operated and semiautonomous machines have become a major component in the arsenals of industrial nations around the world. By the year 2015 the United States military plans to have one-third of their combat aircraft and ground vehicles robotically controlled. Although there are many reasons for the use of robots on the battlefield, perhaps one of the most interesting assertions are that these machines, if properly designed and used, will result in a more just and ethical implementation of warfare. This (...) paper will focus on these claims by looking at what has been discovered about the capability of humans to behave ethically on the battlefield, and then comparing those findings with the claims made by robotics researchers that their machines are able to behave more ethically on the battlefield than human soldiers. Throughout the paper we will explore the philosophical critique of this claim and also look at how the robots of today are impacting our ability to fight wars in a just manner. (shrink)

John Norton says that philosophers have been led astray for thousands of years by their attempt to treat induction formally. He is correct that such an attempt has caused no end of trouble, but he is wrong about the history. There is a rich tradition of non-formal induction. In fact, material theories of induction prevailed all through antiquity and from the Renaissance to the mid-1800s. Recovering these past systems would not only fill lacunae in Norton’s own theory but would (...) highlight areas where Norton has not freed himself from the straightjacket of formal induction as much as he might think. This essay begins that recovery. (shrink)

A philosopher once wrote the following words:If I examine the PTOLOMAIC and COPERNICAN systems, I endeavour only, by my enquiries, to know the real situation of the planets; that is, in other words, I endeavour to give them, in my conception, the same relations, that they bear towards each other in the heavens. To this operation of the mind, therefore, there seems to be always a real, though often an unknown standard, in the nature of things; nor is truth or (...) falsehood variable by the various apprehensions of mankind. Though all human race should for ever conclude, that the sun moves, and the earth remains at rest, the sun stirs not an inch from his place for all these reasonings; and such conclusions are eternally false and erroneous. (shrink)

Machine generated contents note: 1. Introduction: class, liberty, and popular government; Part I: 2. Peoples, patricians, and the prince; 3. Democratic republics and the oppressive appetite of young nobles; Part II: 4. The benefits and limits of popular participation and judgment; 5. Elections, lotteries and class specific institutions; 6. Political trials and 'the free way of life'; Part III: 7. Republicanism and democracy; 8. Post-electoral republics and the people's tribunate revived.

The debate over whether brain death is death has focused on whether individuals who have sustained total brain failure have satisfied the biological definition of death as “the irreversible loss of the integration of the organism as a whole.” In this paper, I argue that what it means for an organism to be integrated “as a whole” is undefined and vague in the views of those who attempt to define death as the irreversible loss of the integration of the organism (...) as a whole. I show how what it means for a living thing to be integrated as a whole depends on the sortal concept by which it is identified. Since interests, values, and ontological considerations besides strictly biological ones affect the concepts by which we individuate and identify living things, those non-biological considerations have a bearing on what it means for a particular kind of living thing to exist as a whole and thus what it means for one of us to die. Even if our bodies may remain organically integrated in some sense despite total brain failure, this fact should not lead us to reject brain death as death. Artificially sustained brain-dead human bodies are not human beings, but the remains of them. While such bodies may be alive in some sense, they are not human beings or human persons. They are not one of us. (shrink)

The form of nominalism known as 'mathematical fictionalism' is examined and found wanting, mainly on grounds that go back to an early antinominalist work of Rudolf Carnap that has unfortunately not been paid sufficient attention by more recent writers.

The complexity of the set of truths of arithmetic is determined for various theories of truth deriving from Kripke and from Gupta and Herzberger.

A new axiomatization of set theory, to be called Bernays-Boolos set theory, is introduced. Its background logic is the plural logic of Boolos, and its only positive set-theoretic existence axiom is a reflection principle of Bernays. It is a very simple system of axioms sufficient to obtain the usual axioms of ZFC, plus some large cardinals, and to reduce every question of plural logic to a question of set theory.

Neurobiology-based interventions for mental diseases and searches for useful biomarkers of treatment response have largely failed. Clinical trials should assess interventions related to environmental and social stressors, with long-term follow-up; social rather than biological endpoints; personalized outcomes; and suitable cluster, adaptive, and n-of-1 designs. Labor, education, financial, and other social/political decisions should be evaluated for their impacts on mental disease.

By utilizing new information from both clinical and experimental (lesion, electrophysiological, and gene-activation) studies with animals, the anatomy underlying anterograde amnesia has been reformulated. The distinction between temporal lobe and diencephalic amnesia is of limited value in that a common feature of anterograde amnesia is damage to part of an comprising the hippocampus, the fornix, the mamillary bodies, and the anterior thalamic nuclei. This view, which can be traced back to Delay and Brion (1969), differs from other recent models in (...) placing critical importance on the efferents from the hippocampus via the fornix to the diencephalon. These are necessary for the encoding and, hence, the effective subsequent recall of episodic memory. An additional feature of this hippocampalanterior thalamic and the perirhinal–medial dorsal thalamic systems are compromised, leading to severe deficits in both recall and recognition. (shrink)

Saul Kripke has been a major influence on analytic philosophy and allied fields for a half-century and more. His early masterpiece, _Naming and Necessity_, reversed the pattern of two centuries of philosophizing about the necessary and the contingent. Although much of his work remains unpublished, several major essays have now appeared in print, most recently in his long-awaited collection _Philosophical Troubles_. In this book Kripke’s long-time colleague, the logician and philosopher John P. Burgess, offers a thorough and self-contained guide (...) to all of Kripke’s published books and his most important philosophical papers, old and new. It also provides an authoritative but non-technical account of Kripke’s influential contributions to the study of modal logic and logical paradoxes. Although Kripke has been anything but a system-builder, Burgess expertly uncovers the connections between different parts of his oeuvre. Kripke is shown grappling, often in opposition to existing traditions, with mysteries surrounding the nature of necessity, rule-following, and the conscious mind, as well as with intricate and intriguing puzzles about identity, belief and self-reference. Clearly contextualizing the full range of Kripke’s work, Burgess outlines, summarizes and surveys the issues raised by each of the philosopher’s major publications. _Kripke_ will be essential reading for anyone interested in the work of one of analytic philosophy’s greatest living thinkers. (shrink)

(2013). Informed Consent, Big Data, and the Oxymoron of Research That Is Not Research. The American Journal of Bioethics: Vol. 13, No. 4, pp. 40-42. doi: 10.1080/15265161.2013.768864.

The source, status, and significance of the derivation of the necessity of identity at the beginning of Kripke’s lecture “Identity and Necessity” is discussed from a logical, philosophical, and historical point of view.

The publication of a new intellectual biography of George Cheyne provides a "propitious" occasion for "a thoroughly skeptical review" of the question which has long exercised Hume scholars, whether Cheyne was the intended recipient of David Hume's fascinating pre-Treatise Letter to a Physician, the letter which describes his own hypochondriacal physical and mental symptoms and gives an account of his early philosophical development. Hume's nineteenth-century biographer, John Hill Burton, argued that Hume was probably writing to Cheyne, while Ernest Mossner (...) claimed to definitively refute that hypothesis in an article entitled "Hume's Epistle to Dr. Arbuthnot," published in 1944. Anita Guerrini's intellectual biography does not discuss Cheyne as a possible recipient of Hume's letter, but she does present a well-rounded picture of this interesting eighteenth-century physician from which we can judge his appropriateness as its addressee. In the following discussion I will make use of the biographical material found in this new biography of Cheyne, as well as other sources, to show that Mossner's arguments are less than definitive, and that it would be wrong to dismiss the possibility that the letter was sent to George Cheyne. This is a possibility that, for reasons that I will make clear, makes good biographical and philosophical sense. At the same time, it is important to keep a proper suspense of judgment as Burton did, for the evidence that the letter was either intended for or actually sent to Cheyne is not definitive. (shrink)

Psyche and Soma is a multi-disciplinary exploration of the history of understanding of the human mind or soul and its relationship to the body, through the course of more than two thousand years. Thirteen specially commissioned chapters, each written by a recognized expert, discuss such figures as the doctors Hippocrates and Galen, the theologians St Paul, Augustine, and Aquinas, and philosophers from Plato to Leibniz.

This is the first in-depth critical appraisal in English of the political, legal, and cultural writings of Carl Schmitt, perhaps this century's most brilliant critic of liberalism. It offers an assessment of this most sophisticated of fascist theorists without attempting either to apologise for or demonise him. Schmitt's Weimar writings confront the role of technology as it finds expression through the principles and practices of liberalism. Contemporary political conditions such as disaffection with liberalism and the rise of extremist political organizations (...) have rendered Schmitt's work both relevant and insightful. John McCormick examines why technology becomes a rallying cry for both right- and left-wing intellectuals at times when liberalism appears anachronistic, and shows the continuities between Weimar's ideological debates and those of our own age. (shrink)

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel’s incompleteness theorems, but also a large number of optional topics, from Turing’s theory of computability to Ramsey’s theorem. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a (...) traditional stumbling block for students on the way to the Godel incompleteness theorems. (shrink)