Which concepts should we use to think and talk about the world and to do all of the other things that mental and linguistic representation facilitates? This is the guiding question of the field that we call ‘conceptual ethics’. Conceptual ethics is not often discussed as its own systematic branch of normative theory. A case can nevertheless be made that the field is already quite active, with contributions coming in from areas as diverse as fundamental metaphysics and social/political philosophy. In (...) this pair of papers, we try to unify the field, reflecting on its basic nature, structure, and methodology. (shrink)

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)

Conceptual engineering and conceptual ethics are branches of philosophy concerned with questions about how to assess and ameliorate our representational devices (such as concepts and words). It's a part of philosophy concerned with questions about which concepts we should use (and why), how concepts can be improved, when concepts should be abandoned, and how proposals for amelioration can be implemented. Central parts of the history of philosophy have engaged with these issues, but the focus of this volume is on applications (...) to work in contemporary philosophy of language and mind, epistemology, gender and race theory, ethics, philosophy of science, and philosophical logic. This is the first volume devoted entirely to conceptual engineering and conceptual ethics. The volume explores the possibilities, benefits, problems, and applications of conceptual engineering and conceptual ethics. It consists of twenty chapters written by leading philosophers. (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. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a (...) simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual. (shrink)

Which concepts should we use to think and talk about the world, and to do all of the other things that mental and linguistic representation facilitates? This is the guiding question of the field that we call ‘conceptual ethics’. Conceptual ethics is not often discussed as its own systematic branch of normative theory. A case can nevertheless be made that the field is already quite active, with contributions coming in from areas as diverse as fundamental metaphysics and social/political philosophy. In (...) this pair of papers, we try to unify the field, reflecting on its basic nature, structure, and methodology. (shrink)

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)

This is a concise, advanced introduction to current philosophical debates about truth. A blend of philosophical and technical material, the book is organized around, but not limited to, the tendency known as deflationism, according to which there is not much to say about the nature of truth. In clear language, Burgess and Burgess cover a wide range of issues, including the nature of truth, the status of truth-value gaps, the relationship between truth and meaning, relativism and pluralism about truth, and (...) semantic paradoxes from Alfred Tarski to Saul Kripke and beyond. Following a brief introduction that reviews the most influential traditional and contemporary theories of truth, short chapters cover Tarski, deflationism, indeterminacy, realism, antirealism, Kripke, and the possible insolubility of semantic paradoxes. The book provides a rich picture of contemporary philosophical theorizing about truth, one that will be essential reading for philosophy students as well as philosophers specializing in other areas. (shrink)

This is the first systematic survey of modern nominalistic reconstructions of mathematics, and for this reason alone it should be read by everyone interested in the philosophy of mathematics and, more generally, in questions concerning abstract entities. In the bulk of the book, the authors sketch a common formal framework for nominalistic reconstructions, outline three major strategies such reconstructions can follow, and locate proposals in the literature with respect to these strategies. The discussion is presented with admirable precision and clarity, (...) and should be accessible even to readers with only minimal background in logic and mathematics. There will be many who will turn directly to these pages and use them as a brief manual on the state of the art of nominalism in mathematics. But the most intriguing parts of this elegant book—at least in my view—are the introduction and the conclusion, where the authors examine the significance of reconstructive nominalism. (shrink)

This fourth edition of one of the classic logic textbooks has been thoroughly revised by John Burgess. The aim is to increase the pedagogical value of the book for the core market of students of philosophy and for students of mathematics and computer science as well. This book 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. John Burgess has now enhanced the book by adding a selection of problems at the end of each chapter, and by reorganising and rewriting chapters to make them more independent of each other and thus to increase the range of options available to instructors as to what to cover and what to defer. (shrink)

The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework for modern abstract mathematics. Over the past couple of decades, however, logicians and philosophers have discovered that much more is salvageable from the rubble of Frege's system than had previously been assumed. A variety of repaired systems have been (...) proposed, each a consistent theory permitting the development of a significant portion of mathematics. 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 each. John Burgess considers every proposed fix, each with its distinctive philosophical advantages and drawbacks. These systems range from those barely able to reconstruct the rudiments of arithmetic to those that go well beyond the generally accepted axioms of set theory into the speculative realm of large cardinals. For the most part, Burgess finds that attempts to fix Frege do less than advertised to revive his system. This book will be the benchmark against which future analyses of the revival of Frege will be measured. (shrink)

In recent years, there has been growing discussion amongst philosophers about “conceptual engineering”. Put roughly, conceptual engineering concerns the assessment and improvement of concepts, or of other devices we use in thought and talk (e.g., words). This often involves attempts to modify our existing concepts (or other representational devices), and/or our practices of using them. This paper explores the relation between conceptual engineering and conceptual ethics, where conceptual ethics is taken to encompass normative and evaluative questions about concepts, words, and (...) other broadly “representational” and/or “inferential” devices we use in thought and talk. We take some of the central questions in conceptual ethics to concern which concepts we should use and what words should mean, and why. We put forward a view of conceptual engineering in terms of the following three activities: conceptual ethics, conceptual innovation, and conceptual implementation. On our view, conceptual engineering can be defined in terms of these three activities, but not in a straightforward, Boolean way. Conceptual engineering, we argue, is made up of mereologically complex activities whose parts fall into the categories associated with each of these three different activities. (shrink)

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)

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)

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

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 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.

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.

Metasemantics comprises new work on the philosophical foundations of linguistic semantics, by a diverse group of established and emerging experts in the philosophy of language, metaphysics, and the theory of content. The science of semantics aspires to systematically specify the meanings of linguistic expressions in context. The paradigmatic metasemantic question is accordingly: what more basic or fundamental features of the world metaphysically determine these semantic facts? Efforts to answer this question inevitably raise others, including: where are the boundaries of semantics?; (...) what is the essence of the meaning relation?; which framework should we use for semantic theorizing?; and what are the intrinsic natures of semantic values? Metasemantic inquiry has long been recognized as a central part of the philosophy of language, but recent developments in metaphysics and semantics itself now allow us to approach these classic questions with an unprecedented degree of precision. The essays collected here provide promising new perspectives on old problems, pose questions that suggest novel research projects, and taken together, greatly sharpen our understanding of linguistic representation. (shrink)

Rigorous proof is supposed to guarantee that the premises invoked imply the conclusion reached, and the problem of rigor may be described as that of bringing together the perspectives of formal logic and mathematical practice on how this is to be achieved. This problem has recently raised a lot of discussion among philosophers of mathematics. We survey some possible solutions and argue that failure to understand its terms properly has led to misunderstandings in the literature.

The question, "Which modal logic is the right one for logical necessity?," divides into two questions, one about model-theoretic validity, the other about proof-theoretic demonstrability. The arguments of Halldén and others that the right validity argument is S5, and the right demonstrability logic includes S4, are reviewed, and certain common objections are argued to be fallacious. A new argument, based on work of Supecki and Bryll, is presented for the claim that the right demonstrability logic must be contained in S5, (...) and a more speculative argument for the claim that it does not include S4.2 is also presented. (shrink)

BackgroundThe COVID-19 pandemic presents significant challenges to research ethics committees (RECs) in balancing urgency of review of COVID-19 research with careful consideration of risks and benefits. In the African context, RECs are further challenged by historical mistrust of research and potential impacts on COVID-19 related research participation, as well as the need to facilitate equitable access to effective treatments or vaccines for COVID-19. In South Africa, an absent National Health Research Ethics Council (NHREC) also left RECs without national guidance for (...) a significant duration of the COVID-19 pandemic. We conducted a qualitative descriptive study that explored the perspectives and experiences of RECs regarding the ethical challenges of COVID-19 research in South Africa.MethodsWe conducted in-depth interviews with 21 REC chairpersons or members from seven RECs at large academic health institutions across South Africa that were actively involved in the review of COVID-19 related research from January to April 2021. In-depth interviews were conducted remotely via Zoom. Interviews (60–125 min) were conducted in English using an in-depth interview guide, until data saturation was achieved. Audio-recordings were transcribed verbatim and field notes were converted into data documents. Line-by-line coding of transcripts was performed, and data were organised into themes and sub-themes. An inductive approach to thematic analysis was used to analyse data.ResultsFive main themes were identified, namely: rapidly evolving research ethics landscape, extreme vulnerability of research participants, unique challenges to informed consent, challenges to community engagement during COVID-19, and overlapping research ethics and public health equity issues. Sub-themes were identified for each main theme.ConclusionsNumerous, significant ethical complexities and challenges were identified by South African REC members in the review of COVID-19 related research. While RECs are resilient and adaptable, reviewer and REC member fatigue were major concerns. The numerous ethical issues identified also highlight the need for research ethics teaching and training, especially in informed consent, as well as the urgent requirement for the development of national guidelines for research ethics during public health emergencies. Further, comparative analysis between different countries is needed to develop the discourse around African RECs and COVID-19 research ethics issues. (shrink)

Background: Medical Assistance in Dying, also known as euthanasia or assisted suicide, is expanding internationally. Canada is the first country to permit Nurse Practitioners to provide euthanasia. These developments highlight the need for nurses to reflect upon the moral and ethical issues that euthanasia presents for nursing practice. Purpose: The purpose of this article is to provide a narrative review of the ethical arguments surrounding euthanasia in relationship to nursing practice. Methods: Systematic search and narrative review. Nine electronic databases were (...) searched using vocabulary developed from a stage 1 search of Medline and CINAHL. Articles that analysed a focused ethical question related to euthanasia in the context of nursing practice were included. Articles were synthesized to provide an overview of the literature of nursing ethics and euthanasia. Ethical Considerations: This review was conducted as per established scientific guidelines. We have tried to be fair and respectful to the authors discussed. Findings: Forty-three articles were identified and arranged inductively into four themes: arguments from the nature of nursing; arguments from ethical principles, concepts and theories; arguments for moral consistency; and arguments from the nature of the social good. Key considerations included nursing’s moral ontology, the nurse–patient relationship, potential impact on the profession, ethical principles and theories, moral culpability for acts versus omissions, the role of intention and the nature of the society in which euthanasia would be enacted. In many cases, the same assumptions, values, principles and theories were used to argue both for and against euthanasia. Discussion: The review identified a relative paucity of literature in light of the expansion of euthanasia internationally. However, the literature provided a fulsome range of positions for nurses to consider as they reflect on their own participation in euthanasia. Many of the arguments reviewed were not nursing-specific, but rather are relevant across healthcare disciplines. Arguments explicitly grounded within the nature of nursing and nurse–patient relationships warrant further exploration. (shrink)

Population-level biomedical research offers new opportunities to improve population health, but also raises new challenges to traditional systems of research governance and ethical oversight. Partly in response to these challenges, various models of public involvement in research are being introduced. Yet, the ways in which public involvement should meet governance challenges are not well understood. We conducted a qualitative study with 36 experts and stakeholders using the World Café method to identify key governance challenges and explore how public involvement can (...) meet these challenges. This brief report discusses four cross-cutting themes from the study: the need to move beyond individual consent; issues in benefit and data sharing; the challenge of delineating and understanding publics; and the goal of clarifying justifications for public involvement. The report aims to provide a starting point for making sense of the relationship between public involvement and the governance of population-level biomedical research, showing connections, potential solutions and issues arising at their intersection. We suggest that, in population-level biomedical research, there is a pressing need for a shift away from conventional governance frameworks focused on the individual and towards a focus on collectives, as well as to foreground ethical issues around social justice and develop ways to address cultural diversity, value pluralism and competing stakeholder interests. There are many unresolved questions around how this shift could be realised, but these unresolved questions should form the basis for developing justificatory accounts and frameworks for suitable collective models of public involvement in population-level biomedical research governance. (shrink)

The species of indeterminist tense logic called Peircean by A. N. Prior is proved to be recursively decidable.

Nominalism is the view that mathematical objects do not exist. This chapter delimits several types of nominalistic projects: revolutionary programs that attempt to change mathematics and hermeneutic programs that attempt to interpret mathematics. Some programs accord with naturalism, and some oppose naturalism. Steven Yablo’s fictionalism is brought into the fold and discussed at some length.

Perhaps if the future existed, concretely and individually, as something that could be discerned by a better brain, the past would not be so seductive: its demands would he balanced by those of the future. Persons might then straddle the middle stretch of the seesaw when considering this or that object. It might be fun. But the future has no such reality (as the pictured past and the perceived present possess); the future is but a figure of speech, a specter (...) of thought. (shrink)

Today there appears to be a widespread impression that W. V. Quine's notorious critique of modal logic, based on certain ideas about reference, has been successfully answered. As one writer put it some years ago: “His objections have been dead for a while, even though they have not yet been completely buried.” What is supposed to have killed off the critique? Some would cite the development of a new ‘possible-worlds’ model theory for modal logics in the 1960s; others, the development (...) of new ‘direct’ theories of reference for names in the 1970s.These developments do suggest that Quine's unfriendliness towards any formal logics but the classical and indifference towards theories of reference for any singular terms but variables were unfortunate. (shrink)

One thousand stones, suitably arranged, might form a heap. If we remove a single stone from a heap of stones we still have a heap; at no point will the removal of just one stone make sufficient difference to transform a heap into something which is not a heap. But, if this is so, we still have a heap, even when we have removed the last stone composing our original structure. So runs the Sorites paradox. Similar paradoxes can be constructed (...) with any predicate which, like 'heap', displays borderline vagueness. Although I have frequently heard it said that there is no completely credible and satisfying dissolution of the paradoxes of the Sorites family; and although there is no possible approach to dissolution which has not been at least partially explored, philosophers continue glibly to use vague language as though it were entirely unproblematic. Since no argument has ever been produced which would justify our ignoring the para~doxes, this situation is extremely unsatisfactory. (shrink)

A concept of diversity is an understanding of what makes a group diverse that may be applicable in a variety of contexts. We distinguish three diversity concepts, show that each can be found in discussions of diversity in science, and explain how they tend to be associated with distinct epistemic and ethical rationales. Yet philosophical literature on diversity among scientists has given little attention to distinct concepts of diversity. This is significant because the unappreciated existence of multiple diversity concepts can (...) generate unclarity about the meaning of “diversity,” lead to problematic inferences from empirical research, and obscure complex ethical-epistemic questions about how to define diversity in specific cases. We illustrate some ethical-epistemic implications of our proposal by reference to an example of deliberative mini-publics on human tissue biobanking. (shrink)

Extant semantic theories for languages containing vague expressions violate intuition by delivering the same verdict on two principles of classical propositional logic: the law of noncontradiction and the law of excluded middle. Supervaluational treatments render both valid; many-Valued treatments, Neither. The core of this paper presents a natural deduction system, Sound and complete with respect to a 'mixed' semantics which validates the law of noncontradiction but not the law of excluded middle.