Anti-exceptionalism about logic takes logical theories to be continuous with scientific theories. Scientific theories are subject to criteria of theoretical equivalence. This article compares two types of theoretical equivalence – one syntactic and one semantic – in the context of logical anti-exceptionalism, and argues that the syntactic approach leads to undesirable consequences. The anti-exceptionalist should therefore take a semantic approach when evaluating whether logical theories, understood as scientific theories, are equivalent. This article argues for a particular semantic approach, in terms (...) of categorical equivalence, to determine whether logical theories are equivalent. (shrink)

_ doi:10.1093/analys/anx072 _, published: 27 June 2017.

Linnebo and Pettigrew have recently developed a version of non-eliminative mathematical structuralism based on Fregean abstraction principles. They recognize that this version of structuralism is vulnerable to the well-known problem of non-rigid structures. This paper offers a solution to the problem for this version of structuralism. The solution involves expanding the languages used to describe mathematical structures. We then argue that this solution is philosophically acceptable to those who endorse mathematical structuralism based on Fregean abstraction principles.

Thought: A Journal of Philosophy, EarlyView.

This paper describes a modal conception of sets, according to which sets are 'potential' with respect to their members. A modal theory is developed, which invokes a naive comprehension axiom schema, modified by adding `forward looking' and `backward looking' modal operators. We show that this `bi-modal' naive set theory can prove modalized interpretations of several ZFC axioms, including the axiom of infinity. We also show that the theory is consistent by providing an S5 Kripke model. The paper concludes with some (...) discussion of the nature of the modalities involved, drawing comparisons with noneism, the view that there are some non-existent objects. (shrink)

Øystein Linnebo and Richard Pettigrew have recently developed a version of non-eliminative mathematical structuralism based on Fregean abstraction principles. They argue that their theory of abstract structures proves a consistent version of the structuralist thesis that positions in abstract structures only have structural properties. They do this by defining a subset of the properties of positions in structures, so-called fundamental properties, and argue that all fundamental properties of positions are structural. In this article, we argue that the structuralist thesis, even (...) when restricted to fundamental properties, does not follow from the theory of structures that Linnebo and Pettigrew have developed. To make their account work, we propose a formal framework in terms of Kripke models that makes structural abstraction precise. The formal framework allows us to articulate a revised definition of fundamental properties, understood as intensional properties. Based on this revised definition, we show that the restricted version of the structuralist thesis holds. 1Introduction 2The Structuralist Thesis 3LP-Structuralism 4Purity 5A Formal Framework for Structural Abstraction 6Fundamental Relations 7The Structuralist Thesis Vindicated 8Conclusion. (shrink)

In this paper, we explore the idea that sets depend on, or are grounded in, their members. It is said that a set depends on each of its members, and not vice versa. Members do not depend on the sets that they belong to. We show that the intuitive modal truth conditions for dependence, given in terms of possible worlds, do not accurately capture asymmetric dependence relations between sets and their members. We extend the modal truth conditions to include impossible (...) worlds and give a more satisfactory account of the dependence of a set on its members. Focusing on the case of singletons, we articulate a logical framework in which to evaluate set-theoretic dependence claims, using a normal first-order modal logic. We show that on this framework the dependence of a singleton on its single members follows from logic alone. However, the converse does not hold. (shrink)

Øystein Linnebo and Richard Pettigrew have recently developed a version of non-eliminative mathematical structuralism based on Fregean abstraction principles. They argue that their theory of abstract structures proves a consistent version of the structuralist thesis that positions in abstract structures only have structural properties. They do this by defining a subset of the properties of positions in structures, so-called fundamental properties, and argue that all fundamental properties of positions are structural. In this paper, we argue that the structuralist thesis, even (...) when restricted to fundamental properties, does not follow from the theory of structures that Linnebo and Pettigrew have developed. To make their account work, we propose a formal framework in terms of Kripke models that makes structural abstraction precise. The formal framework allows us to articulate a revised definition of fundamental properties, understood as intensional properties. Based on this revised definition, we show that the restricted version of the structuralist thesis holds. (shrink)

Conceptions of Set and the Foundations of Mathematics By IncurvatiLucaCambridge University Press, 2020. xvi + 238 pp.

Mathematical structuralism can be understood as a theory of mathematical ontology, of the objects that mathematics is about. It can also be understood as a theory of the semantics for mathematical discourse, of how and to what mathematical terms refer. In this paper we propose an epistemological interpretation of mathematical structuralism. According to this interpretation, the main epistemological claim is that mathematical knowledge is purely structural in character; mathematical statements contain purely structural information. To make this more precise, we invoke (...) a notion that is central to mathematical epistemology, the notion of (informal) proof. Appealing to the notion of proof, an epistemological version of the structuralist thesis can be formulated as: Every mathematical statement that is provable expresses purely structural information. We introduce a bi-modal framework that formalizes the notions of structural information and informal provability in order to draw connections between them and confirm that the epistemological structuralist thesis holds. (shrink)

Structuralism, the view that mathematics is the science of structures, can be characterized as a philosophical response to a general structural turn in modern mathematics. Structuralists aim to understand the ontological, epistemological, and semantical implications of this structural approach in mathematics. Theories of structuralism began to develop following the publication of Paul Benacerraf’s paper ‘What numbers could not be’ in 1965. These theories include non-eliminative approaches, formulated in a background ontology of sui generis structures, such as Stewart Shapiro’s ante rem (...) structuralism and Michael Resnik’s pattern structuralism. In contrast, there are also eliminativist accounts of structuralism, such as Geoffrey Hellman’s modal structuralism, which avoids sui generis structures. These research projects have guided a more systematic focus on philosophical topics related to mathematical structuralism, including the identity criteria for objects in structures, dependence relations between objects and structures, and also, more recently, structural abstraction principles. Parallel to these developments are approaches that describe mathematical structure in category-theoretic terms. Category-theoretic approaches have been further developed using tools from homotopy type theory. Here we find a strong relationship between mathematical structuralism and the univalent foundations project, an approach to the foundations of mathematics based on higher category theory. (shrink)

This new edition includes a substantial postscript by the author, in which he responds to thirty years of discussion, criticism and further work in the field to ...

Natural Law and Natural Rights is widely recognised as a seminal contribution to the philosophy of law, and an essential reference point for all students of the subject. This new edition includes a substantial postscript by the author responding to thirty years of comment, criticism, and further work in the field.

This launch volume in the Founders of Modern Political and Social Thought series presents a critical examination of Aquinas' thought, combining an accessible, historically-informed account of his work with an assessment of his central ideas and arguments. John Finnis presents a richly-documented critical review of Aquinas's thought on morality, politics, law, and method in social science. Unique in his coverage of Aquinas's primary and secondary texts and his own vigorous argumentation on many themes, the author focuses on the philosophy (...) in Aquinas's texts, and demonstrates how this interconnects with the theological elements. Professor Finnis shows how Aquinas, despite some medieval limitations, makes clear and profound contributions to present debates. (shrink)

SYMBOLIC LOGIC. CHAPTER I. ON THE FORMS OF LOGICAL PROPOSITION. IT has been mentioned in the Introduction that the System of Logic which this work is ...

The main theme of this book is the challenge to ethics from philosophical scepticism and from contemporary forms of consequentialism.

With precision and profundity born of 30 years of devoted study, John Boyle offers an essential introduction to St. Thomas Aquinas on Scripture, shedding helpful light on the goals, methods, and commitments that animate the Angelic Doctor's engagement with the sacred page. Because the genius of St. Thomas's approach to the Bible lies not so much in its novelty but rather in the fidelity and clarity with which he recapitulates the riches of the preceding interpretive Tradition, this initiation into (...) St. Thomas's vision of Scripture is itself an orientation to the Church's vision of Scripture, from the Fathers through and beyond the Middle Ages. St. Thomas's embeddedness within the Church's Tradition and his own historical context is integral to his approach to Scripture, yet it sets him at some distance from modern readers, for whom his interpretive vision may seem perplexing or even impenetrable. In this Primer, Boyle first provides an acclimation to this medieval context through a survey and explanation of pertinent technical terminology used by St. Thomas and characteristic of the scholastic theology of the time. With an eye to the medieval practice of considering Scripture according to the fourfold division of causes, Boyle builds on this initial foundation by exploring in turn St. Thomas's accounts of the end or use of Scripture (final cause), its divine and human authorship (efficient cause), its order and division (material cause), and its literary styles or genres (formal cause). Drawing on writings from across St. Thomas's corpus, but especially his work On the Commendation and Division of Sacred Scripture and the prologues to his biblical commentaries, Boyle masterfully elucidates both the hermeneutical principles and deep wisdom of the Angelic Doctor's approach to Scripture, imparting invaluable guidance not only for reading and understanding St. Thomas and other great masters of the Tradition, but also-and ultimately-for understanding Scripture in light of this Tradition and reading it with greater benefit and joy. (shrink)

The notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master. In particular, undergraduate mathematics students often experience difficulties in understanding and constructing proofs. Understanding Mathematical Proof describes the nature of mathematical proof, explores the various techniques that mathematicians adopt to prove their results, and offers advice and strategies for constructing proofs. It will improve students’ ability to understand proofs and construct correct proofs of their own. The (...) first chapter of the text introduces the kind of reasoning that mathematicians use when writing their proofs and gives some example proofs to set the scene. The book then describes basic logic to enable an understanding of the structure of both individual mathematical statements and whole mathematical proofs. It also explains the notions of sets and functions and dissects several proofs with a view to exposing some of the underlying features common to most mathematical proofs. The remainder of the book delves further into different types of proof, including direct proof, proof using contrapositive, proof by contradiction, and mathematical induction. The authors also discuss existence and uniqueness proofs and the role of counter examples. (shrink)

Despite recurring efforts, a gap exists across a variety of contexts between the protection of patients' safety in theory and in practice. This timely Research Handbook highlights these critical issues and suggests both legal and policy changes are necessary to better protect patients' safety. Multidisciplinary in nature, this Research Handbook features contributions from eminent academics, policy makers and medical practitioners from the Global North and South, discussing the essential facets concerning patient safety and the law. It highlights how the role (...) of legislation and case law has the potential to influence, both positively and negatively, medical practice and the quality of care. Chapters explore patient safety and the global health agenda; physiotherapy; 'non-therapeutic' clinical research with children; patient safety awareness in healthcare education; and the increasing use of robotics and artificial intelligence in healthcare. Outlining a wide range of international perspectives on patient safety and the law, this Research Handbook will appeal to academics and researchers specialising in health and medical law, human rights and healthcare regulation. It will also serve as a valuable resource for legal and medical practitioners alike, as well as clinicians and professionals working in healthcare governance. (shrink)

For this second edition, the editors have returned to Austin's original lecture notes, amending the printed text where it seemed necessary.

This two-volume work, first published in 1843, was John Stuart Mill's first major book. It reinvented the modern study of logic and laid the foundations for his later work in the areas of political economy, women's rights and representative government. In clear, systematic prose, Mill disentangles syllogistic logic from its origins in Aristotle and scholasticism and grounds it instead in processes of inductive reasoning. An important attempt at integrating empiricism within a more general theory of human knowledge, the work (...) constitutes essential reading for anyone seeking a full understanding of Mill's thought. Continuing the discussion of induction, Volume 2 concludes with Book VI, 'On the Logic of the Moral Sciences', in which Mill applies empirical reasoning to human behaviour. A crucial early formulation of his thinking regarding free will and necessity, this book establishes the centrality of 'the social science' to Mill's philosophy. (shrink)

The Machiavellian Moment is a classic study of the consequences for modern historical and social consciousness of the ideal of the classical republic revived by Machiavelli and other thinkers of Renaissance Italy. J.G.A. Pocock suggests that Machiavelli's prime emphasis was on the moment in which the republic confronts the problem of its own instability in time, and which he calls the "Machiavellian moment." After examining this problem in the thought of Machiavelli, Guicciardini, and Giannotti, Pocock turns to the revival of (...) republican thought in Puritan England and in Revolutionary and Federalist America. He argues that the American Revolution can be considered the last great act of civic humanism of the Renaissance. He relates the origins of modern historicism to the clash between civic, Christian, and commercial values in the thought of the eighteenth century. (shrink)

Dewey's book on Democracy and Education established his credentials in the field of education and once counted as his most important book. It has been re-published in many editions and continuously in print ever since the original publication in 1916.

Though the revised edition of A Theory of Justice, published in 1999, is the definitive statement of Rawls's view, so much of the extensive literature on Rawls's theory refers to the first edition. This reissue makes the first edition once again available for scholars and serious students of Rawls's work.

In recent years, the phenomena of hormonal control, embryonic determination and pattern formation have been receiving intensive scrutiny from molecular biologists. In the following «Roots» contribution, Professor Sir Vincent B. Wigglesworth reviews some of the seminal work that he did on these subjects in the insect Rhodnius prolixus.

The book also includes a chronological table of significant events, select bibliography, succinct explanatory notes, and an index--all of which supply ...

This book continues and revises the ideas of justice as fairness that John Rawls presented in _A Theory of Justice_ but changes its philosophical interpretation in a fundamental way. That previous work assumed what Rawls calls a "well-ordered society," one that is stable and relatively homogenous in its basic moral beliefs and in which there is broad agreement about what constitutes the good life. Yet in modern democratic society a plurality of incompatible and irreconcilable doctrines--religious, philosophical, and moral--coexist within (...) the framework of democratic institutions. Recognizing this as a permanent condition of democracy, Rawls asks how a stable and just society of free and equal citizens can live in concord when divided by reasonable but incompatible doctrines? This edition includes the essay "The Idea of Public Reason Revisited," which outlines Rawls ' plans to revise _Political Liberalism,_ which were cut short by his death. "An extraordinary well-reasoned commentary on _A Theory of Justice_...a decisive turn towards political philosophy." --_Times Literary Supplement_. (shrink)

The renowned philosopher John Searle reveals the fundamental nature of social reality. What kinds of things are money, property, governments, nations, marriages, cocktail parties, and football games? Searle explains the key role played by language in the creation, constitution, and maintenance of social reality. We make statements about social facts that are completely objective, for example: Barack Obama is President of the United States, the piece of paper in my hand is a twenty-dollar bill, I got married in London, (...) etc. And yet these facts only exist because we think they exist. How is it possible that we can have factual objective knowledge of a reality that is created by subjective opinions? This is part of a much larger question: How can we give an account of ourselves, with our peculiar human traits DS mind, reason, freedom, society - in a world that we know independently consists of mindless, meaningless particles? How can we account for our social and mental existence in a realm of brute physical facts? In answering this question, Searle avoids postulating different realms of being, a mental and a physical, or worse yet, a mental, a physical, and a social. There is just one reality: Searle shows how the human reality fits into that one reality. Mind, language, and civilization are natural products of the basic facts of the physical world described by physics, chemistry and biology. Searle explains how language creates and maintains the elaborate structures of human social institutions. These institutions serve to create and distribute power relations that are pervasive and often invisible. These power relations motivate human actions in a way that provides the glue that holds human civilization together. Searle shows how this account illuminates human rationality, free will, political power, and human rights. Our social world is a world created and maintained by language. (shrink)

This book comprises all of John Bell's published and unpublished papers in the field of quantum mechanics, including two papers that appeared after the first edition was published. It also contains a preface written for the first edition, and an introduction by Alain Aspect that puts into context Bell's great contribution to the quantum philosophy debate. One of the leading expositors and interpreters of modern quantum theory, John Bell played a major role in the development of our current (...) understanding of the profound nature of quantum concepts. First edition Hb (1987): 0-521-33495-0 First edition Pb (1988): 0-521-36869-3. (shrink)

In The Construction of Social Reality, John Searle argues that there are two kinds of facts--some that are independent of human observers, and some that require..

Reissued here in its corrected second edition of 1864, this essay by John Stuart Mill argues for a utilitarian theory of morality. Originally printed as a series of three articles in Fraser's Magazine in 1861, the work sought to refine the 'greatest happiness' principle that had been championed by Jeremy Bentham, defending it from common criticisms, and offering a justification of its validity. Following Bentham, Mill holds that actions can be judged as right or wrong depending on whether they (...) promote happiness or 'the reverse of happiness'. Although attracted by Bentham's consequentialist framework based on empirical evidence rather than intuition, Mill separates happiness into 'higher' and 'lower' pleasures, arguing for a weighted system of measurement when making and judging decisions. Dissected and debated since its first appearance, the essay is Mill's key discussion on the topic and remains a fundamental text in the study of ethics. (shrink)

A Norton Library edition of Locke's Second Treatise of Government, edited by A. John Simmons.

Much as we would like to conceive empirical thought as rationally grounded in experience, pitfalls await anyone who tries to articulate this position, and ...

John Henry Newman was a theologian and vicar at the university church in Oxford who became a leading thinker in the Oxford Movement, which sought to return Anglicanism to its Catholic roots. Newman converted to Catholicism in 1845 and became a cardinal in 1879. He published widely during his lifetime; his work included novels, poetry and the famous hymn 'Lead, Kindly Light', but he is most esteemed for his sermons and works of religious thought. This volume, first published in (...) 1870, is an ambitious examination of the logical processes that underpin religious faith. Newman discusses how it is possible to believe what cannot be proven empirically, and postulates that the mind has the facility to bridge the logic gap to allow for humans to believe in things that they do not fully comprehend. A lucid and masterful work which remains relevant to contemporary discussions of faith. (shrink)