Philosophical concerns rarely force their way into the average mathematician’s workday. But, in extreme circumstances, fundamental questions can arise as to the legitimacy of a certain manner of proceeding, say, as to whether a particular object should be granted ontological status, or whether a certain conclusion is epistemologically warranted. There are then two distinct views as to the role that philosophy should play in such a situation. On the first view, the mathematician is called upon to turn to the counsel (...) of philosophers, in much the same way as a nation considering an action of dubious international legality is called upon to turn to the United Nations for guidance. After due consideration of appropriate regulations and guidelines (and, possibly, debate between representatives of different philosophical factions), the philosophers render a decision, by which the dutiful mathematician abides. Quine was famously critical of such dreams of a ‘first philosophy.’ At the opposite extreme, our hypothetical mathematician answers only to the subject’s internal concerns, blithely or brashly indifferent to philosophical approval. What is at stake to our mathematician friend is whether the questionable practice provides a proper mathematical solution to the problem at hand, or an appropriate mathematical understanding; or, in pragmatic terms, whether it will make it past a journal referee. In short, mathematics is as mathematics does, and the philosopher’s task is simply to make sense of the subject as it evolves and certify practices that are already in place. In his textbook on the philosophy of mathematics (Shapiro, 2000), Stewart Shapiro characterizes this attitude as ‘philosophy last, if at all.’. (shrink)

Contributors discuss the work of thinkers such as Cass Sunstein and Jeremy Waldron in their exploration of the relations between philosophical theories and everyday life. They elucidate major attempts to reconcile theory with practice in the Western tradition, from Herodotus to Heidegger, and discuss topics such as the role of theory in judicial decision-making and the political implication of theory. Of interest to philosophers, lawyers, and social scientists. Annotation copyright by Book News, Inc., Portland, OR.

Stewart Shapiro's ambition in Vagueness in Context is to develop a comprehensive account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary according to their context: a person can be tall with respect to male accountants and not tall (even short) with respect to professional basketball players. The key feature of Shapiro's account is that the extensions of (...) vague terms also vary in the course of conversations and that, in some cases, a competent speaker can go either way without sinning against the meaning of the words or the non-linguistic facts. As Shapiro sees it, vagueness is a linguistic phenomenon, due to the kinds of languages that humans speak; but vagueness is also due to the world we find ourselves in, as we try to communicate features of it to each other. (shrink)

As idealized descriptions of mathematical language, there is a sense in which formal systems specify too little, and there is a sense in which they specify too much. On the one hand, formal languages fail to account for a number of features of informal mathematical language that are essential to the communicative and inferential goals of the subject. On the other hand, many of these features are independent of the choice of a formal foundation, so grounding their analysis on a (...) particular choice of a formal system introduces unnecessary specificity. This chapter begins to map out the design features of mathematical language without descending to the level of formal implementation, drawing on examples from the mathematical literature and insights from the design of computational proof assistants and their libraries. (shrink)

We examine George Boolos's proposed abstraction principle for extensions based on the limitation-of-size conception, New V, from several perspectives. Crispin Wright once suggested that New V could serve as part of a neo-logicist development of real analysis. We show that it fails both of the conservativeness criteria for abstraction principles that Wright proposes. Thus, we support Boolos against Wright. We also show that, when combined with the axioms for Boolos's iterative notion of set, New V yields a system equivalent to (...) full Zermelo-Fraenkel set theory with a principle of global choice. This advances Boolos's longstanding interest in the foundations of set theory. (shrink)

The revisionary approach to semantic paradox is commonly thought to have a somewhat uncomfortable corollary, viz. that, on pain of triviality, we cannot affirm that all valid arguments preserve truth (Beall2007, Beall2009, Field2008, Field2009). We show that the standard arguments for this conclusion all break down once (i) the structural rule of contraction is restricted and (ii) how the premises can be aggregated---so that they can be said to jointly entail a given conclusion---is appropriately understood. In addition, we briefly rehearse (...) some reasons for restricting structural contraction. (shrink)

Next SectionIntensification of poverty and degradation of health infrastructure over recent decades in countries most affected by HIV/AIDS present formidable challenges to clinical research. This paper addresses the overall standard of health care (SOC) that should be provided to research participants in developing countries, rather than the narrow definition of SOC that has characterised the international debate on standards of health care. It argues that contributing to sustainable improvements in health by progressively ratcheting the standard of care upwards for research (...) participants and their communities is an ethical obligation of those in resource-rich countries who sponsor and implement research in poorer ones. (shrink)

Cells are cognitive entities possessing great computational power. DNA serves as a multivalent information storage medium for these computations at various time scales. Information is stored in sequences, epigenetic modifications, and rapidly changing nucleoprotein complexes. Because DNA must operate through complexes formed with other molecules in the cell, genome functions are inherently interactive and involve two-way communication with various cellular compartments. Both coding sequences and repetitive sequences contribute to the hierarchical systemic organization of the genome. By virtue of nucleoprotein complexes, (...) epigenetic modifications, and natural genetic engineering activities, the genome can serve as a read-write storage system. An interactive informatic conceptualization of the genome allows us to understand the functional importance of DNA that does not code for protein or RNA structure, clarifies the essential multidirectional and systemic nature of genomic information transfer, and emphasizes the need to investigate how cellular computation operates in reproduction and evolution. (shrink)

Most of us believe that partiality applies in a broad range of relationships. One relationship on which there is much disagreement is co-nationality. Some writers argue that co-national partiality is not justified in certain cases, like killing in war, since killing in defense of co-nationals is intuitively impermissible in other contexts. I argue that this approach overlooks an important structural feature of partiality—namely, that its scope is sometimes restricted. In this essay, I show how some relationships that generate reasons of (...) partiality are restricted in scope—that is, they generate reasons within particular contexts or with respect to particular goods. I then argue that co-national partiality is scope restricted. I then show how this fact helps proponents of co-national partiality overcome the aforementioned objection to its application in cases like war. (shrink)

I respond to Fishkin?s critique of my book The State of Democratic Theory. I reiterate my defense of a competitive model of democracy geared to reducing domination, rather than Fishkin?s deliberative model that deploys structured discussion to enlighten mass preferences. In light of the literatures on framing effects and the value of mutually independent judgments, I question whether the procedures Fishkin recommends would produce outcomes that are better informed rather than differently informed. Recognizing that deliberation might sometimes be helpful in (...) reducing domination, I note that sometimes it will not, and I fault Fishkin for his indiscriminate embrace of exceedingly costly deliberative mechanisms that promise dubious benefits? notably his and Bruce Ackerman?s?Deliberation Day? (shrink)

The contractarian theory elaborated by John Rawls in A Theory of Justice exploits the difference principle in a great many ways. Rawls argues that, when used as part of a set of guiding principles for structuring the basic institutions of society, it simplifies the problem of interpersonal comparisons (91-4)1, helps compensate for the arbitrariness of natural endowments (101-3), promotes a harmony of interests between citizens (104-5), reintroduces the principle of fraternity to democratic society (105-6), and, what is critical to his (...) contractarian theory, it is an essential part of the principles of justice which would be chosen by free, equal, and rational persons in the original position. (shrink)

Building on recent work, I present sequent systems for the non-classical logics LP, K3, and FDE with two main virtues. First, derivations closely resemble those in standard Gentzen-style systems. Second, the systems can be obtained by reformulating a classical system using nonstandard sequent structure and simply removing certain structural rules (relatives of exchange and contraction). I clarify two senses in which these logics count as “substructural.”.

Plato is often acknowledged as the first philosophical critic of democracy and his Republic is regularly taken as a paradigm of an anti-democratic work. While it is true that Plato objected to much about the democracy of his own time, Plato’s political theorizing also reveals an interest in improving democratic institutions. This chapter explores three themes in Plato’s thinking about democracy: firstly, Plato's insistence that rulers should be knowledgeable and his claim that most people are politically incompetent (§1); secondly, Plato's (...) criticisms of oratory and the corrupting effects of public rhetoric (§2); thirdly, Plato's use of democratic institutions in the Laws (§3). Once we appreciate these different evaluations of democratic practices, we can see that Plato was not simply ‘anti-democratic’ or ‘pro-democratic’ but thought some democratic practices should be abandoned, some reformed, and some adopted. (shrink)

Of all the demands that mathematics imposes on its practitioners, one of the most fundamental is that proofs ought to be correct. It has been common since the turn of the twentieth century to take correctness to be underwritten by the existence of formal derivations in a suitable axiomatic foundation, but then it is hard to see how this normative standard can be met, given the differences between informal proofs and formal derivations, and given the inherent fragility and complexity of (...) the latter. This essay describes some of the ways that mathematical practice makes it possible to reliably and robustly meet the formal standard, preserving the standard normative account while doing justice to epistemically important features of informal mathematical justification. (shrink)

The COVID-19 global pandemic has shone a light on several important ethical questions, ranging from fairness in resource allocation to the ethical justification of government mandates. In addition to these institutional issues, there are also several ethical questions that arise at the interpersonal level. This essay focuses on several of these issues. In particular, I argue that, despite the insistence in public health messaging that avoiding infecting others constitutes ‘saving lives’, virus transmission that results in death constitutes an act of (...) killing. Whether this killing is wrongful depends on several factors. I consider one intuitively plausible view—namely, that in many cases, killing via unintentional transmission is not wrongful, because the parties in question have implicitly waived their rights against this harm, often via reciprocal risk imposition. I argue that this view is mistaken, but that its central insight can be better captured by identifying the appropriate standards of blame that we ought to apply during a pandemic. I conclude by showing how these conclusions can be fruitfully applied to certain institutional questions, such as helping to justify restricting government mandates. (shrink)

We discuss from a philosophical perspective the way in which the normal concept of time might be said to `emerge' in a quantum theory of gravity. After an introduction, we briefly discuss the notion of emergence, without regard to time. We then introduce the search for a quantum theory of gravity ; and review some general interpretative issues about space, time and matter. We then discuss the emergence of time in simple quantum geometrodynamics, and in the Euclidean approach. Section 6 (...) concludes. (shrink)

"Arguing that debates over legitimacy, political violence, freedom, and justice would benefit greatly from cross-tradition theorizing, this book shows how putting analytic and continental political theory in conversation would help us to overcome these intractable problems"--.

It's often said that according to deflationary theories of truth, truth is not a ‘substantial’ property. While this is a fine slogan, it is far from transparent what deflationists mean (or ought to mean) in saying that truth is ‘insubstantial’. Focusing so intently upon the concept of truth and the word ‘true’, I argue, deflationists and their critics have been insufficiently attentive to a host of metaphysical complexities that arise for deflationists in connection with the property of truth. My aim (...) is to correct several misunderstandings as to what deflationists are after here—including some harboured by deflationists themselves—and to offer an account of the commitments about truth's nature that they ought to undertake. In developing this account, I focus particularly upon the issue of what metaphysics of truth a Horwichian minimalist ought to adopt. (shrink)

This volume makes available one of the central texts in the development of utilitarian tradition, in the authoritative 1977 edition prepared by Professors Burns and Hart as part of Bentham's Collected Works. Certain that history was on his side, Bentham sought to rid the world of the hideous mess wrought by legal obfuscation and confusion, and to transform politics into a rational, scientific activity, premised on the fundamental axiom that "it is the greatest happiness of the greatest number that is (...) the measure of right and wrong.". (shrink)

Debates about the semantics and pragmatics of predicates of personal taste have largely centered on contextualist and relativist proposals. In this paper, I argue in favor of an alternative, absolutist analysis of PPT. Theorists such as Max Kölbel and Peter Lasersohn have argued that we should dismiss absolutism due to its inability to accommodate the possibility of faultless disagreement involving PPT. My aim in the paper is to show how the absolutist can in fact accommodate this possibility by drawing on (...) an account of faultless disagreement that improves upon a recent proposal due to Karl Schafer. In amending Schafer’s proposal, I put forward an empirically informed view of our beliefs regarding matters of personal taste, as well as an account of our assertions concerning such matters. I also argue that absolutists should take disagreement about these matters to be conative, rather than doxastic, in nature. The anticipated result is an independently compelling account of faultless disagreement about matters of personal taste that fits naturally with absolutism. (shrink)

The new critical edition of the works and correspondence of Jeremy Bentham is being prepared and published under the supervision of the Bentham Committee of University College London. In spite of his importance as jurist, philosopher, and social scientist, and leader of the Utilitarian reformers, the only previous edition of his works was a poorly edited and incomplete one brought out within a decade or so of his death. Eight volumes of the new Collected Works, five of correspondence, and (...) three of writings on jurisprudence, appeared between 1968 and 1981, published by the Athlone Press. Further volumes in the series since then are published by Oxford University Press. The overall plan and principles of the edition are set out in the General Preface to The Correspondence of Jeremy Bentham, vol. 1, which was the first volume of the Collected Works to be published.An Introduction to the Principles of Morals and Legislation, Jeremy Bentham's best-known work, is a classic text in modern philosophy and jurisprudence. First published in 1789, it contains the important statement of the foundations of utilitarian philosophy and a pioneering study of crime and punishment, both of which remain at the heart of contemporary debates in moral and political philosophy, economics, and legal theory. Printed here in full is the definitive edition, edited by the distinguished scholars J. H. Burns and H. L. A. Hart. An introductory essay by Hart, first published in 1982 and a widely acknowledged classic in its own right, is reprinted here. It contains an important analysis of Bentham's principle of utility, theory of action, and an account of the relationship between law and morality.A new introduction by the leading Bentham scholar F. Rosen, specially written for this Clarendon Paperback edition, provides students with a helpful survey of Bentham's main ideas and an extensive bibliographical study of recent critical work on Bentham. Professor Rosen's essay also contains a new analysis of the principle of utility in Bentham's philosophy which is compared with its use in Hume and J. S. Mill. (shrink)

In a wide range of fields, the word “modular” is used to describe complex systems that can be decomposed into smaller systems with limited interactions between them. This essay argues that mathematical knowledge can fruitfully be understood as having a modular structure and explores the ways in which modularity in mathematics is epistemically advantageous.

Foucault and Religion seeks to unearth a new dimension of Foucault scholarship. Renowned Foucault scholar Jeremy Carrette reveals not simply how Foucault's work can be applied to religion but how a religious question at the heart of Foucault's own work offers a radical challenge to religious ideas. Carrette argues that Foucault offers a twofold critique of Christianity by bringing the body and sexuality into religious practice and exploring a political spirituality of the self. This first major commentary on Foucault (...) and religion opens up the diverse religious questions the philosopher raises in his work, and sheds new light on how Foucault challenges religious thinking and transforms religious understanding. (shrink)

While Descartes’s Passions of the Soul has been taken to hold a place in the history to human physiology, until recently philosophers have neglected the work. In this research summary, I set Descartes’s last published work in context and then sketch out its philosophical significance. From it, we gain further insight into Descartes’s solution to the Mind--Body Problem -- that is, to the problem of the ontological status of the mind--body union in a human being, to the nature of body--mind (...) causation, and to the way body-caused thoughts represent the world. In addition, the work contains Descartes’s developed ethics, in his account of virtue and of the passion of générosité in particular. Through his taxonomy of the passions and the account of their regulation, we also learn more about his moral psychology. (shrink)

This paper provides a method for characterizing space events using the framework of conceptual spaces. We focus specifically on estimating and ranking the likelihood of collisions between space objects. The objective is to design an approach for anticipatory decision support for space operators who can take preventive actions on the basis of assessments of relative risk. To make this possible our approach draws on the fusion of both hard and soft data within a single decision support framework. Contextual data is (...) also taken into account, for example data about space weather effects, by drawing on the Space Domain Ontologies, a large system of ontologies designed to support all aspects of space situational awareness. The framework is coupled with a mathematical programming scheme that frames a mathematically optimal approach for decision support, providing a quantitative basis for ranking potential for collision across multiple satellite pairs. The goal is to provide the broadest possible information foundation for critical assessments of collision likelihood. (shrink)

This essay argues that techniques for assessing testimonial credibility were well established in English legal contexts before they appeared in English natural philosophy. ‘Matters of fact’ supported by testimony referred to human actions and events before the concept was applied to natural phenomena. The article surveys English legal views about testimony and argues that the criteria for credible testimony in both legal and scientific venues were not limited to those of gentle status. Natural philosophers became concerned with testimony when they (...) shifted their attention from universal statements about nature to particular natural and experimental events. Testimony thus became important in the construction of natural and experimental histories constructed by English naturalists. The shift to a more Baconian approach to natural investigation, itself shaped in part by legal concepts and practice, made it possible for members of the Royal Society to adopt an already familiar and societally approved approach to testimony. However, the essay also suggests how the use of scientific instruments and the desire to avoid the adversarial processes of the law modified legal conditions for fact determination, and made it possible for later generations to associate the concept of fact, supported by credible testimony, with the natural rather than the human sciences.Author Keywords: Natural history; Natural philosophy; Testimony; Credibility; Science and law. (shrink)

In this paper, I discuss two concerns for pluralist truth theories: a concern about a key detail of these theories and a concern about their viability. The detail-related concern is that pluralists have relied heavily upon the notion of a domain, but it is not transparent what they take domains to be. Since the notion of a domain has been present in philosophy for some time, it is important for many theorists, not only truth pluralists, to be clear on what (...) domains are and what work they can do. The viability-related concern is that it’s not clear how a pluralist truth theory could explain the truth-conditions of mixed atomic propositions. To address this concern, truth pluralists should recognize something to which they have not been sufficiently attentive: that some atomic propositions belong to more than one domain. But, recognizing this requires rethinking the relationships between the nature of propositions, their membership in domains, and their truth. I address these issues and propose an understanding of them that is preferable to the best existing account of them, that offered by Michael Lynch. (shrink)