Category theory and topos theory have been seen as providing a structuralist framework for mathematics autonomous vis-a-vis set theory. It is argued here that these theories require a background logic of relations and substantive assumptions addressing mathematical existence of categories themselves. We propose a synthesis of Bell's many-topoi view and modal-structuralism. Surprisingly, a combination of mereology and plural quantification suffices to describe hypothetical large domains, recovering the Grothendieck method of universes. Both topos theory and set theory can be carried out (...) relative to such domains; puzzles about ‘large categories’ and ‘proper classes’ are handled in a uniform way, by relativization, sustaining insights of Zermelo. (shrink)

The value of rational choice theory for the social sciences has long been contested. It is argued here that, in the debate over its role, it is necessary to distinguish between claims that people maximise manifest payoffs, and claims that people maximise their utility. The former version has been falsified. The latter is unfalsifiable, because utility cannot be observed. In principle, utility maximisation can be adapted to fit any form of behaviour, including the behaviour of non-human organisms. Allegedly 'inconsistent' behaviour (...) is also impossible to establish without qualification. This utility-maximising version of rational choice theory has the character of a universal 'explanation' that can be made to 'fit' any set of events. This is a sign of weakness rather than strength. In its excessive quest for generality, utility-maximising rational choice theory fails to focus on the historically and geographically specific features of socio-economic systems. As long as such theory is confined to ahistorical generalities, then it will remain highly limited in dealing with the real world. Instead we have to consider the real social and psychological determinants of human behaviour. (shrink)

Hellman and Shapiro explore the development of the idea of the continuous, from the Aristotelian view that a true continuum cannot be composed of points to the now standard, entirely punctiform frameworks for analysis and geometry. They then investigate the underlying metaphysical issues concerning the nature of space or space-time.

Recent technical developments in the logic of nominalism make it possible to improve and extend significantly the approach to mathematics developed in Mathematics without Numbers. After reviewing the intuitive ideas behind structuralism in general, the modal-structuralist approach as potentially class-free is contrasted broadly with other leading approaches. The machinery of nominalistic ordered pairing (Burgess-Hazen-Lewis) and plural quantification (Boolos) can then be utilized to extend the core systems of modal-structural arithmetic and analysis respectively to full, classical, polyadic third- and fourthorder number (...) theory. The mathenatics of many structures of central importance in functional analysis, measure theory, and topology can be recovered within essentially these frameworks. (shrink)

The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the book considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical possibilities, (...) and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives. (shrink)

Some remarks on determination, physicalism, model theory, and logical truth.//An attempt to defend physicalism against objections that its bases are indeterminate.

Several leading topics outstanding after John Earman's Bayes or Bust? are investigated further, with emphasis on the relevance of Bayesian explication in epistemology of science, despite certain limitations. (1) Dutch Book arguments are reformulated so that their independence from utility and preference in epistemic contexts is evident. (2) The Bayesian analysis of the Quine-Duhem problem is pursued; the phenomenon of a "protective belt" of auxiliary statements around reasonably successful theories is explicated. (3) The Bayesian approach to understanding the superiority of (...) variety of evidence is pursued; a recent challenge (by Wayne) is converted into a positive result on behalf of the Bayesian analysis, potentially with far-reaching consequences. (4) The condition for applying the merger-of-opinion results and the thesis of underdetermination of theories are compared, revealing significant limitations in applicability of the former. (5) Implications concerning "diachronic Dutch Book" arguments and "non-Bayesian shifts" are drawn, highlighting the incompleteness, but not incorrectness, of Bayesian analysis. (shrink)

A plurality of approaches to foundational aspects of mathematics is a fact of life. Two loci of this are discussed here, the classicism/constructivism controversy over standards of proof, and the plurality of universes of discourse for mathematics arising in set theory and in category theory, whose problematic relationship is discussed. The first case illustrates the hypothesis that a sufficiently rich subject matter may require a multiplicity of approaches. The second case, while in some respects special to mathematics, raises issues of (...) ontological multiplicity and relativity encountered in the natural sciences as well. (shrink)

Originally published in 1967, this book aims to develop an ethical theory which remedies the defects of Utilitarianism while recognising the truths upon which Utilitarians have insisted. Its thesis is offered as a challenge to all schools of moral philosophy which have flourished in the twentieth century. Dr Grice argues that there are two kinds of Judgement of moral obligation. Social Contract theory, in a form which avoids the classical objections, is employed in setting out the ground of basic obligations; (...) and the ultra obligations of individual men are found to be grounded in their own characters. He then demonstrates that the theory offered, unlike Utilitarianism, throws light on judgements of rights and justice. Moral good is seen eventually as the coping stone, not the foundation stone of morality. (shrink)

Moral patients deserve moral consideration and concern – they have moral standing. What factors drive attributions of moral standing? Understanding these factors is important because it indicates how broadly individuals conceptualize the moral world, and suggests how they will treat various entities, both human and non-human. This understanding has recently been advanced by a series of studies conducted by both psychologists and philosophers, which have revealed three main drivers of moral standing: the capacity to suffer, intelligence or autonomy, and the (...) nature of an entity's disposition. These studies have also revealed causal links between moral standing and other variables of interest, namely, mental state attributions and moral behavior. In this review, I consider this recent research, aiming to clarify what the balance of evidence indicates about how moral standing is judged and about its links to mind perception and behavior. I conclude by suggesting open questions for future research on this exciting topic. (shrink)

Prior research on the psychology of retribution is complicated by the difficulty of separating retributive and general deterrence motives when studying human offenders . We isolate retribution by investigating judgments about punishing animals, which allows us to remove general deterrence from consideration. Studies 2 and 3 document a “victim identity” effect, such that the greater the perceived loss from a violent animal attack, the greater the belief that the culprit deserves to be killed. Study 3 documents a “targeted punishment” effect, (...) such that the responsive killing of the actual “guilty” culprit is seen as more deserved than the killing of an almost identical yet “innocent” animal from the same species. Studies 4 and 5 extend both effects to participants' acceptance of inflicting pain and suffering on the offending animal at the time of its death, and show that both effects are mediated by measures of retributive sentiment, and not by consequentialist concerns. (shrink)

Traditional theories of associative learning have found no place for the possibility that the way in which events are perceived might change as a result of experience. Evidence for the reality of perceptual learning has come from those studied by learning theorists. The work reviewed in this book shows that learned changes in perceptual organization can in fact be demonstrated, even in experiments using procedures of the type on which associative theories have been based. These results come from procedures that (...) have been the focus of detailed theoretical and empirical analysis; and from this analysis emerges an outline of the mechanisms responsible. Some of these are themselves associative; others require the addition of nonassociative mechanisms to the traditional theory. The result is an extended version of associative theory which, it is argued, will be relevant not only to the experimental procedures discussed in this book but to the entire range of instances of perceptual learning. (shrink)

This paper considers on what basis justice may require that people be treated as equals. It begins with an examination of the argument that people are to be treated as equals because they are equals, and suggests reasons for thinking that such an argument is unlikely to succeed. The remainder of the paper considers, and tries to make plausible, the argument that justice requires people be treated as equals because they are individuals. Thus the paper offers some support for the (...) view that the proper foundation of egalitarianism is individualism. (shrink)

Hird, G.R., Recursive properties of relations on models, Annals of Pure and Applied Logic 63 241–269. We prove general existence theorems for recursive models on which various relations have specified recursive properties. These capture common features of results in the literature for particular algebraic structures. For a useful class of models with new relations R, S, where S is r.e., we characterize those for which there is a recursive model isomorphic to on which the relation corresponding to S remains r.e., (...) while that corresponding to R is not r.e.; immune; hyperimmune. The results are applied to vector spaces, Boolean algebras and abelian groups. In the case of vector spaces, this leads to a new kind supermaximal subspace of V∞. (shrink)

It is often supposed that there is a relationship between desert and responsibility: that to be deserving we must be responsible for that which makes us deserving. Indeed, there seems little doubt that a supposed relationship between desert and responsibility, combined with a growing tendency to view less and less as the responsibility of the individual, contributed to the reluctance to appeal to desert which has been a feature of much recent moral and political philosophy. Certainly, if to be deserving (...) we need to be responsible for that which makes us deserving ‘all the way down,’ it is not easy to see how anyone could ever be deserving of anything.I will argue that the claim that we can deserve only on the basis of that for which we are responsible — the desert-responsibility thesis — is false. There is no conceptual connection between desert and responsibility. Nevertheless, it is true that many claims to deserve are undermined if there is a lack of responsibility. (shrink)

In a recent paper, while discussing the role of the notion of analyticity in Carnap’s thought, Howard Stein wrote: “The primitive view–surely that of Kant–was that whatever is trivial is obvious. We know that this is wrong; and I would put it that the nature of mathematical knowledge appears more deeply mysterious today than it ever did in earlier centuries – that one of the advances we have made in philosophy has been to come to an understanding of just ∗I (...) am grateful to audiences at the Steinfest, University of Chicago, May 21-23, 1999, and at the Philosophy of Mathematics Conference at the University of California, Santa Barbara, Feb. 4-6, 2000, and especially to Stewart Shapiro and Tony Anderson, for helpful comments on earlier drafts of this paper. (shrink)

This book brings together a number of essays that are optimistic about the ways certain neuroscientific insights might advance philosophical ethics, and other essays that are more circumspect about the relevance of neuroscience to philosophical ethics. As a whole, the essays form a self-reflective body of work that simultaneously seeks to derive normative ethical implications from neuroscience, and to question whether and how that may be possible at all. In doing so, the collection brings together psychology, neuroscience, philosophy of mind, (...) ethics, and philosophy of science. Neuroscience seeks to understand the biological systems that guide human behavior and cognition. Normative ethics, on the other hand, seeks to understand the system of abstract moral principles dictating how people ought to behave. By studying how the human brain makes moral judgments, can philosophers learn anything about the nature of morality itself? A growing number of researchers believe that neuroscience can, indeed, provide insights into the questions of philosophical ethics. However, even these advocates acknowledge that the path from neuroscientific is to normative ethical ought can be quite fraught. (shrink)

The rate‐limiting step in the uptake and metabolism of Dglucose by insulin target cells is thought to be glucose transport mediated by glucose transporters (primarily the GLUT4 isoform) localized to the plasma membrane. However, subcellular fractionation, photolabelling and immunocytochemical studies have shown that the pool of GLUT4 present in the plasma membrane is only one of many subcellular pools of this protein. GLUT4 has been found in occluded vesicles at the plasma membrane, clathrin‐coated pits and vesicles, early endosomes, and tubulo‐vesicular (...) structures; the latter are analogous to known specialized secretory compartments. Tracking the movement of GLUT4 through these compartments, and defining the mechanism and site of action of insulin in stimulating this subcellular trafficking, are major topics of current investigation. Recent evidence focuses attention on the exocytosis of GLUT4 as the major site of insulin action. Increased exocytosis may be due to decreased retention of glucose transporters in an intracellular pool, or possibly to increased assembly of a vesicle docking and fusion complex. Although details are unknown, the presence in GLUT4 vesicles of a synaptobrevin homologue leads us to propose that a process analogous to that occurring in synaptic vesicle trafficking is involved in the assembly of GLUT4 vesicles into a form suitable for fusion with the plasma membrane. Evidence that the pathways of signalling from the insulin receptor and of GLUT4 vesicle exocytosis may converge at the level of the key signalling enzyme, phosphatidylinositol 3‐kinase, is discussed. (shrink)

This paper explores the status of the von Neumann-Luders state transition rule (the "projection postulate") within "real-logic" quantum logic. The entire discussion proceeds from a reading of the Luders rule according to which, although idealized in applying only to "minimally disturbing" measurements, it nevertheless makes empirical claims and is not a purely mathematical theorem. An argument (due to Friedman and Putnam) is examined to the effect that QL has an explanatory advantage over Copenhagen and other interpretations which relativize truth-value assignments (...) to experimental arrangements. Two versions of QL, the lattice-theoretic (LT) and partial-Boolean-algebra (PBA), are considered. It turns out that the projection postulate is intimately connected with the choice of conditional connective for QL. The effect of the projection postulate is obtained with the Sasaki conditional. However, this choice is found to require extra assumptions, on both the LT and PBA versions, which are either just as ad hoc as the projection postulate itself or indefensible from within the real-logic QL framework. (shrink)

This is a critical examination of Quine's "Two Dogmas" that leaves nothing much of Quine's paper still standing. It concludes with a short study of a bit of bad work in philosophy that results from following the doctrines of "Two Dogmas".

An essential guide to an essential book, this first anthology on Camera Lucida offers critical perspectives on Barthes's influential text. Roland Barthes's 1980 book Camera Lucida is perhaps the most influential book ever published on photography. The terms studium and punctum, coined by Barthes for two different ways of responding to photographs, are part of the standard lexicon for discussions of photography; Barthes's understanding of photographic time and the relationship he forges between photography and death have been invoked countless times (...) in photographic discourse; and the current interest in vernacular photographs and the ubiquity of subjective, even novelistic, ways of writing about photography both owe something to Barthes. Photography Degree Zero, the first anthology of writings on Camera Lucida, goes beyond the usual critical orthodoxies to offer a range of perspectives on Barthes's important book. Photography Degree Zero includes essays written soon after Barthes's book appeared as well as more recent rereadings of it, some previously unpublished. The contributors' approaches range from psychoanalytical to Buddhist ; they include a history of Barthes's writings on photography and an account of Camera Lucida and its reception; two views of the book through the lens of race; and a provocative essay by Michael Fried and two responses to it. The variety of perspectives included in Photography Degree Zero, and the focus on Camera Lucida in the context of photography rather than literature or philosophy, serve to reopen a vital conversation on Barthes's influential work. (shrink)

Gers (Biol Philos, 2011) provides a positive and constructive view of the project to generalise Darwinian principles in Geoffrey Hodgson and Thorbjørn Knudsen’s Darwin’s Conjecture. We note considerable overlap with his work and ours, and also with important recent work of Godfrey-Smith ( 2009 ), which Gers cites extensively. But we also note that there are differences in research objectives between Gers and Godfrey-Smith, on the one hand, and ourselves, on the other. Gers and Godfrey-Smith focus on the elucidation (...) of the most general principles possible. Our aim is to derive principles that are sufficiently abstract to span the natural and human social worlds, and then add additional principles to help understand the Darwinian evolution of human society. Furthermore, Gers and Godfrey-Smith critique a replicator concept that is different from ours. Once these points are made apparent, the criticisms are essentially disabled, and we end up in a position with different but complementary and overlapping research projects. (shrink)

The recent appearance of generative artificial intelligence (AI) platforms has been seen by many as disruptive for education. In this paper I attempt to locate the source of tension between educational goals and new information technologies including AI. I argue that this tension arises from new conceptions of epistemic agency that are incompatible with educational aims. I describe three competing theories of epistemic agency which I refer to as Makers, Managers, and Inforgs. I contend that educators are correct in maintaining (...) the first of these, which is rooted in the educational theories of Locke and Dewey, as their main educational purpose. Competing theories do not serve the goals of learners, even as they must prepare for life in a very different epistemic environment. (shrink)

Descartes believed that causation is intelligible only if the cause and effect are similar, since it is impossible to understand how the reality of an effect can owe anything to the reality of its cause if the two have nothing in common. I argue first that Descartes has a coherent and reasonably strong metaphysical justification for his condition of causal similarity. Second, I defend Descartes from the charge that his conception of similarity renders the condition trivial by making practically everything (...) similar to everything else. Third, I discuss the familiar objection that if the similarity condition is not trivial, then it is incompatible with Cartesian mind–body interaction. I argue that the condition is consistent with, and indeed explains, Descartes's late view of interaction. (shrink)

Probably there is no position in Goodman’s corpus that has generated greater perplexity and criticism than Goodman’s “nominalism”. As is abundantly clear from Goodman’s writings, it is not “abstract entities” generally that he questions—indeed, he takes sensory qualia as “basic” in his Carnap-inspired constructional system in Structure—but rather just those abstracta that are so crystal clear in their identity conditions, so fundamental to our thought, so prevalent and seemingly unavoidable in our discourse and theorizing that they have come to form (...) the generally accepted framework for the most time-honored, exact, sophisticated, refined, central, and secure branch of human knowledge yet devised, mathematics itself! Of all the abstracta to question, why sets? Of course, Goodman gave his “reasons”, the unintelligibility of “generating” an infinitude of “constructed objects” automatically from any given object or objects. But critics have been quick to point out that set theory is intended not as a theory of what can be “generated” or “constructed” from given objects in any literal sense but rather as a theory of a certain realm of objects independently existing in their own right. “Construction” is a metaphor. (shrink)

Geoffrey Lloyd engages in a wide-ranging exploration of what we can learn from the study of ancient civilisations that is relevant to fundamental problems, both intellectual and moral, that we still face today. How far is it possible to arrive at an understanding of alien systems of belief? Is it possible to talk meaningfully of 'science' and of its various constituent disciplines, 'astronomy', 'geography', 'anatomy', and so on, in the ancient world? Are logic and its laws universal? Is there (...) one ontology - a single world - to which all attempts at understanding must be considered to be directed? When we encounter apparently very different views of reality, how far can that be put down to a difference in conceptions of what needs explaining, or of what counts as an explanation, or to different preferred modes of reasoning or styles of inquiry? Do the notions of truth and belief represent reliable cross-cultural universals? In another area, what can ancient history teach us about today's social and political problems? Are the discourses of human nature and of human rights universally applicable? What political institutions do we need to help secure equity and justice within nation states and between them? Lloyd sets out to answer all these questions, and to convince us that the science and culture of ancient Greece and China provide precious resources to advance modern debates. (shrink)

The Scottish philosopher Norman Kemp Smith (1872–1958) is best known for his 1929 English translation of Kant’s Critique of Pure Reason, and for his incisive commentaries on Descartes, Hume, and Kant. These achievements have overshadowed his original philosophical work in several areas, including the experience of time. A realist with idealist sympathies, Kemp Smith developed a non-transcendental version of Kant’s conception of time as a ‘pure intuition’ (though he insisted that temporal perception involved ‘categories’). He employed this conception to solve (...) a problem that was widely discussed in early twentieth-century European and American philosophy, which William James dubbed the ‘specious present’: how can we perceive an extended duration, like a full golf swing, or the cadence of a brief tune, if we only perceive the present? A closely related problem: if we only ever perceive the present, how can we distinguish among the future, present, and past? In this paper, I explain Kemp Smith’s proposed solution, and compare it with two of his contemporary influences: Samuel Alexander and George F. Stout. Finally, I suggest that these problems are still with us, and are likely to be for some time, especially if we ignore the insights offered by earlier discussions. (shrink)