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.

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)

A history of the pre-Socratic philosophers, with selected writings and texts.

It is possible to learn multiple layers of non-linear features by backpropagating error derivatives through a feedforward neural network. This is a very effective learning procedure when there is a huge amount of labeled training data, but for many learning tasks very few labeled examples are available. In an effort to overcome the need for labeled data, several different generative models were developed that learned interesting features by modeling the higher order statistical structure of a set of input vectors. One (...) of these generative models, the restricted Boltzmann machine (RBM), has no connections between its hidden units and this makes perceptual inference and learning much simpler. More significantly, after a layer of hidden features has been learned, the activities of these features can be used as training data for another RBM. By applying this idea recursively, it is possible to learn a deep hierarchy of progressively more complicated features without requiring any labeled data. This deep hierarchy can then be treated as a feedforward neural network which can be discriminatively fine-tuned using backpropagation. Using a stack of RBMs to initialize the weights of a feedforward neural network allows backpropagation to work effectively in much deeper networks and it leads to much better generalization. A stack of RBMs can also be used to initialize a deep Boltzmann machine that has many hidden layers. Combining this initialization method with a new method for fine-tuning the weights finally leads to the first efficient way of training Boltzmann machines with many hidden layers and millions of weights. (shrink)

Though Descartes is traditionally associated with the moderately nativist doctrine that our ideas of God, of eternal truths, and of true and immutable natures are innate, on two occasions he explicitly argued that all of our ideas, even sensory ideas, are innate in the mind. One reason it is surprising to find Descartes endorsing universal innateness is that such a view seems to leave no role for bodies in the production of our ideas of them.

Macmillan papermac 3003. Bibliography: p. 80-81.

Chomsky’s highly influential Syntactic Structures ( SS ) has been much praised its originality, explicitness, and relevance for subsequent cognitive science. Such claims are greatly overstated. SS contains no proof that English is beyond the power of finite state description (it is not clear that Chomsky ever gave a sound mathematical argument for that claim). The approach advocated by SS springs directly out of the work of the mathematical logician Emil Post on formalizing proof, but few linguists are aware of (...) this, because Post’s papers are not cited. Chomsky’s extensions to Post’s systems are not clearly defined, and the arguments for their necessity are weak. Linguists have also overlooked Post’s proofs of the first two theorems about effects of rule format restrictions on generative capacity, published more than ten years before SS was published. (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)

Standard proofs of generalized Bell theorems, aiming to restrict stochastic, local hidden-variable theories for quantum correlation phenomena, employ as a locality condition the requirement of conditional stochastic independence. The connection between this and the no-superluminary-action requirement of the special theory of relativity has been a topic of controversy. In this paper, we introduce an alternative locality condition for stochastic theories, framed in terms of the models of such a theory (§2). It is a natural generalization of a light-cone determination condition (...) that is essentially equivalent to mathematical conditions that have been used to derive Bell inequalities in the deterministic case. Further, it is roughly equivalent to a condition proposed by Bell that, in one investigation, needed to be supplemented with a much stronger assumption in order to yield an inequality violated by some quantum mechanical predictions. It is shown here that this reflects a very general situation: from the proposed locality condition, even adding the strict anticorrelation condition and the auxiliary hypotheses needed to derive experimentally useful (and theoretically telling) inequalities, no Bell-type inequality is derivable. (These independence claims are the burden of §4.) A certain limitation on the scope of the proposed stochastic locality condition is exposed (§5), but it is found to be rather minor. The conclusion is thus supported that conditional stochastic independence, however reasonable on other grounds, is essentially stronger than what is required by the special theory.Our results stand in apparent contradiction with a class of derivations purporting to obtain generalized Bell inequalities from locality alone. It is shown in Appendix (B) that such proofs do not achieve their goal. This fits with our conclusion that generalized Bell theorems are not straightforward generalizations of theorems restricting deterministic hidden-variable theories, and that, in fact, such generalizations do not exist. This leaves open the possibility that a satisfactory, non-deterministic account of the quantum correlation phenomena can be given within the framework of the special theory. (shrink)

Although the mathematization of nature is a distinctive and crucial feature of the emergence of modern science in the seventeenth century, this volume shows that it was a far more complex, contested, and context-dependent phenomenon than the received historiography has indicated.0.

The Spanish philosopher Miguel de Unamuno and the American social scientist Ernest Becker see death as humanity’s fundamental anxiety. My essay explores the ethical ramifications attendant upon making that anxiety a well-spring of human activity. More specifically, I am interested in humanity’s effort to escape death via the secular milieu of social remembrance. Does such an effort produce a vista where the other exhibits an intrinsic value? Alternatively, does the other become a mere means in light of one’s project of (...) self-preservation? Pursuing such questions, this reflection will explore both positive and negative responses. It will take up the Columbine school shootings in reference to the latter and a notion of protest with regard to the former. The treatise will culminate with a discussion of Unamuno’s ethics of irreplaceability and its potential to engender a universal human respect while also endorsing one’s commitment to her concrete individuality. (shrink)

How would a liberation theologian respond to Marx’s famous critique that religious belief and, even more specifically, a hope for heaven is “the opium of the people”? I utilize the conceptual resources found within the work of liberation theologians Gustavo Gutiérrez, Enrique Dussel, and Jon Sobrino to argue that a belief in heaven is able to constitute a protest against oppressed persons’ present hell. To strengthen the connection between a believer’s heavenly hope and a commitment to worldly struggle, I examine (...) how the hope must be conceived as the completion and fulfillment of a process of temporal transformation. (shrink)

La création d’un système de santé public a été l’un des éléments clés de la Révolution tranquille dans les années 1960 au Québec. Toutefois, le développement de nouveaux traitements et de nouvelles technologies, en particulier des produits pharmaceutiques, ont fait naître un nouveau débat sur la gestion de notre système de santé. En se basant sur une analyse récente des valeurs libérales dans la société québécoise par Claude Ryan, l’auteur souligne l’importance que le gouvernement doit accorder à ces valeurs dans (...) la modernisation de notre système de santé. À la lumière des recommandations présentées par la commission Clair au provincial et par la commission Romanow au fédéral, la situation se prête bien à une modernisation du système de soins au Québec. Les valeurs libérales ont fourni une base au système de santé public ; elles sont plus pertinentes qu’elles ne l’ont jamais été alors que le débat sur notre système de santé est engagé. (shrink)

On Civic Republicanism explores the enduring relevance of the ancient concepts of republicanism and civic virtue to modern questions about political engagement and identity.".

What is courage and why is it one of the oldest and most universally admired virtues? How is it relevant in the world today, and what contemporary forms does it take? In this insightful and crisply written book, Geoffrey Scarre examines these questions and many more. He begins by defining courage, asking how it differs from fearlessness, recklessness and fortitude, and why people are often more willing to ascribe it to others than to avow it for themselves. He also (...) asks whether courage can serve bad ends as well as good, and whether it can sometimes promote confrontation over compromise and dialogue. On Courage explores the ideas of Aristotle, Aquinas and many later philosophers who have written about courage, as well as drawing on classic and recent examples of courage in politics and fiction, including the German anti-Nazi "White Rose Movement", the modern phenomenon of "whistle-blowing", and Stephen Crane’s The Red Badge of Courage. (shrink)

Quantum logic as genuine non-classical logic provides no solution to the "paradoxes" of quantum mechanics. From the minimal condition that synonyms be substitutable salva veritate, it follows that synonymous sentential connectives be alike in point of truth-functionality. It is a fact of pure mathematics that any assignment Φ of (0, 1) to the subspaces of Hilbert space (dim. ≥ 3) which guarantees truth-preservation of the ordering and truth-functionality of QL negation, violates truth-functionality of QL ∨ and $\wedge $ . Thus, (...) from within both the classical framework and that of any QL that preserves elementary set theory, two distinct (nonsynonymous) sets of connectives are discernible. Classical derivations of QM paradoxes are all available unless the language of QM is not classically closed. Maintaining this requires a strong and selfdefeating verification theory of meaning, the philosophical cornerstone of the Copenhagen interpretation to which QL was to provide an alternative. (shrink)

Amartya Sen reconsiders the idea of 'the standard of living'. He rejects the more conventional economic interpretations in terms of 'unity' and of wealth or 'opulence', and suggests an interpretation in terms of the 'capabilities and freedoms' that states of affairs do or do not allow. His argument is conceptual, but it refers to a wide range of examples. In elaborations of it, John Muellbauer explains how parts of it might be applied; Ravi Kanbur discusses the difficulties raised by choice (...) ex ante, under uncertainty, and choice ex post; Keith Hart discusses the ways in which one might think about living standards in societies in which there is a substantial amount of what he calls 'self provisioning' outside the market; and Bernard Williams reflects on some of the moral and political implications of Sen's argument. There is a bibliography of most of the more important works on the subject. The book will be of interest to economists, sociologists, students of development and moral and political philosophers; it will also be of interest to those concerned with public policy. (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 takes the thinking of Quentin Skinner, Philip Pettit and J. G. A. Pocock on republican liberty and explores the way in which this idea of liberty can be used to illuminate educational practice. It argues that republican liberty is distinct from both positive and negative liberty, and its emphasis on liberty as non-dependency gives the concept of liberty a particularly critical role in contemporary society. Each chapter formulates and expounds the idea that an empire of liberty requires the (...) existence of what are termed 'liberty-bearing agents', and shows how education - with a particular emphasis on knowledge - is needed to foster the human powers which allow people to become liberty-bearing. It is also emphasised, however, that republican liberty is non-perfectionist and non-eudaimonic: the core values enshrined in an empire of liberty centre on non-dependency rather than the promulgation of a certain way of life. Drawing on prominent seventeenth century contract theorists, the link between liberty and authority is explained, suggesting that appropriate authoritative structures need to underpin the provision of education, and especially schooling, if educational practice devoted to the pursuit of liberty is to flourish. Liberty and Education will be of value to both educational theorists unfamiliar with republican theory, as well as republican theorists interested in how their theory might play out in education. It will also be of interest to researchers and students from the fields of politics and the philosophy of education. (shrink)

An acclaimed critical history of social theory from the eighteenth century onwards.

After some introductory remarks on "experimental metaphysics", a brief survey of the current situation concerning the major types of hidden-variable theories and the inexistence proofs is presented. The category of stochastic, contextual, local theories remains open. Then the main features of a logical analysis of "locality" are sketched. In the deterministic case, a natural "light-cone determination" condition helps bridge the gap that has existed between the physical requirements of the special theory of relativity and formal conditions used in proving the (...) Bell -Wigner theorem. Natural generalization to the stochastic type, taking account of the distinction between epistemic and physical probabilities, leads to a series of independence claims constituting some significant limitations on generalized Bell theorems. In particular, the conditional stochastic independence requirement is seen both to go beyond the demand of compliance with the STR and to be a genuine necessity in deriving any Bell theorem for the stochastic case. The conclusion is also supported that, if determinism is given up, the Bell theorems and experiments do not pose an additional obstacle to unifying relativity theory and quantum mechanics beyond what is already posed by the "instantaneous" collapse of the wave function. (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)