The large cardinal axioms of the title assert, respectively, the existence of a nontrivial elementary embedding j:Vλ→Vλ, the existence of such a j which is moreover , and the existence of such a j which extends to an elementary j:Vλ+1→Vλ+1. It is known that these axioms are preserved in passing from a ground model to a small forcing extension. In this paper the reverse directions of these preservations are proved. Also the following is shown : if V is a model (...) of ZFC and V[G] is a -generic forcing extension of V, then in V[G], V is definable using the parameter Vδ+1, where. (shrink)

The rank-into-rank and stronger large cardinal axioms assert the existence of certain elementary embeddings. By the preservation of the large cardinal properties of the embeddings under certain operations, strong implications between various of these axioms are derived.

Say that the property Φ of a cardinal λ strongly implies the property Ψ. If and only if for every λ,Φ implies that Ψ and that for some λ′<λ,Ψ. Frequently in the hierarchy of large cardinal axioms, stronger axioms strongly imply weaker ones. Some strong implications are proved between axioms of the form “there is an elementary embedding j:Lα[Vλ+1]→Lα[Vλ+1] with ”.

In connection with his interest in selfdistributive algebra, Richard Laver established two deep results with potential applications in low-dimen\-sional topology, namely the existence of what is now known as the Laver tables and the well-foundedness of the standard ordering of positive braids. Here we present these results and discuss the way they could be used in topological applications.

In this commemorative article, the work of Richard Laver is surveyed in its full range and extent.

A selection of speeches and essays from the author's second decade as president of Yale University.

In 2020, it is clear that racism must be a moral priority for white American Catholics, as for all white Americans. To face racism maturely, our consciences need more robust formation than we received as children preparing for First Reconciliation—or as adolescents at Confirmation, when we were instructed that we must be prepared to act boldly to defend our commitment to Christ. One way to build a racially-mature conscience is to seek feedback from anti-racism accountability partners, as the author did. (...) Another is to explore the distinction in Catholic moral theology between invincible and vincible ignorance—what we can know and what we cannot—in order to discern whether an action or inaction is moral. Much of what liberal whites claim we can’t know without input from Blacks is readily available if we have ears to hear. (shrink)

Carnap's position on mathematical truth in The Logical Syntax of Language has been attacked from two sides: Kreisel argues that it is formalistic but should not be, and Friedman argues that it is not formalistic but needs to be. In this paper I argue that the Carnap of Syntax does not eliminate our ordinary notion of mathematical truth in favour of a formal analogue; so Carnap's notion of mathematical truth is not formalistic. I further argue that there is no conflict (...) between Carnap's use of informal notions and his principle of tolerance; so Carnap's definition of mathematical truth need not be formalistic. CiteULike Connotea Del.icio.us What's this? (shrink)

This collection of new essays addresses emotion in relation to the arts. The essays consider such topics as the paradox of fiction, emotion in the pure and abstract arts, and the rationality and ethics of emotional responses to art.

Thinking through the body: educating for the humanities -- The body as background -- Self-knowledge and its discontents: from Socrates to somaesthetics -- Muscle memory and the somaesthetic pathologies of everyday life -- Somaesthetics in the philosophy classroom: a practical approach -- Somaesthetics and the limits of aesthetics -- Somaesthetics and Burke's sublime -- Pragmatism and cultural politics: from textualism to somaesthetics -- Body consciousness and performance -- Somaesthetics and architecture: a critical option -- Photography as performative process -- Asian (...) ars erotica and the question of sexual aesthetics -- Philosophy as awakened life : everyday aesthetics of embodiment in American transcendentalism and Japanese Zen practice -- Somatic style. (shrink)

Most recent accounts of will-power have tried to explain it as reducible to the operation of beliefs and desires. In opposition to such accounts, this paper argues for a distinct faculty of will-power. Considerations from philosophy and from social psychology are used in support.

This paper argues that Carnap both did not view and should not have viewed Frege's project in the foundations of mathematics as misguided metaphysics. The reason for this is that Frege's project was to give an explication of number in a very Carnapian sense — something that was not lost on Carnap. Furthermore, Frege gives pragmatic justification for the basic features of his system, especially where there are ontological considerations. It will be argued that even on the question of the (...) independent existence of abstract objects, Frege and Carnap held remarkably similar views. I close with a discussion of why, despite all this, Frege would not accept the principle of tolerance. (shrink)

Most individuals realise that we have a moral obligation to avoid the evils of war. But this realization raises a host of difficult questions when we, as responsible individuals, witness harrowing injustices such as ""ethnic cleansing"" in Bosnia or starvation in Somalia. With millions of lives at stake, is war ever justified? And, if so, for what purpose? In this book, Richard J. Regan confronts these controversial questions by first considering the basic principles of just-war theory and then applying (...) those principles to historical and ongoing conflicts. Part One presents two opposing viewpoints: first, that war is not subject to moral norms and, second, that war is never morally permissible. The author rejects both perspectives, and moves to define the principles of just-war theory. He evaluates the roles of the president, Congress and, most importantly, the UN Security Council in determining when long-term US military involvement is justified. The moral limits of war conduct and the moral problem of using, or threatening to use, nuclear weapons are also discussed. On the just cause to wage war, Regan argues that defense of nations and nationals - whether in self-defense or in defense of others - remains the ""only"" classical cause that in the modern world would justify resorting to war. With respect to military intervention in secessionist and revolutionary wars, he contends that such intervention might be justified, but that prudence dictates extreme caution. In considering acceptable war conduct, Regan elaborates the specific principle of discrimination and proportionality; he maintains that civilians uninvolved in the enemy's war should not be directly targeted and that the costs of military action must be proportionate to the anticipated benefits of destroying military targets. The second part of the book presents case studies of eight historical wars - World War I, the Vietnam War, the Falklands War, the revolution and civil war in Nicaragua, the civil war in El Salvador, the Gulf War, the intervention in Somalia, and the Bosnian War - and poses several provocative questions about each. It invites readers and students to apply just-war principles to complex war-related situations and to understand the factual contingencies involved in moral judgements about war decisions. The book should be of particular interest to students of the moral issues of international relations and to readers interested more generally in philosophy, theology and political science. (shrink)

This book gives a descriptive analysis of specific Madhyamika texts. It compares the ideology of Kumarajiva (a translator of the four Madhyamika treatises 400 A.D.) with the ideologies of the three Chinese contemporaries - HuiYuan, Seng-Jui and Seng-Chao. It envisages an intercultural transmission of religious and philosophical ideas from India to China.

This is the third edition of a classic book first published in 1960, which has sold thousands of copies in two paperback edition and has been translated into several foreign languages. Popkin's work ha generated innumerable citations, and remains a valuable stimulus to current historical research. In this updated version, he has revised and expanded throughout, and has added three new chapters, one on Savonarola, one on Henry More and Ralph Cudworth, and one on Pascal. This authoritative treatment of the (...) theme of scepticism and its historical impact will appeal to scholars and students of early modern history now as much as ever. (shrink)

If aesthetics is both surface and depth, impassioned immediacy yet also critical distance of judgment, how can this doubleness be held together in one ...

From 1953 to 1959 Gödel worked on a response to Carnap’s philosophy of mathematics. The drafts display Gödel’s familiarity with Carnap’s position from The Logical Syntax of Language, but they received a dismissive reaction on their eventual, posthumous, publication. Gödel’s two principal points, however, will here be defended. Gödel, though, had wished simply to append a few paragraphs to show that the same arguments apply to Carnap’s later views. Carnap’s position, however, had changed significantly in the intervening years, and to (...) a significant extent, this mature position realizes much of what Gödel himself wanted out of a philosophy of mathematics. (shrink)

Logical Forms explains both the detailed problems involved in finding logical forms and also the theoretical underpinnings of philosophical logic. In this revised edition, exercises are integrated throughout the book. The result is a genuinely interactive introduction which engages the reader in developing the argument. Each chapter concludes with updated notes to guide further reading.

This paper will deal with three questions regarding Carnap's transition from the position he held at the time of writing Syntax to the doctrines he held during his semantic phase: (1) What was Carnap's attitude towards truth at the time of writing Syntax? (2) What was Carnap's position regarding questions of reference and ontology at the time of writing Syntax? (3) Was Carnap's acceptance of Tarski's analysis of truth and reference detrimental to his philosophical project? Section 1 of this paper (...) will deal with the first of these questions. Special attention will be paid to identifying what it was that prevented Carnap from defining a truth predicate for descriptive languages in Syntax. Section 2 of this paper will deal with the question of Carnap's attitude towards reference and ontology in Syntax. It will be shown that the attempt in Syntax to address ontological questions is seriously defective. Section 3 of this paper addresses the last of the questions posed above. It is argued that in the light of what is established in Sections 1 and 2, Carnap could not have retained the position of Syntax with respect to truth and reference. (shrink)

The book begins with an overview that introduces the Theorem and the issues surrounding it, and explores how the essays that follow contribute to our understanding of those issues.

"Ce livre propose une enquête philosophique explorant le rapport à la mort dans nos sociétés. C’est une invitation à penser les liens humains à la fin de la vie. On évoque les liens intimes, mais également les liens sociaux encadrés par la loi. Dans un tel contexte, comment discerner les raisons anciennes et nouvelles convenant au bien de la cité? L’ouvrage s’adresse aux accompagnants en soins palliatifs. Il concerne également toute personne soucieuse pour elle-même et ses proches de réfléchir à (...) son voyage au bout de la vie. Nous sommes mortels, nous le savons et le fil de nos existences provoque des occasions de nous le rappeler. Dans la solitude de mourir s’inscrit l’appel à la compassion. Ainsi, pour les Grecs de l’Antiquité, l’image de la cigogne symbolisait la prise en charge des vieux par les jeunes, un signe de l’amitié politique. L’émergence de la culture palliative est intimement liée aux changements qui ont affecté l’évolution récente de la vie démocratique. Cette culture est née et s’est développée dans des circonstances politiques particulières. À l’observer, on peut déchiffrer certains codes de notre vie civique, ses aspirations, mais aussi ses ambiguïtés. Louis-André Richard propose d’examiner les questions actuelles en compagnie de Platon, d’Aristote, d’Augustin ou de Tocqueville. Grâce à eux, la philosophie, symbolisée par la sagesse de Minerve, est mise à contribution pour explorer la genèse et les métamorphoses de concepts comme la dignité et l’autonomie. Comment se déploie la dynamique de la raison et de la liberté à l’heure de notre mort? Tel est l’enjeu pour les roseaux pensants que nous sommes. Si notre frêle espèce appelle à la sollicitude de la cigogne, elle ne saurait négliger de convoquer aussi la sagesse de Minerve."--Résumé de l'éditeur. (shrink)

This paper discusses Frege's account of definition by induction in Grundgesetze and the two key theorems Frege proves using it.

This paper investigates the relation between Carnap and Quine’s views on analyticity on the one hand, and their views on philosophical analysis or explication on the other. I argue that the stance each takes on what constitutes a successful explication largely dictates the view they take on analyticity. I show that although acknowledged by neither party (in fact Quine frequently expressed his agreement with Carnap on this subject) their views on explication are substantially different. I argue that this difference not (...) only explains their differences on the question of analyticity, but points to a Quinean way to answer a challenge that Quine posed to Carnap. The answer to this challenge leads to a Quinean view of analyticity such that arithmetical truths are analytic, according to Quine’s own remarks, and set theory is at least defensibly analytic. (shrink)