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.

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)

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)

This classic, provocative introduction to classical metaphysical questions focuses on appreciating the problems, rather than attempting to proffer answers.

The Exchange of Words is a philosophical exploration of human testimony, specifically as a form of intersubjective understanding in which speakers communicate by making themselves accountable for the truth of what they say. This account weaves together themes from philosophy of language, moral psychology, action theory, and epistemology, for a new approach to this basic human phenomenon.

The paper argues for the centrality of believing the speaker (as distinct from believing the statement) in the epistemology of testimony, and develops a line of thought from Angus Ross which claims that in telling someone something, the kind of reason for belief that a speaker presents is of an essentially different kind from ordinary evidence. Investigating the nature of the audience's dependence on the speaker's free assurance leads to a discussion of Grice's formulation of non-natural meaning in an epistemological (...) light, concentrating on just how the recognition of the speaker's self-reflexive intention is supposed to count for his audience as a reason to believe P. This is understood as the speaker's explicitly assuming responsibility for the truth of his statement, and thereby constituting his utterance as a reason to believe. (shrink)

In this volume Rorty offers a Deweyan account of objectivity as intersubjectivity, one that drops claims about universal validity and instead focuses on utility for the purposes of a community. The sense in which the natural sciences are exemplary for inquiry is explicated in terms of the moral virtues of scientific communities rather than in terms of a special scientific method. The volume concludes with reflections on the relation of social democratic politics to philosophy.

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.

Øystein Linnebo*. Philosophy of Mathematics. Princeton University Press, 2017. ISBN: 978-0-691-16140-2 ; 978-1-40088524-4. Pp. xviii + 203.

Richard Swinburne offers an original treatment of a question at the heart of epistemology: what makes a belief rational, or justified in holding? He maps the rival accounts of philosophers on epistemic justification ("internalist" and "externalist"), arguing that they are really accounts of different concepts. He distinguishes between synchronic justification (justification at a time) and diachronic justification (synchronic justification resulting from adequate investigation)--both internalist and externalist. He also argues that most kinds of justification are worth having because they are (...) indicative of truth; however, it is only justification of internalist kinds that can guide a believer's actions. Swinburne goes on to show the usefulness of the probability calculus in elucidating how empirical evidence makes beliefs probably true. (shrink)

This paper explores some aspects of the relation between different ways of achieving a consensus on the judgemental values of a group of indviduals; in particular, aggregation and deliberation. We argue firstly that the framing of an aggregation problem itself generates information that individuals are rationally obliged to take into account. And secondly that outputs of the deliberative process that this initiates is in tension with constraints on consensual values typically imposed by aggregation theory, at least when deliberation is modelled (...) as process of learning from others compatible with Bayesian updating principles. (shrink)

Atheism is a familiar kind of skepticism about religion. Moral error theory is an analogous kind of skepticism about morality, though less well known outside academic circles. Both kinds of skeptic face a "what next?" question: If we have decided that the subject matter (religion/morality) is mistaken, then what should we do with this way of talking and thinking? The natural assumption is that we should abolish the mistaken topic, just as we previously eliminated talk of, say, bodily humors and (...) unicorns. The fictionalist, however, offers a less obvious recommendation. According to the fictionalist, engaging in the topic in question provides pragmatic benefits that do not depend on its truth-in a way roughly analogous to engaging with a novel or a movie. The religious fictionalist maintains that even if we were atheists, we should carry on talking, thinking, and acting as if religion were true. The moral fictionalist maintains a similar view regarding moral talk, thought, and action. Both forms of fictionalism face serious challenges. Some challenges can be levelled at either form of fictionalism (or at any form of fictionalism), whereas others are problems unique to moral fictionalism or to religious fictionalism. There are important questions to be asked about the relationship between these two kinds of fictionalism. Could moral fictionalism be plausible even if religious fictionalism is not (or vice versa)? This is a volume of thirteen previously unpublished papers on the topics of religious fictionalism, moral fictionalism, and the relation between these views. (shrink)

This book brings together twenty articles giving a comprehensive view of the work of the Aristotelian commentators.... The importance of the commentators is partly that they represent the thought and classroom teaching of the Aristotelian and Neoplatonist schools and partly that they provide a panorama of a thousand years of anicient Greek philosophy, revealing many original quotations from lost works. Even more significant is the profound influence... that they exert on later philosophy, Islamic and Western. Not only did they preserve (...) anti-Aristotelian marterial which helped inspire Medieval and Renaissance science, but they presented Aristotle in a form that made him acceptable to the Christian Church. It is not Aristotle, but Aristotle transformed and embedded in the philosophy of the commentators, that so often lies behind the views of later thinkers. --From book jacket. (shrink)

In his final work, Richard Rorty provides the definitive statement of his political thought. Rorty equates pragmatism with anti-authoritarianism, arguing that because there is no authority we can rely on to ascertain truth, we can only do so intersubjectively. It follows that we must learn to think and care about what others think and care about.

Richard Swinburne presents a powerful new case for substance dualism and for libertarian free will. He argues that pure mental events are distinct from physical events and interact with them, and claims that no result from neuroscience or any other science could show that interaction does not take place. Swinburne goes on to argue for agent causation, and claims that it is we, and not our intentions, that cause our brain events. It is metaphysically possible that each of us (...) could acquire a new brain or continue to exist without a brain; and so we are essentially souls. Brain events and conscious events are so different from each other that it would not be possible to establish a scientific theory which would predict what each of us would do in situations of moral conflict. Hence, we should believe that things are as they seem to be: that we make choices independently of the causes which influence us. It follows that we are morally responsible for our actions. (shrink)

Philosophy and literature enjoy a close, complex relationship. Elucidating the connections between these two fields, this book examines the ways philosophy deploys literary means to advance its practice, particularly as a way of life that extends beyond literary forms and words into physical deeds, nonlinguistic expression, and subjective moods and feelings.

_Heidegger_ is a classic introduction to Heidegger's notoriously difficult work. Truly accessible, it combines clarity of exposition with an authoritative handling of the subject-matter. Richard Polt has written a work that will become the standard text for students looking to understand one of the century's greatest minds.

Richard Kilvington (ca. 1302-1361) was one of the most original and influential thinkers among the Oxford Calculators. His impact on late medieval philosophy and theology remains unquestionable. His physical, logical, and ethical solutions were extensively debated and referred to, paving the way for new approaches in philosophy and theology. This volume presents a critical edition of question 4 from Kilvington's Quaestiones super libros Sententiarum, complete with an introduction to the edition and a guide to Kilvington's theological concepts.

The sixteen essays in this volume confront the current debate about the relationship between philosophy and its history. On the one hand intellectual historians commonly accuse philosophers of writing bad - anachronistic - history of philosophy, and on the other, philosophers have accused intellectual historians of writing bad - antiquarian - history of philosophy. The essays here address this controversy and ask what purpose the history of philosophy should serve. Part I contains more purely theoretical and methodological discussion, of such (...) questions as whether there are 'timeless' philosophical problems, whether the issues of one epoch are commensurable with those of another, and what style is appropriate to the historiography of the subject. The essays in Part II consider a number of case-histories. They present important revisionist scholarship and original contributions on topics drawn from ancient, early modern and more recent philosophy. All the essays have been specially commissioned, and the contributors include many of the leading figures in the field. The volume as a whole will be of vital interest to everyone concerned with the study of philosophy and of its history. (shrink)

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)

This Element, written for researchers and students in philosophy and the behavioral sciences, reviews and critically assesses extant work on number concepts in developmental psychology and cognitive science. It has four main aims. First, it characterizes the core commitments of mainstream number cognition research, including the commitment to representationalism, the hypothesis that there exist certain number-specific cognitive systems, and the key milestones in the development of number cognition. Second, it provides a taxonomy of influential views within mainstream number cognition research, (...) along with the central challenges these views face. Third, it identifies and critically assesses a series of core philosophical assumptions often adopted by number cognition researchers. Finally, the Element articulates and defends a novel version of pluralism about number concepts. (shrink)

Disagreement is common: even informed, intelligent, and generally reasonable people often come to different conclusions when confronted with what seems to be the same evidence. Can the competing conclusions be reasonable? If not, what can we reasonably think about the situation? This volume examines the epistemology of disagreement. Philosophical questions about disagreement arise in various areas, notably politics, ethics, aesthetics, and the philosophy of religion: but this will be the first book focusing on the general epistemic issues arising from informed (...) disagreement. Ten leading philosophers offer specially written essays which together will offer a starting-point for future work on this topic. (shrink)