Merging of opinions results underwrite Bayesian rejoinders to complaints about the subjective nature of personal probability. Such results establish that sufficiently similar priors achieve consensus in the long run when fed the same increasing stream of evidence. Initial subjectivity, the line goes, is of mere transient significance, giving way to intersubjective agreement eventually. Here, we establish a merging result for sets of probability measures that are updated by Jeffrey conditioning. This generalizes a number of different merging results in the literature. (...) We also show that such sets converge to a shared, maximally informed opinion. Convergence to a maximally informed opinion is a (weak) Jeffrey conditioning analogue of Bayesian “convergence to the truth” for conditional probabilities. Finally, we demonstrate the philosophical significance of our study by detailing applications to the topics of dynamic coherence, imprecise probabilities, and probabilistic opinion pooling. (shrink)

According to ante rem structuralism a branch of mathematics, such as arithmetic, is about a structure, or structures, that exist independent of the mathematician, and independent of any systems that exemplify the structure. A structure is a universal of sorts: structure is to exemplified system as property is to object. So ante rem structuralist is a form of ante rem realism concerning universals. Since the appearance of my Philosophy of mathematics: Structure and ontology, a number of criticisms of the idea (...) of ante rem structures have appeared. Some argue that it is impossible to give identity conditions for places in homogeneous ante rem structures, invoking a version of the identity of indiscernibles. Others raise issues concerning the identity and distinctness of places in different structures, such as the the natural number 2 and the real number 2. The purpose of this paper is to take the measure of these objections, and to further articulate ante rem structuralism to take them into account. (shrink)

The dominant response to this problem of the criterion focuses on the alleged requirement that we need to know a belief source is reliable in order for us to acquire knowledge by that source. Let us call this requirement, “The KR principle”.

We are sceptical of concerns over the opacity of algorithmic decision tools. While transparency and explainability are certainly important desiderata in algorithmic governance, we worry that automated decision-making is being held to an unrealistically high standard, possibly owing to an unrealistically high estimate of the degree of transparency attainable from human decision-makers. In this paper, we review evidence demonstrating that much human decision-making is fraught with transparency problems, show in what respects AI fares little worse or better and argue that (...) at least some regulatory proposals for explainable AI could end up setting the bar higher than is necessary or indeed helpful. The demands of practical reason require the justification of action to be pitched at the level of practical reason. Decision tools that support or supplant practical reasoning should not be expected to aim higher than this. We cast this desideratum in terms of Daniel Dennett’s theory of the “intentional stance” and argue that since the justification of action for human purposes takes the form of intentional stance explanation, the justification of algorithmic decisions should take the same form. In practice, this means that the sorts of explanations for algorithmic decisions that are analogous to intentional stance explanations should be preferred over ones that aim at the architectural innards of a decision tool. (shrink)

The purpose of this article is to delimit what can and cannot be claimed on behalf of second-order logic. The starting point is some of the discussions surrounding my Foundations without Foundationalism: A Case for Secondorder Logic.

Would Aquinas hold the view that a patient in a persistent vegetative state (PVS) is something other than a human being? Some recent interpreters have argued for this position. I contend that this reading is grounded in a false symmetry between the three stages of Aquinas’s embryology and the (alleged) three-stage process of death. Instead, I show that there are textual grounds for rejecting the view that the absence of higher brain activity in a patient would lead Aquinas to say (...) that the patient no longer has a rational soul. On my reading of Aquinas, the patient in PVS has a rational soul and is unequivocally a human being. (shrink)

For two ideally rational agents, does learning a finite amount of shared evidence necessitate agreement? No. But does it at least guard against belief polarization, the case in which their opinions get further apart? No. OK, but are rational agents guaranteed to avoid polarization if they have access to an infinite, increasing stream of shared evidence? No.

This paper defends the view that standards, which are typically social in nature, play a role in determining whether a subject has knowledge. While the argument focuses on standards that pertain to reasoning, I also consider whether there are similar standards for memory and perception.Ultimately, I argue that the standards are context sensitive and, as such, we must view attributions of knowledge as indexical. I exploit similarities between this view and a version of the relevant alternatives reply to skepticism in (...) order to defend this reply against the objection that it is ad hoc. (shrink)

This paper compares two kinds of epistemic principles---an underdetermination principle and a deductive closure principle. It argues that each principle provides the basis for an independently motivated skeptical argument. It examines the logical relations between the premises of the two kinds of skeptical argument and concludes that the deductive closure argument cannot be refuted without refuting the underdetermination argument. The underdetermination argument, however, can be refuted without refuting the deductive closure argument. In this respect, the deductive closure argument is the (...) stronger of the two. (shrink)

The traditional view in epistemology is that we must distinguish between being rational and being right (that is also, by the way, the traditional view about practical rationality). In his paper in this volume, Williamson proposes an alternative view according to which only beliefs that amount to knowledge are rational (and, thus, no false belief is rational). It is healthy to challenge tradition, in philosophy as much as elsewhere. But, in this instance, we think that tradition has it right. In (...) this paper we defend our version of the traditional view and argue against Williamson’s alternative. (shrink)

Just about every theorist holds that vague terms are context-sensitive to some extent. What counts as ?tall?, ?rich?, and ?bald? depends on the ambient comparison class, paradigm cases, and/or the like. To take a stock example, a given person might be tall with respect to European entrepreneurs and downright short with respect to professional basketball players. It is also generally agreed that vagueness remains even after comparison class, paradigm cases, etc. are fixed, and so this context sensitivity does not solve (...) the problems with vague terms. In this paper, I briefly sketch the main features of my broadly contextualist account of vagueness, that of the late Ruth Manor, and that of Agustín Rayo, showing how the three accounts relate to, and reinforce, each other, noting a seeming difference. A key item used to articulate my own view is David Lewis's notion of conversational score. This is used to track which borderline cases have been called in the course of a conversation. Manor alludes to Lewis's notion of accommodation, a key aspect of the kinematics of conversation, and Rayo invokes Stalnaker's notion of common ground. I'll show how the conversational score could be employed to develop and extend their views, showing how vague terms, as they construe them, are (or can be) deployed in conversation, consistent with both the underlying indeterminacy of the terms and normal communicative goals. To help develop all three views further, I invoke Craige Roberts's notion of Retrievability, a tool developed to show how definites, such as definite descriptions, singular pronouns, and proper names, are deployed in conversation, in a Lewis-style scorekeeping framework. This, I think, is exactly the right way to understand conversations in what Manor calls non-sorities situations and, to invoke my own view, in sorites situations as well. (shrink)

There is an interesting logical/semantic issue with some mathematical languages and theories. In the language of (pure) complex analysis, the two square roots of i’ manage to pick out a unique object? This is perhaps the most prominent example of the phenomenon, but there are some others. The issue is related to matters concerning the use of definite descriptions and singular pronouns, such as donkey anaphora and the problem of indistinguishable participants. Taking a cue from some work in linguistics and (...) the philosophy of language, I suggest that i functions like a parameter in natural deduction systems. This may require some rethinking of the role of singular terms, at least in mathematical languages. (shrink)

cannot understand the language.”[1] This is not intended to cover (easily imaginable) cases of recording one's experiences in a personal code, for such a code, however obscure in fact, could in principle be deciphered. What Wittgenstein had in mind is a language conceived as necessarily comprehensible only to its single originator because the things which define its vocabulary are necessarily inaccessible to others.

Moral philosophers and theologians have long debated the classic moral dilemma of lying to an intruder in order to save a refugee. This dilemma presents an especially difficult challenge to those who reject consequentialist reasoning. Many contemporary defenders of Thomas Aquinas have argued that lying is never permissible under any circumstances, but none has offered a satisfactory answer to the question of what one ought to do when facing such a dilemma. I argue that there can be no morally satisfying (...) answer to this question, because every possible action will involve some degree of sin, even if lying is the least sinful action. This should not lead us to redefine what it means to tell a lie, nor to say that lying to the intruder is a good or right action; rather, it should lead us to acknowledge the tragic dimension of life in a fallen world. (shrink)

ABSTRACT Michael Rescorla has argued that it makes sense to compute directly with numbers, and he faulted Turing for not giving an analysis of number-theoretic computability. However, in line with a later paper of his, it only makes sense to compute directly with syntactic entities, such as strings on a given alphabet. Computing with numbers goes via notation. This raises broader issues involving de re propositional attitudes towards numbers and other non-syntactic abstract entities.

I argue that Hobbes isn't really a materialist in the early 1640s (in, e.g., the Third Objections to Descartes's Meditations). That is, he doesn't assert that bodies are the only substances. However, he does think that bodies are the only substances we can think about using imagistic ideas.

Hobbes denies in Leviathan that we have an idea of God. He does think, though, that God exists, and does not even deny that we can think about God, even though he says we have no idea of God. There is, Hobbes thinks, another cognitive mechanism by means of which we can think about God. That mechanism allows us only to think a few things about God though. This constrains what Hobbes can say about our knowledge of God, and grounds (...) his belief in a fairly strong version of the thesis that God is incomprehensible. (shrink)

The is an old question over whether there is a substantial disagreement between advocates of different logics, as they simply attach different meanings to the crucial logical terminology. The purpose of this article is to revisit this old question in light a pluralism/relativism that regards the various logics as equally legitimate, in their own contexts. We thereby address the vexed notion of translation, as it occurs between mathematical theories. We articulate and defend a thesis that the notion of “same meaning” (...) is itself context-sensitive, depending on the purposes of a given conversation. (shrink)

STEWART SHAPIRO; Mathematical Structuralism, Philosophia Mathematica, Volume 4, Issue 2, 1 May 1996, Pages 81–82, https://doi.org/10.1093/philmat/4.2.81.

The purpose of the Cambridge Edition of the Works of Schopenhauer is to offer translations of the best modern German editions of Schopenhauer's work in a uniform format for Schopenhauer scholars, together with philosophical introductions and full editorial apparatus. The World as Will and Representation contains Schopenhauer's entire philosophy, ranging through epistemology, metaphysics, philosophy of mind and action, aesthetics and philosophy of art, to ethics, the meaning of life and the philosophy of religion. This second volume was added to the (...) work in 1844, and revised in 1859. Its chapters are officially 'supplements' to the first volume, but are indispensable for a proper appreciation of Schopenhauer's thought. Here we have his most mature reflections on many topics, including sex, death, conscious and unconscious desires, and the doctrines of salvation and liberation in Christian and Indian thought. Schopenhauer clarifies the nature of his metaphysics of the will, and synthesizes insights from a broad range of literary, scientific and scholarly sources. This new translation reflects the eloquence and power of Schopenhauer's prose, and renders philosophical terms accurately and consistently. It offers an introduction, glossary of names, bibliography, and succinct editorial notes. (shrink)

"This book describes the power of the human mind and the cognitive processes that take place through the use of our external senses. Among these cognitive processes is memory, which receives extensive coverage in the essays. The book also contains a preface section providing an account of the author's life and writings. This section is written by Dugald Stewart, who details the philosophy and publications of the deceased Thomas Reid, the book's author." (PsycINFO Database Record (c) 2009 APA, all (...) rights reserved). (shrink)

Inclusive fitness theory provides a compelling explanation for the evolution of altruism among kin. However, a completely satisfactory account of non-kin altruism is still lacking. The present study compared the level of altruism found among siblings with that found among friends and mates and sought to reconcile the findings with an evolutionary explanation for human altruism. Participants (163 males and 156 females) completed a questionnaire about help given to a sibling, friend, or mate. Overall, participants gave friends and mates as (...) much or more help than they gave siblings. However, as the cost of help increased, siblings received a progressively larger share of the help, whereas friends and mates received a progressively smaller share, despite the fact that participants were closer emotionally to friends and mates than they were to siblings. These findings help to explain the relative standing of friends and mates as recipients of altruistic aid. (shrink)

Thomas Hobbes (1588-1679), whose current reputation rests largely on his political philosophy, was a thinker with wide ranging interests. In philosophy, he defended a range of materialist, nominalist, and empiricist views against Cartesian and Aristotelian alternatives. In physics, his work was influential on Leibniz, and lead him into disputes with Boyle and the experimentalists of the early Royal Society. In history, he translated Thucydides's History of the Peloponnesian War into English, and later wrote his own history of the Long Parliament. (...) In mathematics he was less successful, and is best remembered for his repeated unsuccessful attempts to square the circle. But despite that, Hobbes was a serious and prominent participant in the intellectual life of his time. (shrink)

The purpose of this note is to examine the relationship between the practice of mathematics and the philosophy of mathematics, ontology in particular. One conclusion is that the enterprises are (or should be) closely related, with neither one dominating the other. One cannot 'read off' the correct way to do mathematics from the true ontology, for example, nor can one ‘read off’ the true ontology from mathematics as practiced.

A decade on after it first published to international acclaim, the seminal Handbook of Organization Studies has been updated to capture exciting new developments in the field. Providing a retrospective and prospective overview of organization studies, this Handbook continues to challenge and inspire readers with its synthesis of knowledge and literature. As ever, contributions have been selected to reflect the diversity of the field. New chapters cover areas such as organizational change, knowledge management and organizational networks.

This chapter examines the ways in which French philosopher Gilles Deleuze offers conceptual resources for an enactive account of language, in particular his extensive consideration of language in The Logic of Sense. Specifically, Deleuze’s distinction between the nonsense of Lewis Carroll’s portmanteau creations and that of Antonin Artaud’s “transla- tion” of Carroll’s Jabberwocky highlights the need for an enactive, rather than merely embodied, approach to sense-making, particularly with regard to the general category of what Jakobson and Halle (1956) call “sound (...) symbolism”. (shrink)

The purpose of this paper is to describe briefly the institutional arrangements which condition the activities of accountants in the United States; to heighten an awareness of the values which are embodied in the existing structures of accountability; to appraise the consistency with which the established ideals of society have been actualised in financial reporting, and to discern the shape of the emerging history of financial reporting in the light of new values and possibilities. I suggest that the tradition of (...) fair presentation in financial reporting is in danger of being eliminated by a purely political response to previous abuses. Mandatory accounting standards do have a role in preventing these abuses, but they can also be seen as instruments of distributive justice. To promote an awareness and discussion of the issues, I point out some of the goals and values underlying a few of the major structures designed for the distribution of economic costs and benefits. (shrink)

Books Reviewed in this Article: Reason, Truth and History. By Hilary Putnam. Pp.xii, 222, Cambridge University Press, 1982, £15.00 , £4.95 . Fundamentals of philosophy. By David Stewart and H. Gene Blocker. Pp.xiii, 378, New York, Macmillan, 1982, £12.95. Modern Philosophy: An Introduction. By A.R. Lacey. Pp.vii, 246, London and Boston, Routledge & Kegan Paul, 1982, £7.95 , £3.95 . Merleau‐Ponty's Philosophy. By Samuel B. Mallin. Pp.xi, 302, New Haven and London, Yale University Press, 1979, £14.20. Thought and Object: (...) Essays on Intentionality. Edited by Andrew Woodfield. Pp.xvi, 316, Oxford, Clarendon Pressl Oxford University Press, 1982, £16.00. Philosophical Ethics: An Introduction to Moral Philosophy. By Tom L. Beauchamp. Pp.xv, 396, New York & London, McGraw‐Hill, 1982, £14.25. The Limits of Obligation. By James S. Fishkin. Pp.viii, 184, New Haven and London, Yale University Press, 1982, £12.95. Religion and the One: Philosophies East and West. By Frederick Copleston. Pp.281, London, Search Press, 1982, £10.50. Religious Experience and Christian Faith. By F.W. Dillistone. Pp.viii, 120. London, SCM Press, 1982, £4.95. Exploring Inner Space: Scientists and Religious Experience. By David Hay. Pp.256, Harmondsworth, Penguin Books, 1982, £2.95. Judaism and Psychoanalysis. Edited by Mortimer Ostrow. Pp.ix, 305, New York, Ktav, 1982, $20.00. Ecclesial Reflection: An Anatomy of Theological Method. By Edward Farley. Pp.xix, 380, Philadelphia, Fortress Press, 1982, $29.95. The Pastoral Nature of the Ministry. By Frank Wright. Pp.89, London, SCM Press, 1980, £2.50. Power and Authority in the Catholic Church. By Charles Dahm in collaboration with Robert Ghelardi. Pp.xviii, 334, Notre Dame, University of Notre Dame Press, 1981, £12.35. Religion in Sociological Perspective. By Bryan Wilson. Pp.vii. 187, Oxford University Press, 1982, £8.50. Myth, Religion and Society: Structuralist Essays. By M. Detienne, L. Gernet, J.‐P. Vernant and P. Vidal‐Naquet. Pp.xviii, 306, Cambridge University Press, 1981, £20.00 , £6.95 . Seven Theories of Human Society. By Tom Campbell. Pp.244, Oxford, Clarendon Press: Oxford University Press, 1981, £10.00. The Aims of Education Restated. By John White. Pp.xi, 177, London, Routledge & Kegan Paul, 1982, £8.95 , £4.95 . Love and Meaning in Religious Education: An Incarnational Approach to Teaching Christianity. By D.J. O'Leary and T. Sallnow. Pp.147, Oxford University Press, 1982, £3.50. Servant and Son: Jesus in Parable and Gospel. By J. Ramsey Michaels. Pp.xiii, 323, Atlanta, John Knox Press, 1981, £7.80. Parables for Now. By Edmund Flood. Pp.98, London, Darton, Longman and Todd, 1981, £2.50. More Parables for Now. By Edmund Flood. Pp.102, London, Darton, Longman and Todd, 1981, £2.50. Councils and Synods: With other Documents relating to the English Church, Vol.1 , A.D. 871–1204. Edited by D. Whitelock, M. Brett and C.N. Brooke. Pp.1 xxix, xii, 1151, Oxford University Press, 1981, £65.00. The Architectural History of Canterbury Cathedral. By Francis Woodman. Pp.xviii, 282, London, Routledge and Kegan Paul, 1981, £35.00. The Correspondence of Erasmus, Volume VI. Translated by R.A.B. Mynors and D.F.S. Thomson, annotated by Peter G. Bietenholz. Pp.xxii, 448, Toronto, University of Toronto Press, 1982, £56.25. Erasme: Vie de Jean Vitrier et de John Colet. Edited by Andrd Godin. Pp.160, Angers, Editions Moreana, 1982, $7.00. Erasme, lecteur d'Origène. By André Godin. Pp.ix, 724, Geneva, Librairie Droz, 1982, no price given. Thomas More: history and providence. By Alistair Fox. Pp.xi, 271, Oxford, Basil Blackwell, 1982, no price given. Thomas More: Essays on the Icon. Edited by D. Grace and B. Byron. Pp.129, Melbourne, Dove Communications, 1980, no price given. The Cambridge Connection and the Elizabethan Settlement of 1559. By W.S. Hudson. Pp.x, 158, Durham , Duke University Press, 1980, $14.75. Faith by Statute: Parliament and the Settlement of Religion, 1559. By Norman L. Jones. Pp.viii, 245 , London, Royal Historical Society, 1982, £17.52. Richard Hooker and the Politics of a Christian England. By Robert K. Faulkner. Pp.x, 190, Berkeley, University of California Press, 1981, £15.75. Icon and Conquest. By Bernadette Bucher. Pp.xvii, 220, Chicago, The University of Chicago Press, 1981, £9.95. The Wooden Churches of Eastern Europe: An Introductory Survey. By David Buxton. Pp.viii, 405, Cambridge University Press, 1982, £42.50. American Catholics: A History of the Roman Catholic Community in the United States. By James Hennessey. Pp.xii, 397, New York, Oxford University Press, 1981, £13.50. Peter Maurin: Prophet in the Twentieth Century. By Marc H. Ellis. Pp.191, Ramsey, New Jersey and Leominster, England, Paulist Press/Fowler Wright Books, 1981, £7.45. The Newman Movement: Roman Catholics in American Higher Education, 1883–1971. By John Whitney Evans. Pp.xvi, 248, Notre Dame, University of Notre Dame Press, 1980, $14.95. Priests and People in Pre‐Famine Ireland, 1780–1845. By S.J. Connolly. Pp.338, Dublin, Gill & Macmillan, 1982, £17.00. The Nonconformist Conscience: Chapel and Politics, 1870–1914. By D.W. Bebbington. Pp.x, 193, London, George Allen and Unwin, 1982, £10.00. Heinrich Pesch: sein Leben und seine Lehre. By Franz H. Mueller. Pp.220, Cologne, J.P. Bachem, 1980, no price given. Beyond Survival: Reflections on the Future of Judaism. By Dow Marmur. Pp.xix, 218, London, Darton, Longman and Todd, 1982, £7.95. (shrink)

Famously, Michael Dummett argues that considerations concerning the role of language in communication lead to the rejection of classical logic in favor of intuitionistic logic. Potentially, this results in massive revisions of established mathematics. Recently, Neil Tennant (“The law of excluded middle is synthetic a priori, if valid”, Philosophical Topics 24 (1996), 205-229) suggested that a Dummettian anti-realist can accept the law of excluded middle as a synthetic, a priori principle grounded on a metaphysical principle of determinacy. This article shows (...) that the for the anti-realist, the law of excluded middle entails that humans have wildly implausible abilities. The proposed synthesis between anti-realism and classical mathematics thus fails. (shrink)