In mathematics, various representations of real numbers have been investigated. All these representations are mathematically equivalent because they lead to the same real structure – Dedekind-complete ordered field. Even the effective versions of these representations are equivalent in the sense that they define the same notion of computable real numbers. Although the computable real numbers can be defined in various equivalent ways, if “computable” is replaced by “primitive recursive” , these definitions lead to a number of different concepts, which we (...) compare in this article. We summarize the known results and add new ones. In particular we show that there is a proper hierarchy among p. r. real numbers by nested interval representation, Cauchy representation, b -adic expansion representation, Dedekind cut representation, and continued fraction expansion representation. Our goal is to clarify systematically how the primitive recursiveness depends on the representations of the real numbers. (shrink)

This paper discusses the metaphor of projection in relation to Hume’s treatment of causal necessity. I argue that the best understanding of projection shows it to be compatible with taking Hume to be a ‘sceptical realist’ about causal necessity, albeit an agnostic one.

Speech variability facilitates non-tonal language speakers’ lexical tone learning. However, it remains unknown whether tonal language speakers can also benefit from speech variability while learning second language (L2) lexical tones. Researchers also reported that the effectiveness of speech variability was only shown on learning new items. Considering that the first language (L1) and L2 probably share similar tonal categories, the present study hypothesizes that speech variability only promotes the tonal language speakers’ acquisition of L2 tones that are different from the (...) tones in their L1. To test this hypothesis, the present study trained native Mandarin (a tonal language) speakers to learn Cantonese tones with either high variability (HV) or low variability (LV) speech materials, and then compared their learning performance. The results partially supported this hypothesis: only Mandarin subjects’ productions of Cantonese low level and mid level tones benefited from the speech variability. They probably relied on the mental representations in L1 to learn the Cantonese tones that had similar Mandarin counterparts. This learning strategy limited the impact of speech variability. Furthermore, the results also revealed a discrepancy between L2 perception and production. The perception improvement may not necessarily lead to an improvement in production. (shrink)

Traditionally Hume is seen as offering an ‘empiricist’ critique of ‘rationalism’. This view is often illustrated – or rejected – by comparing Hume's views with those of Descartes'. However the textual evidence shows that Hume's most sustained engagement with a canonical ‘rationalist’ is with Nicolas Malebranche. The author shows that the fundamental differences (among the many similarities) between the two on the self and causal power do indeed rest on a principled distinction between ‘rationalism’ and ‘empiricism’, and that there is (...) some truth in the traditional story. This, however, is very far from saying that Hume's general orientation is an attack on something called ‘rationalism’. (shrink)

Religion and the external world -- Projection, religion, and the external world -- The senses, reason and the imagination -- Realism, meaning and justification : the external world and religious belief -- Modality, projection and realism -- 'Our profound ignorance' : causal realism, and the failure to detect necessity -- Spreading the mind : projection, necessity and realism -- Into the labyrinth : persons, modality, and Hume's undoing -- Value, projection, and realism -- Gilding : projection, value and secondary qualities (...) -- The gold : good, evil, belief and desire -- The golden : relational values, realism and a moral sense. (shrink)

Christian Emden’s informative book has a number of explicit aims: the first aim is to “reconstruct Nietzsche’s philosophical naturalism”; the second aim is to show “that there are specific historical reasons why Nietzsche came to adopt a position best understood in terms of philosophical naturalism”; and the third aim is to show “how Nietzsche’s naturalism and his understanding of the life sciences tie in with genealogy.”1 In pursuit of these aims, Emden divides the book into three parts, one titled “Varieties (...) of Philosophical Naturalism,” the second “Evolution and the Limits of Teleology,” and the third “Genealogy, Nature and Normativity.” In this article I shall concentrate mainly on Emden’s discussion of... (shrink)

An inclusive vision of mathematics-- its beauty, its humanity, and its power to build virtues that help us all flourish. For mathematician Francis Su, a society without mathematical affection is like a city without museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a diverse audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves personal reflections, puzzles, and stories to (...) show how mathematics meets basic human desires and cultivates virtues essential for human flourishing. Readers will explore mathematical concepts-- and see how mathematical thinking can even fulfill such longings as for love, play, freedom, justice, and community. Some lessons come from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher Jackson's letters to the author appear throughout the book and show how this intellectual pursuit can-- and must-- be open to all. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume Studies Volume 29, Number 1, April 2003, pp. 43-61 Conceivability and Modality in Hume: A Lemma in an Argument in Defense of Skeptical Realism PETER KAIL Introduction: A Realist View of Necessity and the Key Objection Those who seek to defend a skeptical realist reading of Hume on causal necessity have a number of textual and philosophical hurdles to clear. This paper attempts to clear one and only (...) one hurdle. So one should not look here for a complete case in favor of a skeptical realist reading: I merely attempt to dispose of what looks like a decisive objection to a conception of objective necessary connection which, I believe, Hume endorses. The skeptical realist Hume, as I and others read him, is a Hume who wishes to deny that human beings have the cognitive wherewithal to perceive or grasp the necessary connection which relates the objects of genuine causal relations. His "skeptical conclusion" is that we cannot grasp in re necessity, nor that there is no necessity. That bald statement, of course, leaves us with a whole host of questions: why should we think that Hume believes that there really is causal necessity? Is this position compatible with his positive account of our idea of necessary connection, or his theory of belief (and of ideas in general)? What of Hume's talk of "necessity in the objects" lacking a meaning? And how does Peter Kail is Lecturer in the Department of Philosophy, The University of Edinburgh, David Hume Tower, George Square, Edinburgh ΕΗ8 9JX, United Kingdom, e-mail: [email protected] 44 Peter Kail such a skeptical realist reading mesh with Hume's general philosophical project (or, indeed, what does it tell us about that)? None of these questions can be addressed here.1 Instead, as I said, I want to defend a conception of necessary connection that seems vulnerable to a decisive objection. First, then, I need to spell out what that conception is. Hume takes acquaintance with necessary connection (the "power, force or efficacy") to entail certain conceptual-cum-epistemological consequences. Roughly, acquaintance with necessary connection would entail (a) the possibility of a priori knowledge of the relevant cause's effect and (b) the impossibility of conceiving the cause without its effect. He tells us that: From the first appearance of an object, we can never conjecture what effect will result from it. But were the power or energy of any cause discoverable by the mind, we could foresee the effect, even without experience; and might, at first, pronounce with certainty concerning it, by the mere dint of thought and reasoning. (EHU 7.1.7; SBN 63) A similar claim is made in the Treatise: We must distinctly and particularly conceive the connection betwixt cause and effect, and be able to pronounce, from a simple view of the one, that it must be follow'd or preceded by the other. This is the true manner of conceiving a particular power in a particular body. (T 1.3.14.13; SBN 161) These aspects of Hume's treatment of necessity constitute what Galen Strawson has called the "AP Property."2 Notice that the AP Property furnishes a thin, but nevertheless contentful, specification of that of which we are ignorant when Hume says we are ignorant of necessary connection. Necessary connection is that feature, acquaintance with which, would yield what is specified in the AP Property. One can go further by suggesting that what the AP Property picks out are unknown (and, for reasons of deep contingency, unknowable) essences.3 This thought is intimated by a number of things Hume says: 'Tis easy to observe, that in tracing this relation, the inference we draw from cause to effect, is not deriv'd merely from a survey of these particular objects, and from such a penetration into their essences as may discover the dependence of the one upon the other. (T 1.3.6.1; SBN 86 (my emphasis)) Hume Studies Conceivability and Modality 45 And: It has been observ'd already, that in no single instance the ultimate connexion of any objects is discoverable, either by our senses or reason, and that we can never penetrate... (shrink)

스페인 시인 씰로트의 상징사전을 토대로 국내외 문학작품을 예로 들어 주제별, 가나다순으로 수록한 문 학평론가의 상징사전.

This chapter provides summaries of the chapter of this book and introduces the major themes and debates addressed in the volume. Discussed are Nietzsche’s metaphysics; his philosophy of mind in light of contemporary views; the question of panpsychism of Beyond Good and Evil 36; the rejection of dualism in favour of monism, in particular a monism of value; Nietzsche’s positions on consciousness and embodied cognition in light of recent cognitive science; a conception of freedom and agency based on an intrinsically (...) motivating; embodied sense of self-efficacy; a Nietzschean account of valuing understood as drive-induced affective orientations of which an agent approves; the idea of ressentiment conceived as a process of intentional, not reflectively strategic, self-deception about one’s own conscious mental states; and a defence of a Nietzschean naturalism. (shrink)

Hume's 'Natural History of Religion' offers a naturalized account of the causes of religious thought, an investigation into its 'origins' rather than its 'foundation in reason'. Hume thinks that if we consider only the causes of religious belief, we are provided with a reason to suspend the belief. I seek to explain why this is so, and what role the argument plays in Hume's wider campaign against the rational acceptability of religious belief. In particular, I argue that the work threatens (...) a form of fideism which maintains that it is rationally permissible to maintain religious belief in the absence of evidence or of arguments in its favour. I also discuss the 'argument from common consent', and the relative superiority of Hume's account of the origins of religious belief. (shrink)

He is the darling of naturalism or the bogeyman of scepticism, a friend to virtue or an unwitting party to incipient nihilism. He is politically conservative, or a liberator from old views. He is a fideist, an advocate of faith over reason, or a precursor of Richard Dawkins.

The original occasion for most of the chapters contained in this book was the result of a wish to establish a forum where Hume scholars of various provenances and convictions could meet and discuss all matters Humean, profiting from the very differences that commonly would make it difficult for them to cross paths with each other. This wish materialised in an interdisciplinary workshop, ‘Hume Studies in Britain’, held in Cambridge in September 2000. The title of the book is intended to (...) reflect that original interdisciplinary approach: Hume has made different impressions on the different areas of investigation here represented. Thus his writings can be taken as transparent vehicles for philosophical intuitions, problems, and arguments that are still at the centre of philosophical reflection today. On the other hand, there are readings that try to locate Hume's views against the background of concerns, debates and discussions of his own time. Hume's texts may be read as highly sophisticated literary-cum-philosophical creations: in such cases, the reader's attention tends to be directed at issues of genre and persuasive strategies rather than philosophical questions and arguments. Or they may be regarded as moments in the construction of the ideology of modernity, and as contributions to the legitimation of a given social order. As the true classics that they are, Hume's works are typical ‘open texts’, in which readers keep finding an ever new and varied bounty of inspirations. The borders between these approaches are far from neat; and this book intends to promote as much trespassing as possible between them. (shrink)

This paper discusses the metaphor of projection in relation to Hume’s treatment of causal necessity. I argue that the best understanding of projection shows it to be compatible with taking Hume to be a ‘sceptical realist’ about causal necessity, albeit an agnostic one.

This paper examines the ramifications of Hume's view of the relation of conceivability to metaphysical possibility. It argues that the limitations Hume places of the representations involved in moves to conceivability to metaphysical possibility preclude any straightforward argument against full-blooded causal realism in Hume from conceivability. Furthermore, our finding certain states of affairs conceivable when they are not metaphysically possible is perfectly compatible with the thrust of the causal realist position.

Impressions of Hume collects brand-new essays from leading scholars in different philosophical, historiographical, and literary traditions within which Hume is a canonical figure. To some his writings are vehicles for intuitions, problems, and arguments which are at the center of contemporary philosophical reflection; others locate Hume's views against the background of concerns and debates of his own time. Hume's texts may be read as highly sophisticated literary-cum-philosophical creations, or as moments in the construction of the ideology of modernity; these are (...) "open" texts which present their reader with a bounty of different materials and inspirations. (shrink)

In mathematics, various representations of real numbers have been investigated. All these representations are mathematically equivalent because they lead to the same real structure - Dedekind-complete ordered field. Even the effective versions of these representations are equivalent in the sense that they define the same notion of computable real numbers. Although the computable real numbers can be defined in various equivalent ways, if computable is replaced by primitive recursive (p. r., for short), these definitions lead to a number of different (...) concepts, which we compare in this article. We summarize the known results and add new ones. In particular we show that there is a proper hierarchy among p. r. real numbers by nested interval representation, Cauchy representation, b -adic expansion representation, Dedekind cut representation, and continued fraction expansion representation. Our goal is to clarify systematically how the primitive recursiveness depends on the representations of the real numbers. (shrink)

The full-text of this article is not currently available in ORA, but you may be able to access the article via the publisher copy link on this record page. Citation: Kail, P. J. E. . 'Naturalism, method and genealogy in Beyond Selflessness', European Journal of Philosophy, 17, 113-120. Copyright © 2009 Blackwell Publishing Ltd.

The full-text of this article is not available in ORA, but you may be able to access the article via the publisher copy link on this record page.

This chapter contains section titled: Introduction Meaning and the Copy Principle External Objects Causal Power The Self and Necessary Connection Acknowledgments References.

This paper examines Hume’s ‘Title Principle’ and its role in a response to one of the ‘manifest contradictions’ he identifies in the conclusion to Book I of A Treatise on Human Nature. This ‘contradiction’ is a tension between two ‘equally natural and necessary’ principles of the imagination, our causal inferences and our propensity to believe in the continued and distinct existence of objects. The problem is that the consistent application of causal reason undercuts any grounds with have for the belief (...) in continued and distinct existence, and yet that belief is as ‘natural and necessary’ as our propensity to infer effects from causes. The TP appears to offer a way to resolve this ‘contradiction’. It statesWhere reason is lively, and mixes itself with some propensity, it ought to be assented to. Where it does not, it never can have any title to operate upon us.’ In brief, if it can be shown that the causal inferences that undermine the belief in external world are not ‘lively’ nor mixed with some propensity’ then we have grounds for think that they have no normative authority. This is in part a response to another ‘manifest contradiction’, namely the apparently self-undermining nature of reason. In this paper I examine the nature and grounds of the TP and its relation to these ‘manifest contradictions’. (shrink)

The full-text of this article is not currently available in ORA, but you may be able to access the article via the publisher copy link on this record page. Citation: Kail, P. J. E.. 'Naturalism, method and genealogy in Beyond Selflessness', European Journal of Philosophy, 17, 113-120. Copyright © 2009 Blackwell Publishing Ltd.

This is a review essay of Richman and Read (eds.) _The New Hume Debate (London: Routledge, 2000). The essay is highly critical of how the debate concerning whether Hume is a causal realist is presently conceived by its opponents, and argues in favour of a _New Hume position.

This paper discusses some key connections between Berkeley's reflections on language in the introduction to his Treatise on the Principles of Human Knowledge and the doctrines espoused in the body of that work, in particular his views on vulgar causal discourse and his response to the objection that his metaphysics imputes massive error to ordinary thought. I argue also that there is some mileage in the view that Berkeley's thought might be an early form of non-cognitivism.