The use of figurate numbers (e. g. in the context of elementary number theory) can be considered a heuristic in the field of problem solving or proving. In this paper, we want to discuss this heuristic from the perspectives of the semiotic theory of Peirce (“diagrammatic reasoning” and “collateral knowledge”) and cognitive psychology (“schema theory” and “Gestalt psychology”). We will make use of several results taken from our research to illustrate first-year students’ problems when dealing with figurate numbers in the (...) context of proving. The considerations taken from both theoretical perspectives will help to partly explain such phenomena. It will be shown that the use of figurate numbers must not be considered to be any kind of help for learners or some way of ‘easy’ mathematics. Working in this representational system has to be learned and practiced as another kind of knowledge is necessary for working with figurate numbers. The named findings also touch upon the concept of ‘proofs that explain’. Finally, we will highlight some implications for teaching and point to a number of demands for future research. (shrink)

Responds to comments by G. Kempen (see record 1996-00289-001) regarding L. Frazier's (see record 1995-31821-001) comments regarding G. Kempen's (see record 1995-31826-001) comments on Frazier et al's (see record 1994-32229-001) article on processing discontinuous words. There are serious problems with Kempen's account of the data of Frazier et al. These problems involve the principle of uncertainty invoked by Kempen. It is unclear that all control items in the original Frazier et al study were open to a (...) complex verb analysis. Kempen's alternative account of the results is not only incomplete, but it is inconsistent with the English data and with half of the Dutch data, in addition to relying on a principle of parsing that is otherwise unmotivated. (PsycINFO Database Record (c) 2000 APA, all rights reserved) (unassigned). (shrink)

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

While philosophers are often concerned with the conditions for moral knowledge or justification, in practice something arguably less demanding is just as, if not more, important – reliably making correct moral judgments. Judges and juries should hand down fair sentences, government officials should decide on just laws, members of ethics committees should make sound recommendations, and so on. We want such agents, more often than not and as often as possible, to make the right decisions. The purpose of this paper (...) is to propose a method of enhancing the moral reliability of such agents. In particular, we advocate for a procedural approach; certain internal processes generally contribute to people’s moral reliability. Building on the early work of Rawls, we identify several particular factors related to moral reasoning that are specific enough to be the target of practical intervention: logical competence, conceptual understanding, empirical competence, openness, empathy and bias. Improving on these processes can in turn make people more morally reliable in a variety of contexts and has implications for recent debates over moral enhancement. (shrink)

This paper aims to show that Godel's ontological argument can be parodied in much the same kind of way in which Gaunilo parodied Anselm's Proslogion argument. The parody in this paper fails; there is a patch provided in "Reply to Gettings" (Analysis 60, 4, 2000, 363-7).

This book presents G. A. Cohen's Gifford Lectures, delivered at the University of Edinburgh in 1996. Focusing on Marxism and Rawlsian liberalism, Cohen draws a connection between these thought systems and the choices that shape a person's life. In the case of Marxism, the relevant life is his own: a communist upbringing in the 1940s in Montreal, which induced a belief in a strongly socialist egalitarian doctrine. The narrative of Cohen's reckoning with that inheritance develops through a series of sophisticated (...) engagements with the central questions of social and political philosophy. In the case of Rawlsian doctrine, Cohen looks to people's lives in general. He argues that egalitarian justice is not only, as Rawlsian liberalism teaches, a matter of rules that define the structure of society, but also a matter of personal attitude and choice. Personal attitude and choice are, moreover, the stuff of which social structure itself is made. Those truths have not informed political philosophy as much as they should, and Cohen's focus on them brings political philosophy closer to moral philosophy, and to the Judeo-Christian ethical tradition, than it has recently been. (shrink)

Our ultimate purpose is to give an axiomatic treatment of recursion theory sufficient to develop the priority method. The direct or abstract approach is to keep in mind as clearly as possible the methods actually used in recursion theory, and then to formulate them explicitly. The indirect or experimental approach is to look first for other mathematical theories which seem similar to recursion theory, to formulate the analogies precisely, and then to search for an axiomatic treatment which covers not only (...) recursion theory but also the analogous theories as particular cases.The first approach is more general because it does not depend on the existence of analogues. A concrete mathematical theory, it seems, need have no such analogues and still be important, as e.g. classical number theory. In such a case, an axiomatic treatment may still be useful for exhibiting the mathematical structure of the theory considered and the assumptions on which it rests. However, it will lack one of the most heavily advertised advantages of the axiomatic method, namely, the “economy of thought” which results from an uniform theory for several different and interesting cases: we cannot hope for this if, by hypothesis, we know of only one particular case. In contrast, the second approach, if successful at all, is bound to achieve such “economy” because we start out with several interesting particular cases. Another possible virtue of the second approach is that of field work over insight: the abstract pattern that we are looking for and hoping to formalize in axioms, may not be evident in any one mathematical theory, but may spring to the eye if one happens to look simultaneously at several theories which happen to realize the pattern. (shrink)

This paper offers a short extension of the dialogue between Anselm and the Fool that is contained in "The Ontological Argument Simplified" by Gary Matthews and Lynne Rudder Baker. My extension of the dialogue ends with the Fool proclaiming that "what looks like an argument of elegant simplicity turns out to be no argument at all".

This article is a reply to Michael Gettings' criticisms of a previous paper of mine on Godel's ontological argument. (All relevant bibliographical details may be found in the article.) I provide a patch to my previous -- faulty -- attempt to provide a parody of Godel's ontological argument on the model of Gaunilo's parody of Anselm's Proslogion 2 argument.

Tracing a central theme of Plato's Republic , G. R. F. Ferrari reconsiders in this study the nature and purpose of the comparison between the structure of society and that of the individual soul. In four chapters, Ferrari examines the personalities and social status of the brothers Glaucon and Adeimantus, Plato's notion of justice, coherence in Plato's description of the decline of states, and the tyrant and the philosopher king—a pair who, in their different ways, break with the terms of (...) the city-soul analogy. In addition to acknowledging familiar themes in the interpretation of the Republic —the sincerity of its utopianism, the justice of the philosopher's return to the Cave—Ferrari provocatively engages secondary literature by Leo Strauss, Bernard Williams, and Jonathan Lear. With admirable clarity and insight, Ferrari conveys the relation between the city and the soul and the choice between tyranny and philosophy. City and Soul in Plato's Republic will be of value to students of classics, philosophy, and political theory alike. (shrink)

In these essays, we are concerned with virtue in journalism and the media but are mindful of the tension between the commercial foundations of publishing and broadcasting, on the one hand, and journalism's democratic obligations on the other. Adam outlines, first, a moral vision of journalism focusing on individualistic concepts of authorship and craft. Next, Craft attempts to bridge individual and organizational concerns by examining the obligations of organizations to the individuals working within them. Finally, Cohen discusses the importance of (...) resisting the powerful corporate logic that pervades the news media in the United States and calls on journalists to be courageous. (shrink)

Meillassoux seeks knowledge of transcendental reality, blaming Kant for the ‘correlationist’ proscription of independent access to either thought or being. For Meillassoux, correlationism blocks an account of the meaning of ‘ancestral statements’ regarding reality prior to humans. I examine three charges on which Meillassoux’s argument depends: (1) Kant distorts ancestral statements’ meaning; (2) Kant fallaciously infers causality’s necessity; (3) Kant’s transcendental idealism cannot grasp ‘the great outdoors’. I reject these charges: (1) imposes a Cartesian misreading, hence Meillassoux’s false assumption that, (...) for Kant, objects don’t exist without subjects; (2) misreads Kant, who infers causality’s necessity from the possibility of experience; (3) casts Kant’s idealism as subjective, ignoring his perspectival portrayal of it. (shrink)

I criticise a paper by Peter Forrest in which he argues that a principle of unrestricted countable fusion has paradoxical consequences. I argue that the paradoxical consequences that he exhibits may be due to his Whiteheadean assumptions about the nature of spacetime rather than to the principle of unrestricted countable fusion.

Philosophers and logicians have long debated how best to understand conditional or hypothetical sentences. William G. Lycan has a distinctive approach to this debate, attending not just to the semantics of such sentences, but equally to their syntax. He shows how insights from linguistic theory help to illuminate problems about the meaning and function of conditionals. For instance, philosophers and logicians have had problems analysing the locutions 'only if', 'unless', and 'even if'. Lycan sets out a general semantic theory of (...) conditionals which works for all such sentences; he assigns meanings to them in a way that explains how and why those meanings depend upon features of utterance context. According to Lycan's theory the 'if'-clauses refer to items called 'events', 'circumstances', or 'conditions'.Real Conditionals gives at last the definitive presentation of this original approach to a topic at the intersection of philosophy, logic, and linguistics. Lycan's characteristically lively and witty expository style ensures that it can be enjoyed by readers from all three disciplines. (shrink)

In this book G. W. Leibniz presents not only his reflections on predestination and election but also a more detailed account of the problem of evil than is found in any of his other works apart from the _Theodicy_. Surprisingly, his _Dissertation on Predestination and Grace_ has never before been published in any form. Michael J. Murray's project of translating, editing, and providing commentary for the volume will therefore attract great interest among scholars and students of Leibniz's philosophy and theology. (...) Leibniz addresses such topics as free will, moral responsibility, divine causation, justice, punishment, divine foreknowledge, and human freedom, revealing crucial aspects of the genesis of his mature metaphysics and the theological motivations behind it. (shrink)

G. E. Moore 's 1912 work Ethics has tended to be overshadowed by his famous earlier work Principia Ethica. However, its detailed discussions of utilitarianism, free will, and the objectivity of moral judgements find no real counterpart in Principia, while its account of right and wrong and of the nature of intrinsic value deepen our understanding of Moore 's moral philosophy. Moore himself regarded the book highly, writing late in his career, "I myself like [it] better than Principia Ethica, because (...) it seems to me to be much clearer and far less full of confusions and invalid arguments." Short but philosophically rich, and written with impressive precision and intellectual candor, Ethics is a minor classic which repays careful study. This new edition includes Moore 's essay "The Nature of Moral Philosophy" as well as editorial notes, an introduction, and a guide to further reading. (shrink)

G. E. R. Lloyd explores the amazing diversity of views that humans have held on being, humanity, and understanding. In a cross-cultural study that ranges from ancient to modern times, he asks how far we are bound by the conceptual systems to which we belong, and explores topics such as ontology, morality, philosophy of language, and communication.

The foregoing considerations support the conjecture that prototypes are semi-compositional in the sense that there exist unboundedly many combinations of nouns with non-exceptional adjectives, which satisfy the rule default-to-prototype and hence are compositional. Presumably there also exist unboundedly many combinations of nouns with exceptional adjectives, which violate DP and hence are non-compositional. An analysis of the connection between productivity and compositionality has been suggested by Robbins. He argues that, for the explanation of productivity, one need not assume that conceptual meanings (...) always compose—it is enough that they compose in infinitely many cases. Since semi-compositionality entails the existence of unboundedly many non-compositional cases, non-compositionality cannot be dealt away with a finite list of idiomatic exceptions, but is a genuine feature of prototype semantics in natural language. (shrink)

An alleged moral right to informational privacy assumes that we should have control over information about ourselves. What is the philosophical justification for this control? I think that one prevalent answer to this question—an answer that has to do with the justification of negative rights generally—will not do.

The practice of paternalism has changed along with developments in medicine, philosophy, law, sociology and psychology. Physicians have learned that a patient's values are a factor in determining what is best for that patient. Modern paternalism continues to be guided by the principle that the physician decides what is best for the patient and pursues that course of action, taking into account the values and interests of the patient. In the autonomy model of the doctor-patient relationship, patient values are decisive. (...) In the paternalistic model, they are but one among several factors the physician must consider in making a medical decision. Although difficult to practise because of limitations in empathising with another person, modern paternalism remains a way to achieve maximum patient benefit. (shrink)

The first English translation of Fichte’s second set of 1804 lectures on the Wissenschaftslehre.