Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. (...) The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists. (shrink)

Scholars of Plato are divided between those who emphasize the literature of the dialogues and those who emphasize the argument of the dialogues, and between those who see a development in the thought of the dialogues and those who do not. In this important book Russell Dancy focuses on the arguments and defends a developmental picture. He explains the Theory of Forms of the Phaedo and Symposium as an outgrowth of the quest for definitions canvassed in the Socratic dialogues, by (...) constructing a Theory of Definition for the Socratic dialogues based on the refutations of definitions in those dialogues, and showing how that theory is mirrored in the Theory of Forms. His discussion, notable for both its clarity and its meticulous scholarship, ranges in detail over a number of Plato's early and middle dialogues, and will be of interest to readers in Plato studies and in ancient philosophy more generally. (shrink)

Dancy (philosophy, Florida State U.) presents two new interpretations of the evidence regarding the metaphysical ideas of two important figures in Plato's Academy, Eudoxus and Speusippus, and of Aristotle's reaction to those ideas.

We argue that thoughts are structures of concepts, and that concepts should be individuated by their origins, rather than in terms of their semantic or epistemic properties. Many features of cognition turn on the vehicles of content, thoughts, rather than on the nature of the contents they express. Originalism makes concepts available to explain, with no threat of circularity, puzzling cases concerning thought. In this paper, we mention Hesperus/Phosphorus puzzles, the Evans-Perry example of the ship seen through different windows, and (...) Mates cases, and we believe that there are many additional applications. (shrink)

ARISTOTLE'S PROGRAM Aristotle says outright that the law of non-contradiction cannot be demonstrated: you can't prove everything, and among the things you ...

Are fictional characters such as Sherlock Holmes real? What can fiction tell us about the nature of truth and reality? In this excellent introduction to the problem of fictionalism R. M. Sainsbury covers the following key topics: what is fiction? realism about fictional objects, including the arguments that fictional objects are real but non-existent; real but non-factual; real but non-concrete the relationship between fictional characters and non-actual worlds fictional entities as abstract artefacts fiction and intentionality and the problem of irrealism (...) fictionalism about possible worlds moral fictionalism. R. M. Sainsbury makes extensive use of examples from fiction, such as Sherlock Holmes, Anna Karenina and Madame Bovary and examines the work of philosophers who have made significant contributions to the topic, including Meinong, David Lewis, and Bas Van Fraassen. Additional features include chapter summaries, annotated further reading and a glossary of technical terms, making _Fiction and Fictionalism_ ideal for those coming to the issue for the first time. (shrink)

Few residency training programmes explicitly require substantive exposure to issues in medical ethics and fewer still have a formal curriculum in this area. Traditional undergraduate medical ethics courses teach preclinical students to identify ethical issues and analyse them at a theoretical level. Residency training, however, is the ideal time to establish the critical behavioural link which makes ethics truly useful in clinical medicine. The General Internal Medicine Residency Training Program at Rhode Island Hospital has developed an integrated, three-year curriculum with (...) the goals of helping residents to perceive ethical issues in clinical practice, to utilise basic philosophical principles in resolving ethical dilemmas and to communicate these issues clearly and sensitively to patients. The curriculum has been well received by residents and has had a hospital-wide impact. We believe that training residents in medical ethics and communication skills is an effective approach to developing physicians' humane qualities. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Plato and Aristotle in Agreement? Platonists on Aristotle from Antiochus to PorphyryR. M. DancyGeorge E. Karamanolis. Plato and Aristotle in Agreement? Platonists on Aristotle from Antiochus to Porphyry. Oxford: Clarendon Press, 2006. Pp. x + 419. Cloth, $125.00.Coleridge wrote: “Every man is born an Aristotelian or a Platonist. I do not think it possible that anyone born an Aristotelian can become a Platonist; and I am sure that (...) no born Platonist can ever change into an Aristotelian. They are two classes of man, beside which it is next to impossible to conceive a third.”Ancient Platonists could not be counted on to accept this kind of dichotomy, and that is what Karamanolis’s book is about. (It may be usefully compared with Lloyd P. Gerson’s 2005 book, Aristotle and Other Platonists.) It covers Antiochus (second century BC), Plutarch [End Page 634] of Chaeronea, Numenius, Atticus, Ammonius Saccas, Plotinus, and Porphyry (third century AD). And it does so with incredible thoroughness, making it a tough read. The book began as a dissertation; it still has something of the air of one.The longest chapter is devoted to Porphyry, whom Karamanolis claims to be the first Platonist to write commentaries on books of Aristotle, and the first to adopt the view that Aristotle simply was in agreement with Plato—the founder of a tradition in scholarship to the effect that “Plato is named as the authority in metaphysics, and Aristotle in logic” (330). His concluding paragraph is this:It is this understanding of philosophizing which lies behind the formation of the Pla-tonist syllabus I described in the beginning of this book. This remains the situation until the Renaissance. When Renaissance humanists revive ancient philosophy, especially Platonism, as happened in Renaissance Florence, they re-establish this very model. Few other shifts in the history of Western philosophy are of such significance as the one which we, quite rightly, attribute to Porphyry.(330)The “Platonist syllabus” to which Karamanolis here adverts is perhaps summed up when he says that “from the third to the sixth century AD... Aristotle was appropriated by Platonists because they found his philosophy, if properly studied, a prerequisite for, and conducive to, an understanding of Plato’s thought” (4). More precisely, Karamanolis’s book is about Porphyry’s view and the background of its formation.Answering Karamanolis’s title question is not what is at stake; rather, he is concerned with how the Platonists listed above answered it. So we are not getting a history of the reading of Plato and Aristotle as agreeing or disagreeing from the very beginning. The early Academy and the skeptical Academy before Antiochus, for example, do not figure, except incidentally, in Karamanolis’s story (although there is a useful appendix on the early peripatetics). There is enough here to keep us busy without this.Dealing with any of Karamanolis’s Platonists is made more difficult by the nature of the material that remains: except for Plutarch and Plotinus, it is almost entirely fragmentary. So it is a question of interpreting not just the target authors, whose works we do not possess, but the sources we have for them, who have their own hobby-horses to ride, and hence are not always reliable. Karamanolis pays suitable attention to such details. But the back-and-forth discussion required can make it difficult to keep the larger picture in view.Karamanolis’s Platonists do not uniformly go for the agreement of Plato and Aristotle. As Karamanolis has it, Porphyry is the only one to swallow it whole: “... nowhere does Porphyry criticize Aristotle,” he concludes (322). This requires him to explain away what he regards as misunderstandings of the evidence (243–45 records some disagreements, and the Porphyry chapter throughout is dedicated to rebuttal). Karamanolis is at least prima facie convincing. At the opposite end of the spectrum are Atticus and Numenius, whose antipathy toward Aristotle is universal.For the rest, whether we are to say that Plato and Aristotle were in agreement obviously depends on what the agreement is to be about. There is, among Karamanolis’s Platonists, a good deal of interesting variation over that. Most of those who... (shrink)

This chapter contains sections titled: A Socratic Theory of Definition The Meno: Between Definitions and Forms Forms.

Recently, Bohr’s complementarity principle was assessed in setups involving delayed choices. These works argued in favor of a reformulation of the aforementioned principle so as to account for situations in which a quantum system would simultaneously behave as wave and particle. Here we defend a framework that, supported by well-known experimental results and consistent with the decoherence paradigm, allows us to interpret complementarity in terms of correlations between the system and an informer. Our proposal offers formal definition and operational interpretation (...) for the dual behavior in terms of both nonlocal resources and the couple work-information. Most importantly, our results provide a generalized information-based trade-off for the wave–particle duality and a causal interpretation for delayed-choice experiments. (shrink)

The solution of the outer multiplicity problem in the tensor product of U(3) irreducible representations (irreps) developed by Biedenharn et al.(1–7) and realized through the well-known Draayer-Akiyama (DA) computer code(8) is extended to the quantum algebra Uq(3). An analytic formula for special stretched Uq(3) Wigner coefficients, $$\left\langle {(\lambda _1 \mu _1 ) H_1 , (\lambda _2 \mu _2 ) \varepsilon _2 \Lambda _2 m_2 \left| { (\lambda _3 \mu _3 ) H_3 } \right.} \right\rangle _{\max }^q $$ is derived using (...) a projection operator method.(9–10) In this expression Hi denotes the highest weight vector of the (λiμi) irrep; the subscript “max” means coefficients corresponding to a unit tensor operator with a maximal characteristic null space; and q is the usual quantum label so the standard U(3) Wigner coefficient, which is required in the DA code, can be obtained in the q→1 limit of the theory. To illustrate the theory, some Uq(3) Wigner coefficients for the tensor product (22)×(22) are calculated. The procedure for evaluating nonhighest weight Wigner Uq(3) coefficients follow the DA prescription. (shrink)