For an educational zeitgeist so rooted, and understandably so, in measurable, scalable, and replicable results, it is difficult to entertain the idea of an unquantifiable goalpost. Although terms l...

Alan Weir’s new book is, like Darwin’s Origin of Species, ‘one long argument’. The author has devised a new kind of have-it-both-ways philosophy of mathematics, supposed to allow him to say out of one side of his mouth that the integer 1,000,000 exists and even that the cardinal ℵω exists, while saying out of the other side of his mouth that no numbers exist at all, and the whole book is devoted to an exposition and defense of this new view. (...) The view is presented in the book in a way that can make it difficult for the reader to trace the main line of argument: with a great deal of apparatus, and with a great many digressions into subordinate issues. In what follows I will try to stick to what I take to be the essentials, even at the risk of oversimplifying some central but complicated issues, and at the cost of neglecting some interesting but peripheral ones.In chapter 1, the author introduces a distinction between what he calls ‘two aspects of meaning’ and dubs informational content and metaphysical content. Informational content is the aspect of meaning of primary interest to linguists, and the one of which speakers themselves are generally aware, at least upon reflection. Metaphysical content is supposed to be another aspect of meaning primarily of interest to philosophers. The basic idea is that if there are standards of correctness for assertions of a certain kind, then such an assertion may be called ‘true’ when those standards are met, even though the kind of correctness involved is not correctness in representing how the world is. What the world must be like in order for the utterance to be true is the metaphysical content of the assertion, but it need not be part of its …. (shrink)

The latest book of Reviel Netz presents a highly erudite analysis of the style of Hellenistic mathematics. Besides the Introduction and Conclusion the book is composed of four chapters. Before turning to more general remarks I would like first to outline the contents of the book.The Introduction starts with the presentation of Archimedes’ Spiral lines. In a condensed form, the author outlines his approach and calls attention to the stylistic peculiarities of that work. Most of the themes discussed in more (...) detail in the following chapters, such as the analysis of the narrative structure of the treatise, its working with surprise, the exposition of the rhetorical devices, the discussion of technical tools, and the breaking of genre-boundaries emerge here side by side in a single treatise.The first chapter, called The carnival of calculation, starts with another work of Archimedes, the Stomachion, for which Netz offers a new interpretation as a treatise in geometrical combinatorics. Then he turns to Archimedes’ On the measurement of the circle, where, in a detailed analysis of the calculations made by Archimedes, Netz presents a pattern that he identifies in several other works of Hellenistic mathematics, a pattern he calls ‘asymptotic calculation’. It consists in a combination of strict geometric arguments with calculations of proportions, some precise, some only approximate, which together with rather arbitrary simplifications lead to a result that is achieved after an abrupt and unexpected halt. Netz shows that, according to the surviving testimonies, a similar pattern can be found in many Hellenistic authors, such as Aristarchus, Hipparchus, and Apollonius of Perga. "[I]n many Hellenistic mathematical works we see calculations that give rise to values that are big and unwieldy, or else are only asymptotically found. Such calculations end up not with the satisfaction of having simplified … ". (shrink)

Conditional judgements—judgements employing ‘if’—are essential to practical reasoning about what to do, as well as to much reasoning about what is the case. We handle them well enough from an early...

Susan Wolf, Meaning in Life and Why it Matters Content Type Journal Article Pages 1-2 DOI 10.1007/s10677-011-9321-8 Authors Simon Derpmann, Westfälische Wilhelms-Universität Münster, Philosophisches Seminar, Domplatz 23, 48143 Münster, Germany Journal Ethical Theory and Moral Practice Online ISSN 1572-8447 Print ISSN 1386-2820.

Targeted killing has become a staple tactic in the “war in terror”. Since the beginning of the second Intifada, Israel is estimated to have killed over four hundred Palestinians in targeted strikes, while the US has killed over two thousand in Pakistan alone since 2004. These statistics include the deaths of innocent bystanders caught in the wrong place at the wrong time—“collateral damage”—as well as the deaths of the terrorists themselves. Be that as it may, the American and Israeli publics (...) have largely settled into an acceptance of the targeted killings carried out in their name.In Anna Goppel’s Killing Terrorists: A Moral and Legal Analysis, even the staunchest defender of targeted killing will find good reason to reconsider. The book does not bother developing an absolute, in-principle objection to targeted killing; it concedes to advocates of the practice that there are conceivable circumstances under which it might be justified. But these circumstances are shown to b .. (shrink)

IntroductionThis title is an important collection of articles on the principles, methods, and facts of human reasoning. It is of interest to argumentation theorists, philosophers, psychologists, cognitive scientists, and researchers in related fields. Out of the 53 articles, 16 were written specifically for this volume by prominent representatives of their fields, and it makes an important contribution to the research on reasoning. The size of the collection enables it to include papers from classic philosophical articles to important new theorizing on (...) the psychology of reasoning, so it can be used as material for a variety of courses with different emphases and levels of expertise. The “comingling” of the empirical and the philosophical keeps the reading experience refreshing for readers of different academic denominations. Both the philosophical and the empirical develop their mutual and distinct debates, though the selection of philosophical texts naturally favors those that link wi .. (shrink)