Preface -- 1. Propositional logic : proofs from axioms and inference rules -- 2. First order logic : proofs with quantifiers -- 3. Set theory : proofs by detachment, contraposition, and contradiction -- 4. Mathematical induction : definitions and proofs by induction -- 5. Well-formed sets : proofs by transfinite induction with already well-ordered sets -- 6. The axiom of choice : proofs by transfinite induction -- 7. applications : Nobel-Prize winning applications of sets, functions, and relations -- 8. Solutions (...) to some odd-numbered exercises. (shrink)

This volume shows how late medieval dream-poetry explored problems arising from the reception of Aristotle's philosophical work concerning human knowledge. Marco Nievergelt explores how the work of three medieval poets in the genre of allegorical fiction addressed these problems in distinctive, non-academic terms.

Circadian rhythm abnormalities in bipolar disorder have led to a search for genetic abnormalities in circadian "clock genes" associated with BD. However, no significant clock gene findings have emerged from genome-wide association studies. At least three factors could account for this discrepancy: complex traits are polygenic, the organization of the clock is more complex than previously recognized, and/or genetic risk for BD may be shared across multiple illnesses. To investigate these issues, we considered the clock gene network at three levels: (...) essential "core" clock genes, upstream circadian clock modulators, and downstream clock controlled genes. Using relaxed thresholds for GWAS statistical significance, we determined the rates of clock vs. control genetic associations with BD, and four additional illnesses that share clinical features and/or genetic risk with BD. Then we compared the results to a set of lithium-responsive genes. Associations with BD-spectrum illnesses and lithium-responsiveness were both enriched among core clock genes but not among upstream clock modulators. Associations with BD-spectrum illnesses and lithium-responsiveness were also enriched among pervasively rhythmic clock-controlled genes but not among genes that were less pervasively rhythmic or non-rhythmic. Our analysis reveals previously unrecognized associations between clock genes and BD-spectrum illnesses, partly reconciling previously discordant results from past GWAS and candidate gene studies. (shrink)

The thirteenth-century allegorical dream vision, the Roman de la Rose, transformed how medieval literary texts engaged with philosophical ideas. Written in Old French, its influence dominated French, English and Italian literature for the next two centuries, serving in particular as a model for Chaucer and Dante. Jean de Meun's section of this extensive, complex and dazzling work is notable for its sophisticated responses to a whole host of contemporary philosophical debates. This collection brings together literary scholars and historians of philosophy (...) to produce the most thorough, interdisciplinary study to date of how the Rose uses poetry to articulate philosophical problems and positions. This wide-ranging collection demonstrates the importance of the poem for medieval intellectual history and offers new insights into the philosophical potential both of the Rose specifically and of medieval poetry as a whole. (shrink)

Book review r A. (2004). "Book review: Yves nievergelt, foundations of ...

This is a review of Yves Nievergelt, Foundations of Logic and Mathematics: Applications to Computer Science and Cryptography, Birkäuser Verlag, Boston, 2002, €90, pp. 480, ISBN 0-8176-4249-8, hardcover.

Epistemische Tugenden sind Eigenschaften des forschenden Subjekts, die in wissenschaftlichen Kulturen als Bedingung fur die Produktion, Vermittlung oder den Erwerb von Wissen angesehen werden. Sie lassen sich nicht auf ein abstraktes Sollen reduzieren, wie es oft von Ethikkommissionen oder politischen Bewegungen an die Wissenschaft herangetragen wird. Die methodische Erzeugung von Wissen ware kaum moglich, wenn es nicht erkenntnisfordernde Tugenden wie Geduld, Aufmerksamkeit, Genauigkeit, Intuition, Wahrhaftigkeit, Neugierde, Strenge oder Zuverlassigkeit gabe, die den an sich prekaren Erkenntnisprozess stabilisieren und in eine bestimmte (...) Richtung lenken. Die Beitrage dieses Sammelbandes befassen sich mit epistemischen Tugenden aus (wissenschafts-)historischer, philosophischer, medien- und literaturwissenschaftlicher Perspektive. Ein Schwerpunkt liegt dabei auf dem Verhaltnis von wissenschaftlichen und soziokulturellen beziehungsweise moralischen Normen. Mit Beitragen von: Lorraine Daston, Martin Doll, Andreas Gelhard, Raymond Geuss, Ruben Hackler, Michael Hagner, Jens Kertscher, Markus Krajewski, Marcel Lepper, Martin Mulsow, Oliver Nievergelt, Tanja Paulitz, Robert Proctor, Katja Sabisch, Sandro Zanetti, Cornelia Zumbusch. (shrink)