In the paper below the authors describe three super-tasks. They show that although the abstract notion of a super-task may be, as Benacerraf suggested, a conceptual mismatch, the completion of the three super-tasks involved can be defined rather naturally, without leading to inconsistency, by means of a particular kinematical interpretation combined with a principle of continuity.

ABSTRACT:Many companies engage in dialogue with nongovernmental organizations about societal issues. The question is what a regulative ideal for such dialogues should be. In the literature on corporate social responsibility, the Habermasian notion of communicative action is often presented as a regulative ideal for stakeholder dialogue, implying that actors should aim at consensus and set strategic considerations aside. In this article, we argue that in many cases, communicative action is not a suitable regulative ideal for dialogue between companies and NGOs. (...) We contend that there is often an adversarial element in the relation between companies and NGOs, and that an orientation towards consensus can be in tension with this adversarial relation. We develop an alternative approach to stakeholder dialogue called ‘agonistic deliberation.’ In this approach, conflict and strategic considerations play a legitimate and, up to a certain point, desirable role. (shrink)

In this book, which is both a philosophical and historiographical study, the author investigates the fallibility and the rationality of mathematics by means of rational reconstructions of developments in mathematics. The initial chapters are devoted to a critical discussion of Lakatos' philosophy of mathematics. In the remaining chapters several episodes in the history of mathematics are discussed, such as the appearance of deduction in Greek mathematics and the transition from Eighteenth-Century to Nineteenth-Century analysis. The author aims at developing a notion (...) of mathematical rationality that agrees with the historical facts. A modified version of Lakatos' methodology is proposed. The resulting constructions show that mathematical knowledge is fallible, but that its fallibility is remarkably weak. (shrink)

In an earlier paper the authors discussed some super-tasks by means of a kinematical interpretation. In the present paper we show a semi-formal way that a more abstract treatment is possible. The core idea of our approach is simple: if a super-task can be considered as a union of (finite) tasks, it is natural to define the effect of the super-task as the union of the effects of the finite tasks it consists of. We show that this approach enables us (...) to handle two of the three super-tasks that we discussed earlier. We also argue that recent objections against our original kinematical interpretation do not hold water. One of our arguments is based on the construction of an elegant correspondence between the first of those three super-tasks and Zeno's Achilles and the Tortois. (shrink)

Mathematics and the Divine seem to correspond to diametrically opposed tendencies of the human mind. Does the mathematician not seek what is precisely defined, and do the objects intended by the mystic and the theologian not lie beyond definition? Is mathematics not Man's search for a measure, and isn’t the Divine that which is immeasurable? The present book shows that the domains of mathematics and the Divine, which may seem so radically separated, have throughout history and across cultures, proved to (...) be intimately related. Religious activities such as the building of temples, the telling of ritual stories or the drawing of enigmatic figures all display distinct mathematical features. Major philosophical systems dealing with the Absolute and theological speculations focussing on our knowledge of the Ultimate have been based on or inspired by mathematics. A series of chapters by an international team of experts highlighting key figures, schools and trains of thought is presented here. Chinese number mysticism, the views of Pythagoras and Plato and their followers, Nicholas of Cusa's theological geometry, Spinozism and intuitionism as a philosophy of mathematics are treated side by side among many other themes in an attempt at creating a global view on the relation of mathematics and Man’s quest for the Absolute in the course of history. (Elsevier). (shrink)

Mathematics and the Divine seem to correspond to diametrically opposed tendencies of the human mind. Does the mathematician not seek what is precisely defined, and do the objects intended by the mystic and the theologian not lie beyond definition? Is mathematics not Man's search for a measure, and isn’t the Divine that which is immeasurable? The present book shows that the domains of mathematics and the Divine, which may seem so radically separated, have throughout history and across cultures, proved to (...) be intimately related. Religious activities such as the building of temples, the telling of ritual stories or the drawing of enigmatic figures all display distinct mathematical features. Major philosophical systems dealing with the Absolute and theological speculations focussing on our knowledge of the Ultimate have been based on or inspired by mathematics. A series of chapters by an international team of experts highlighting key figures, schools and trains of thought is presented here. Chinese number mysticism, the views of Pythagoras and Plato and their followers, Nicholas of Cusa's theological geometry, Spinozism and intuitionism as a philosophy of mathematics are treated side by side among many other themes in an attempt at creating a global view on the relation of mathematics and Man’s quest for the Absolute in the course of history. (Elsevier). (shrink)

Ivor Grattan-Guinness, Routes of Learning: Highways, Pathways and Byways in the History of Mathematics. Baltimore: The John Hopkins University Press, 2009. xii + 372 pp. $75.00. ISBN 10:978-0-8018-...

In the present paper the roots of the Art of the Catalan philosopher Ramon Llull are examined. Moreover the impact of the Art on seventeenth mathematics is briefly discussed.

This article contains an outline of the development of the classic wind mill with some additional attention to developments in the Netherlands.

Comparative genomics has proven a fruitful approach to acquire many functional and evolutionary insights into core cellular processes. Here it is argued that in order to perform accurate and interesting comparative genomics, one first and foremost has to be able to recognize, postulate, and revise different evolutionary scenarios. After all, these studies lack a simple protocol, due to different proteins having different evolutionary dynamics and demanding different approaches. The authors here discuss this challenge from a practical (what are the observations?) (...) and conceptual (how do these indicate a specific evolutionary scenario?) viewpoint, with the aim to guide investigators who want to analyze the evolution of their protein(s) of interest. By sharing how the authors draft, test, and update such a scenario and how it directs their investigations, the authors hope to illuminate how to execute molecular evolution studies and how to interpret them. Also see the video abstract here https://youtu.be/VCt3l2pbdbQ. (shrink)

Floor Brouwer, Teunis van Rheenan, Shivcharn S. Dhillion, and Anna Martha Elgersma (eds.) Sustainable Land Management: Strategies to Cope with the Marginalisation of Agriculture Content Type Journal Article Pages 1-21 DOI 10.1007/s10806-011-9313-7 Authors Douglas Seale, 21 Turner Ridge Road, Marlborough, MA 01752, USA Journal Journal of Agricultural and Environmental Ethics Online ISSN 1573-322X Print ISSN 1187-7863.