Past and present societies world-wide have employed well over 100 distinct notational systems for representing natural numbers, some of which continue to play a crucial role in intellectual and cultural development today. The diversity of these notations has prompted the need for classificatory schemes, or typologies, to provide a systematic starting point for their discussion and appraisal. The present paper provides a general framework for assessing the efficacy of these typologies relative to certain desiderata, and it uses this framework to (...) discuss the two influential typologies of Zhang & Norman and Chrisomalis. Following this, a new typology is presented that takes as its starting point the principles by which numerical notations represent multipliers (the principles of cumulation and cipherization), and bases (those of integration, parsing, and positionality). Many different examples show that this new typology provides a more refined classification of numerical notations than the ones put forward previously. In addition, the framework provided here can be used to assess typologies not only of numerical notations, but also of many other domains. (shrink)

Recent work on kinetoplast DNA and on CAP‐DNA and Eco RI‐DNA complexes shows that certain sequences cause DNA to be highly bent, and that other sequences bend in response to the sequence‐specific binding of proteins. These results demonstrate that alterations of DNA structure may facilitate gene regulation and DNA packaging.

This chapter contains sections titled: Nietzsche's (Artful) Naturalism The Subject Naturalized Nietzsche's Artful Naturalism Toward an Ethos of the Agonized Subject.

In this article I address Schiller’s first response in his Kallias Briefe or Concerning the Beautiful, Letters to Gottfried Körner to Kant’s analysis of the beautiful in the first part of the Critique of Judgment. My main intention in the paper is to investigate Schiller’s emphasis on the notion of resistance (Widerstand) in his reading of Kant’s concept of beauty, and to ask how does this relate to Schiller’s own approach to aesthetics as an ethico-political realm. I am particularly interested (...) in the turn, in Schiller’s case, from Kant’s critique of aesthetics to the idea of aesthetics as critique. (shrink)

This chapter contains sections titled: Epistemological Background Educational Applications On Not Addressing Epistemological Controversies.

Scholarship on Xenophanes’s F1 has had two foci, one on the rules of the symposium and the other on the religious program posed at its close. Thus far, the two areas of focus have been treated as either separate issues or as the religious program proposed in the service of the sympotic objectives. Instead, I will argue that the sympotic norms Xenophanes espouses are in the service of the broader program of rational theology.

Duchamp’s aspiration to become more philosophical in his art mirrors Heidegger’s aspiration to become more poetical in his philosophy. Their shared mistrust of subjectivity led them to question the continued viability of art on the one hand and of philosophy on the other. This article examines Heidegger’s essay in juxtaposition to Duchamp’s work, highlighting Heidegger’s (often underappreciated) playful approach to his weighty task, and, in regard to Duchamp, revealing just how serious art can be when it doesn’t appear to take (...) itself too seriously. (shrink)

This chapter contains sections titled: Early Years in Stageira First Athenian Period Period of Travels Second Period in Athens Last Year in Chalcis, Euboia Notes Bibliography.

This chapter contains sections titled: Introduction Aristotle's Presuppositions and Demonstration Induction (epagôgê) and Comprehension or Intuition (nous) Collecting Facts and Finding Causes Dialectic and its Uses Notes Bibliography.

This chapter contains sections titled: Catalogues and Editions of Aristotle's Works Chronology of Aristotle's Works The Development of Aristotle's Thought Notes Bibliography.

Translations of the “myths” from Plato’s Protagoras (320c-324d), Symposium (189c-193d), Republic (614b-621d), Timaeus (20d-25d and 29d-34b), and Kritias (108e-121c).

Religion has surprised the secular elites of North American and European societies. Not only has religion survived the treacherous passage from village to metropolis, from medieval superstition to modern science, and from state support (and coercion) to voluntary membership. Apparently, it has thrived and gained new sources of strength amidst these transformations. Far from being relegated to the proverbial ash‐heap of history, modern religions and the activist movements they generate find themselves positioned at the centre of modern debates – and (...) modern wars – over territory, political sovereignty, human rights, global and local economy, scientific research and popular culture. Among these activist movements, the most virulent and sustained are ‘fundamentalisms’ – increasingly sophisticated reactions against secular modernity that seek to fight back against the enemies of traditional religion by constructing religiously inspired and quintessentially modern alternatives to ‘godless’, idolatrous governments, institutions and political and cultural elites. (shrink)