Through criticism and analysis of ancient traditions, Kahn reconstructs the pattern of Anaximander’s thought using historical methods akin to the reconstructive techniques of comparative linguists.

An examination of the emergence of the phenomenon of deductive argument in classical Greek mathematics.

The question as to whether Ian Hacking’s project of scientific styles of thinking entails epistemic relativism has received considerable attention. However, scholars have never discussed it vis-à-vis Wittgenstein. This is unfortunate: not only is Wittgenstein the philosopher who, together with Foucault, has influenced Hacking the most, but he has also faced the same accusation of ‘relativism’. I shall explore the conceptual similarities and differences between Hacking’s notion of style of thinking and Wittgenstein’s conception of form of life. It is a (...) fact that whether or not the latter entails epistemic relativism is still a controversial question. From my comparative analysis, it will emerge that there are stronger reasons to conclude that Hacking’s notion of style leads to epistemic relativism than there are to reach the same conclusion in the case of Wittgenstein’s conception of form of life. This point will be at odds with the anti-relativistic stance that Hacking has taken in his more recent writings. (shrink)

The analytical notion of ‘scientific style of reasoning’, introduced by Ian Hacking in the middle of the 1980s, has become widespread in the literature of the history and philosophy of science. However, scholars have rarely made explicit the philosophical assumptions and the research objectives underlying the notion of style: what are its philosophical roots? How does the notion of style fit into the area of research of historical epistemology? What does a comparison between Hacking’s project on styles of thinking and (...) other similar projects suggest? My aim in this paper is to answer these questions. Hacking has denied that his project of styles of thinking falls into the field of historical epistemology. I shall challenge his remark by tracing out the connections of the notion of style with historical epistemology and, more in general, with a tradition of thought born in France in the beginning of twentieth-century. (shrink)

This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that (...) proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities. (shrink)

Geoffrey Lloyd engages in a wide-ranging exploration of what we can learn from the study of ancient civilizations that is relevant to fundamental problems, both intellectual and moral, that we still face today. These include, in philosophy of science, the question of the incommensurability of paradigms, the debate between realism and relativism or constructivism, and between correspondence and coherence conceptions of truth. How far is it possible to arrive at an understanding of alien systems of belief? Is it possible to (...) talk meaningfully of 'science' and of its various constituent disciplines, 'astronomy' 'geography' 'anatomy' and so on, in the ancient world? Are logic and its laws universal? Is there one ontology - a single world - to which all attempts at understanding must be considered to be directed? When we encounter apparently very different views of reality, how far can that be put down to a difference in conceptions of what needs explaining, or of what counts as an explanation, or to different preferred modes of reasoning or styles of inquiry? Do the notions of truth and belief represent reliable cross-cultural universals? In another area, what can ancient history teach us about today's social and political problems? Are the discourses of human nature and of human rights universally applicable? What political institutions do we need to help secure equity and justice within nation states and between them? Lloyd sets out to answer all these questions, and to argue that the study of the science and culture of ancient Greece and China provided a precious resource in order to advance a wealth of modern debates. (shrink)

The essay considers synthetically the passages of Hesiod’s Theogony concerning Khaos, Gaia, Uranòs, and Tàrtaros as describing the cosmic structure at its very beginning and at its present state. The final result of the cosmogenetic process consists of three solid parallel disks of equal size separated from one another by the space of Khaos/Aèr. The whole structure is conceived of as an ideal cylinder, whose superior base is Uranòs, the inferior one is Tàrtaros and the median section is Gaia, dividing (...) the whole cylinder into two high semicylinders full of Khaos/Aèr. From this Khaos/Aèr, the primal Four Elements derive, as plants do from their roots, from which all other substances of the universe originate in turn. Thus, Khaos is arkhè not only in the chronological-historical sense, but also in the sense of an eternal generative substance of all things. We may conclude that the Hesiodic word khaos is a lexical ancestor of the later physical and philosophical term hyle because it conveys the primeval notion of ‘matter’. (shrink)

Places the development of Anaximander's thought within social, political, cosmological, astronomical, and technological contexts.