Edward Halper

By examining Klein’s discussion of the difference between Plato and Aristotle regarding the ontology of number, this article aims to spells out the significanceof that debate both in itself and for the development of the later mathematical sciences. This is accomplished by explicating and expanding Klein’s account of the differences that exist in the understanding of number presented by these two thinkers. It is ultimately argued that Klein’s analysis can be used to show that the transition from the ancient to the modern number concept has some roots in this disagreement between Plato and Aristotle regarding number. This, in turn, sets up that dispute as an essential part of the background to the more general break between ancient and modern conceptuality, the uncovering of whichis Klein’s main concern.

Why should the work of the ancient and the medievals, so far as it relates to nature, still be of interest and an inspiration to us now? The contributions to this enlightening volume explore and uncover contemporary scholarship's debt to the classical and medieval past. Thinking About the Environment synthesizes religious thought and environmental theory to trace a trajectory from Mesopotamian mythology and classical and Hellenistic Greek, through classical Latin writers, to medieval Christian views of the natural world and our relationship with it. The work also offers medieval Arabic and Jewish views on humanity's inseparability from nature. The volume concludes with a study of the breakdown between science and value in contemporary ecological thought. Thinking About the Environment will be a invaluable source book for those seeking to address environmental ethics from a historical perspective.

In the first lines of Metaphysics 3, Aristotle argues that any progress in this discipline hinges on carefully working through the problems peculiar to it, the metaphysical aporiai; and he devotes all of book 3 to drawing up these problems. Despite this warning, book 3 and its doublet, book 11.1–2, have received relatively little attention. Many of the problems Aristotle sets out here are not addressed explicitly elsewhere in the Metaphysics, their discussion in book 3 is inconclusive, and most seem today of little intrinsic interest on their own. Book 3 has often been read as a merely historical record of that stage in his development when Aristotle personally struggled with Platonism, other philosophies, or his own earlier philosophy. Since there is no detailed and thorough study of book 3 in the recent literature, Madigan’s contribution is sorely needed and a worthy addition to the Clarendon Aristotle series. Like other volumes in the series, this one includes a literal translation followed by a line by line commentary that aims to explore different construals of Aristotle’s arguments and a glossary. Madigan also provides a few pages of textual notes that, unlike the rest of the book, presuppose some knowledge of Greek. A lengthy introduction does a good job of connecting book 3 to the rest of the Metaphysics. Book 11 receives relatively little attention—three pages in the introduction, six in the commentary. Madigan divides the text by aporia, he works through each argument that falls under each aporia, emphasizing in the process Aristotle’s frequent shifts in focus and assumption; Madigan tries to trace the origin of the various assumptions; and he concludes his discussion of each aporia by explaining where and how Aristotle solves it. Additionally, Madigan groups some of book 3’s aporiai and provides, either for the group or each nongrouped aporia, an introduction and an epilogue that lists the premises mentioned explicitly in each aporia along with a statement of whether or not Aristotle continued to accept each or how his view changed. Madigan counts 124 such premises in the whole of book 3. His conclusion is that “working through the aporiai of book 3 would heighten one’s awareness of the difficulties of the issues, but book 3 does not state in so many words what the ‘knots’ in our thinking are, much less how to untie them”.

IT IS well-known that Plato and Aristotle disagree on the possibility of knowledge of nature. Plato maintains that knowledge, in contrast with belief, is never mistaken, that the objects of knowledge are always the same and never becoming, and that what we sense is always becoming. He concludes that knowledge is possible only of objects that are unchanging and separate from sensibles, i.e., the forms. Aristotle rejects this conclusion and recognizes knowledge of sensibles. Surprisingly, though, he accepts Plato's assumptions. He too maintains that knowledge is not sometimes true and sometimes false, but always true ; he distinguishes the sensibles from the unchanging eternal beings ; and he asserts that the objects of knowledge "always are or are for the most part", and occasionally he even claims that they cannot be otherwise. The problem is, how can Aristotle accept Plato's assumptions about the nature and objects of knowledge and still maintain that knowledge of nature is possible?