The N.A., as Peirce somewhat affectionately called it, consists of a “nest of three arguments for the Reality of God.” The first arises from “Musement” and is perhaps best described in terms of the psychology of discovery. Yet musement “inevitably” leads to “the hypothesis of God’s Reality.” Thus this, the “Humble Argument,” then gives way to the N.A. proper, which is in part reminiscent of the traditional argument from design. Also every human heart “will be ravished by the beauty and (...) adorability of the Idea” of God’s reality, by the notion of an Ens necessarium. Indeed, “a latent tendency toward belief in God is a fundamental ingredient of the soul.”. (shrink)

“Ordinary algebra in its modern developments,” Whitehead observed in 1897, “is studied as being a large body of propositions, inter-related by deductive reasoning, and based upon conventional definitions which are generalizations of fundamental conceptions.” The use of ‘based upon’ here is perhaps too weak, for some “propositions” must of course be picked out as determinative of the kind of algebra in question by way of axioms. The definitions are then ancillary devices of notational abbreviation and may or may not be (...) of terms or phrases previously introduced, and may or may not be of a “generalized” form. “Thus a science is being created [ordinary algebra in its modern developments],” Whitehead continues, “which by reason of its fundamental character has relation to almost every event, phenomenal or intellectual, which can occur…. Such algebras are mathematical sciences which are not essentially concerned with number or quantity; and this bold extension beyond the traditional domain of pure quantity forms their peculiar interest. The ideal of mathematics should be to erect a calculus to facilitate reasoning in connection with every province of thought, or of external experience, in which the succession of thought, or of events can be definitely ascertained and precisely stated. So that all serious thought which is not philosophy, or inductive reasoning, or imaginative literature, shall be mathematics developed by means of a calculus.”. (shrink)

We may paraphrase Charles Péguy by noting that the philosophical classics are new every morning and nothing is as old as today’s latest philosophical fad. Even fads are not without their value, however, if some new approach or method is introduced and shown to be really contributory to “progress in clarification” in either historical understanding or in the pursuit of new knowledge. In any case, the great enduring philosophical views present a continual challenge to be updated in the light of (...) new knowledge. We know much more now about individuals, classes, relations, predication, identity, and the like, than was known in the days of Peirce and Bradley. It may be helpful to examine the views of these writers on these topics, especially as concerns continuous relations, in the light of what we now know. The result will be not only an updating but to some extent a defense and rational reconstruction of some views which have long been in disrepute among writers who pride themselves upon logical clarity. (shrink)

This magisterial volume achieves a remarkable new synthesis of work on the deep roots of the Homeric poems in Indo-European antiquity with fine-grained historical analyses of the period when the text was crystallizing. Frame’s unmatched range of learning in specialized subjects from Vedic meter and Greek noun morphology to the tangled web of Ionian inter-state relations in the archaic era enables him to buttress a massive structure of argumentation arrayed with architectural artistry over five large parts. The result should change (...) views not just of the underlying poetic structure of the Iliad and Odyssey but also of the place, date, and circumstances of their composition. Few Classics books containing 782 pages of text can be said to reward reading of every paragraph; this one does. (shrink)