Libertarians such as J.R. Lucas have abandoned traditional Christian doctrines because they cannot reconcile them with the freedom of the will. Traditional Christian thinkers such as Augustine have repudiated libertarianism because they cannot reconcile it with the dogmas of the Faith. In Free Will and the Christian Faith, W.S. Anglin demonstrates that free will and traditional Christianity are ineed compatible. He examines, and solves, puzzles about the relationships between free will and omnipotence, omniscience, and God's goodness, using the idea of (...) free will to answer the question of why God allows evil, and presenting arguments that link free will to eternal life and to the nature of revelation. Topics covered include the meaning of life, the soul and Lesbegue measure, and strategies for discerning the voice of God. (shrink)

The authors' novel approach to some interesting mathematical concepts - not normally taught in other courses - places them in a historical and philosophical setting. Although primarily intended for mathematics undergraduates, the book will also appeal to students in the sciences, humanities and education with a strong interest in this subject. The first part proceeds from about 1800 BC to 1800 AD, discussing, for example, the Renaissance method for solving cubic and quartic equations and providing rigorous elementary proof that certain (...) geometrical problems posed by the ancient Greeks cannot be solved by ruler and compass alone. The second part presents some fundamental topics of interest from the past two centuries, including proof of G del's incompleteness theorem, together with a discussion of its implications. (shrink)

In 1962 a mimeographed sheet of paper fell into my possession. It had been prepared by Ernest Adams of the Philosophy Department at Berkeley as a handout for a colloquim. Headed 'SOME FALLACIES OF FORMAL LOGIC' it simply listed eleven little pieces of reasoning, all in ordinary English, and all absurd. I still have the sheet, and quote a couple of the arguments here to give the idea. • If you throw switch S and switch T, the motor will start. (...) There fore, either if you throw switch S the motor will start, or, if you throw switch T the motor will start. • It is not the case that if John passes history he will graduate. Therefore, John will pass history. The disconcerting thing about these inferences is, of course, that under the customary truth-functional interpretation of and, or, not, and if-then, they are supposed to be valid. What, if anything, is wrong? At first I was not disturbed by the examples. Having at that time consider able personal commitment to rationality in general and formal logic in par ticular, I felt it my duty and found myself easily able (or so I thought) to explain away most of them. But on reflection I had to admit that my expla nations had an ad hoc character, varying suspiciously from example to example. (shrink)

A fundamental philosophical question that arises in connection with evolutionary theory is whether the fittest patterns of behavior are always the most rational. Are fitness and rationality fully compatible? When behavioral rationality is characterized formally as in classical decision theory, the question becomes mathematically meaningful and can be explored systematically by investigating whether the optimally fit behavior predicted by evolutionary process models is decision-theoretically coherent. Upon investigation, it appears that in nontrivial evolutionary models the expected behavior is not always in (...) accord with the norms of the standard theory of decision as ordinarily applied. Many classically irrational acts, e.g. betting on the occurrence of one event in the knowledge that the probabilities favor another, can under certain circumstances constitute adaptive behavior.One interesting interpretation of this clash is that the criterion of rationality offered by classical decision theory is simply incorrect (or at least incomplete) as it stands, and that evolutionary theory should be called upon to provide a more generally applicable theory of rationality. Such a program, should it prove feasible, would amount to the logical reduction of the theory of rational choice to evolutionary theory. (shrink)

Heidegger’s characterization of Dasein as Being-in-the-world suggests a natural relation to environmental philosophy. Among environmentalists, however, closer inspection must raise alarm, both since Heidegger’s approach is in some senses inescapably anthropocentric and since Dasein discovers its environment through its usability, serviceability, and accessibility. Yet Heidegger does not simply adopt a traditionally modern, instrumental view. The conditions under which the environment appears imply neither that the environment consists only of tools, nor that what is true of the parts is also true (...) of the whole, nor that an orientation to use—where appropriate—precludes any other orientation. Heidegger’s anthropocentric commitments thus do not rule out the possibility of a non-instrumental perspective on the natural world. (shrink)

This is a concise introductory textbook for a one semester course in the history and philosophy of mathematics. It is written for mathematics majors, philosophy students, history of science students and secondary school mathematics teachers. The only prerequisite is a solid command of pre-calculus mathematics. It is shorter than the standard textbooks in that area and thus more accessible to students who have trouble coping with vast amounts of reading. Furthermore, there are many detailed explanations of the important mathematical procedures (...) actually used by famous mathematicians, giving more mathematically talented students a greater opportunity to learn the history and philosophy by way of problem solving. Several important philosophical topics are pursued throughout the text, giving the student an opportunity to come to a full and consistent knowledge of their development. These topics include infinity, the nature of motion, and Platonism. This book offers, in fewer pages, a deep penetration into the key mathematical and philosophical aspects of the history of mathematics. (shrink)

This text is organized around the distinction between finite and infinite. It includes a brief overview of what different philosophers have said about infinity, and looks at some of the arguments to the effect that one should adopt a pro-infinity attitude. Other chapters contain an exposition of the ontological schools; interactions among these schools and various theories of truth; the relationship between mathematics and values; a history of mathematics; an analysis of mathematical knowledge; the role of mathematics in eduction; the (...) implications of religion for the philosophy of mathematics; and referenc eto mathematical objects. (shrink)

In an article on ‘The Name of the Euxine Pontus’ in C.Q.xxxiv , pp. 123 ff., A. C. Moorhouse rejects the suggestion made by M. Vasmer and supported by Boisacq that the original Greek title ξενος was a popular rendering of the Avestan adjective αχṦαệνα, ‘of dark colour’. Moorhouse raises the following objections to this theory: i. There is no direct evidence of the Avestan adjective ever being applied to the Black Sea. ii. In historical times ‘Avestan is a long (...) way from Greek’ and in prehistorical times it is doubtful whether the speakers of Avestan had any close connexion with the Black Sea. iii. Assuming πόντος to denote ‘way’, ‘the dark way’ would be a fantastic name for any sea. iv. The early Greek form is ξενος, and only metri gratia ξεινος, whereas if the word is a loan from αχṧαēνα we should expect the phonetically closer form ξενος. (shrink)

Since my article in C.Q. xli, pp. 86 ff., a further discussion of the problem has come to my notice. H. Jacobsohn, in an article entitled Σκνθικ in Zeitschr. f. vergleichende Sprachforschung, liv, pp. 254 ff., anticipates my point that the Greek ᾊξενƿς is borrowed not from Avestan but from some other Iranian language, probably Scythian. He also makes outan attractive case, based on the word παφδεισ¿ς, for considering the Iranian pronunciation at the period when the loan occurred to have (...) been αχšēna, with ē from original ai. It is unfortunate that he should have supported his case with the argument that a form αχšaina is too remote from Greek ξειν¿ς for the identification to have taken place: this insistence on complete homonymy in folk-etymology I have already criticized in discussing Moorhouse's article; and in any case it is by no means certain that ξεινႿς is the earliest form of the name in Greek. (shrink)

We now know that the epitomes prefixed to the plays of Euripides in the medieval manuscripts were written not for this purpose but as part of a complete collection of Euripidean epitomes, arranged alphabetically by initial,and intended presumably to make the subject-matter of the plays available to persons unable or unwilling to read the plays themselves. The first direct proof of the existence of this collection came with the publication in 1933 of a fragment containing Rhesos, Rhadamanthys, Skyrioi ; we (...) now have parts of it in three other papyri as well, and may reasonably suppose that P. Oxy. 420 is also from the same work. (shrink)