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)

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)

Since the appearance of Dodds's edition of Gorgias a number of the dialogues in tetr. I-VII have benefited from a re-examination of the evidence for the Platonic text—most notably Meno, tetr. IV, Parmenides, and Phaedrus. Recently the textual tradition of Phaedo has been studied by A. Carlini in a useful book which traces the fortunes of the text from antiquity until the time of the major manuscripts. The evidence thus accumulated goes some way to lessening a problem which has long (...) been obvious—the difficulty of studying the tradition of any single dialogue in isolation from the rest of the Platonic corpus. I propose to argue, however, that the bulk of evidence now available for several dialogues should not blind us to another hazard—that of attempting to fit dialogues showing different textual features into what is basically a single stemmatic pattern. (shrink)

Modern knowledge of servo systems and computing machines makes it possible to specify a circuit that can and will induce the rules and winning moves in a game like chess when they are given only ostensibly, that is, by playing against opponents who quit when illegal or losing moves are made. Such circuits enjoy a value social in the sense that it is shared by the players.La connaissance moderne des servomécanismes et des machines à calculer permet de concevoir un circuit (...) qui pourra suivre des règles et décider les coups décisifs dans un jeu comme le jeu d'échecs tout au moins quand les coups sont joués de faÇon apparente, c'est-à-dire contre des adversaires qui abandonneront dans le cas de coups irréguliers ou de coups absurdes.De tels circuits possèdent une „valeur” sociale dans la mesure où elle est partagée par les autres joueurs.Moderne Kenntnissen im Gebiete von Folgegeraeten und Rechenmaschinen ermoeglichen es einen elektrischen Kreis aufzuwerfen, der die Regeln und gewinnbringende Zuege eines Spieles wie Schach induktiv erfassen kann und wird, wenn diese Regeln und Zuege nur ostensiv gegeben sind; d.h. indem mit Gegnern gespielt wird, die das Spiel einstellen sobald regelwidrige oder verlustbringende Zuege gemacht werden. Solche Kreise schaffen demnach einen Wert, der gesellschaftlich in dem Sinn ist, dass er auch von den Mitspielern geteilt wird. (shrink)

By arguing that his use of representations at the core of Durkheim's sociological thought, this book makes a unique contribution to Durkheimian studies which have recently been dominated by postivist and functionalist interpretaions, and reveals a thinker very much in tune with contemporary developments in philosophy, linguistics and sociology.

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)

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)

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)

by W. S. F. Pickering Durkheim's sociological approach to morals and moral systems has always aroused considerable interest, be it by way of criticism or ...

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)

Although other quasi-Kantian theories have been adapted, Jürgen Habermas’s discourse theory has been largely ignored in discussions of environmental ethics. Indeed on some versions of what an environmental philosophy must entail, Habermas’s anthropocentric approach must be disqualified from the start. Yet, there are some environmentally friendly implications of his discourse theory. They may not give us everything we would wish, but in the contemporary political context we must treasure any moral theory that can draw on the still-extensive theoretical and political (...) resources of liberalism. (shrink)

'Thick neural event' is introduced to mean an event that requires firings of more than one neuron and a substantive (i.e. additional to merely temporal and spatial) relation among them. It is shown that some well regarded theories (e.g. by Lamme, Koch, etc.) strongly suggest that neural correlates of consciousness (NCCs) are thick neural events. It is then shown that thin (= not thick) neural events provide sufficient causation for neural events leading to behaviour, and that there are good reasons (...) to reject overdetermination by thick events. Thus, any physicalism that recognizes legitimacy of a search for NCCs must either reject theories that embrace thickness of NCCs, or accept the epiphenomenalistic view that the properties in virtue of which we are conscious are not properties in virtue of which events causally contribute to our behaviour. (shrink)

The general significance of Ovid's Apollo-Dapbne within its immediate context seems plain enough. Ovid's technique, as Otis remarks, is to set epic pretensions beside elegiac behaviour and thus to show a struggle between incompatible styles of life and poetry. Yet the episode still poses certain problems. These mainly concern the significance of the story within the wider context of the opening of Ovid's poem. One difficulty is hinted at by Otis himself. He observes that with the Apollo-Dapbne and Jupiter-10 Ovid (...) has ‘deflated his divine prologue’. Yet elsewhere3 Otis remarks that in one sense the gap between the behaviour of the gods in the concilium deorum and their philandering in the Daphne and Io stories is very slight. (shrink)

In two shocking articles that appeared in 1968 and 1974, Garrett Hardin argued that the population explosion was producing a “tragedy of the commons.” Since we lack an effective method of sharing common resources, the strong incentive for individuals to appropriate them selfishly would soon lead to their collapse. To mitigate this danger, Hardin proposed a “lifeboat ethic”: less populated and -polluted Western countries should deny food aid to developing nations, where it would save lives only to increase population pressure, (...) and they should close their borders to immigration to prevent their lifeboats from becoming overcrowded and going down with the rest. This paper challenges and complicates Hardin’s account of the tragedy. While there is something right about his view, its vulnerability to a series of empirical challenges reflects its conceptual limitations. I argue that we need to develop a broadly ethical and arguably religious solution to the twin challenges of population growth and pollution. If the liberal commitment to negative freedom is, ironically, largely responsible for our current ecological bind, our only hope of escape is to build bridges between traditions in search of a thicker sense of ethicopolitical obligation. (shrink)

Over the last few years, the concept of “wilderness” has come under attack by environmentalists deeply committed to sustaining the natural world. Their criticisms are pointed and undeniably strong; moreover as I will argue, very similar critiques could be made of its putative counter-concept, “the city.” Yet in both cases, we need not simply reject the concepts themselves as incoherent; our challenge is rather to develop resources rich enough to show that and why they must stand in a constructive tension. (...) I will close by outlining the possibility and productivity of this development through hermeneutic reflections inspired by the work of Hans-Georg Gadamer. (shrink)