For 20th century mathematicians, the role of Cantor's sets has been that of the ideally featureless canvases on which all needed algebraic and geometrical structures can be painted. (Certain passages in Cantor's writings refer to this role.) Clearly, the resulting contradication, 'the points of such sets are distinc yet indistinguishable', should not lead to inconsistency. Indeed, the productive nature of this dialectic is made explicit by a method fruitful in other parts of mathematics (see 'Adjointness in Foundations', Dialectia 1969). This (...) role of Cantor's theory is compared with the role of Galois theory in algebraic geometry. (shrink)

The heart of philosophy is metaphysics, and at the heart of the heart lie two questions about existence. What is it for any contingent thing to exist? Why does any contingent thing exist? Call these the nature question and the ground question, respectively. The first concerns the nature of the existence of the contingent existent; the second concerns the ground of the contingent existent. Both questions are ancient, and yet perennial in their appeal; both have presided over the burial of (...) so many of their would-be undertakers that it is a good induction that they will continue to do so. For some time now, the preferred style in addressing such questions has been deflationary when it has not been eliminativist. Ask Willard Quine what existence is, and you will hear that "Existence is what existential quantification expresses. "! Ask Bertrand Russell what it is for an individual to exist, and he will tell you that an individual can no more exist than it can be numerous: there 2 just is no such thing as the existence of individuals. And of course Russell's eliminativist answer implies that one cannot even ask, on pain of succumbing to the fallacy of complex question, why any contingent individual exists: if no individual exists, there can be no question why any individual exists. Not to mention Russell's modal corollary: 'contingent' and 'necessary' can only be said de dicto (of propositions) and not de re (of things). (shrink)

W. F. R. Hardie; X—Aristotle's Doctrine that Virtue is a “Mean”, Proceedings of the Aristotelian Society, Volume 65, Issue 1, 1 June 1965, Pages 183–204, https.

`Folk Psychology' - our everyday talk of beliefs, desires and mental events - has long been compared with the technical language of `Cognitive Science'. Does folk psychology provide a correct account of the mental causes of our behaviour, or must our everyday terms ultimately be replaced by a language developed from computational models and neurobiology? This broad-ranging book addresses these questions, which lie at the heart of psychology and philosophy. Providing a critical overview of the key literature in the field, (...) including the seminal work of Fodor and Churchland, the author explores the classic `Frame Problem' and assesses the future prospects of cognitive science. The scope of the frame problem, touching on connec. (shrink)

The words “free will” have uses in ordinary talk as in “free will offering” and, most commonly, in the expression “of my own free will.” We all know what states of affairs make this expression applicable, and its standard use is defined by this application. Yet philosophers discuss, or used to discuss, whether the will is free, libertarians saying that it is and determinists denying this. Are they, or were they, asking whether anyone ever acts of his own free will? (...) If so, the question asked was absurd. (shrink)

In this module, which first appeared in Vol. 9, Nos. 2&3, pp. 168-170, 1989, an error in a formula appeared three times: CO2 and C2HSOH should read CO2. The entire article is reprinted here. The editors apoligize for this and regret any confusion this may have caused.

Aristotle maintains that every man has, or should have, a single end, a target at which he aims. The doctrine is stated in E.N. I 2. ‘If, then, there is some end of the things we do which we desire for its own sake, and if we do not choose everything for the sake of something else, clearly this must be the good and the chief good. Will not the knowledge of it, then, have a great influence on life? Shall (...) we not, like archers who have a mark to aim t, be more likely to hit upon what is right?’. Aristotle does not here prove, nor need we understand him as claiming to prove, that there is only one end which is desired for itself. He points out correctly that, if there are objects which are desired but not desired for themselves, there must be some object which is desired for itself. The passage further suggests that, if there were one such object and one only, this fact would be important and helpful for the conduct of life. (shrink)

Let g E(m, n)=o mean that n is the Gödel-number of the shortest derivation from E of an equation of the form (m)=k. Hao Wang suggests that the condition for general recursiveness mn(g E(m, n)=o) can be proved constructively if one can find a speedfunction s s, with s(m) bounding the number of steps for getting a value of (m), such that mn s(m) s.t. g E(m, n)=o. This idea, he thinks, yields a constructivist notion of an effectively computable function, (...) one that doesn't get us into a vicious circle since we intuitively know, to begin with, that certain proofs are constructive and certain functions effectively computable. This paper gives a broad possibility proof for the existence of such classes of effectively computable functions, with Wang's idea of effective computability generalized along a number of dimensions. (shrink)

Rapid developments in Artificial Intelligence are leading to an increasing human reliance on machine decision making. Even in collaborative efforts with Decision Support Systems (DSSs), where a human expert is expected to make the final decisions, it can be hard to keep the expert actively involved throughout the decision process. DSSs suggest their own solutions and thus invite passive decision making. To keep humans actively ‘on’ the decision-making loop and counter overreliance on machines, we propose a ‘reflection machine’ (RM). This (...) system asks users questions about their decision strategy and thereby prompts them to evaluate their own decisions critically. We discuss what forms RMs can take and present a proof-of-concept implementation of a RM that can produce feedback on users’ decisions in the medical and law domains. We show that the prototype requires very little domain knowledge to create reasonably intelligent critiquing questions. With this prototype, we demonstrate the technical feasibility to develop RMs and hope to pave the way for future research into their effectiveness and value. (shrink)

G. W. F. Hegel is an immensely important yet difficult philosopher. Philosophy of Mind is the third part of Hegel's Encyclopaedia of the Philosophical Sciences, in which he summarizes his philosophical system. It is one of the main pillars of his thought. Michael Inwood presents this central work to the modern reader in an intelligible and accurate new translation---the first into English since 1894---that loses nothing of the style of Hegel's thought. In his editorial introduction Inwood offers a philosophically sophisticated (...) evaluation of Hegel's ideas which includes a survey of the whole of Hegel's thought and detailed analysis of the terminology he used. (shrink)

Does Aristotle in the Nicomachean Ethics give one consistent answer to the question what life is best or two mutually inconsistent answers? In the First Book he says that we can agree to say that the best life is eudaimonia or eupraxia but must go on to say in what eudaimonia consists. By considering the specific nature of man as a thinking animal he reaches a conclusion: eudaimonia, the human good, is the activity of soul in accordance with virtue, and (...) if there are more than one virtue in accordance with the best and most complete, and in a complete life. Aristotle states that his formula is no more than a sketch or outline, but that a good sketch is important since, if the outline is right, anyone can articulate it and supply details. He seems to be thinking here not just of the rest of his own treatise but of the work of pupils and successors; he speaks, as at the end of the Topics, of progress in a science. (shrink)

The majority of studies on absorptive capacity (AC) underscore the importance of absorbing technological knowledge from other firms to create economic value. However, to preserve moral legitimacy and create social value, firms must also discern and adapt to (shifts in) societal values. A comparative case study of eight firms in the food industry reveals how organizations prioritize and operationalize the societal value health in product innovation while navigating inter- and intravalue conflicts. The value-sensitive framework induced in this article extends AC (...) by explaining how technically savvy, economic value–creating firms diverge in their receptivity, articulation, and reflexivity of societal values. (shrink)

The, Contrasted with the Intuitional-Causal Approach. There are two states of sophistication in the attitude which men of science have taken towards theories of natural phenomena. In the more abstract state, the purpose has been to seek the most harmonious scheme of coordination of the phenomena without raising the question of underlying causes and without adherence to some, or any, set of preconceived principles regarded primarily as fundamental starting points. In this state, the starting points have been sought in the (...) phenomena themselves. (shrink)