We show that the solvability of matching problems in the simply typed λ-calculus, up to β equivalence, is not decidable. This decidability question was raised by Huet [4].Note that there are two variants of the question: that concerning β equivalence, and that concerning βη equivalence.The second of these is perhaps more interesting; unfortunately the work below sheds no light on it, except perhaps to illustrate the subtlety and difficulty of the problem.

This paper provides characterisations of the equational theory of the PER model of a typed lambda calculus with inductive types. The characterisation may be cast as a full abstraction result; in other words, we show that the equations between terms valid in this model coincides with a certain syntactically defined equivalence relation. Along the way we give other characterisations of this equivalence; from below, from above, and from a domain model, a version of the Kreisel-Lacombe-Shoenfield theorem allows us to transfer (...) the result from the domain model to the PER model. (shrink)

Many philosophres have attempted to argue from the "Humean Theory of Motivation" (HTM) and the "Internalism Requirement" (IR) to the "Humean Theory of Practical Reason" (HTPR). This argument is familiar, but it has rarely been stated with sufficient precision. In this paper, I shall give a precise statement of this argument. I shall then rely on this statement to show two things. First, the HTPR is false: it is incompatible with some extremely plausible assumptions about weakness of will or akrasia. (...) Second, this argument for the HTPR is invalid: even if the HTM and the IR are true, they do not provide any support whatsoever to the HTPR. (shrink)

Philosophers have long distinguished between practical and theoretical rationality. The first section of this chapter begins by discussing the ways in which this distinction was drawn by Aristotle and Kant; then it sketches what seems to be the general consensus today about how, at least roughly, the distinction should be drawn. The rest of this chapter explores what practical and theoretical rationality have in common: in the second section, several parallels between practical and theoretical rationality are outlined, and it is (...) argued that these parallels make it plausible that a unifying account of rationality can be given. Finally, in the third section, a number of such unifying accounts of practical and theoretical rationality are surveyed. These include accounts that are inspired in various ways by Hume and by the results of formal decision theory, as well as views that appeal to reasons and to the distinctive value of correct or appropriate attitudes. (shrink)

In this article i defend the claim that an individual is no more and no less than a bundle of instances of properties against the following objections: (1) the concept of an instance of a property presupposes the concept of an individual. i argue that it presupposes only that no instance of a property exists independently of other instances. (2) if a thing were only a bundle of instances of properties, then properties would qualify properties. this objection commits the fallacy (...) of composition. (3) a bundle constituting an individual needs a component which is not a property to individuate it. i argue that such a bundle individuates itself. (4) the bundle theory makes change impossible. i argue against this claim by distinguishing a thing's numerical identity from its "complete" identity. (5) the bundle theory makes all true statements about individuals analytically true. i show that, at least for one interpretation of 'analytically true', this is not so. (shrink)

The _Symbolic Forms_ has long been considered the greatest of Cassirer’s works. Into it he poured all the resources of his vast learning about language and myth, religion, art, and science—the various creative symbolizing activities and constructions through which man has expressed himself and given intelligible objective form to this experience. “These three volumes alone make an outstanding contribution to epistemology and to the human power of abstraction. It is rather as if ‘The Golden Bough’ had been written in philosophical (...) rather than in historical terms.”—F.I.G. Rawlins, _Nature_. (shrink)

The 25th volume of Research in the Social Scientific Study of Religion continues to provide readers with an interdisciplinary assortment of high quality research studies aimed at capturing salient, contemporary trends in the field. The current volume presents a special section examining the role of spiritual and religious themes in sexuality research.

In this paper, we discuss the macroscopic quantum behavior of simple superconducting circuits. Starting from a Lagrangian for electromagnetic field with broken gauge symmetry, we construct a quantum circuit model for a superconducting weak link (SQUID) ring, together with the appropriate canonical commutation relations. We demonstrate that this model can be used to describe macroscopic excitations of the superconducting condensate and the localized charge states found in some ultrasmall-capacitance weak-link devices.

Reductionist explanations in biology generally assume that biological mechanisms are highly deterministic and basically similar between individuals. A contrasting view has emerged recently that takes into account the degeneracy of biological processes—the ability to arrive at a given endpoint by a variety of available paths, even within the same individual. This perspective casts significant doubt on the prospects for the ability to predict behavior accurately based on brain imaging or genotyping, and on the ability of neuroscience to stipulate ethics.

In this article, I reply to the comments that Richard Holton, Peter Railton, and James Lenman have made on my 2007 book "The Nature of Normativity".