It is generally believed that the uncertainty relation Δq Δp≥1/2ħ, where Δq and Δp are standard deviations, is the precise mathematical expression of the uncertainty principle for position and momentum in quantum mechanics. We show that actually it is not possible to derive from this relation two central claims of the uncertainty principle, namely, the impossibility of an arbitrarily sharp specification of both position and momentum (as in the single-slit diffraction experiment), and the impossibility of the determination of the path (...) of a particle in an interference experiment (such as the double-slit experiment). (shrink)

We discuss some recent work by Tim Maudlin concerning Black Hole Information Loss. We argue, contra Maudlin, that there is a paradox, in the straightforward sense that there are propositions that appear true, but which are incompatible with one another. We discuss the significance of the paradox and Maudlin's response to it.

This book, first published in 1938, is based on the Muirhead Lectures given at Birmingham University in February and March of 1937. The first half of this book is mainly devoted to an exposition of the principles of genetics, whilst the second half deals with more controversial topics, with the text providing an insight into the ideology of the time. This title will be of interest to students of politics and history.

We investigate the relative probabilistic support afforded by the combination of two analogies based on possibly different, structural similarity (as opposed to e.g. shared predicates) within the context of Pure Inductive Logic and under the assumption of Language Invariance. We show that whilst repeated analogies grounded on the same structural similarity only strengthen the probabilistic support this need not be the case when combining analogies based on different structural similarities. That is, two analogies may provide less support than each would (...) individually. (shrink)

Although the existence of tachyons is not ruled out by special relativity, it appears that causal paradoxes will arise if there are tachyons. The usual solutions to these paradoxes employ some form of the reinterpretation principle. In this paper it is argued first that the principle is incoherent, second that even if it is not, some causal paradoxes remain, and third, the most plausible “solution,” which appeals to boundary conditions of the universe, will conflict with special relativity.

Girard and Reynolds independently invented System F to handle problems in logic and computer programming language design, respectively. Viewing F in the Curry style, which associates types with untyped lambda terms, raises the questions of typability and type checking. Typability asks for a term whether there exists some type it can be given. Type checking asks, for a particular term and type, whether the term can be given that type. The decidability of these problems has been settled for restrictions and (...) extensions of F and related systems and complexity lower-bounds have been determined for typability in F, but this report is the first to resolve whether these problems are decidable for System F. This report proves that type checking in F is undecidable, by a reduction from semi-unification, and that typability in F is undecidable, by a reduction from type checking. Because there is an easy reduction from typability to type checking, the two problems are equivalent. The reduction from type checking to typability uses a novel method of constructing lambda terms that simulate arbitrarily chosen type environments. All of the results also hold for the λI-calculus. (shrink)

Plato's "Politicus" (Statesman) stands, both in date and in political thought, between the "Republic" and the "Laws". It presents his thought at the point when he was chastened by disappointment with his attempts to put theory into practice at Syracuse. The dialogue reflects contemporary controversies on the method of definition; but its logical exercises and the impressive 'myth' of the two cosmic eras serve to bring out its essential political teaching. This volume contains the text in translation. In this second (...) edition, Skemp made corrections to his extensive introduction and running commentary, and added a new appendix taking into account scholarship since the first (1952) edition. (shrink)

In the seventeenth and eighteenth centuries rationalism about morality was repeatedly used to reject strong divine command theories of ethics. Such theories were morally unacceptable to many devout Christians. But deism, rationalist through and through, seemed to make revelation unnecessary, and with it most of Christianity. William Law, an influential divine command theorist of Hume's time, argued that Christians must consequently find rationalism unacceptable. Hume's effort to destroy moral rationalism functions to force his readers into a dilemma: either a morally (...) horrifying divine command view of morals, or almost no religion at all. (shrink)

What is the function of moral principles within the body of moral knowledge? And what must be the nature of moral principles in order for them to carry out this function? A specific set of answers to these questions is widely accepted among moral philosophers – so widely accepted as almost to constitute a sort of orthodoxy. The answers embody a view of the place of principles within the body of morality which crosses the lines between cognitivism and non-cognitivism. Though (...) I have put the question in cognitivist terms and shall discuss it in those terms, I think a similar question and a more or less parallel discussion could be given in non-cognitivist terms. Perhaps the time-honoured debate between the two positions can be suspended, at least temporarily, while we examine, not the nature of morality, but its structure. (shrink)

Sidgwick is usually considered to be a utilitarian, and with good reason. In an autobiographical fragment he tells us that his “first adhesion to a definite Ethical system was to the Utilitarianism of Mill”, and that after a variety of intellectual changes he became “a Utilitarian again, but on an Intuitional basis.” He refers to himself in other works and in letters as a utilitarian, and he was so viewed by his contemporaries. Hence it is understandable that Albee should view (...) The Methods of Ethics as “an independent contribution to the literature of Utilitarianism”, labelling it “the last authoritative utterance of traditional Utilitarianism”, and that almost everyone who discusses the book should agree with this classification of it. Yet Sidgwick did not himself say that the Methods is a defense or a restatement of utilitarianism. On the contrary: he was from the first at pains to disavow any intention of proving a system of morality and to insist that he is presenting only an examination of “the different methods of obtaining reasoned convictions as to what ought to be done which are to be found … in the moral consciousness of mankind generally.” In the “Preface” to the second edition he bemoans the misunderstanding which led critics to suppose that he was “writing as an assailant of two of the methods” he examines. One critic, he complains, thought he was giving “mere hostile criticism” of intuitionism, another “has constructed an article on the supposition that my principal object is ‘the suppression of Egoism’”. Yet a third critic, he remarks dryly, referring to a savage attack by F. H. Bradley, “has gone to the length of a pamphlet under the impression that the ‘main argument’ of my treatise is a demonstration of Universalistic Hedonism. I am concerned”, he comments, “to have caused so much misdirection of criticism”; and he goes on to reiterate his position about the two forms, egoistic and universalistic, of hedonism: “I do not hold the reasonableness of aiming at happiness generally with any stronger conviction than I do that of aiming at one’s own.”. (shrink)

Paralleling the formal derivation of general relativity as a flat spacetime theory, we introduce in addition a preferred temporal foliation. The physical interpretation of the formalism is considered in the context of 5-dimensional “parametrized” and 4-dimensional preferred frame contexts. In the former case, we suggest that our earlier proposal of unconcatenated parametrized physics requires that the dependence on τ be rather slow. In the 4-dimensional case, we consider and tentatively reject several areas of physics that might require a preferred foliation, (...) but find a need for one in the process (“flowing”) theory of time. We then suggest why such a foliation might reasonably be unobservable. (shrink)