We present a one per cent measurement of the cosmic distance scale from the detections of the baryon acoustic oscillations in the clustering of galaxies from the Baryon Oscillation Spectroscopic Survey, which is part of the Sloan Digital Sky Survey III. Our results come from the Data Release 11 sample, containing nearly one million galaxies and covering approximately 8500 square degrees and the redshift range 0.2 < z < 0.7. We also compare these results with those from the publicly released (...) DR9 and DR10 samples. Assuming a concordance Λ cold dark matter cosmological model, the DR11 sample covers a volume of 13 Gpc3 and is the largest region of the Universe ever surveyed at this density. We measure the correlation function and power spectrum, including density-field reconstruction of the BAO feature. The acoustic features are detected at a significance of over 7σ in both the correlation function and power spectrum. Fitting for the position of the acoustic features measures the distance relative to the sound horizon at the drag epoch, rd, which has a value of rd,fid = 149.28 Mpc in our fiducial cosmology. We find DV = at z = 0.32 and DV = at z = 0.57. At 1.0 per cent, this latter measure is the most precise distance constraint ever obtained from a galaxy survey. Separating the clustering along and transverse to the line of sight yields measurements at z = 0.57 of DA = and H =. Our measurements of the distance scale are in good agreement with previous BAO measurements and with the predictions from cosmic microwave background data for a spatially flat CDM model with a cosmological constant. © 2014 The Author Published by Oxford University Press on behalf of the Royal Astronomical Society. (shrink)

Originally published in Proceedings of the British Academy 60 (1974), 339-359.

A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.

The idea of a 'logic of quantum mechanics' or quantum logic was originally suggested by Birkhoff and von Neumann in their pioneering paper [1936]. Since that time there has been much argument about whether, or in what sense, quantum 'logic' can be actually considered a true logic (see, e.g. Bell and Hallett [1982], Dummett [1976], Gardner [1971]) and, if so, how it is to be distinguished from classical logic. In this paper I put forward a simple and natural semantical framework (...) for quantum logic which reveals its difference from classical logic in a strikingly intuitive way, viz. through the fact that quantum logic admits (suitably formulated versions of) the characteristic quantum-mechanical notions of superposition and incompatibility of attributes. That is, precisely the features that distinguish quantum from classical physics also serve, within this framework, to distinguish quantum from classical logic. Some light is shed on the question of whether quantum logic is a genuine logical system by introducing a natural entailment relation for quantum-logical formulas with the implication symbol. The novelty is that, although implication behaves as it should (i.e. the 'deduction theorem' holds), the order of introduction of premises is significant. The fact that a reasonable entailment relation can be formulated for quantum logic supports the view that it is a genuine logical system and not merely an algebraic formalism. (shrink)

‘Unfair to Facts’ is a follow-up on Ch. 5, addressing objections Peter Strawson raised against Austin’s view of truth as a description of the conditions that must be satisfied if we are to say of a statement that it is true. Austin addresses the objection that his description of these conditions is due to a misunderstanding about the use of ‘fact’, arguing, against Strawson, that facts are not pseudo-entities and that the notion of ‘fitting the facts’ is not a useless (...) notion. (shrink)

_The Foundations of Arithmetic_ is undoubtedly the best introduction to Frege's thought; it is here that Frege expounds the central notions of his philosophy, subjecting the views of his predecessors and contemporaries to devastating analysis. The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly influenced developments in the philosophy of mathematics and in general ontology.

In this paper (a sequel to [4]) I put forward a "local" interpretation of mathematical concepts based on notions derived from category theory. The fundamental idea is to abandon the unique absolute universe of sets central to the orthodox set-theoretic account of the foundations of mathematics, replacing it by a plurality of local mathematical frameworks - elementary toposes - defined in category-theoretic terms.

Austin takes on the problem of other minds, of how to respond to the question ‘how do you know?’, if this question is raised with regard to the thoughts, feelings, sensations, minds of other creatures. This problem has traditionally been understood as the problem of justifying our belief in the existence of other minds. Austin argues that believing in other persons, in authority and testimony, is an essential part of the act of communicating, and as such is an irreducible part (...) of our experience. While we can state certain advantages of communicative performances, there is no justification for our doing them as such. (shrink)

Questions of religious liberty have become flashpoints of controversy in virtually every area of life around the world. Despite protection of religious liberty at both supranational and individual state levels, there is an increasing number of conflicts concerning the proper way to recognize it, both in modern secular states, and in countries with an established religion or theocratic mode of government. This book provides an analysis of the general concept of religious liberty with a close study of important cases that (...) serve as a test bed for proposals. It combines the insights of both pure academics and experienced practitioners in law to take a fresh look at the nature, scope and limits of religious liberty. Divided into two parts, the collection presents a blend of legal and philosophical approaches, and draws on cases from a wide range of jurisdictions, including Brazil, India, Australia, USA, Netherlands, and Canada. Presenting a broad range of views, this often provocative volume makes fascinating reading for academics and researchers working in the areas of law and religion, legal philosophy and human rights. (shrink)

Genealogía y lógica de la ratio imperial romana -- Racionalización ética judía y religión de salvación cristiana -- La revolución teológica de Pablo y sus consecuencias -- Teología política imperial y militancia cristiana -- La teología trinitaria y el destino de la teología imperial -- Hilario, Ambrosio y el camino del catolicismo en Occidente -- Mal y salvación: Augstín de Hipona.

It will be noticed that, in the stemma above, no line of descent is marked from the first generation registered therein to the following generations. The genealogy of the Emperor Nerva is customarily traced back to the consul of 36 b.c., M. Cocceius Nerva. This short note will underline the ancient testimony found amongst the Pseudacroniana tracing his descent from the latter's brother, the consummate diplomat. There are ramifications. Amongst the items of interest will be the light shone upon what (...) Dio and Eutropius understood to be Nerva's standing at the time of his accession. Before passing on to Pseudacron's datum, it might be worthwhile pausing on that point, as well as briefly contemplating the factors that actually bore upon the emperor's ancestral training. (shrink)

In a single volume intended for philosophy students of all levels as well as their teachers, this reader provides modern, accurate translations of the texts necessary for a careful study of most aspects of Aristotle's philosophy. Professor Ackrill has drawn on his broad experience of teaching graduate classes in selecting the texts, and his choice reflects issues of current philosophical interest as well as the perennial themes. Only recent translations which achieve a high level of accuracy have been chosen: the (...) aim is to place the reader without Greek, as nearly as possible, in the position of a reader of Greek. As an aid to study, a valuable guide to the key topics covered is also suppied, giving references to works or passages contained in the reader, an indication of their interrelation, and a currnet bibliography. (shrink)

Autobiographical memories typically give rise either to memory reports (“I remember going swimming”) or to first person past-tense judgements (“I went swimming”). This article focuses on first person past-tense judgements that are (epistemically) based on autobiographical memories. Some of these judgements have the IEM property of being immune to error through misidentification. This article offers an account of when and why first person past-tense judgements have the IEM property.

This paper is an introduction to topos theory which assumes no prior knowledge of category theory. It includes a discussion of internal logic in a topos, A characterization of the category of sets, And an investigation of the notions of topology and sheaf in a topos.

In this paper, we revisit the long-standing debate of whether there is a pattern in the evolution of organisms towards greater complexity, and how this hypothesis could be tested using an interdisciplinary lens. We argue that this debate remains alive today due to the lack of a quantitative measure of complexity that is related to the teleonomic (i.e. goal-directed) nature of living systems. Further, we argue that such a biological measure of complexity can indeed be found in the vast literature (...) produced within life history theory. We propose that an ideal method to quantify this complexity lies within life history strategies (i.e., schedules of survival and reproduction across an organism’s life cycle), as it is precisely these strategies that are under selection to optimise the organism’s fitness. In this context, we set an agenda for future steps: (1) how this complexity can be measured mathematically, and (2) how we can engage in a comparative analysis of this complexity across species to investigate the evolutionary forces driving increases or for that matter decreases in teleonomic complexity. (shrink)

Esta obra es un viaje por el camino recorrido por la filosofía trascendente, que pone de relieve la pervivencia de conceptos como "sujeto", "crítica" o "reflexión". El núcleo fundamental del libro está en el estudio de la situación terminal a la que conduce el planteamiento fenomenológico husserliano y en el hallazgo de nuevos ámbitos de trascendentalidad. Puede advertirse cómo la vieja filosofía de sujeto-conciencia llega a transformarse y girar, para dar cabida a nuevos temas: la corporeidad, la intersubjetividad, el lenguaje, (...) que tradicionalmente habían sido silenciados o infravalorados. (shrink)

Deals with the question of whether there is a use of ‘is true’ that is the primary or generic name for that which at bottom we are always saying ‘is true’. Austin discusses the views that truth is primarily a property of beliefs and of true statements. He goes on to argue that the word ‘true’ denotes the validity of an intended correspondence between a representation and what it represents, and dismantles confusions about the meaning of the words that underlie (...) such a view, such as ‘fact that’ and ‘corresponds’. (shrink)

A key idea in both Frege's development of arithmetic in theGrundlagen[7] and Zermelo's 1904 proof [10] of the well-ordering theorem is that of a “type reducing” correspondence between second-level and first-level entities. In Frege's construction, the correspondence obtains betweenconceptandnumber, in Zermelo's (through the axiom of choice), betweensetandmember. In this paper, a formulation is given and a detailed investigation undertaken of a system ℱ of many-sorted first-order logic (first outlined in the Appendix to [6]) in which this notion of type reducing (...) correspondence is accorded a central role and which enables Frege's and Zermelo's constructions to be presented in such a way as to reveal their essential similarity. By adapting Bourbaki's version of Zermelo's proof of the well-ordering theorem, we show that, within ℱ, any correspondencecbetween second-level entities (here calledconcepts) and first-level ones (here calledobjects) induces a well-ordering relationW(c) in a canonical manner. We shall see that, whencis the “Fregean” correspondence between concepts and cardinal numbers,W(c) is (the well-ordering of) the ordinalω+ 1, and whencis a “Zermelian” choice function on concepts,W(c) is a well-ordering of the universal concept embracing all objects.In ℱ an important role is played by the notion ofextensionof a concept. To each conceptXwe assume there is assigned an objecte(X) in such a way that, for any conceptsX, Ysatisfying a certain predicateE, we havee(X) =e(Y) iff the same objects fall underXandY. (shrink)

The infinitesimal methods commonly used in the 17th and 18th centuries to solve analytical problems had a great deal of elegance and intuitive appeal. But the notion of infinitesimal itself was flawed by contradictions. These arose as a result of attempting to representchange in terms ofstatic conceptions. Now, one may regard infinitesimals as the residual traces of change after the process of change has been terminated. The difficulty was that these residual traces could not logically coexist with the static quantities (...) traditionally employed by mathematics. The solution to this difficulty, as it turns out, is to regard these quantities asalso being subject to (a form of) change, for then they will have the same nature as the infinitesimals representing the residual traces of change, and will become,ipso facto, compatible with these latter.In fact, the category-theoretic models which realize the Principle of Infinitesimal Linearity may themselves be regarded as representations of a general concept of variation (cf. Bell (1986)). While the static set-theoretical models represent change or motion by making a detour through the actual (but static) infinite, the varying category-theoretic models enable such change to be representeddirectly, thus permitting the introduction of geometric infinitesimals and, as we have attempted to demonstrate in this paper, the virtually complete incorporation of the methods of the early calculus.It is surely a remarkable — even an ironic — fact that the contradiction between the flux of the objective world and the stasis of mathematical entities has found its resolution in category theory, a branch of mathematics commonly, and, as one now sees, mistakenly, regarded as the summit of gratuitous abstraction. (shrink)