Philosophy & Public Affairs, Volume 50, Issue 1, Page 6-49, Winter 2022.

We analyse the extent of possible computations following Hogarth ([2004]) conducted in Malament–Hogarth (MH) spacetimes, and Etesi and Németi ([2002]) in the special subclass containing rotating Kerr black holes. Hogarth ([1994]) had shown that any arithmetic statement could be resolved in a suitable MH spacetime. Etesi and Németi ([2002]) had shown that some relations on natural numbers that are neither universal nor co-universal, can be decided in Kerr spacetimes, and had asked specifically as to the extent of computational limits there. (...) The purpose of this note is to address this question, and further show that MH spacetimes can compute far beyond the arithmetic: effectively Borel statements (so hyperarithmetic in second-order number theory, or the structure of analysis) can likewise be resolved: Theorem A. If H is any hyperarithmetic predicate on integers, then there is an MH spacetime in which any query ? n H ? can be computed. In one sense this is best possible, as there is an upper bound to computational ability in any spacetime, which is thus a universal constant of that spacetime. Theorem C. Assuming the (modest and standard) requirement that spacetime manifolds be paracompact and Hausdorff, for any spacetime there will be a countable ordinal upper bound, , on the complexity of questions in the Borel hierarchy computable in it. Introduction 1.1 History and preliminaries Hyperarithmetic Computations in MH Spacetimes 2.1 Generalising SADn regions 2.2 The complexity of questions decidable in Kerr spacetimes An Upper Bound on Computational Complexity for Each Spacetime CiteULike Connotea Del.icio.us What's this? (shrink)

El propósito de este texto es ofrecer una visión general de la relación entre nación e historia en los debates que se generaron por parte de los historiadores y otros intelectuales de las ciencias sociales a finales del siglo XIX y durante gran parte del siglo XX. La reflexión central que se plantea consiste entonces en estudiar y mostrar cómo al mismo tiempo que las naciones modernas eran objeto de un proceso de redefinición política, en el escenario intelectual de las (...) ciencias sociales, y en particular de los historiadores, fueron apareciendo también un conjunto de debates y obras que intentaban problematizar y someter a consideración las relaciones que pretendían establecerse entre la nación y la historia como un elemento que las justificaba. (shrink)

An edition of the letters of Erasmus, regarded as one of the greatest humanist writers. All 12 volumes of this work have been reissued, complete with their scholarly apparatus of commentary and notes, as well as plates.

An edition of the letters of Erasmus, regarded as one of the greatest humanist writers. All 12 volumes of this work have been reissued, complete with their scholarly apparatus of commentary and notes, as well as plates.

This article examines the question of the existence of non-Adamic persons-both terrestrial and extra-terrestrial-in early modern Europe. More particularly it looks at how the existence of non-Adamites seriously called into question the credibility of the central themes of the Christian story of the creation, fall and redemption in Jesus Christ in early modern Europe. It analyses the impact on the Christian view of history caused by the discovery of the inhabitants of the New World, speculations about the polygenetic origins of (...) the human race, and discussions about the plurality of worlds. It concludes with some reflections on the monogenetic and polygenetic accounts of the origin of humans in a post-Darwinian context. (shrink)

A Remark about the Analysis of the Illocutionary Act of Assertion. The starting point of this article is the Searleian analysis of the illocutionary act of assertion. I try to sketch an alternative interpretation of the illocutionary act of assertion based on the arguments brought forward by John R. Searle, Paul Grice, Rom Harré, Robert Brandom. This possible interpretation might help us raise some questions about the Searleian interpretation.

Both the Correspondence Theory of Truth and the Redundancy/Performative Theory of Truth appear to be unquestionably correct and yet each seems to be inconsistent with the other. As a result we have a puzzle. The way out of this dilemma is to be found by taking a closer look at the role that ‘Is’ and its cognates play in the structure of the standard statement. Once this is done it can be seen that both theories are compatible with one another.

This paper discusses a number of different aspects of Moore’s reading of Hume as engaged in the metaphysics of ‘sense-making’. After a brief discussion of the semantic strains, I turn to consider Moore’s views of Hume on epistemic ‘sense-making’ where I criticize Moore’s reading of Hume’s epistemology as assimilated to the more basic natural process of human beings. I consider some of the ways in which Moore thinks that Hume is involved in a positive metaphysical project.

Abstract In this paper, I attempt to throw light on the phenomenon of postmodernism by comparing it with the understanding of other cultures such as the Indian and Chinese. One can say that postmodernism, like, say Mahayana Buddhism, Taoism and Advaita Vedanta recognise the impossibility of finding an absolute in the world. However, unlike the latter three, rather than moving on beyond finite things, postmodernism seems content to simply sit and play around with the non?absolutes that it has found (even (...) if ?ironically'). Comparison with the philosophies of other cultures, and also the message of Christianity, show clearly the mistake that postmodernism makes in doing this. Finally, I note some of the responsibilities that Western postmodern philosophers have. (shrink)

Husserl's investigations of internal time-consciousness take sound as the primary temporal object. However, in these investigations, the structure of the flux of temporal subjectivity is established to the detriment of the rich tonal content of sound. Just as Husserl has enlarged the significance of the spatial object of mathematical physics to include the historically-sedimented layers of its appearance, so the temporal object will receive additional intelligibility if the rich texture of musical sound is taken into consideration. Particularly useful for this (...) task is Bergson's philosophy of the listening experience. (shrink)

It is consistent that there exists a set mapping $F: \lbrack\omega_2\rbrack^2 \rightarrow \lbrack\omega_2\rbrack^{<\omega}$ such that $F(\alpha, \beta) \subseteq \alpha$ for $\alpha < \beta < \omega_2$ and there is no infinite free subset for F. This solves a problem of A. Hajnal and A. Mate.

Originally published in 1960, The Future of Man is a chronicle of Professor Medwar's Reith lectures of 1959. The book outlines his predictions about the future estate of man, with the 'process of foretelling, rather than with what is actually foretold'. He asks, can we predict the future size of populations? What is the evidence and theoretical background for the belief that human intelligence is declining? Could human beings become uniformly excellent or is inborn diversity and inequality a necessary part (...) of the texture of human populations? The lectures tried to answer these questions and attempts to end with a definition of the biological standing of man. This book will be of interest to anthropologists, biologists and natural historians. (shrink)

First published in 1972, The Hope of Progress presents collection of essays and lectures dealing with the history of scientific ideas and the impact of science on society. The principle piece in this volume is the author's 1969 presidential address to the British Association 'On The Effecting of All Things Possible', an argument for believing in the ability of science to solve the problems it has itself created, and which too many of us believe insoluble. It contains author's Romanes Lecture (...) on 'Science and Literature' and a well known critique of J.D. Watson's notorious account of the discovery of the molecular structure of DNA, The Double Helix. Other chapters discuss the possibility of the control and domination by science of the body and mind of Man- though the author concludes in 'The Genetic Improvement of Man' 'I think that, in the main, for many centuries to come, we shall have to put up with human beings as they are at present constituted'. This book will be useful for scholars and researchers of history of science, philosophy of science, natural science, and philosophy in general. (shrink)