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Socratic Club Speakers and Dates from the Marion E. Wade Center
Socratic Club Speakers and Dates - To Accompany the Stella Aldwinckle Papers Marion E. Wade Center, Wheaton College, Wheaton, IL Name(s) Lecture Title Date Notes Prof. Krner Science and Moral Responsibility ? Dr. Mason, Prof. Demant Marxian View of Religion ? Won't Mankind outgrow Christianity in R.E. Havard, M.D. the face of the advance of science January 26, 1942 and of modern ideologies? In Socratic Dr. William Stevenson Is God a wish-fulfilment? February 2, 1942 Digest Was Christ really any more than a Stella Aldwinckle, M.A. February 9, 1942 great teacher and prophet? W. B. Merchant, M.A. and C.S. Lewis, Scepticism and Faith. February 16, 1942 M.A. Is Christianity obscurantism hindering Lord Elton February 23, 1942 social progress? Are there any valid objections to free- In Socratic Charles Williams March 2, 1942 love? Digest Dr. L. W. Grensted Is prayer auto-suggestion? March 9, 1942 Some ambiguities in the use of the D. M. MacKinnon, M.A. April 29, 1942 word 'rational.' Is it rational to believe in a 'personal' Prof. W. G. De Burgh God? (postponed until May 27 due to May 6, 1942 illness of the speaker) Rev. A. M. Farrer and Prof. R. Eisler Did Christ rise from the dead? May 13, 1942 Can science render religion In Socratic Prof. H. A. Hodges May 20, 1942 unnecessary? Digest Is it rational to believe in a 'personal' Prof. W.G. De Burgh May 27, 1942 God? Has man a special place in the Dr. R. W. Kosterlitz June 3, 1942 universe? In Socratic Mr. -
Moral Reason
Moral Reason OXFORD PHILOSOPHICAL MONOGRAPHS Editorial Committee ANITA AVRAMIDES R. S. CRISP WILLIAM CHILD ANTONY EAGLE STEPHEN MULHALL OTHER TITLES IN THIS SERIES INCLUDE Nietzsche and Metaphysics Peter Poellner Understanding Pictures Dominic Lopes Things That Happen Because They Should: A Teleological Approach to Action Rowland Stout The Ontology of Mind: Events, Processes, and States Helen Steward Wittgenstein, Finitism, and the Foundations of Mathematics Mathieu Marion Semantic Powers: Meaning and the Means of Knowing in Classical Indian Philosophy Jonardon Ganeri Hegel’s Idea of Freedom Alan Patten Metaphor and Moral Experience A. E. Denham Kant’s Empirical Realism Paul Abela Against Equality of Opportunity Matt Cavanagh The Grounds of Ethical Judgement: New Transcendental Arguments in Moral Philosophy Christian Illies Of Liberty and Necessity: The Free Will Debate in Eighteenth-Century British Philosophy James A. Harris Plato and Aristotle in Agreement? Platonists on Aristotle from Antiochus to Porphyry George E. Karamanolis Aquinas on Friendship Daniel Schwartz The Brute Within: Appetitive Desire in Plato and Aristotle Hendrik Lorenz Moral Reason Julia Markovits 1 1 Great Clarendon Street, Oxford, ox2 6dp, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Julia Markovits 2014 The moral rights of the author have been asserted First Edition published in 2014 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. -
A Simplified Version of Gödel's Theorem Michael Redhead
A Simplified Version of Gödel’s Theorem Michael Redhead “Isn’t it a bad thing to be deceived about the truth and a good thing to know what the truth is?” Plato Abstract The Lucas - Penrose argument is considered. As a special case we consider sorites arithmetic and explain how the argument actually works. A comparison with Gödel’s own treatment is made. Truth is valuable. But certifiable truth is hard to come by! The Case of Mathematics Does truth equate with proof? No: Gödel showed famously that truth outruns proof, even in the case of the natural numbers 0, 1, 2, 3, … The Lucas-Penrose argument The argument that ascertainable truth outruns proof in mathematics has been used by John Lucas and Roger Penrose to claim that human minds can do things which computers can’t do, and hence that minds can’t be (digital) machines. Quote from Lucas and myself: We are dealing with a different style of reasoning… an informal semantics concerned with truth rather than proof. Sceptics deny that we have such a concept of truth. We cannot prove to them that we have… (but) we have many intimations of truth, not all of which can be articulated as proofs. Sorites arithmetic This is the sort of arithmetic you learnt at school. The basic operation is moving from one number to the next along the number line and repeating the operation a finite number of times. Addition and multiplication are defined recursively in the usual way. So, addition is effectively reduced to adding one and one and one… repeatedly, and multiplication is repeated addition. -
Blackwell Guide to the Philosophy of Religion Blackwell Philosophy Guides Series Editor: Steven M
The Blackwell Guide to the Philosophy of Religion Blackwell Philosophy Guides Series Editor: Steven M. Cahn, City University of New York Graduate School Written by an international assembly of distinguished philosophers, the Blackwell Philosophy Guides create a groundbreaking student resource – a complete critical survey of the central themes and issues of philosophy today. Focusing and advancing key arguments throughout, each essay incorporates essential background material serving to clarify the history and logic of the relevant topic. Accordingly, these volumes will be a valuable resource for a broad range of students and readers, including professional philosophers. 1 The Blackwell Guide to EPISTEMOLOGY Edited by John Greco and Ernest Sosa 2 The Blackwell Guide to ETHICAL THEORY Edited by Hugh LaFollette 3 The Blackwell Guide to the MODERN PHILOSOPHERS Edited by Steven M. Emmanuel 4 The Blackwell Guide to PHILOSOPHICAL LOGIC Edited by Lou Goble 5 The Blackwell Guide to SOCIAL AND POLITICAL PHILOSOPHY Edited by Robert L. Simon 6 The Blackwell Guide to BUSINESS ETHICS Edited by Norman E. Bowie 7 The Blackwell Guide to the PHILOSOPHY OF SCIENCE Edited by Peter Machamer and Michael Silberstein 8 The Blackwell Guide to METAPHYSICS Edited by Richard M. Gale 9 The Blackwell Guide to the PHILOSOPHY OF EDUCATION Edited by Nigel Blake, Paul Smeyers, Richard Smith, and Paul Standish 10 The Blackwell Guide to PHILOSOPHY OF MIND Edited by Stephen P. Stich and Ted A. Warfield 11 The Blackwell Guide to the PHILOSOPHY OF THE SOCIAL SCIENCES Edited by Stephen P. Turner and Paul A. Roth 12 The Blackwell Guide to CONTINENTAL PHILOSOPHY Edited by Robert C. -
B Academy Review
The British Academy THE NATIONAL ACADEMY FOR THE HUMANITIES AND SOCIAL SCIENCES REVIEW July – December 2000 The British Academy 10 Carlton House Terrace, London SW1Y 5AH Telephone:020 7969 5200 Fax: 020 7969 5300 Email: [email protected] Web site: www.britac.ac.uk © The British Academy 2001 Some contents of the Review may also be found in electronic form on the Academy’s web site at www.britac.ac.uk Cover illustration: ??????? iii Foreword The British Academy publishes a regular account of its activities by means of its biannual Review. Some readers may be unfamiliar with what the Academy is and what it does.The following pages seek to give a flavour of the variety of Academy activities, which range across a broad spectrum of scholarly endeavour both within the UK and on the international stage. First and foremost, the Academy is a Fellowship of scholars, elected for outstanding academic achievement in one or more of the disciplines of the humanities and social sciences. The active participation of these Fellows enables the Academy to conduct a wide variety of activities to support academic research, to stimulate scholarly debate and to promote the role of the humanities and social sciences to a wider audience. The activities undertaken by the Academy include the organisation of lectures and conferences, the sponsoring of major infrastructural projects that are adopted as Academy Research Projects, running a flourishing publications programme, facilitating international networks, and allocating research awards.This Review contains a section on each of the major areas of the Academy’s work. As well as material customarily to be found in a formal Annual Report, extracts from lectures and publications and specially commissioned articles are included that seek to offer an insight into the variety of academic endeavour promoted by the Academy. -
Gödelian Arguments Against AI
Gödelian arguments against AI Master’s Thesis ARTIFICIAL INTELLIGENCE Department of Information and Computing Sciences Faculty of Science Utrecht University Author: Jesús Rodríguez Pérez Supervisor: Dr. Gerard Vreeswijk Second reviewer: Prof. Dr. Albert Visser 2015 ii Acknowledgements I would like to thank my supervisor Dr. Gerard Vreeswijk for his guidance and support in this project; for pointing to multiple suggestions and possible improvements regarding not only the content of this thesis, and in particular technical inaccuracies, but most valuably its form and discursive structure. His personal guidance on writing argumentative essays have proved to be a valuable source. I am also indebted to Prof. Dr. Albert Visser for proofreading this text and providing useful feedback in the form of sticky notes. I hope this work reflects the advice that in such respect I received from him. Last, but not least, a word of gratitude goes to my sisters and parents, for the contin- uous loving support they demonstrated me along the way. Without their everyday words of encouragement this thesis would not have come about in its current shape. iii Contents I Predicate logic, axiomatic systems and Gödel’s theorems 4 1 Preliminaries 5 2 The undecidability results 9 2.1 Generalization and acceptance . 10 3 An informal exposition of the proof 15 II The Gödelian arguments and learning systems 21 4 The arguments against Computationalism 22 4.1 Lucas’ argument . 23 4.2 Goedel’s argument . 27 4.3 The counter-argument from the standpoint of mathematical cognition -
BASIL MITCHELL Basil George Mitchell 1917–2011
BASIL MITCHELL Basil George Mitchell 1917–2011 Career Outline ALTHOUGH BASIL MITCHELL was eventually to make his reputation as a philosopher of religion, his first interests suggested a somewhat different trajectory, perhaps in comparative religion. Born on 9 April 1917 to middle class parents in Bath (his father was a quantity surveyor), it was while living in Southampton that his mother became permanently confined to bed as a result of severe rheumatoid arthritis and remained there for the last twenty years of her life (1928–47). Although Basil was confirmed in the Church of England, his parents’ search for some relief for his mother’s condition led him along with the rest of his family to attend Sufi services of universal worship that included extracts from the sacred texts of all the major religions. Indeed, that search included taking his mother in 1938 to the Paris headquarters of Hazrat Inayat Khan who had brought this par ticular version of Sufism from India. Although Basil’s decision to read Greats at The Queen’s College, Oxford was quite conventional, it is signifi cant that he confesses to not finding the way philosophy was then taught particularly interesting and that the real satisfaction of his desires came when he was awarded a scholarship to study Indian philosophy under Radhakrishnan, then a professor at Oxford, and began to learn Sanskrit.1 1 Further details are available in Basil’s autobiography, B. G. Mitchell, Looking Back: on Faith, Philosophy and Friends in Oxford (Durham, 2009), and, more briefly, in ‘War and friendship’, in K. -
Oxfordcolleges
Oxford colleges Oxford University is made up of different colleges. Colleges are academic communities. They are where students usually have their tutorials. Each one has its own dining hall, bar, common room and library, and lots of college groups and societies. If you study here you will be a member of a college, and probably have your tutorials in that college. You will also be a member of the wider University, with access to University and department facilities like laboratories and libraries, as well as hundreds of University groups and societies. You would usually have your lectures and any lab work in your department, with other students from across the University. There is something to be said for an academic atmosphere wherein everyone you meet is both passionate about what they are studying and phenomenally clever to boot. Ziad 144| Does it matter which college I go to? What is a JCR? No. Colleges have a lot more in common than Junior Common Room, or JCR, means two they have differences. Whichever college you go different things. Firstly, it is a room in college: to, you will be studying for the same degree at the a lively, sociable place where you can take time end of your course. out, eat, watch television, play pool or table football, and catch up with friends. The term Can I choose my college? JCR also refers to all the undergraduates in a college. The JCR elects a committee which Yes, you can express a preference. When you organises parties, video evenings and other apply through UCAS (see ‘how to apply’ on p 6) events, and also concerns itself with the serious you can choose a college, or you can make an side of student welfare, including academic ‘open application’. -
Dasgupta UMBC, 1000 Hilltop Circle, Baltimore, Maryland 21250
A New Approach Refuting Penrose’s Gödelian Argument Arghya Dasgupta UMBC, 1000 Hilltop Circle, Baltimore, Maryland 21250 Abstract Background Related Work Possible Approaches Sir Roger Penrose, though one of the greatest minds in pure In the case of Peano arithmetic or any familiar explicitly Hilary Putnam, G.Boolos and others have already pointed out to know this, we must also prove (or know) that ∀e ∀x(A(e, x) mathematics and physics, is known for his insistence in using axiomatized theory T, it is possible to define the consistency "Con some of Penrose’s technical errors, and he has conceded several ⇒ Φ(e, x)↑ That is, we have to know that A is a sound method Gödel’s incompleteness theorems to support a non-computationist (T)" of T in terms of the non-existence of a number with a certain of the technical points, but there does not seem to be a complete for deciding that our own computations fail to halt: whenever it and even a non-algorithmic view point in studying consciousness. property, as follows: "there does not exist an integer coding a statement of the fundamental problems with this kind of argument. claims that a computation is non-terminating, then in fact that Repeatedly, in books like “The Emperor’s New Mind” (1989), sequence of sentences, such that each sentence is either one of Benacerraf (1967) made two points against the original Lucas computation does not terminate. An alternative resolution of the “Shadows of the Mind” (1994) and “The Large, the Small and the the (canonical) axioms of T, a logical axiom, or an immediate argument, both of which we will develop more precisely here. -
1 Zuse's Thesis, Gandy's Thesis, and Penrose's Thesis Jack Copeland
Zuse's Thesis, Gandy's Thesis, and Penrose's Thesis Jack Copeland, Oron Shagrir, Mark Sprevak 1. Introduction Computer pioneer Konrad Zuse (1910-1995) built the world's first working program- controlled general-purpose digital computer in Berlin in 1941. After the Second World War he supplied Europe with cheap relay-based computers, and later transistorized computers. Mathematical logician Robin Gandy (1919-1995) proved a number of major results in recursion theory and set theory. He was Alan Turing's only PhD student. Mathematician Roger Penrose (1931- ) is famous for his work with Stephen Hawking. What we call Zuse's thesis, Gandy's thesis, and Penrose's thesis are three fundamental theses concerning computation and physics. Zuse hypothesized that the physical universe is a computer. Gandy offered a profound analysis supporting the thesis that every discrete deterministic physical assembly is computable (assuming that there is an upper bound on the speed of propagation of effects and signals, and a lower bound on the dimensions of an assembly's components). Penrose argued that the physical universe is in part uncomputable. We explore these three theses. Zuse's thesis we believe to be false: the universe might have consisted of nothing but a giant computer, but in fact does not. Gandy viewed his claim as a relatively apriori one, provable on the basis of a set-theoretic argument that makes only very general physical assumptions about decomposability into parts and the nature of causation. We maintain that Gandy's argument does not work, and that Gandy's thesis is best viewed, like Penrose's, as an open empirical hypothesis. -
2016 Clifton Henry.Pdf
The Foundations of Mathematics History, Concepts, and Applications in Higher Level Mathematics by Clifton Henry A CAPSTONE PROJECT submitted in partial fulfillment of the requirements for the acknowledgement Honors Distinction Mathematics School of Engineering, Mathematics, and Science TYLER JUNIOR COLLEGE Tyler, Texas 2016 When people hear the word mathematics, some think numbers and others think solving for x and y. In all truth, the field of mathematics is more than numbers and equations. Mathematics was founded based off the principle of counting in 50,000 B.C.E. Mathematical contributions and ideas increased from the Babylonian Empire in 2000 BC to the 18th century, where mathematicians and philosophers developed ideas in algebra, geometry and calculus. It can be argued that mathematical contributions in the 19th century shaped the field of mathematics and set in place the true foundations of mathematics. In the 19th century, mathematical logic was founded, followed by the development of set theory, and then came the concept of mathematical function. Logic, set theory, and function are some of the foundations of mathematics, and the three revolutionized the field of mathematics as a whole. Mathematical fields, such as topology, abstract algebra, and probability rely heavily on the three foundations. Instead of being seen as numbers and equations, mathematics is the field of logic and proof that is based off the mathematical foundations of logic, set theory, and function. It is important to know how the ideas were developed and put to use in order for mathematics to have its meaning and significance. After understanding how the foundations were developed, it is important to understand how they apply in advanced mathematical fields such as topology, abstract algebra, and probability. -
Logic in Philosophy of Mathematics
Logic in Philosophy of Mathematics Hannes Leitgeb 1 What is Philosophy of Mathematics? Philosophers have been fascinated by mathematics right from the beginning of philosophy, and it is easy to see why: The subject matter of mathematics| numbers, geometrical figures, calculation procedures, functions, sets, and so on|seems to be abstract, that is, not in space or time and not anything to which we could get access by any causal means. Still mathematicians seem to be able to justify theorems about numbers, geometrical figures, calcula- tion procedures, functions, and sets in the strictest possible sense, by giving mathematical proofs for these theorems. How is this possible? Can we actu- ally justify mathematics in this way? What exactly is a proof? What do we even mean when we say things like `The less-than relation for natural num- bers (non-negative integers) is transitive' or `there exists a function on the real numbers which is continuous but nowhere differentiable'? Under what conditions are such statements true or false? Are all statements that are formulated in some mathematical language true or false, and is every true mathematical statement necessarily true? Are there mathematical truths which mathematicians could not prove even if they had unlimited time and economical resources? What do mathematical entities have in common with everyday objects such as chairs or the moon, and how do they differ from them? Or do they exist at all? Do we need to commit ourselves to the existence of mathematical entities when we do mathematics? Which role does mathematics play in our modern scientific theories, and does the em- pirical support of scientific theories translate into empirical support of the mathematical parts of these theories? Questions like these are among the many fascinating questions that get asked by philosophers of mathematics, and as it turned out, much of the progress on these questions in the last century is due to the development of modern mathematical and philosophical logic.