Darrell P. Rowbottom - Probability

1. Guy Axtell, Objectivity
2. Heather Battaly, Virtue
3. Lisa Bortolotti, Irrationality
4. Ben Bradley, Well-Being
5. Joseph Keim Campbell, Free Will
6. Roy T. Cook, Paradoxes
7. Douglas Edwards, Properties
8. Ian Evans & Nicholas D. Smith, Knowledge
9. Bryan Frances, Disagreement
10. Amy Kind, Persons and Personal Identity
11. Douglas Kutach, Causation
12. Carolyn Price, Emotion
13. Daniel Speak, The Problem of Evil
14. Mathew Tulbert, Moral Responsibility
15. Deborah Perron Tollefsen, Groups as Agents
16. Joshua Weisberg, Consciousness
17. Chase Wrenn, Truth

Copyright Darrell P. Rowbottom 2015

The right of Darrell P. Rowbottom to be identified as Author of this Work has been asserted in accordance with the UK Copyright, Designs and Patents Act 1988.

First published in 2015 by Polity Press

Polity Press

65 Bridge Street

Cambridge CB2 1UR, UK

Polity Press

350 Main Street

Malden, MA 02148, USA

All rights reserved. Except for the quotation of short passages for the purpose of criticism and review, no part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher.

ISBN-13 978-0-7456-5256-6

ISBN-13 978-0-7456-5257-3 (pb)

A catalogue record for this book is available from the British Library.

Library of Congress Cataloging-in-Publication Data

Rowbottom, Darrell P., 1975

Probability / Darrell Rowbottom.

pages cm

Includes bibliographical references and index.

ISBN 978-0-7456-5256-6 (hardback : alk. paper) ISBN 978-0-7456-5257-3 (pb) 1. ProbabilitiesPhilosophy. 2. Decision makingPhilosophy. I. Title.

QA273.A35R69 2015

519.2dc23

2015005729

Typeset in 10.5 on 12 pt Sabon

by Toppan Best-set Premedia Limited

Printed and bound in the UK by CPI Group (UK) Ltd, Croydon, CRO 4YY

The publisher has used its best endeavours to ensure that the URLs for external websites referred to in this book are correct and active at the time of going to press. However, the publisher has no responsibility for the websites and can make no guarantee that a site will remain live or that the content is or will remain appropriate.

Every effort has been made to trace all copyright holders, but if any have been inadvertently overlooked the publisher will be pleased to include any necessary credits in any subsequent reprint or edition.

For further information on Polity, visit our website:

politybooks.com

To my parents, Errol and Jean, in gratitude for forty years of loving support

I have aimed to produce a highly accessible introduction to the philosophy of probability, which will be of interest to students in any discipline where probabilties are used. It doesn't just present the many different ways that probabilities may be interpreted, and the arguments for and against each, with reference to everyday life. It puts the findings to work too. It explains several common fallacies in probabilistic reasoning (in ).

Writing the book has been a labour of love, because most of the prestige in academia nowadays is associated with research productivity. As such, sadly, writing an introductory book isn't typically in one's own best interest (especially as a junior academic). (I began writing this book in 2010, when I was indeed a junior academic, and was supposed to finish it by 2012. I am a very naughty author!) It will be reward enough for me, though, if my passion for the subject comes across in what I've written, and inspires you to study it further (if you haven't already). If it does or if you have any questions about anything in here then let me know!

I have many debts of gratitude. First, I'd like to offer my sincere thanks to everyone who has commented on drafts of this book, or parts thereof: Chris Atkinson, Jenny Hung, William Peden, Mauricio Surez, Jon Williamson, Jiji Zhang, previous students on my Probability and Scientific Method course, and the anonymous reviewers appointed by Polity. Second, I'd like to express my gratitude to Donald Gillies, who inspired my interest in the philosophy of probability, and taught me much of what I know about it. Third, I must thank several editors at Polity Emma Hutchinson, Sarah Lambert, and Pascal Porcheron for their heroic patience in helping me to see this project through. Fourth, and finally, I am grateful to Sarah Dancy for her meticulous copyediting, and for removing many an unwarranted exclamation mark!

A book on how to understand probability may not sound interesting; in fact, it probably doesn't sound interesting if you're not interested in maths. But if you don't understand probability, then you'll probably find yourself making some bad decisions. (Maybe it would pique your interest if I told you that I made a lot of money, from people who didn't know as much about probability as they should have, during my student days? More on this in .) Sometimes you'll act when you shouldn't, and other times you'll fail to act when you should. Don't take my word for it. Let's think about scenarios in which claims involving probabilities are relevant in everyday life.

Imagine you're intent on climbing a mountain, and you consult the weather forecast for the day. On the report, you see that the probability of precipitation in the relevant mountain range or what is sometimes called the chance of rain is just one in twenty, or 5 per cent. Should you take waterproof gear with you?

Obviously this will depend a little bit on context, so let's fill some of that out. Imagine you don't have any waterproof gear, and that it will be quite a hassle to get some, but that you don't want to get wet. Overall, you think that getting wet would be more unpleasant than going through the trouble of getting the gear; in an ideal world, however, you'd neither get the gear nor get wet. It's possible to assign a number to each possible outcome, a utility, to make this kind of discussion more precise. Let's avoid complicating things unnecessarily, though. We can instead rank the four possible outcomes in order of your preference: no gear and no rain (best), gear and rain (2nd best), gear and no rain (3rd best), and no gear and rain (worst). (It's always helpful in such scenarios to think about whether anything has been assumed which hasn't been explicitly mentioned. I encourage you to do this throughout the book. In this case, for example, gear and rain has been ranked more highly than gear and no rain. I did this because I figured you'd be a bit irritated at having the gear if it didn't rain; you'd be thinking I shouldn't have bothered to get this gear! But perhaps I should have added this as a stipulation in presenting the context.)

The order of preference makes it clearer what's at stake in this hypothetical scenario. If you take the gear, you miss out on the best possible outcome. But you also protect yourself from the worst possible outcome (while giving yourself a shot at the second and third best outcomes). Now if the order of preference were the only information you had, your choice might depend only on your attitude towards risk; some people are more