Argument and Evidence: Critical Analysis for the Social Sciences

260 Pages·1996·1.92 MB·English

by  Peter Phelan

Argument and evidence
How do we know whether or not an argument is valid? What counts as
evidence? How does one make reliable estimates when the evidence is
incomplete? Argument and Evidence offers an integrated treatment of
these questions by bringing together the various approaches
traditionally found in separate disciplines and literatures.
The ability to evaluate arguments in terms of their internal logic
and to appraise the available evidence is critical in all fields of
academic enquiry. Peter Phelan and Peter Reynolds present aspects of
informal logic and statistical theory in an accessible way, enabling
readers to acquire critical thinking skills without formal training in the
more difficult aspects of those disciplines.
Throughout, the authors draw on examples from the human and
social sciences, and relate the theoretical discussion to issues of
current or recent media controversy. Each chapter ends with a
summary of the main points discussed.
Argument and Evidence will enable students to develop a range of
skills that can easily be transferred between academic disciplines and
that will prove useful well beyond their undergraduate studies.
Peter Phelan is Lecturer in Business Ethics at Staffordshire University.
Peter Reynolds is Head of the Economics Division at Staffordshire
University.

Argument and evidence
Critical analysis for the social sciences
Peter Phelan and Peter Reynolds
London and New York
First published 1996
by Routledge
11 New Fetter Lane, London EC4P 4EE
This edition published in the Taylor & Francis e-Library, 2001.
Simultaneously published in the USA and Canada
by Routledge
29 West 35th Street, New York, NY 10001
© 1996 Peter Phelan and Peter Reynolds
All rights reserved. No part of this book may be reprinted or
reproduced or utilized in any form or by any electronic,
mechanical, or other means, now known or hereafter invented,
including photocopying and recording, or in any information
storage or retrieval system, without permission in writing from
the publishers.
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library.
Library of Congress Cataloging in Publication Data
A catalogue record for this book has been requested.
ISBN 0-415-11372-5 (hbk)
ISBN 0-415-11373-3 (pbk)
ISBN 0-203-20074-8 Master e-book ISBN
ISBN 0-203-20077-2 (Glassbook Format)
Contents
List of illustrations vii
Preface and acknowledgements xi
1 Introduction 1
2 Argument and evidence 12
3 Context, convention and communication 26
4 An informal analysis of arguments 34
5 Patterns of reasoning 45
6 Establishing validity 58
7 Critical analysis in practice 75
8 Assumptions 89
9 Evidence as ground for belief 99
10 What counts as evidence? 110
11 Presenting and summarising evidence 127
12 Furthering knowledge 148
13 Probability and uncertainty 160
14 Probability theory applied 175
15 Estimation and reliability 187
16 Testing hypotheses 205
Appendices 223
Notes 230
References 238
Index 242

Illustrations
FIGURES
2.1 Source of radiation exposure of the UK population 18
5.1 Simple Venn diagram 50
5.2 Positive particular proposition 51
5.3 Negative particular proposition 51
5.4 Negative universal proposition 51
5.5 Positive universal proposition 51
5.6 Reversed universal 52
6.1 Universe of discourse 68
6.2 Venn diagram for Example 6.10 69
6.3 Conclusion of Example 6.10 69
6.4 Venn diagram for Example 4.9 70
6.5 Venn diagram for Example 6.11 72
7.1 A valid argument form 75
7.2 The ‘all negative premises’ fallacy 78
7.3 Incomplete reasoning 81
7.4 Completed argument 82
7.5 Metaphysical poetry 84
8.1 A model of ‘pathways’ 96
9.1 Predicate form and Venn diagram for Example 9.1 106
11.1 A blank Excel spreadsheet 130
11.2 Family study 131
11.3 Two sets of data in a spreadsheet 136
11.4 Calculating a variance 137
11.5 Graduate incomes 139
11.6 Frequency distribution for graduate incomes 140
11.7 Histogram 140
11.8 Calculation of cumulative and relative frequency
distributions 141
viii Illustrations
11.9 Ogive and frequency polygon 142
11.10 Lorenz curves to compare income distribution in Brazil
and Hungary 143
11.11 Alternative ways of presenting data 145
11.12 Scatter diagram 146
12.1 Methodological positions 154
12.2 The hypothetico-deductive method 155
13.1 Probability distribution for Example 13.2 168
13.2 Sample space for Example 13.4 169
13.3 Probability distribution for Example 13.4 169
13.4 Probability distribution for Example 13.4 170
13.5 Probability distribution for rolling a die 170
13.6 Probability distribution for the number of heads from
three tosses of a coin 170
13.7 Worksheet for calculation of the mean, variance and
standard deviation of a random variable 173
14.1 Simple probability density function 176
14.2 The normal distribution 177
14.3 Illustration of the central limit theorem 178–9
14.4 The standard normal distribution 182
14.5 Use of standard normal tables (1) 183
14.6 Use of standard normal tables (2) 184
14.7 Probability density functions for X and Z in Example 14.1 185
15.1 Probability distribution for X 189
i
15.2 Probability distribution for X¯ 189
15.3 The students’ t-distribution 198
16.1 Sampling distribution of test statistic 208
16.2 The students’ t-distribution 210
16.3 The chi-square distribution 217
A.1 Valid arguments in predicate form 224
A.2–A.9 Venn diagrams representing patterns of valid
arguments in predicate forms 225–6
TABLES
2.1 Airborne radioactive discharges from UK nuclear
installations, 1978 20
15.1 Formulae for population mean and standard deviation 187
15.2 Calculation of sample standard deviation 194
16.1 Observed and expected results from tossing a die 600 times 218
16.2 Contingency table relating voting intention to family size 219
16.3 Contingency table of examination results and gender 220
Illustrations ix
16.4 Expected frequencies for examination results by gender 221
A.1 The normal distribution 227
A.2 The students’ t-distribution 228
A.3 The χ2 distribution 229