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John Butterworth and Geoff Thwaites Thinking Skills Critical Thinking and Problem Solving Second edition



John Butterworth and Geoff Thwaites Thinking Skills Critical Thinking and Problem Solving Second edition

cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK www.cambridge.org Information on this title: www.cambridge.org/9781107606302 © Cambridge University Press 2005, 2013 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2005 Second edition 2013 Printed in Italy by L.E.G.O. S.p.A. A catalogue record for this publication is available from the British Library ISBN 978-1-107-60630-2 Paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Information regarding prices, travel timetables and other factual information given in this work is correct at the time of first printing but Cambridge University Press does not guarantee the accuracy of such information thereafter.

Contents 1 7 Unit 1 Thinking and reasoning 13 1.1 Thinking as a skill  16 1.2 An introduction to critical thinking  21 1.3 Solutions not problems  28 33 Unit 2 Critical thinking: the basics 38 43 2.1 Claims, assertions, statements 50 2.2 Judging claims 58 2.3 Argument  63 2.4 Identifying arguments 70 2.5 Analysing arguments 2.6 Complex arguments  79 2.7 Conclusions  82 2.8 Reasons  86 2.9 Assumptions  90 2.10 Flaws and fallacies 93 98 Unit 3 Problem solving: basic skills 102 106 3.1 What do we mean by a ‘problem’? 112 3.2 How do we solve problems? 116 3.3 Selecting and using information 119 3.4 Processing data 123 3.5 Finding methods of solution 3.6 Solving problems by searching 126 3.7 Recognising patterns 137 3.8 H ypotheses, reasons, explanations and inference 144 3.9 Spatial reasoning 150 3.10 Necessity and sufficiency 156 3.11 Choosing and using models 163 3.12 Making choices and decisions Contentsiii Unit 4 Applied critical thinking 4.1 Inference 4.2 Explanation 4.3 Evidence 4.4 Credibility  4.5 Two case studies 4.6 Critical thinking and science

4.7 Introducing longer arguments 170 4.8 Applying analysis skills 177 4.9 Critical evaluation 183 4.10 Responding with further argument  191 4.11 A self-assessment 195 Unit 5 Advanced problem solving  205 211 5.1 C ombining skills – using imagination 220 5.2 Developing models 225 5.3 Carrying out investigations 5.4 Data analysis and inference 231 235 Unit 6 Problem solving: further techniques 240 246 6.1 Using other mathematical methods 6.2 Graphical methods of solution 249 6.3 Probability, tree diagrams and decision trees 254 6.4 Have you solved it? 262 269 Unit 7 Critical reasoning: Advanced Level 279 287 7.1 Conditions and conditionals 295 7.2 S oundness and validity: a taste of logic 301 7.3 Non-deductive reasoning 7.4 Reasoning with statistics 311 7.5 Decision making 342 7.6 Principles 344 7.7 An argument under the microscope 345 7.8 Critical writing  Answers to assignments Appendix Acknowledgements Index iv Contents

Unit 1 Thinking and reasoning 1.1 Thinking as a skill This book is about thinking. But it is not about there are advanced skills like gymnastics or any thinking. It is about those kinds of woodwork or piano playing. It doesn’t make thinking that take conscious effort, and which much sense to talk about jumping ‘well’ can be done well or badly. Most of our unless you mean jumping a significant thinking takes little or no conscious effort. We distance, or clearing a high bar, or just do it. You could almost say that we think somersaulting in mid-air and landing on without thinking! If I am asked whether I your feet. There has to be a degree of would like coffee or tea, I don’t have to challenge in the task. But even when the exercise skill to reply appropriately. Similarly if challenge is met, there is still more to be said I am asked a factual question, and I know the about the quality of the performance. One answer, it takes no skill to give it. Expressing a gymnast may look clumsy and untidy, preference or stating a fact are not in another perfectly controlled and balanced. themselves thinking skills. There are language Both have performed the somersault, but one and communication skills involved, of course, has done it better than the other: with more and these are very considerable skills in their economy of effort, and more skilfully. own right. But they are contributory skills to the activities which we are calling ‘thinking’. The first of these two criteria also applies to thinking. Once we have learned to count and This distinction is often made by assigning add, tell the time, read and understand a text, some skills a ‘higher order’ than others. Much recognise shapes, and so on, we do these work has been done by psychologists, things without further thought, and we don’t educationalists, philosophers and others to really regard them as skilled. You don’t have classify and even rank different kinds of to think ‘hard’ unless there is a hard problem thinking. Most would agree that activities to solve, a decision to make, or a difficult such as analysis, evaluation, problem solving concept to understand. So, as with physical and decision making present a higher order of performance, we judge thinking partly by the challenge than simply knowing or recalling or degree of challenge posed by the task. If a understanding facts. What distinguishes student can solve a difficult problem, within higher orders of thinking is that they apply a set time, that is usually judged as a sign of knowledge, and adapt it to different purposes. greater skill than solving an easier one. They require initiative and independence on the part of the thinker. It is skills of this order However, when it comes to assessing the that form the content of this book. quality of someone’s thinking, matters are more complicated. Mental performance is Skills are acquired, improved, and judged largely hidden inside a person’s head, unlike by performance. In judging any skill, there physical performance which is very visible. If are two key criteria: (1) the expertise with two students give the same right answer to a which a task is carried out; (2) the difficulty of question, there is no telling from the answer the task. We are very familiar with this in the alone how it was reached. One of the two case of physical skills. There are basic skills may simply have known the answer, or have like walking and running and jumping; and learned a mechanical way to obtain it – or 1.1 Thinking as a skill 1

even just guessed it. The other may have to suggest that there are two distinct ways of worked it out independently, by reasoning thinking: cold hard reason on one hand and and persistence and imagination. Although free-ranging creativity on the other. In fact, the difference may not show from the answer there is so much overlap and interdependence given, the second student scores over the first between the two that it is very difficult to say in the long term, because he or she has the where one begins and the other ends. Clearly ability to adapt to different challenges. The there are times when a seemingly insoluble first is limited to what he or she knew and problem has been cracked by an imaginative could recall, or simply guessed correctly. leap rather than a methodical process. Some of the greatest advances in science have been the Reasoning result of creative thinking that appeared to conflict with reason when first put forward. Reasoning is the ability most closely Yet it is just as clear that many apparent associated with human advancement. It is flashes of genius, which seem to come ‘out of often cited as the faculty which marks the the blue’, actually come on the back of a lot of difference between humans and other careful and methodical work. Likewise, new animals. The famous apes studied by the and creative ideas have to be understood and psychologist Wolfgang Köhler learned ways to explained to be of any practical value. overcome problems, such as using a stick to Reasoning is required both to enable and to get at food that was beyond their reach; but apply creative thinking, just as creative they discovered the solution by trial and error, thinking is needed to give a spark to and then remembered it for the next time. reasoning. This is evidence of animal intelligence, and certainly of skill; but it is not evidence that Reflection apes can ‘reason’. As far as we can tell, no animal ever draws conclusions on the basis of Another quality that is evidently exclusive to observable facts. None of Köhler’s apes human thinking is reflection. Reflecting thought anything like, ‘That banana is further means giving deep or serious or concentrated from the bars than the length of my arm. thought to something, beyond the immediate Therefore I need to find a stick’; or ‘If this response to stimuli. When we are engaged in stick is too short, I will need a longer one.’ reflection we don’t just make up our minds on impulse, but carefully consider alternatives, Reasoning is the process by which we think about consequences, weigh up available advance from what we know already to new evidence, draw conclusions, test hypotheses knowledge and understanding. Being rational and so on. Critical thinking, problem solving is recognising that from some facts or beliefs and decision making are all forms of reflective others follow, and using that understanding thinking. to make decisions or form judgements with confidence. If there is one overriding aim of Moreover, the reflective thinker does not this book it is to improve students’ focus only on the problem to be solved, the confidence in reasoning. decision to be made, or the argument to be won, but also on the reasoning processes that Creative thinking go into those activities. Reflecting on the way we think – or thinking about thinking – helps Reasoning is not the only higher thinking us to evaluate how effective our thinking is, skill, nor the only kind of rationality. what its strengths are, where it sometimes Imaginative and creative activities are no less goes wrong and, most importantly, how it important in the history of human can be improved. development and achievement. But that is not 2 Unit 1 Thinking and reasoning

Using this book examination are covered, though not necessarily in the same order as they appear in Throughout the book there are activities and the specification. The book does not follow discussion topics to prompt and encourage the syllabus step by step or confine itself to reflection on thinking and reasoning just one examination. If it did it would not themselves. At regular intervals in the chapters help you either to think more effectively or to you will find ‘Activity’ panels. You can use do well in your exam. Critical thinking and these as opportunities to close the book, or problem solving are very broad skills, not cover up the rest of the page, and think or talk bodies of knowledge to be learned and – or both – about the question or task. Each repeated. A competent thinker is one who is activity is followed by a commentary offering able to deal with the unexpected as well as the an appropriate answer, or some guidance on expected. This book therefore takes you well the task, before returning to the chapter. By beyond the content of one particular exam comparing the discussion or solution in the and equips you with a deeper understanding commentary with your own reflections and of the processes involved, as well as a flexible, responses, you can judge whether to go back adaptive approach to the tasks you are set. and look at a section again, or whether to move on to the next one. Because thinking skills are general and transferable, the topics and concepts dealt Although it is not essential to do all of these with in the coming units will also prepare activities, you are strongly urged to give some you for many other awards that involve time to them, as they will help greatly with critical thinking and/or problem solving. The your understanding of the concepts and table on pages 342–43 shows a range of procedures that make up the Thinking Skills public examinations and admissions tests syllabus. The tasks also act as opportunities for whose content is covered by some or all of self-assessment, both of your own personal the chapters. These include A Level Critical responses, and of those of your colleagues if Thinking (OCR and AQA); the BioMedical you are working in groups. Small-group Admissions Test (BMAT); Cambridge discussion of the tasks is particularly valuable Thinking Skills Assessment (TSA); Singapore because it gives you insight into other ways to H2 Knowledge and Inquiry; and Theory think and reason besides your own. You have of Knowledge in the International the opportunity to compare your responses Baccalaureate (IB). with those of others, as well as with the responses suggested in the commentary. The Other subjects activities and commentaries are like a dialogue between you and the authors of the book. Finally, the value of developing your thinking skills extends far beyond passing exams called The book can be used either for a school or ‘Thinking Skills’! It has been shown, college course in thinking skills, or by the student unsurprisingly, that confidence and aptitude for individual study. It is divided into seven units in critical thinking and problem solving will with varying numbers of chapters within them. assist students to achieve higher grades across Although it is not a straight-line progression, all the subjects that they study. Accordingly there is an overall advance from basic skills to you will find critical thinking, problem applied skills and to higher levels of challenge. solving and presenting well-reasoned argument among the learning and assessment Preparing for examinations objectives of just about every senior-school or university course, whether in the sciences or The backbone of this book is the Cambridge the arts and humanities. syllabus for A and AS Level Thinking Skills. All of the assessment objectives for that 1.1 Thinking as a skill 3

Beyond that, too, these are sought-after N o more than one of the statements on each qualities in a great many professions and envelope is false. occupations. Hardly surprisingly, employers want staff who can think for themselves, On envelope X it says: solve problems, make decisions and construct arguments. A The jailhouse key is solid brass. B The jailhouse key is not in this What to expect envelope. To give a taste of the structure and style of the book, this chapter ends with an activity On envelope Y it says: similar to those which appear at regular intervals in all of the coming units. You can C The jailhouse key is not in this think of it as a trial run. The task is to solve a envelope either. puzzle entitled ‘The Jailhouse Key’. It is a simple puzzle, but it introduces some of the D The jailhouse key is in envelope Z. reasoning skills you will encounter in future chapters, giving a foretaste of all of three On envelope Z it says: disciplines: problem solving, critical thinking and decision making. E The jailhouse key is solid silver. F The jailhouse key is not in envelope X. Activity The prisoners may look inside the envelopes Two prisoners are held in a dungeon. One if they wish, before deciding. They have five night a mysterious visitor appears in their cell minutes to make up their minds. and offers them a chance to escape. It is only a chance because they must first reason Decide which envelope the prisoners to a decision which will determine whether or should choose in order to escape from not they actually do go free. the cell. Their cell is at the bottom of a long flight The best way to do this activity is to of steps. At the top is the outer door. Three discuss it with a partner, just as the two envelopes, marked X, Y and Z, are placed on prisoners would do in the story. As well as the table in the prisoners’ cell. One of them, deciding which envelope to choose, answer they are told, contains the key to the outer this further question: door, but they may take only one envelope when they attempt to leave the cell. If they Why is the envelope you have chosen the choose the wrong one, they will stay locked right one; and why can it not be either of the up forever, and the chance will not come others? again. It is an all-or-nothing decision. Commentary There are six clues, A to F, to help them – Throughout this book you will be given or puzzle them, depending on how you look at questions to answer, problems to solve, ideas it. Two are printed on each envelope. There is to think about or discuss, followed, as we have also a general instruction, on a separate said, by commentaries. The commentaries will card, which stipulates: vary: some will provide the correct answer, if there is one. Some will suggest various possible answers, or different directions you could have taken in your thinking. The purpose of the activities and commentaries is to allow you to assess your own progress and to give you useful advice for tackling future tasks. 4 Unit 1 Thinking and reasoning

Sometimes you may question or disagree It also tells you that: with the commentary, especially later on when you have gained experience. On other [1b] The statements on any one envelope occasions you will see from the commentary cannot both be false. where you went wrong, or missed an important point, or reasoned ineffectively. Although [1a] says exactly the same as the Don’t be disheartened if you do find you have card, it states it in a positive way rather than a taken the wrong tack. It is part of the learning negative one. Negative statements can be process. Very often we learn more from making confusing to work with. A positive statement mistakes than we do from easy successes. may express the information more practically. [1b] also says the same as the card, and In the present example there is only one although it is negative it restates it in a plainer answer to the question: the key is in envelope way. Just rewording statements in this kind of Z. The clues, although they seem confusing way draws useful information from them, and and contradictory, do give you all the helps you to organise your thoughts. information you need to make the correct decision. Nonetheless, there are any number Now let’s look at the envelopes and ask of different ways to get to the solution, and what more we can learn from the clues on you may have found a quicker, clearer or them. Here are some suggestions: more satisfying procedure than the one you are about to see. You may even have taken [2] Statements B and F are both true or one look at the puzzle and ‘seen’ the solution both false (because they say the same straight away. Occasionally this happens. thing). However, you still have to explain and/or justify your decision. That is the reflective part [3] A and E cannot both be true. (You only of the task. have to look at them to see why.) Procedures and strategies Taking these two points together, we can apply Procedures and strategies can help with a useful technique known as ‘suppositional puzzles and problems. These may be quite reasoning’. Don’t be alarmed by the name. You obvious; or you may find it hard even to know do this all the time. It just means asking where to begin. One useful opening move is to questions that begin: ‘What if . . .?’ For look at the information and identify the parts example: ‘What if B and F were both false?’ that seem most relevant. At the same time you Well, it would mean A and E would both have can write down other facts which emerge from to be true, because (as we know from [1a]) at them. Selecting and interpreting information least one statement on each envelope has to be in this way are two basic critical thinking and true. But, as we know from [3], A and E cannot problem solving skills. both be true (because no key can be solid silver and solid brass). Start with the general claim, on the card, that: Therefore: [1] No more than one of the statements on [4] B and F have to be true: the key is not in each envelope is false. envelope X: it is in either Y or Z. This also tells you that: This is a breakthrough. Now all the clues we need are on envelope Y. Using suppositional [1a] At least one of the statements on each reasoning again we ask: What if the key were in envelope must be true. Y? Well, then C and D would both be false. But we know (from [1b]) that they can’t both be false. Therefore the key must be in envelope Z. 1.1 Thinking as a skill 5

Thinking about thinking Take a statement – we’ll call it S – and ask You may have approached the puzzle in a yourself: ‘If S is true, what else would have to completely different way. For instance, you may be true too?’ If the second statement can’t be not have started with the clues on X and Z, but true, then nor can S. You can do the same gone for eliminating Y first. This is perfectly thing asking: ‘What if S is false?’ If you find possible and perfectly sensible. If the key were that that would lead to something that can’t in Y, both the clues on Y would be false. So it possibly be true, then you know that S can’t could not be there and must be in X or Z. Then be false but must be true. (If you do Sudoku you could eliminate X, as in the solution above. puzzles you will be very familiar with this way of thinking, although you may not have a You may not have used the ‘What if . . .?’ name for it.) strategy at all. (Or you may have used it but without calling it that or thinking of it that Whether you proceeded this way or not, way.) Different people have different ways of study the solution carefully and remember doing things and reasoning is no exception. The how it works. Think of it as an addition to method used above is not the only way to get to your logical toolbox. The more procedures the solution, but it is a powerful strategy, and it and strategies that you have in the box, the can be adapted to a wide variety of situations. better your chances of solving future The method, in general terms, is this: problems or puzzles. Summary • When we talk of thinking as a skill we are • Reflection includes ‘thinking about referring to higher-order activities, such as thinking’. In many ways the content of this analysing, evaluating and explaining; and book is thinking about thinking: thinking to challenges such as problem solving and more confidently, more skilfully and more evaluating complex arguments. independently. • Three broad categories of higher-order thinking are reasoning, creativity and reflection. They all overlap. 6 Unit 1 Thinking and reasoning

1.2 An introduction to critical thinking What makes some thinking critical, others Critical Thinking uncritical? (and critical ­thinking) ‘Critical’, ‘criticism’ and ‘critic’ all We should also be aware of the difference originate from the ancient Greek word between ‘critical thinking’, as a general kritikos, meaning able to judge, discern or descriptive term, and Critical Thinking (with decide. In modern English, a ‘critic’ is a large C and T), which is the name of an someone whose job it is to make evaluative academic discipline with a broadly defined judgements, for example about films, books, syllabus. This book addresses both. In Units music or food. Being ‘critical’ in this sense 2, 4 and 7 it covers the Critical Thinking (CT) does not merely mean finding fault or component of the Cambridge and other expressing dislike, although that is another syllabuses. But it goes well beyond the meaning of the word. It means giving a fair confines of exam preparation. In fact, having and unbiased opinion of something. Being mentioned the distinction, we can largely critical and thinking critically are not the ignore it. To have maximum value, thinking same thing. skills have to be transferable from one task or context to others. The aim of this book is to If critical thinking did just mean judging, instil in students a critical approach to wouldn’t that mean that anyone could do it reading, listening and reasoning generally; simply by giving an opinion? It takes no and to provide the conceptual tools and skills special training or practice to pass a that enable them to respond critically to a judgement. If I watch a film and think that wide range of texts. The CT syllabus gives the it is boring, even though it has had good book its structure but not its whole purpose. reviews, no one can really say that my judgement is wrong and the professional The objects of critical focus are referred to critics are right. Someone can disagree with generically as ‘texts’. The word is used in its me, but that is just another judgement, no broadest sense. In real life a ‘text’ can be better or worse, you might say, than mine. spoken or written or visual: a television In a limited sense, this is true. But a serious programme, for example, or Tweet or blog; or critical judgement is more than just a just a conversation. In a book, of course, the statement of preference or taste. A critical texts are restricted to objects which can be judgement must have some basis, which placed on a page, so that they are often usually requires a measure of knowledge or referred to instead as documents. Most of the expertise on the part of the person making documents that are used in the coming the judgement. Just saying ‘I like it’ or ‘I chapters are in the form of printed texts. But don’t like it’ is not enough. There have to be some are graphical or numerical; or a mixture some grounds for a judgement before we can of these. Two other generic terms that are call it critical. 1.2 An introduction to critical thinking 7

used are ‘author’ and ‘audience’. The author supports its conclusion; or how strong some of a text is the writer, artist or speaker who piece of evidence is for a claim it is supposed to has produced it. The audience is the receiver: support. reader, watcher or listener. Further argument is self-explanatory. It is Some CT textbooks give the impression that the student’s opportunity to give his or her critical thinking is directed only at arguments. own response to the text in question, by This can be quite misleading if it is taken too presenting a reasoned case for or against the literally. Arguments are of particular interest in claims it makes. CT, but by no means exclusively so. Information, items of evidence, statements and (In most CT examinations, including assertions, explanations, dialogues, statistics, Cambridge, these three tasks are set and news stories, advertisements . . . all of these assessed in roughly equal measure. They are and more may require critical responses. What referred to as the three ‘assessment objectives’.) these various expressions have in common is that they all make claims: that is, utterances Attitude that are meant to be true. Since some claims are in fact untrue, they need to be assessed critically As well as being an exercise of skill and if we, the audience, are to avoid being misled. method, critical thinking also relates to an We cannot just accept the truth of a claim attitude, or set of attitudes: a way of thinking passively. Arguments are especially interesting and responding. Here is a fragment from a because their primary purpose is to persuade or document. It is just a headline, no more. It influence people in favour of some claim. The belongs to an article exploring the history of critical question therefore becomes whether the aviation in the magazine section of a argument succeeds or fails: whether we should newspaper. It challenges the familiar story of allow ourselves to be persuaded by it, or not. the first manned, powered flight in a heavier- than-air machine, by Wilbur and Orville Activities Wright in 1903. The headline reads: The core activities of CT can be summarised WRIGHT BROS NOT FIRST TO FLY under the following three headings: Suppose you have just glanced at the • analysis headline, but not yet read the article. What • evaluation would your immediate reaction be? Would • further argument. you believe it on the grounds that the newspaper would not print it if it wasn’t These recur throughout the book with true? Would you disbelieve it because for so different texts and different levels of long it has been accepted as a historical fact challenge. As they are fully discussed in the that Wilbur and Orville Wright were the coming chapters there is no need to flesh first? Might you even take the cynical view them out in detail here, but they do need a that journalists make claims like this, true brief introduction: or not, just to sell papers? (After all, it would hardly make ‘news’, over a century later, to Analysis means identifying the key parts of announce that the Wright brothers were the a text and reconstructing it in a way that fully first to fly!) and fairly captures its meaning. This is particularly relevant to arguments, especially Such reactions are common enough complex ones. among readers. What they are not is critical. They are either passively accepting, or too Evaluation means judging how successful a quickly dismissive. All suggest a closed mind text is: for example, how well an argument to the question behind the headline. 8 Unit 1 Thinking and reasoning

Critical thinking, by contrast, should judgement – using it to form your own views always be: – is ultimately up to you. • fair and open-minded You cannot evaluate a bare assertion • active and informed without considering the reasons its author has • sceptical for making it. So the whole article is presented • independent. on the next page. Read the document and then have a go at the following question, a Most of these speak for themselves. Without typical critical thinking task. an open mind we cannot judge fairly and objectively whether some statement or story Activity is true or not. It is hard sometimes to set aside or discard an accepted or long-held belief; but How strongly does the information in the we must be willing to do it. Nor can we judge article support the headline claim that the any claim critically if we know nothing about Wright brothers were not the first to fly? it. We have to be ready to take an active interest in the subject matter, and be prepared You can answer this individually, or in a to investigate and enquire. Hasty, uninformed discussion group of two or more. Use your judgements are never critical. At the very least own words. It is an introductory activity, so we would need to read the article before an you are not expected to use any special informed judgement is possible. terms or methods. Some degree of scepticism is also needed: a Commentary willingness to question or to entertain doubt. This is a typical critical thinking question, Scepticism is not the same as cynicism. For and one you will be asked in one form or example, it doesn’t mean doubting everything another many times on different topics. This that journalists write as a matter of course commentary will give you an idea, in quite because you think that they are driven only by basic terms, of the kind of critical responses the wish to grab the reader’s interest, with no you should be making. regard for fact. Critical appraisal requires each claim or argument to be considered on its Firstly, with any document, you need to be merits, not on blanket prejudgements of their clear what it is saying, and what it is doing. authors – however justified those may We know from this article’s style that it is sometimes seem. journalistic. But perhaps the most important point to make about it is that it is an argument. Lastly, critical thinking requires It is an attempt to persuade the reader that one independence. It is fine to listen to others, to of the most widely accepted stories of the 20th respect their beliefs and opinions, to learn century is fundamentally wrong: the Wright from teachers, to get information from books brothers were not the first to fly a powered and/or from online sources. But in order to aeroplane. That claim is, as we have seen, think critically you must also be prepared to made in the headline. It is echoed, though a take some initiative: to ask your own questions bit more cautiously, in the caption beside the and reach your own conclusions. We get very first photograph: ‘Or did they (make history)?’ used to being told or persuaded what to think, The article then goes on to give, and briefly so that being faced with choices or decisions develop, four reasons to support the claim. can be uncomfortable. The methodology of critical thinking can give you greater Two obvious questions need answering: confidence in your own judgements, and (a) whether the claims in the article are more skill at defending them. But exercising the 1.2 An introduction to critical thinking 9

WRIGHT BROS NOT FIRST TO FLY Wilbur and Orville Wright make history at Kitty Hawk, USA, December 1903. machine . . .’, and quoted a Or did they? witness who affirmed: ‘The machine worked perfectly, and Many aviation experts and in Pittsburg, and of signed the operator had no problem historians now believe that affidavits from 20 witnesses. handling it.’ German-born Gustave One was Louis Daravich, Whitehead – seen here with stating that he was present Whitehead was a poor his aeroplane ‘No. 21’ – beat and accompanied Whitehead German immigrant to the the Wright brothers into the on his flight. Randolf tells of United States, whose voice sky by as much as two or even two more flights, in 1901 in was easy to drown out in the three years. a plane that Whitehead debates that followed. The named ‘No. 21’, and another Wrights, by comparison, had In a 1935 article in the in the following year in influential friends and magazine Popular Aviation, ‘No. 22’. supporters. The prestigious and a book published two Smithsonian Institute for years later, author and A headline from the New York Science, in return for historian Stella Randolf tells Herald, dated August 19, 1901 ownership of the Flyer, of a steam-powered flight read: ‘Gustave Whitehead agreed not to publish or made by Whitehead in 1899, travels half a mile in flying exhibit anything referring to flights before 1903. The question we should be asking is: Why? The jury is not so much out. The jury has gone home, and the case is closed. History suggests it is time to reopen it. Jacey Dare Gustave Whitehead, pictured with his aeroplane ‘No. 21’, and his daughter and assistants 10 Unit 1 Thinking and reasoning

believable; and (b) whether they support the Here are three more negative points that headline claim. You cannot be expected to you could have made, and quite probably did know whether or not the claims are true unless make. Firstly, the photograph of Whitehead’s you have done some research. But it can be said plane does not show it in the air. The Wrights’ with some confidence that they are believable. Flyer, by contrast, is doing exactly what its For one thing they could easily be checked. name implies: flying. ‘No. 21’ might have flown. (Apparently some ‘experts’ have As it happens, most if not all of the claims concluded from its design that it was capable in the first four paragraphs are basically true. of flight.) But that is not the same as a Firstly there are people who believe that photograph of it in flight; and had there been Whitehead flew planes successfully before such a photograph, surely Jacey Dare would 1903. (You only need to look up Whitehead have used it in preference to one that shows on the internet to see how many supporters the machine stationary and on the ground. he has. It is hard to say whether they count as The clear implication is that there is no ‘aviation experts’ or ‘historians’, but we can photograph of a Whitehead machine airborne. let that pass.) It is also true that Stella Randolf wrote books and articles in which she refers to Secondly, the New York Herald report is not numerous witnesses giving signed statements a first-hand account: it quotes a single that they saw Whitehead flying. There really unnamed ‘witness’, but the reporter himself was a story in the New York Herald in 1901, clearly was not there, or he would have given reporting a half-mile flight by Whitehead, and his own account. Thirdly Stella Randolf’s quoting a witness as saying that the plane article and book were published 34 years after ‘worked perfectly’. The photograph of the alleged flight of ‘No. 21’, and the Whitehead with his ‘No. 21’ is understood to testimony of Louis Daravich was not made be genuine; and no one disputes that public until then either. Why? There are Whitehead built aircraft. Lastly, it is a fact that many possible reasons; but one, all-too- Whitehead was a poor German immigrant, plausible reason is that it simply wasn’t true. and it is thought that the Smithsonian had some sort of agreement with the Wrights in An overstated conclusion return for their donating the Flyer. Another major weakness in Jacey Dare’s argument is that she claims too much. The If all these claims are so believable, is the evidence she provides does not give headline believable too? No single one of the sufficiently compelling grounds for rewriting claims would persuade anyone, but added the record books. What can be said, however, together they do seem to carry some weight. is that it raises a question mark over the That, however, is an illusion. Even collectively Wright brothers’ claim to fame. For even if the the evidence is inadequate. Not one of the argument fails to show that they were not the claims is a first-hand record of a confirmed first to fly, it doesn’t follow that they were. and dated Whitehead flight pre-1903. All the Lack of evidence for something does not prove evidence consists of is a list of people who that it is false, or that the opposite is true. said that Whitehead flew. Author Jacey Dare reports that author Stella Randolf wrote that There is a way, therefore, to be a little more Louis Daravich said that he flew with positive about the document. We can interpret Whitehead. Such evidence is inherently weak. it as doing no more than opening up a debate. It is what lawyers call ‘hearsay’ evidence, and On that reading, the wording of the headline in legal terms it counts for very little. is just down to journalistic style. If we 1.2 An introduction to critical thinking 11

understand it as a provocative or ‘punchy’ title complex documents and additional concepts rather than a literal claim, and take the last such as evidence and credibility, inference, sentence of the article as the real conclusion, explanation. Unit 7 is entitled: ‘Critical then perhaps Jacey Dare has a more defensible reasoning: Advanced Level’. As the name point. Maybe it is time to reopen the debate. If suggests, it moves into more challenging and that is all she is really saying, then she has a sometimes more technical territory. It draws stronger case. Or you may feel that even that is on some of the methodology of elementary going too far for the evidence available. logic and formal decision making, and concludes with two chapters on drawing Whichever judgement you come to in the together the different strands of critical end, you have now had a taste of critical thinking that have featured in the foregoing thinking, and in particular of two of its core parts of the book. components: analysing (or interpreting) an argument, and evaluating it. You have also Summary seen how the activity sections of the book link up with the instructional part and • Critical thinking consists of making the commentaries. informed, evaluative judgements about claims and arguments. Looking ahead • The main strands of critical thinking are: There are three critical thinking units in the analysis (interpretation), evaluation and book, interspersed – and sometimes further argument. overlapping – with the problem-solving units. Unit 2 is entitled ‘Critical thinking: the basics’, • Critical thinking is characterised by being: which is self-explanatory. It covers the main fair and open-minded; active and informed; concepts and methodologies of the discipline. sceptical; independent. Unit 4 is given over to ‘Applied critical thinking’, introducing longer and more 12 Unit 1 Thinking and reasoning

1.3 Solutions not problems Some people do not like the word ‘problem’; solving (PS). Some of this is due to the nature they say, ‘We don’t have problems, we only of short multiple-choice questions which have solutions.’ The word ‘problem’ is used in mainly deal with testing sub-skills rather than different ways. It can mean something that is looking at the full real-world application of causing us a difficulty. The word ‘problematical’ thinking skills. However, there are areas where implies a situation where we cannot see an easy a more rounded evaluation is carried out, solution to something. However, not all such as the Cambridge A2 papers, BMAT data problems are like this. In some cases we may analysis and inference, and in Unit 2 of the enjoy problems and solve them for fun: for AQA syllabus. Some of the questions in both example, when reading a puzzle book or doing a disciplines will be seen to be ‘hybrid’ where, crossword. Most people have some sorts of for example, you may be asked to draw a problem in their lives and many of these may conclusion or asked about further evidence be solved with a little careful thought. The when presented with a set of numerical data. problem solving we are talking about here is based on logic; it is often related to Although many of the skills used in problem mathematics, in the sense of shape or number, solving in the real world are mathematical in but does not require a high level of formal nature, much of this mathematics is at a mathematics to solve. It is largely based upon relatively elementary level, and needs little the real world and is not abstract like much of more than the basic arithmetical operations mathematics. Many people, from carpenters to taught at elementary school. In fact, many architects, from darts players to lawyers, use this problem-solving tasks do not need arithmetic type of problem solving in their everyday lives. at all. The origins of problem solving as part of a thinking skills examination lie in the On the face of it, critical thinking and processes used by scientists to investigate and problem solving might appear as quite analyse. These were originally defined by separate disciplines. Most critical thinking Robert J. Sternberg (Beyond IQ: A Triarchic Theory questions are primarily textual whilst many of Human Intelligence, Cambridge University problem-solving questions contain numerical Press, 1985) and can be summarised as: information. However, the skills used, especially in the application of logic, are • relevant selection: the ability to identify quite similar and certainly complementary. what is important in a mass of data, and Scientists, politicians and lawyers will thus to recognise what is important in frequently use both verbal and numerical solving the problem in hand data in proposing and advancing an argument and in drawing conclusions. • finding procedures: the ability to put together pieces of information in an One of the reasons why the two disciplines appropriate way and thus to discover the may be thought of as separate is in the nature route to a solution of a problem of thinking skills examination papers, which often present the tests with clear divisions • identifying similarity: the ability to between critical thinking (CT) and problem recognise when new information is similar to old information and thus to be able to understand it better and more quickly. 1.3 Solutions not problems 13

Problem solving in early thinking skills Activity exams was firmly founded on these three basic processes. The BMAT and TSA syllabuses Marina is selling tickets on the door for a still refer to them explicitly. In the Cambridge university play. It costs $11 for most people to examinations, the three basic processes have buy a ticket, but students only have to pay $9. been expanded into a wider range of skills Just after the play starts, she remembers that which are tested at AS Level using multiple- she was supposed to keep track of the number choice questions and at Advanced Level with of students in the audience. When she counts longer, more open-ended questions which the takings, there is a profit of $124. can draw on several of the basic skills. For example, the problem-solving category of How many people in the audience are ‘searching for a solution’ is one of the strands students? of ‘finding procedures’. A 2   B 3   C 4   D 5   E 6 Unit 3 of this book is entitled ‘Problem solving: basic skills’ and deals with these Commentary extended skills. The chapter structure is firmly The $124 is made up of a number of $11 tickets based on the problem-solving skills defined in plus a number of $9 tickets. We need to find the Cambridge syllabus. Unit 5, ‘Advanced out what multiples of 11 and 9 will add to 124. problem solving’, deals with the extension to We can do this systematically by subtracting Advanced Level and wider-ranging questions. multiples of 11 and dividing the remainder by Questions at this level will generally include 9. For example, if there were one audience the use of several of the basic skills. This covers member paying the full ticket price, there the analysis of more complex data sets, and would have been $113 from students. This is mathematical modelling and investigation. not a multiple of 9, so cannot be correct. We These questions have open, rather than can list the possibilities in a table: multiple-choice, answers. Unit 6, ‘Problem solving: further techniques’, deals mainly with Number of Amount paid Remainder mathematical techniques which may be useful in examinations at all levels. full-fee payers from $124 The end-of-chapter assignments have often 1 $11 $113 been left open-ended rather than framed as 2 $22 $102 multiple-choice questions. This is so you will 3 $33 $91 have to solve the problem, rather than 4 $44 $80 eliminating answers or guessing. Some of the 5 $55 $69 activities and questions are marked as ‘harder’ 6 $66 $58 and are intended to stretch candidates. 7 $77 $47 8 $88 $36 Here is a ‘taster’ problem to start with. It is 9 $99 $25 certainly not trivial, but illustrates the essence 10 $110 $14 of problem solving. The problem contains only three relevant numbers and the only mathematics required is the ability to add, subtract and divide some small two-digit numbers. Solving the problem requires no specialised knowledge, either of techniques or skills, just clear thinking. 14 Unit 1 Thinking and reasoning

We found the first multiple of 9 with 8 full- enjoyable experience and one which can help price payers: $124 − $88 = $36, which means you with many things in both your home there were 4 students paying $9. We carried and working life. on checking, just in case there were other solutions. There weren’t any, so C (4) Summary is the correct answer. In practice, most of the working could be done mentally as it is • Problem solving is about the use of logic, quite simple, so the problem could be solved often including simple mathematics, quite quickly. to address real-life situations and aid decision making. Problems you will meet later in the book will have similarities to this in that they are • The fundamental skills of problem solving based on realistic scenarios and reflect the are: selecting relevant data, finding processes needed to function efficiently in appropriate procedures to solve problems much of employment. and comparing data in different forms. The challenges of problem solving are, in • Learning to solve problems successfully principle, no different from doing a puzzle develops skills which are useful in everyday such as Sudoku in a magazine and many are life: at home, in education and at work. the type of thing some people will do for fun. Solving such a challenge is a rewarding and 1.3 Solutions not problems 15

Unit 2 Critical thinking: the basics 2.1 Claims, assertions, statements A claim or assertion is an expression that is or assertion could also be made by sketching supposedly true. It may be spoken or written, and labelling a map showing the two or sometimes just thought. countries next to one another. We have to say ‘supposedly true’ because Since [A], [B] and [C] are all claims, all three obviously not all claims and assertions are true. can be judged to be true or false. You may not Some are deliberate lies; some are based on know whether a particular claim is true, but at mistaken belief. There are also some claims least it makes sense to say that it is; or that you which, as we shall see, are not straightforwardly agree or disagree with it. It makes no sense to true or false, but can still be asserted, or denied. say that a question or command is true. (A denial is a kind of assertion, an assertion that something is not so.) Fact and opinion Here are three illustrative examples: Claims can be divided roughly into those that state facts and those that express opinions. [A] Angola shares a border with Namibia. This is a useful distinction, but it needs some [B] The dinosaurs were cold-blooded. clarification. [C] Top bankers earn too much money. Activity All three sentences are statements. ‘Statement’ here is used in the grammatical sense to Look again at the three expressions above, distinguish between sentences that usually [A], [B] and [C]. They are all grammatical express claims and those which are used to statements. They all express claims. Discuss ask questions or give commands. If you want how, if at all, they differ from each other. a more formal grammatical term, the three sentences are all declaratives (or declarative Commentary sentences), as opposed to interrogatives A fact is a true statement. Of the three (questions) or imperatives (commands). examples, the first, [A], is a fact. What is more, It is important to keep in mind the distinction between an actual sentence – a string of words – and what is expressed by a sentence: the claim. A claim can usually be made in many different ways. For example, [A] could just as well have been expressed by the sentence: [A1] Angola and Namibia are immediate neighbours. The wording is different but the claim is practically the same. Arguably the same claim 16 Unit 2 Critical thinking: the basics

it is a known or an established fact. You can Another way to distinguish this claim check it by looking in an atlas, or going there from the other two claims is to say that it is and crossing the border. Some people may not purely subjective. That means that its truth is be aware of the fact, or even mistakenly think decided by each individual person – or something different; but that doesn’t in any subject – who thinks about it. This is in way alter the fact. If someone says, ‘No, these contrast to the first two, which are objective. two countries do not share a border,’ they are They are true or false regardless of what wrong, and that’s all there is to it. anyone thinks or knows. The fact that the truth is hidden does not mean that there is Note that stating a fact is not the same as no fact to be discovered. claiming it – or making a factual claim. You can state a fact only if it really is a fact. But Value judgements you can claim that something is a fact and be mistaken, or even be lying. Similarly, you can Claims like [C], that something or someone is claim to know something and be mistaken. good, bad, better, nice, nasty, greedy, too rich, But you can’t actually know something that underpaid, and so on, are also called value isn’t true. You can only think you know it. judgements, for the obvious reason that they are opinions about the perceived value or Statement [B] that dinosaurs were cold- worth or rightness or wrongness of things. It is blooded is a claim to fact. But unlike [A], it is not a value judgement to claim that dinosaurs not a known fact, by the author or by had cold blood. Nor would it be a value anybody else. Scientific opinion on the judgement to claim that some bank bosses subject is divided, with grounds for claiming earn more in a week than an average worker either that the dinosaurs were cold-blooded earns in a lifetime. For these are matters of fact (like modern reptiles), or that they were which can be quantified and verified – or warm-blooded (like birds and mammals). The falsified, as the case may be – for example, by best we can therefore say of this claim is that comparing the earnings of actual people. it is a belief (or judgement or opinion); and unless or until there is more factual evidence It becomes a value judgement if you claim available, it will remain so. that there is something ‘wrong’ or ‘excessive’ or ‘obscene’ about a level of earnings; or if This does not mean, however, that this you say that, on the contrary, it is ‘right’ for sentence is neither true nor false. For either such successful and talented individuals to the dinosaurs were cold-blooded or they get huge rewards. It might be difficult to weren’t. Scientists may never know the truth, justify a claim that such huge pay but the truth exists and is there to be differentials are ‘right’; but in the end it discovered – even if it has to wait for the remains a matter of opinion or belief; and invention of a time machine! people may differ in their opinions. The third claim, [C], is purely an opinion. When someone says, therefore, that a value Two people can disagree as to whether it is judgement is true (or false), they are using the true or not, and neither of them is necessarily words in a broad sense to mean something like wrong. It comes down to what they think or ‘true (or false) in my opinion’, or ‘true (or false) believe to be a reasonable wage, and/or what for me’. they think of as ‘too much’. To say that the sentence is true just means that you agree Predictions and probabilities with it, or assent to it. And to say that it is false means you disagree. It can be ‘true’ in Another special kind of claim is a prediction. A your opinion at the same time as being ‘false’ prediction is a claim that something may or in someone else’s. may not be true because it is still in the future, 2.1 Claims, assertions, statements 17

or is as yet unverified. For example, someone often referred to as hypotheses, even when might claim, at a certain time and place: they are generally accepted as true. [D] There’s going to be a storm in the next Take the prediction that, if a dart and an 24 hours. empty drink can are dropped simultaneously from an equal height (under ordinary If there is a storm within one day of the atmospheric conditions), the dart will land sentence being spoken, then you can say, first. This claim is made on the grounds that, looking back, that the prediction (or forecast) whenever two such objects are dropped, the was correct. But you cannot, even with result is always the same – or always has been hindsight, say that the prediction was a fact the same – so that it is entirely reasonable to when it was made, because at the time of expect it to go on being the same in the future. making it, it was not yet known to be true. The observed result is explained by the general principle that thin, arrow-shaped objects Even when a claim cannot be made with encounter less air resistance than bulkier ones, certainty, it can often be made with some allowing the former to accelerate more rapidly degree of probability. If you are playing a game under the same force (in this case gravity) than with five dice, and need five sixes with your the latter. next and final throw, it is a fairly safe prediction that you won’t win, because the The hypothesis has been so well tested that chances of throwing five sixes all at once are the probability of such a claim ever being very low. But it is not impossible. On average, wrong is practically non-existent. We call it a five sixes will come up once in every 7776 (65) ‘hypothesis’, rather than an absolute throws. The claim that you will lose, therefore, certainty, because conceivably the laws of has a high probability of being a correct physics may not be the same in the far, prediction, but it is not a fact. Similarly, if unknowable future, or in all possible worlds. someone said after you had thrown (and lost): ‘I knew you wouldn’t win,’ you could correctly Besides, there have been many scientific reply (as a critical thinker): ‘You didn’t know it. beliefs in the past that no one seriously You predicted it correctly, that’s all.’ doubted, but that have had to be revised because of later discoveries. One of the Hypotheses best-known examples is the belief that the Sun circled the Earth, or actually rose each Strictly speaking, many of the claims that morning from beneath the Earth and travelled scientists treat as fact should be understood across the sky. It was widely accepted by as probabilities of a very high order. These are astronomers before the time of Copernicus. More recently, Albert Einstein’s claim that 18 Unit 2 Critical thinking: the basics

nothing could exceed the speed of light Grammatical note seemed unchallengeable until, in 2011, a We saw earlier in the chapter that claims team of scientists at the Large Hadron Collider typically take the form of statements, or claimed to have measured a tiny subatomic declarative sentences. In some cases, however, particle – a neutrino – travelling fractionally other grammatical forms can be used. faster. Their measurements have yet to be Take [C] again. A similar point could be made confirmed, and may have been proved wrong by ‘asking’: by the time you are reading this page. But whilst any uncertainty remains, Einstein’s [C1] How disgusting are bankers’ wages? assertion is still just a hypothesis, and hence a claim, not a fact. ‘Asking’ is in quotation marks because [C1] is not a genuine question but a rhetorical one. Recommendations (You could alternatively call it an exclamation, and punctuate it with an exclamation mark.) Recommendations or suggestions are claims What defines a rhetorical question is that it is of yet another sort. Here is one example: not really in need of an answer: it is making an assertion. In this case the assertion is: [E] The wages and bonuses of bankers should be capped. [C2] Bankers’ wages are disgusting. This may seem quite similar to [C]: the claim Summary that top bankers earn too much. Both express a similar sentiment, and both are opinions • In this chapter we have discussed and rather than hard facts. However, there is an analysed one of the most basic concepts important difference. [C] is an observation. It in critical thinking: claims. These are describes a situation as the author sees it: the also referred to as ‘assertions’ and way things are in his or her opinion. [E], in ‘statements’. contrast, is a claim about how things ought to be, or what the author thinks should be done • Several important kinds of claim have been in response to the situation. introduced. They include: Recommendations, like value judgements, • claims to fact are not straightforwardly true or false. Two • statements of opinion or belief people – even two people who agree about • value judgements [C] – may disagree about whether the • predictions recommendation to cap wages is the right • hypotheses way to deal with what they see as excessive • recommendations. earnings. Neither of the two will be factually wrong in their judgement. If one person says There will be more discussion of all that it is ‘true’ that bankers’ wages should be of these kinds of claim in the coming capped, it just means that he considers it to chapters. be a good idea. If another says it is ‘false’, she is claiming it is a bad idea. 2.1 Claims, assertions, statements 19

End-of-chapter assignments In what way is each of these different from the others? (You can use a dictionary to 1 Explain briefly, in your own words, the help you answer the question.) difference between a claim and a fact. 5 How would you define the following special 2 Is there any significant difference between kinds of claim? a claim and an assertion? If so, how are they different? If not, what do they have • allegation in common? • accusation • insinuation 3 For each of the five examples [A]–[E] in • confirmation this chapter, suggest two other claims that • denial have the same relation to the truth, but on • verdict different subject matter. 6 The idea of claims is central to the 4 The word ‘hypothesis’ has several close discipline of critical thinking. Why is relatives. Here are four: this so? • conjecture Answers and comments are on page 311. • theory • guess • speculation 20 Unit 2 Critical thinking: the basics

2.2 Judging claims When a claim is made, especially publicly, it The moral of the story is that truth and is natural to think we are being told the truth. trust are both important. People need to be Most of the time we accept claims, especially able to rely on what they are told most of the claims to fact, at face value. For instance, if time; and people who speak the truth need we read in the newspaper that there has been others to believe them most of the time. But a plane crash, we are entitled to assume that that does not mean we should respond with such an event really has taken place. We blind acceptance to everything that we read don’t jump to the conclusion that the and hear. Obviously we cannot assume that statement is false just because we have not just because something has been asserted – in witnessed it ourselves. We hear the football spoken, printed or any other form – it is true, results, or baseball scores, and assume they or we have to agree with it. People do make are correct, and not made up to please the false assertions not only with intent to fans of some clubs. We get a weather forecast deceive, but also out of carelessness or telling us to expect heavy snow, and we plan ignorance. Even when there is a core of truth accordingly: we don’t ignore it just because it in what someone says, it may be exaggerated, is a prediction, and predictions aren’t facts. or over-simplified, or a mere approximation, or a rough guess. There are many ways, Assuming that most of what we are told is besides being plainly false, in which a claim true is entirely reasonable. Indeed, it is may be less than the whole truth. necessary for a normal life, and the functioning of a modern democratic society. None of this means that we should start If we questioned, or refused to believe, routinely doubting everything. But it does everything we read or heard, life as we know mean we should keep an open and inquisitive it would come to a standstill. That is why we mind. all have a responsibility to tell the truth; and why people are understandably annoyed if Justification they are told something that is not true. As you saw in the previous chapter, it is not Everyone knows the story of The Boy Who always possible to know whether a claim is Cried ‘Wolf!’ or a story like it. The boy has a straightforwardly true or false. Knowledge bad habit of raising false alarms, in particular requires certainty and certainties are rare. In frightening his community by shouting out the absence of certainty, the best evaluation that a pack of wolves is approaching the we can give of a claim or belief is to say village. At first the villagers run to safety whether it is justified, or warranted. These two whenever he does this. But after a while they words mean much the same as each other. A stop believing him, until the day comes when warrant is a right or entitlement. We are a real wolf appears. By then, of course, the entitled to hold a belief, or to make a claim, if boy has lost all credibility and his for-once there are strong grounds – for example, genuine warning is ignored. (You can work evidence – to support it. Without such out the ending yourself.) grounds a claim is unwarranted (unjustified). 2.2 Judging claims 21

At first sight it may seem that truth and Judging which of these is the right way to justification amount to the same thing: a respond to a claim is at the heart of the claim is justified if it is true, and unjustified discipline of critical thinking, and is part of (or unwarranted) if not. But neither of these what we mean by ‘evaluation’. is correct. A claim can be true but unjustified if the person making it does not have good Activity grounds for believing it – or in extreme cases may not believe it at all. Suppose, for Recall the example in the last chapter: the example, a crime has been committed. The claim that the prehistoric dinosaurs were victim (we’ll call her Vera) claims that her cold-blooded. Two facts are often cited in neighbour (Nick) was the one who did it, support of this: perhaps because she doesn’t like him, or perhaps because she wants to see someone [A] The dinosaurs were reptiles. convicted, and anyone will do. Other than [B] Modern reptiles, e.g. snakes and this she has no reason for making the allegation, and certainly nothing that would lizards, are all cold-blooded. count as evidence. But then suppose it is discovered that Nick, just as Vera has claimed, Discuss whether these two facts between is guilty of the crime! Would the discovery of them justify the claim that the dinosaurs Nick’s guilt justify Vera’s accusation? No. It were cold-blooded. would just be chance that the claim she had made was true. Given her motives her claim Commentary would still be a lie. The two facts give some support to the claim, but only some. They are grounds for the Conversely, a false claim can be justified in hypothesis that the dinosaurs were cold- some circumstances. Someone may make an blooded inasmuch as they add some weight to assertion on the basis of all the information that side of the debate. If you knew nothing available at the time of making it. If that else about dinosaurs, or reptiles, or evolution information gives convincing grounds for the generally, you might be tempted to accept the claim, then it is fair to say that it is a justified grounds as sufficient. But it would be a big claim to have made, even if it later turns out step to take. For one thing it would mean to be false on the basis of some new assuming that what is true of reptiles now information. must have been true of reptiles 70 million years ago, and earlier. It is not at all impossible In other words, truth and justification are that there were once warm-blooded reptiles different. Justification is provided by the running around, including some of the reasons that can be found and given for a dinosaurs; but that these reptiles became claim, but truth or falsity belong to the claim extinct, leaving only the cold-blooded species itself. We may never know for certain whether surviving today. (Being cold-blooded may a particular claim is true, but we may be able to have given certain reptiles a survival say that there is sufficient evidence or grounds advantage over the warm-blooded ones. or support to justify asserting it. Alternatively Warm-blooded species use more energy than we may say that a claim is unjustified, because those with cold blood, and food sources may there are not sufficient grounds or support for have become scarce.) This possibility alone it, or because there are sufficient grounds to means that the assumption is questionable, cast doubt on it. This is different from saying though not necessarily false. that it is actually false. 22 Unit 2 Critical thinking: the basics

So [A] and [B] on their own do not really truth – by 195 metres. You may have thought justify taking the hypothesis as fact. It could it was fair to say that Katya’s claim was nearly be true, and many scientists consider it more true, or approximately true; but this is really probable than the counter-claim that the just a way of saying that Katya ran nearly a dinosaurs were warm-blooded. But there is no marathon or approximately a marathon. proof one way or the other. Indeed, it is completely true that Katya ran nearly a marathon, even though [C], as it Standards stands, is not true. It should be noted that ‘justified’ is not an Is [C] as it stands justified? That is a more all-or-nothing term like ‘true’ and ‘certain’. A difficult question. It depends on the claim is either true or it is not. You may want circumstances or context in which it was to object that some claims are partly true (or asserted. If it is just a conversational context, partly false); or somewhere in between truth which is what it sounds like, then it would be and falsity. But in strict terms ‘true’ means ‘the plainly silly to call Katya a liar. However, if she whole truth and nothing but the truth’, and had to run at least one complete, officially does not allow degrees or approximations. A recognised marathon – perhaps in a certain claim, on the other hand, can be more or less time – to pass some test, and she was counting justified according to the strength of the the training run as her qualifying run, then supporting grounds and the context in which we have to say that her claim is not justified. the claim is made. What makes the difference is the standard of accuracy or precision required. Here is a simple example. (A ‘marathon’, officially defined, is a running race over The most familiar example of varying 42.195 km. There are various explanations standards of this kind is in the law. Take a and historical accounts for this rather guilty verdict passed in a criminal trial. (A peculiar distance. You may like to do some verdict is a special kind of claim. You were research and find out why. But for present asked to define it in the assignment at the end purposes what matters is that it is a fact.) of Chapter 2.1.) Under the justice systems of many countries, the UK included, a guilty Activity verdict is justified only if it can be proven beyond reasonable doubt. That phrase sets the Let us suppose that Katya has just returned standard. So, even if the jury are pretty sure from a training run of 42 km and announced the defendant is guilty, but there is just a to her friends: small, lingering uncertainty, they must give a verdict of not guilty – or in some countries an [C] I have just run a marathon. ‘open verdict’, or ‘unproven’. Similarly, those who give evidence in a court are instructed Discuss whether her claim is justified (or to tell the truth, the whole truth and nothing warranted), given that it is so close to the but the truth. This, too, sets a very high truth. Is it in any sense ‘true’? Or is it standard on what counts as a justified or altogether ‘false’? warranted assertion. Commentary By contrast, the standard required for a ‘not The assertion is, strictly speaking, untrue. guilty’ verdict is much lower: all that is Even if we allow that by ‘marathon’ Katya required is that there is some room for doubt – means the marathon distance (rather than an at least in societies which hold the principle organised race), her claim is short of the whole that a person is innocent until proven guilty. In 2.2 Judging claims 23

a criminal case there is an imbalance between However, this does not mean we can never the standards that must be met by the use the words ‘know’ or ‘certain’ prosecution and the defence respectively. appropriately. It is perfectly appropriate to say The ‘burden of proof’, it is often said, ‘lies with of some claims that they are certain. The the prosecution’. truths of mathematics and logic are usually spoken of as certainties. No one doubts that The balance of probability 7 + 5 = 12 or that a triangle has three sides, or that an object cannot be red and black all over Outside the criminal law we may find at the same time. Claims like these are often standards lower than proof being needed to said to be true by definition. For example, ‘12’ justify a claim or decision. For instance, in a just means the same as ‘the sum of 7 and 5’. civil case, where both sides are treated equally, a verdict is justified ‘on the balance Also there are claims which are practically of probability’. Obviously it is much harder certain even if they are not logically true. The to justify a claim beyond reasonable doubt old favourite is that the sun will rise tomorrow than on the balance of probability. (as it has always done on previous days). It would be foolish to dispute this claim, despite What this means is that there are degrees of the fact that some freak of nature could justification, depending on context. For conceivably spell the end of the solar system in critical thinking it means that when we judge the next 24 hours. If you had to bet on winning a claim to be justified (warranted), or the lottery or the sun not rising, you would bet unjustified (unwarranted), we need to qualify on winning the lottery every time! the judgement by stating what standard we are applying. Expressions like ‘wholly Complex claims (completely, entirely) justified’ are stronger than ‘well supported’ or ‘highly likely’; and Sentences such as ‘Katya just ran a marathon’ ‘unwarranted’ is stronger than ‘open to or ‘Dinosaurs were reptiles’ express simple question’ or ‘unlikely’. Choosing the right claims. The following, by contrast, are qualification for the judgements we make complex sentences, each expressing two or about claims and their justification is more connected claims: one of the most important critical skills to develop – arguably the most important. [D] Katya just ran a marathon and completed the distance in under four Knowledge and certainty hours. With certainty, on the other hand, there are [E] The dinosaurs were reptiles, yet they no degrees. It is true that people often talk were warm-blooded. about the degree of certainty that can be given to some claim or other; but what they [F] Sea levels are rising around the world really mean by this is the degree to which the because global warming is melting the claim falls short of certainty. The claim that polar ice caps. you will never win the lottery is so highly probable that it can be stated as a near- [G] Many parts of the world will soon be certainty. But near-certainty is not certainty. submerged if nothing is done to reverse Likewise, you don’t know that you won’t win climate change. the lottery. If everyone who bought a lottery ticket claimed to know that they would not Grammatical note win, sooner or later one of them would A simple sentence, when it becomes part of a be wrong! complex sentence, is called a ‘clause’. Words or phrases which express the relation between clauses are called ‘connectives’: for example, 24 Unit 2 Critical thinking: the basics

‘and’, ‘because’, ‘if’. [G] is another complex claim, and one which is quite tricky to analyse accurately. Activity First of all it is not claiming either that parts of the world will soon be underwater, or that What difference does it make to the way we nothing will be done about climate change. judge a claim if it is complex rather than [G] is what we call a conditional claim, or a simple? hypothetical. We will also be returning to these later in the book; but for now all you For each of the examples [D]–[G] discuss need to note is that a conditional is a claim the conditions that would have to be met to that if one thing is true, then so is another. justify the whole claim. For instance, if nothing is done about climate change, then parts of the world will Commentary be underwater. If nothing is done and the When assessing complex claims we also have prediction turns out to a false alarm, then to take note of the connective, and the [G] as a whole is untrue. relation it expresses between the parts. Strong and weak claims In the case of [D] the job is quite straightforward. The connective is ‘and’. This Before concluding the chapter, there is one means that [D] as a whole is true if Katya did more important distinction that needs to be just run a marathon and that she ran it in made. Some claims are stronger than others. under four hours. So, if either of these claims The importance of this is that a strong claim is at all questionable, [D] is not fully justified. is harder to justify than a weak claim. A ‘strong’ claim is one which says a lot, and/or In [E] the connective is ‘yet’ which makes says it very plainly or forcefully. A ‘weak’ [E] a slightly more complex assertion than [D]. claim in comparison is more moderate: it says Again the two connected claims both have to less, and/or qualifies what it says. be true: firstly that dinosaurs were reptiles, and secondly that they had warm blood. But the Suppose for example that whoever asserted use of the connective ‘yet’ also suggests that [G] had said instead: there is something surprising or unusual in this: that the second claim is true despite the [H] Whole regions of the world will soon be first being true. The implication is that reptiles under water as a direct result of man- are usually, or normally, cold-blooded; and if made climate change. this is not the case then the use of ‘yet’ is not really justified, even if both the claims are true This is a very strong claim. It doesn’t say ‘may in themselves. be . . .’, or ‘are at risk of being . . .’, or anything else that softens the impact. It says, [F] also has more to it than just the two categorically, that whole regions will be claims. [F] is an explanation, or more flooded. The whole of [H] is stronger still, precisely a causal explanation, as indicated by because it also claims, just as categorically, the connective ‘because’. Its author not only what the direct cause will be. [H] does not pull asserts that sea levels are rising and that any punches. Moreover, it is clearly implying global warming is melting the ice, but also that climate change is taking place, and that it that the first is caused by the second. If we are is man-made – a claim that some people deny not satisfied that all three parts are true, then or question. It would not make sense to add we are not justified in asserting [F]. (There is that this would be the cause if it were not also more about explanation later in the book.) claimed to be a reality. All of these factors add up to make [H] a strong and far-reaching claim. 2.2 Judging claims 25

Because it says a lot, and says it so forcefully, it problem-solving skills than men. Even so, it would take a lot to justify it in full. would be a generalisation, and a vague one too; and vague generalisations are hard One important point to add about this to justify. distinction is that if a claim is very strong it is easier to challenge, or to cast doubt on, The opposite of the word ‘general’ is the because there is more, potentially, to find word ‘particular’. It would not be a fault with. [H] could be made easier to justify generalisation to select a particular woman, if it were weakened, or modified, for example or group of women, and talk about their like this: thinking skills. Imagine that two teams – one all female, another all male – competed in a [H1] Some parts of the world could one day problem-solving competition, and the be under water, and if so man-made adjudicator concluded at the end that: climate change may be at least partly to blame. [J] The women (in the women’s team) were more organised in their thinking Obviously [H1] needs less to justify it than [H], than the men. and would be easier to defend if a denier of climate change wants to attack or disprove it. This would be a particular claim, not a general Words or phrases such as ‘some’, ‘could’, ‘may’ one, stating that these particular women, on and ‘one day’ are weaker terms than ‘whole’, this particular occasion, were superior to the ‘will’ and ‘soon’; and partial blame is easier to men – at certain particular tasks. Claim [J] pin on something than direct cause. Whereas would be justified if the women won the you need something approaching proof to competition. But no sort of general claim justify [H], you need only danger signs to justify could be made on the strength of [J], [H1]. But then [H1] does not have the impact especially not [I]. (You will meet up with this that [H] has. It is not the same claim any more. topic again in Chapter 2.10.) Generalisations Summary A generalisation is a claim that applies very • We have discussed what is meant by widely – sometimes universally: that is, in justifying a claim, and considered different every single case. For example: standards of justification. [I] Women are better problem solvers • We have looked at simple and complex than men. claims. This is a strong claim because it is about • It has been shown that strong claims are men and women generally. It is especially harder to justify than weak claims. strong if it is taken literally to mean that all women are better at problem solving than • We have seen the distinction between all men. Clearly that would be unwarranted, general and particular claims. since it would take just one or two counter- examples to prove it false. However, [I] could be understood to be the less sweeping claim that on balance women exhibit better 26 Unit 2 Critical thinking: the basics

End-of-chapter assignments 3 Compare these two claims: 1 Invent a story or scenario in which a claim [A] Polar bears will be extinct by the is made that is true but unwarranted. middle of the century. 2 Give an example of a claim that you [B] Polar bears are an endangered consider to be: species. a justified on the balance of probability One of these claims is stronger than the b justified beyond reasonable doubt other. Which one is it, and why? c completely justified; certain. Answers and comments are on page 311. In each case say why your claim matches the description. 2.2 Judging claims 27

2.3 Argument An argument is a complex claim used to This is a very simple argument. It consists of organise and express certain kinds of just one reason and a conclusion, and the reasoning. It is composed of two or more connective ‘so’. The words ‘therefore’ or ‘so’ claims, one of which is a conclusion; the others are typically used before the conclusion of an are reasons for the conclusion. A good argument, and are often called argument argument is one in which the conclusion indicators (or inference indicators) for that follows from the reasons, or is justified by the reason. reasons. However, this is not the only way to This doesn’t simply mean that the construct this argument. It could have been conclusion comes after the reasons. ‘Following written: from’, in the context of an argument, means that the conclusion is adequately supported by [1b] The Earth cannot be flat because (since / the reasons. If the reasons are true, and the given that / . . .) ships appear to sink out argument is a good one, then the conclusion of sight as they sail away from land. must be true as well. Obviously a false conclusion cannot follow, in this sense, from Note that the connective in [1b] reverses the true reasons. order of the claims. Words like ‘because’ and ‘since’ are therefore sometimes referred to as In practical terms arguments exist for the reason indicators (or premise indicators). purpose of persuading others, or of satisfying (‘Premise’ is a more formal word for a reason in oneself, that a particular claim is warranted. an argument.) An example Note also that it is not necessary to include an argument indicator at all: the reasoning Until a few hundred years ago it was generally may be just as clear without it. For example: believed that the world was flat. This was a natural belief to have because the Earth’s [1c] The Earth cannot be flat. Ships appear surface looks flat. But people had also observed to sink out of sight as they sail away. (and been puzzled by the fact) that ships sailing away from land appeared to get lower The form of an argument and lower in the water, as if they were sinking, and appeared to rise up again as they In each of these examples the argument is approached land. Some argued – from this expressed and/or arranged differently. But it is and other observations – that the Earth’s still the same argument, with the same reason surface could not be flat, but was curved. They and same conclusion. Because there are many drew this conclusion because if the Earth were ways in which an argument can be expressed, flat, a ship would just appear to get smaller it is convenient to have one standard form for and smaller until it was too small to see. The setting arguments out. The customary way to argument went like this: do this, both in logic and critical thinking, is to place the reasons in a list, and to separate [1a] Ships appear to sink out of sight as they them from the conclusion by a horizontal sail away. So the Earth cannot be flat. line. The line performs the same function as 28 Unit 2 Critical thinking: the basics

words such as ‘therefore’ or ‘so’ in natural Bart (in a lowered voice): language reasoning. We can set out this Then I’ll tell you something. If simple argument as follows: you go around talking this kind [1] Ships appear to sink out of sight as they of nonsense, someone is going sail away. to lock you up and throw away the key. Or tie you to a post and set you on fire. The Earth cannot be flat. Kris: But just listen – Bart: No, you listen. The Earth is flat. In a formal argument like this, the reason or Kris: It’s round. reasons are also known as ‘premises’. The word Bart: Flat. F-L-A-T, flat! ‘premise’ is derived from Latin and means Kris: ROUND . . . ‘put before’. Activity [1a], [1b] and [1c] are just three out of many ways of expressing [1] in ordinary language. [1] and [2] are both called ‘arguments’. But [1] is the standard way. Reconstructing an do they have anything else in common argument in a standard form helps to make the besides answering to the same word? reasoning clear and assists with its subsequent evaluation. It also helps with the identification Discuss how you would define an of arguments. Obviously the exercise is argument to include both the first kind and unnecessary when an argument is as short and the second. as plain as this one. But with more complex reasoning, which you will encounter as you Commentary progress through the chapters, formal The problem with the English word reconstruction is a valuable tool. ‘argument’ is that it has several meanings. Two of them are given by the following Arguing back dictionary entry: Of course, not everyone has to accept an argument (noun) argument. Sometimes, even when you have 1 a reason or reasons supporting a given your reasons, people may still disagree conclusion; a case made for or against a with your conclusion. This certainly happened point of view. 2 a debate or dispute, hundreds of years ago when the first ‘Round- especially a heated one; quarrel; row. Earthers’ began trying to persuade people that the world was spherical, not flat. As you can see, example [1] is an argument of the first sort whilst [2] is an example of the There may have been conversations like this. second. The main difference is that [2] is a dialogue engaging two or more people. It may [2] Kris: Did you know it’s been proven involve some reasoning from one side or the that the Earth is a huge ball other, or both, but it need not. In [2] there is hanging in space? very little reasoned argument. Kris tries to explain his position, but his opponent shouts Bart: Don’t be ridiculous. Anyone can him down. The two speakers are mostly just see the Earth is flat. exchanging opinions, without giving any developed reasons to back them up. Kris: It can’t be flat. If you just let me explain . . . Bart: There’s nothing to explain. All you have to do is use your eyes. Kris: I am using my eyes, and they tell me the Earth is round. 2.3 Argument 29

However, it would be wrong to think that of belief or opinion. An argument that the Earth the two meanings of ‘argument’ are completely is not flat makes practical sense only if divorced from one another. As stated at the someone – past or present – thinks that it is beginning of the chapter, arguments typically flat, or needs proof that it is. exist to persuade, and it is clear that in a dispute like [2] each of the participants is trying to Evaluating argument change the mind of the other. In [1] there is no context given, but the argument being made is We have seen then that an argument is a obviously aimed at some real or imagined complex claim, made up of simpler claims – opposition. Why else would its author feel any the reasons (premises) and the conclusion. It need to give reasons to support the claim? You is a good argument if the reason or reasons don’t hear people nowadays arguing that the justify the conclusion. It is a poor argument if Earth is spherical, because it is no longer they do not. Evaluating argument means disputed. Arguments of the first kind occur distinguishing good ones from bad ones. typically when some opposition to the Much of the content of this book is about the conclusion has been expressed or is anticipated. critical evaluation of reasoned argument. But here is a taste of what it is like. Conversely, most arguments of the second kind have some elements of reason-giving in Activity them. Even in [2], which is predominantly a quarrel, both men are arguing on the grounds We have established that [3] is a weak of what they claim to see – the evidence of argument; a bad one. Compare it with [1]: their senses. the argument that since ships appear to sink out of sight as they sail away, the Earth Bart: Anyone can see the Earth is flat. cannot be flat. Is [1] a good argument, or Kris: . . . my eyes . . . tell me the Earth is not? Would it persuade you that the Earth’s surface was curved if you had previously round. believed it was flat? If we wanted to interpret Bart’s words as an Commentary argument, we could write it as follows: Argument [1] might seem like a strong argument now, because we already accept that [3] The Earth looks flat (to me); therefore it the Earth is not flat. But, as we also know from is flat. history, arguments like [1] were not enough to convince the general public straight away. You may not think much of this argument now People needed more reasons if they were because you happen to know that, because of going to give up a belief that had persisted for the size of the Earth, appearances are centuries. Judged critically it becomes clear misleading. The Earth does look flat. Therefore that [1] is no better than [3], because [1] also the premise of [3] is true; but the conclusion is argues from appearances. If the flat not. So the conclusion does not follow from the appearance of the Earth does not mean that it reason. [3] is an argument, but it is a bad one. is flat, then surely the appearance of ships sinking does not prove that they are dropping In some textbooks the impression is given out of sight; nor that the curvature of the that critical thinking is concerned only with Earth is the cause of this appearance. It could arguments of type [1], and not with argument be some kind of optical illusion; a kind of in the sense of dispute. But for reasons just mirage perhaps. It isn’t a mirage: it is perfectly given, we cannot understand the full meaning and purpose of arguments if we ignore their most obvious context. Much of our reasoning – perhaps all of it – arises in or from differences 30 Unit 2 Critical thinking: the basics

true both that ships appear to sink and that Obviously [4] is a much stronger argument the Earth’s curvature is the reason. But we than [1]. Whether it actually convinces its know that now independently of the argument. audience will still depend on their willingness The single reason given in [1] does not, on its to accept the evidence. But if they understand own, establish its conclusion. and believe the claims you are making, then it would be irrational of them not to accept More reasons the conclusion also. For an effective argument we usually need more Of course, the ‘if’ is a big one. In all than one reason. Imagine you were sent back in probability the audience from that time would time several hundred years and had to convince not accept your claims because they would not people that the Earth was not flat. What would understand them. What could pictures from you take with you: pictures from space; stories space mean to a 14th-century fisherman? They of people who have sailed round the world? would lock you up – or worse – and carry on These would seem like a good start. Armed with believing what they had always believed and such evidence, you could supplement [1] and could see with their own eyes: a flat Earth thereby make it stronger, for example: surrounded by flat sea. [4] Ships appear to sink lower and lower the This is why ‘claim’ is the right word for the further they are from land. But they statements that appear in arguments. Some of cannot actually be sinking, or they would the claims made in an argument may be not come back. Also, sailors have proved known facts, but others may be forecasts, that if you set off in one general direction, suggestions, beliefs or opinions. Claims may for example east or west, and keep going, also be false. It is perfectly possible to construct you eventually arrive back where you an argument from false claims, either out of started from. These facts show that the ignorance, or out of deceit. (That is probably Earth cannot be flat. Besides, what people hundreds of years ago would have photographs have been taken from space suspected you of doing, as they slammed the that show the Earth’s curvature. dungeon door.) Here four reasons are given in support of the This point is important in understanding conclusion. The conclusion is introduced by what argument is. An argument presents the phrase: ‘These facts show that’, another reasons and a conclusion. It does not way of saying ‘so’. Three of the reasons are guarantee that either the reasons or the given first; then the conclusion; then a conclusion are true. It is still an argument even further, seemingly indisputable, reason. So if the claims in it turn out to be false. the structure of the argument is as follows: Grammatical note Ships appear to sink as they sail away. It was noted in Chapter 2.1 that claims can They can’t actually be sinking or they wouldn’t sometimes take the form of rhetorical come back. questions, or other sentence types: Ships sail in one direction but return to their imperatives, or exclamations. When starting point. reconstructing an argument in which one or P ictures from space show the curvature of the more of the sentences is not a declarative Earth. sentence, but is making a claim nonetheless, it is good practice to transform it into a The Earth cannot be flat. grammatical statement. 2.3 Argument 31

Summary • A good argument is one in which the conclusion follows from the premises, • An argument is a complex construction meaning that if the premises are true then in which one sentence, the conclusion, is the conclusion should be true too, because claimed to follow from another (or others) of the truth of the premises. (But there is a which are reasons. lot more to be said about this point in later chapters.) • A more technical word for a reason, in the context of an argument, is ‘premise’. In this book both terms are used, and have the same meaning unless otherwise stated. End-of-chapter assignments 1 Think of a suitable conclusion that you 2 Think of one or two reasons that could be could add to the following to make it into used to support the following viewpoints, an argument: and use them to construct arguments: P olice forces the world over face a a It is wrong to charge foreign students dilemma. On top of dealing with higher fees than other students. murders and other major incidents, they have to divide their limited time b Private cars with fewer than four and finite resources between tackling occupants should be banned from city minor crimes such as shoplifting and centres. street robbery, and traffic offences such as speeding or careless driving. Of c The stars of football, baseball and other course, the consequences of speeding popular sports deserve every cent of can be as bad as or worse than the theft the millions that they are paid. of a wallet or a mobile phone. They can be fatal. But there is a big difference of 3 Find a short argument published in a another sort. The thief intends to do newspaper or magazine or on the internet. harm and to deprive people of their Copy it down and underline its conclusion. rightful property, whereas any harm that is done by a car-driver, however 4 Write a short argument of your own serious, is usually accidental. consisting of two or three reasons and a conclusion that they support. Answers and comments are on page 311. 32 Unit 2 Critical thinking: the basics

2.4 Identifying arguments Before an argument can be reconstructed and/ often it is left to the reader to interpret how a or evaluated it must first be established that it text is best understood. is an argument. This can be harder than it sounds, especially if the argument is a poor For example, it is not an argument to say: one. In a good argument the conclusion follows from the reasons. In a bad argument it [1] Photographs from space show the does not follow: the reasons do not justify the Earth’s surface as curved. The curvature conclusion. It is this which makes it a bad does not show when a photograph is argument. But how bad does an argument taken from ground level. have to be before we decide that it is not an argument at all? Establishing that some piece How we can establish that [1] is not an of text is an argument may come down to argument is by asking if either of the two deciding whether or not the author meant or claims supports the other, or states a reason intended one of the claims to be a conclusion, for accepting the other. Despite what was and the others to be reasons. Judging an said just now about indicators, a partial test author’s intention, from a text alone, is not a can be applied by inserting ‘therefore’ or ‘so’ very exact science! between the sentences and asking: Does it make sense? If it doesn’t make sense, then Matters are made easier if the conclusion or there is no argument – although the converse reasons are marked by indicators such as does not necessarily apply. Here is the test ‘therefore’, ‘so’, ‘since’ and ‘because’. However, applied to [1]: these connectives have other functions in the language beside signalling argument. They [1a] Photographs from space show the occur frequently, for example, in explanations Earth’s surface as curved. Therefore the (see Chapter 4.2). Just finding two sentences curvature does not show when a joined by ‘so’ or ‘since’ does not automatically photograph is taken from ground level. identify a reasoned argument. Think of the words of the rock ballad: [1b] The curvature does not show when a photograph is taken from ground level, But since you’ve been gone so photographs from space show the I can breathe for the first time . . . Earth’s surface as curved. There is no argument here. ‘Since’ in the song Neither of these makes sense. So [1] is not an means ‘ever since’, which is different from the argument. meaning it has in front of a premise. The same test can be applied to the next Besides, as stated in Chapter 2.3, there are example, only as there are more claims there plenty of examples of natural-language will be more rearrangements to try out. arguments which contain no connectives. An argument may just be conveyed by a pair or [2] Completed tax forms and payments sequence of sentences. Obviously not every must be received by 31 July. Late sequence of sentences is an argument. All too payment may result in a fine not exceeding $100. Your payment did not reach the tax office until 12 August. 2.4 Identifying arguments 33

There are three possible candidates for the went missing when she was in the conclusion of [2], if there is one. So, applying building on her own. the test, we have these possibilities: [5] You are likely to get a fine. Completed tax forms and [2a] Completed tax forms and payments must payments must be received by 31 be received by 31 July. Late payment July and people who miss the may result in a fine not exceeding $100. deadline are usually fined $100. Therefore your payment did not reach the Your payment did not reach the tax office until 12 August. tax office until 12 August. [6] From the 15th century European [2b] Late payment may result in a fine not sailors reached the lands of the east exceeding $100. Your payment did not by sailing west. Those who sailed reach the tax office until 12 August. So on and survived eventually arrived completed tax forms and payments back in Europe. When they must be received by 31 July. claimed they had sailed around the world, few people believed them. [2c] Completed tax forms and payments [7] There are only three possible causes must be received by 31 July. Your of the leak in your system: the pump payment did not reach the tax office could be worn, a hose could be split until 12 August. Therefore late payment or one of the connections could be may result in a fine not exceeding $100. loose. I’ve checked the hoses and tightened all the connections, but In each rearrangement the attempt to use an the machine still leaks. argument indicator sounds unnatural, which indicates that none of the sentences is the kind of claim that could follow from the others in the way that a conclusion follows from reasons. Activity Commentary [3] is an argument. The conclusion, which is Using the ‘therefore/so’ test, and the at the end, is a recommendation. This also is a definition of an argument as reasons and a useful clue: recommendations are often conclusion, decide which of the following accompanied by reasons. Here there are two: could be interpreted as arguments. the time of the train’s departure and the possibility of a 40-minute journey to the For those that are arguments, identify the station. If they are both true, then clearly they conclusion and note what kind of claim it is. justify the conclusion. Lastly, discuss how well supported the [4] is also an argument. The conclusion is a conclusion is, given the reasons. prediction that the police will (definitely) suspect Raisa, firstly because she is the only [3] The Tokyo train leaves at 4.24. It key-holder, and secondly because she was can take up to 40 minutes to get to alone in the building. The argument is the station if the traffic is bad. We perhaps not quite as solid as [3]. Do police should leave for the station by 3.40. always treat people as suspects in these circumstances? The words ‘bound to . . .’ make [4] Raisa is the only person with a key the conclusion a very strong claim. Even if to the safe. The police are bound to both premises are true, there may be other treat her as a suspect. The money 34 Unit 2 Critical thinking: the basics

factors – CCTV footage for instance – that Who wants an argument? show Raisa was nowhere near the safe, and therefore make it less than definite that she In the last unit we discussed arguments in will be treated as a suspect. dialogue form, as well as single arguments. Read the following passage – preferably aloud [5], too, is an argument. The conclusion is with a partner, taking a part each – and then another prediction (of sorts). You could also answer the question that follows. have described it as a statement of probability: ‘You are likely to get a fine.’ The reasoning for SCENE: a table for two in a restaurant the conclusion is that payment did not reach Anita: What are you going to have? the tax office until 12 August, together with (Sound of a mobile phone) the second sentence which establishes that the Bara: Just a minute. I’ve got a message. payment was late and that late payment Anita: Not another! usually results in a fine. The argument is quite Bara: I need to answer it. sound, mainly because the conclusion is a Anita: Why don’t you just switch it off? fairly weak claim. If fines are usual for lateness, then a fine is likely. If the claim had been that Restaurants are places for the person would get a fine, the reasons would conversation. They’re so antisocial, not be adequate. those things. Bara (texting at the same time): [6] is not an argument. None of the three You wouldn’t say that if you had one. sentences makes sense with ‘therefore’ in front You’d be on it all the time. of it, e.g. ‘From the 15th century European Anita: I wouldn’t have one as a gift. sailors reached the lands of the east by sailing Bara: Yes, you would. I’ll give you my old west. Those who sailed on and survived one. eventually arrived back in Europe. Therefore Anita: Keep it. I’m better off without it. In when they claimed they had sailed around the fact the whole world would be better world, few people believed them.’ The off if the wretched things had never connective that makes most sense is ‘but’, not been invented. ‘therefore’. None of the claims is a conclusion Bara: How do you work that out? drawn from either or both of the other two; Anita: Well for a start, you can’t sit and it is the same whichever order the claims anywhere quietly any more without are placed in. having to listen to one end of someone else’s shouted [7] is not an argument either – at least not conversation. Secondly, they’re a an explicit one – because, like [6], none of its health risk because they pour out actual sentences is a natural conclusion. microwaves that cook your brain. However, [7] does point towards a conclusion, Thirdly, they distract drivers and even though it is not stated. In fact there is cause road accidents. So, like I said: really only one conclusion that you could they do more harm than good. draw from [7] – that the pump must be Bara: You just can’t say that. No one worn – because both the other possibilities are thinks they are a health risk any ruled out. What we can say about [7] is that it more. They don’t distract drivers is not complete. It is left to you (the reader or unless the drivers are stupid enough listener) to draw a conclusion – though in this to have them switched on in the car. case it leaves you in little doubt as to what the Not everybody shouts into their conclusion should be. We could say therefore phones, and not everyone finds that [7] is an implicit argument, or that it has them irritating. They help people to an implicit conclusion. 2.4 Identifying arguments 35

keep in touch. They save lives in Commentary emergencies. They access Overall, this conversation is a quarrel, and information when you need it. What parts of it are no more than exchanges of more do you want? opinion, laced with mild insults. But in the Anita (shouting): course of the exchange there are examples of I’m sorry, but people do shout into developed argument as well, coming from them. They don’t even know they’re both sides. doing it. And they do use them when they’re driving, whatever the law The clearest example is Anita’s first long does to stop them. If someone paragraph. This is practically a standard smashed into you because she was argument, with three numbered reasons and a reading a text message, you would conclusion signalled by ‘so’. Bara responds soon change your tune. with a counter-argument. This gives three Bara: Hang on, you’re blaming an reasons which challenge or contradict Anita’s inanimate object for what people do claims, then two further reasons (the value of with it. Of course there are always keeping people in touch, and of saving lives some idiots who misuse stuff. It’s in emergencies) to support a position which is like guns, isn’t it? Guns don’t kill, it’s the complete opposite of Anita’s. Bara’s the people who fire the guns. You’re conclusion is expressed by the first sentence making the same mistake. of the paragraph: ‘You just can’t say that.’ In Anita: I’m not making a mistake. The other words: ‘It is not true that mobile phones machines are to blame. I agree, a do more harm than good,’ (as Anita has just gun can’t kill you until someone fires asserted). In natural-language arguments, it, but you can’t get shot either if conclusions may not always be spelled out in there are no guns to do it with. And full, as they are in a standard argument. people couldn’t be distracted by Expressions such as ‘Yes’, ‘No’, ‘You’re wrong!’ their phones when they’re driving if can be understood as conclusions if it is clear there were no mobile phones. And what they refer to and they are supported you wouldn’t still be sending that by reasons. text and spoiling our lunch. Bara: That’s just silly. You’ve lost that one. In the three paragraphs that follow we see Anita: No I haven’t. Anita and Bara each trying to reinforce their Bara: You have. You’re just old-fashioned, arguments with further reasons and so you can’t see the value of the objections. Then, as their tempers begin to new technology. fray, they go back to mere quarrelling and Anita: I’m not old-fash– personal remarks. Bara: Be quiet, and let me finish this message. I’ll be quicker if you just Summary stop talking. • We have considered ways of identifying Activity arguments using argument indicators. Is the conversation above just a quarrel, or is • The difference between a reasoned there reasoned argument going on here as argument and a mere quarrel has been well? If there is, identify some examples. established. • We have seen examples of arguments in the context of a dialogue. 36 Unit 2 Critical thinking: the basics

End-of-chapter assignments 1 Out of the following passages, only one is C If more cash machines start making an argument. Which is it, and how can it be a fixed charge for each withdrawal, recognised as an argument? Why are the people who draw small amounts others not arguments? will pay more in the long run than those who make larger but fewer A Since the last earthquake in withdrawals. People with low California, engineers have been incomes tend to make smaller investigating what happens to withdrawals, but are more willing man-made structures during a large to look for machines that don’t seismic event. They were surprised charge. that a section of the Bay Bridge, which connects Oakland to San For questions 2 and 3 return to the dialogue Francisco, fell like a trapdoor. They between Anita and Bara. also discovered that in some of the 2 Look back at the dialogue on pages 35–6 older double-decker freeways the joints that connect the lower and find the paragraph that begins: ‘I’m not column to the upper column may making a mistake . . .’ Is it an argument, be suspect. and if so, what is its conclusion? 3 Who do you think ‘wins’ the argument: B The public should not expect the Anita or Bara? Give reasons for your safety of drugs to be guaranteed by judgement. animal testing. Aspirin, which is a Note that this is an entirely open question: safe and effective painkiller for most it is for you to choose which criteria to use humans, is fatal to the domestic cat. in making your judgement, but you must Penicillin poisons guinea pigs. say what they are. These examples show that different species react to drugs differently. Answers and comments are on pages 311–12. 2.4 Identifying arguments 37

2.5 Analysing arguments In Chapter 2.3 you were introduced to the idea Getting it right of a standard form of argument. In natural language an argument can be expressed in Before you can respond critically to an many different ways. Standard form shows argument, by evaluating it or by challenging it what the underlying argument is. If a text with a counter-argument, you need to have a cannot be reduced to a standard form of clear and accurate interpretation, or analysis, of argument, we have to question whether it what the reasoning is. It is no good challenging really is an argument. an argument if you have misunderstood or misrepresented it. That is known as attacking a In critical thinking we use the same basic ‘straw man’ (from the stuffed sacks that soldiers way of formalising arguments as logicians and archers once used for target practice). have used for many centuries: we list the reasons (or premises), and then the What analysis entails is identifying the conclusion. If we use R for ‘reason’ and C for parts of the argument and recognising how ‘conclusion’ we can say that all arguments they relate to each other, especially how the have the form: reasons relate to the conclusion. One convenient way to do this is to reconstruct R1, R2, . . . Rn / C the argument in a standard form. The reasons and conclusion in a standard The simplest kinds of argument have one or argument are all claims. In theory there is no two reasons followed by the conclusion, and no limit to the number of reasons that can be other content besides these. In practice such given for a conclusion. In practice the number arguments don’t really need analysing, as their is usually between one and half-a-dozen. structure is plain enough already. However, we will start with simple examples and build up to The relation between the reasons and more complex, less obvious ones later. conclusion of standard argument is roughly equivalent to the phrase ‘so’, or ‘. . . and so . . .’, Activity which is why inserting ‘so’ or ‘therefore’ into the text is a clue – though not an infallible Here is an example of everyday reasoning, one. What the whole argument states is that which someone might use to persuade R1, R2, etc. are true; and that C follows from another to hurry. them. Or that because R1, R2, etc. are true, C must be true as well. [1] The train doesn’t leave until 4.24, but it can take up to 40 minutes to Another way to say this is that C is true as get to the station, if the traffic’s bad. a consequence of R1, R2, etc. being true. It’s 3.30 now. We need to leave for the station within ten minutes to be Still another way is to say that C can be sure of catching the train. inferred from R1, R2, etc. (Note that it is not correct to say ‘R1, R2, etc. infer C.’ Inferences How would this argument look in standard are always from one or more claims to form? another.) 38 Unit 2 Critical thinking: the basics

Commentary If the next train would do just as well, then The prime purpose of analysis is to identify there is no need to set off within ten minutes. each of the claims that comprise the argument Where possible, analysis abbreviates a text, but and to separate the reasons from the nothing essential can be left out. Sometimes conclusion. Since there are three main for clarification purposes an analysis may even reasons, we can label them R1 to R3, and the need to add explanatory detail. conclusion we can label C: How reasons relate to a conclusion R1 The train leaves at 4.24. R2 It can take 40 minutes to get to the There is more to analysis, even of simple arguments like [1], than simply listing station. premises. We also need to know how the R3 It’s 3.30 now. premises operate in supporting the conclusion. C We need to set off within ten minutes to In some arguments the reasons function be sure of catching the train. independently of one another, each giving support to the conclusion in its own right. If (You can use ‘P’ for premise to replace ‘R’ one premise is taken out, or found to be false, if you prefer.) it doesn’t fatally affect the argument because the other, or others, may still be sufficient. The Notice that in [1] there is no argument argument may be a little weaker for the loss of indicator, such as ‘therefore’, ‘so’ or ‘because’. a premise; but like a plane with two or more That is because none is needed. It is obvious engines, the failure of one does not necessarily which of the claims is the conclusion: it is knock it out of the sky. because of R1, R2 and R3 that the speaker claims C, not the other way round. There are other structures, however, in which the reasons work together in support of Also notice that there are more claims in [1] the conclusion. They are interdependent. This is than there are sentences. The first two reasons more than just an interesting detail. It is an are connected by ‘but’ to form a single important factor when we come to evaluation. compound sentence. Part of the job of analysis In an argument with interdependent premises, is to identify each of the individual claims. So, both or all of them are necessary for the in standard form, these need to be listed conclusion to follow. If one is omitted, or found separately. Logically ‘but’ means the same as to be false, the conclusion cannot be inferred ‘and’ in that both R1 and R2 have to be true from the other (or others) on their own. for the whole compound sentence to be true. ‘But’ has a different meaning from ‘and’ in the In [1] the reasons are interdependent. It is natural-language version. But as far as the the train time together with the time it can take reasoning is concerned all that matters is that to get to the station and the time it is now the train leaves at 4.24 and that the journey that justifies the conclusion. If any of these can take 40 minutes. Nor does it really matter three reasons turned out to be unwarranted, to the argument why the journey to the station then the argument would fail. For example, if sometimes takes 40 minutes: it is sufficient the train were not due until 5.24, then the that it sometimes does. So, when you are other two, on their own, would not establish analysing an argument, it may not be the need for setting off at 3.40. Or if R2 was necessary to include every detail. an exaggeration, and it never took 40 minutes to get to the station, leaving in ten minutes On the other hand, not all detail is would not be necessary. The remaining extraneous: some is essential. For example, the premises would be true, but the conclusion conclusion of [1] is incomplete without the phrase: ‘. . . to be sure of catching the train’. 2.5 Analysing arguments 39

would not follow from them. (If you want to Commentary check this, try crossing out each of the The conclusion is the first sentence. It is premises in turn and see the effect it has on followed by three supporting claims. So in the argument.) standard form the reasoning is as follows: Structure R1 Flying is responsible for ten times the carbon emissions of rail travel. The structure of argument [1] can be represented diagrammatically, for example R2 Flying is twice as stressful (as rail like this: travel). R1 & R2 & R3 C R3 Trains take you to the heart of a city, not to some far-flung airport. The single arrow shows that it is the combination of all three premises that leads to  the conclusion. C Rail travel makes a lot more sense than In comparison, look at the next argument. short-range flights. [2] Short-range flights may have become So far [1] and [2] look to have quite similar cheap, but rail travel makes a lot more shapes: three premises, one conclusion. But sense. Flying is responsible for ten there the similarity ends. In the case of [2] times the carbon emissions of rail travel there is no interdependence between the per passenger/km, and twice as much premises. Each offers a separate line of stress. What is more, trains take you to reasoning to the conclusion. In the case of R3, the heart of a city, not to some far-flung for instance, the inference that rail travel airport. makes more sense is made on the grounds that trains take passengers right into a city centre, Get there unlike planes. (Actually, this is not always the for a bus fare case, but it is what the author claims.) True or with Noisyjet not, R3 does not rely on the truth of either of the other two premises, nor they on it. So, even if you decide that R3 is not a justified reason, you can still argue that rail travel makes more sense on the basis of lower emissions (R1) and less stress (R2). So, if you wanted to represent the structure of [2] in a diagram, you would need three separate arrows for the three independent reasons. For example: R1 R2 R3 Activity C Rewrite [2] in standard form, and comment Indeed, there are grounds for analysing [2] as on the structure of the reasoning. three arguments, rather than just one. All three share the same conclusion, but each one is a separate line of reasoning. 40 Unit 2 Critical thinking: the basics

Note that the first part-sentence, ‘Short- R3 The news is all round the college. range flights may have become cheap’, is not a R4 Rajinder spread a story that I told him reason. In fact it is not part of the argument at all. The fact that flying may be cheaper would, in confidence. if anything, be a reason for choosing to fly, so obviously it does not support the conclusion. C Rajinder cannot be trusted to keep What it does is show why an argument is needed. The author is saying: ‘OK, there may a secret. be a financial reason for going by air, but look at these other reasons for travelling by train.’ The first three reasons depend on each other. In other words, this opening clause puts the Obviously, if I had told several people, or if whole argument into the context of a others had known besides Rajinder, it might potential debate: ‘Which is better: plane or not have been Rajinder who was to blame; and train?’ if the news hadn’t spread there would be no reason to suggest Rajinder had told anyone the Mixed arguments secret. R4, on the other hand, does not have to be true for the conclusion to follow from the In arguments with more than two premises other three. Therefore, although R4 adds there may be some that function strength to the argument, it is separate from independently, and others that combine forces. the other reasons: an additional reason for inferring that Rajinder cannot be trusted. Activity As a diagram: Try rewriting the following argument in standard form, and explaining its structure in R1 & R2 & R3 words or by means of a diagram: R4 C [3] Rajinder cannot be trusted to keep a secret. He was the only person apart Don’t worry if you have structured the from me who knew about Jed and sentences a little differently. For example, Jill getting engaged. I haven’t said a some people might prefer to treat R4 as two word to anyone, yet now the news is reasons: Rajinder spread the story; and R5, I all round the college. And he spread told it to him in confidence. These two reasons another story about Jill that I told would of course be dependent on each other, him in confidence. so the alternative analysis would be: Commentary R1 & R2 & R3 Once again the first sentence is the conclusion, but this time it is supported by R4 & R5 C four or five reasons (depending on how you choose to analyse them). You will find, as you work on more complex arguments, that there can be some differences R1 Rajinder was the only person apart from in the way an argument is analysed. That is me who knew about Jed and Jill getting engaged. R2 I haven’t told anyone. 2.5 Analysing arguments 41

because analysis is a form of interpretation, Summary and different interpretations can be found for the same text. The more complex the text, • We have looked at the workings of some the more room there is for differing relatively simple arguments, and suggested interpretations. some ways of analysing and interpreting them, by identifying the reason(s) and the So, if your way of reconstructing an conclusion, and explaining the structure. argument is not exactly the same as the one suggested in the book, this won’t necessarily • Reasons (premises) can operate mean that yours is wrong. What is important in combination with each other, or is that you recognise the conclusion and the independently. main reasons, and that you are satisfied that you understand the argument and can explain • Some parts of a text may not belong to the it clearly. Analysis helps you to be clear, but it actual argument. should not be a straitjacket. End-of-chapter assignment huge for those who reach the top that the risk will always seem worth taking. Analyse the following arguments using the c No sport should be allowed in which the methods discussed in this unit. prime object is to injure an opponent. Nor should any sport be allowed in which a People shouldn’t be fooled into buying the spectators enjoy seeing competitors bottled mineral water. It’s meant to be inflict physical harm on each other. On safe but there have been several health that score, boxing should be one of the alerts about chemicals found in some first sports to be outlawed. What boxers brands. It costs silly money, and anyway have to do, in order to win matches, is to tap water, which is free, is just as good. batter their opponents senseless in front of large, bloodthirsty crowds. b It is inevitable that every year some athletes will give in to the temptation of Answers and comments are on page 312. taking performance-enhancing drugs. At the highest levels of sport, drugs can make the difference between winning gold and winning nothing. The rewards are so 42 Unit 2 Critical thinking: the basics

2.6 Complex arguments In the last chapter we saw how reasons – Here is an example: independently or in combination – support a conclusion. In every case there was just one [1] In some parts of the world, cars are still conclusion. driven on the left side of the road. This can result in accidents involving drivers But in some arguments there may be more from other countries who are used to than one conclusion. One or more of the traffic being on the right. Pedestrians reasons may lead to an intermediate are also at risk from looking the wrong conclusion, which then leads on to a main or way before crossing the roads. Cities final conclusion. Intermediate conclusions would be safer, therefore, if in all together with their supporting reasons form countries the rule were the same. Since sub-arguments. There may be two or more countries where the drivers keep to the sub-arguments within the larger argument. left are in a minority, those countries should change over to the right. 2.6 Complex arguments 43

Activity distinction between sub-arguments and main arguments – is very important, as you will see Identify the two argument indicators in [1], when we come to evaluating this argument and use them to give an analysis of the and asking whether the reasoning does argument. adequately support its conclusions. Commentary Background information; context With the help of the two connectives, ‘therefore’ and ‘since’, you will have had no You may also have wondered what to do with difficulty identifying two conclusions: the first sentence: ‘In some parts of the world, cars are still driven on the left . . .’ You possibly C1 Cities would be safer if in all countries listed it as a reason. This is not exactly wrong; the rule were the same. in one sense it is because there are some drive-on-the-left countries that there are C2 Countries where drivers keep to the left accidents. But there is another way to look at should change over to the right. this which also makes good sense. The first sentence can be understood as the background The first of these, C1, is drawn from two information, or context, for the argument. It is reasons (or premises): because of the diversity of traffic rules that there is an argument to be had. R1 Driving on the left can cause accidents involving drivers from other countries. Neither interpretation would make your analysis wrong; nor would it make any R2 Pedestrians are also at risk from looking difference to an assessment of the success or the wrong way. failure of the argument. In the interpretation that follows we have chosen to call the first The second conclusion then follows from the sentence ‘context’; but if you prefer to call it a first, making a two-stage argument from R1 reason, you can amend the analysis yourself. and R2 to C1; and from C1 to C2. As stated in the previous chapter, there is often room for different interpretations. As long as To put it another way, we have a sub- you can justify your analysis, and it makes argument – (R1 & R2) → C1 – and a main good sense of the text, you are entitled to give argument, C1 → C2. This means that C1 a different slant. functions as both a conclusion (of one argument) and a premise (of the other). Hence A full analysis we call C1 the intermediate conclusion (IC), and C2 the main conclusion (MC – or just C). Context: In some parts of the world, cars are still driven on the left. However, you may have noticed that within R1 Driving on the left can cause the final sentence there is another reason that directly supports the main conclusion, namely accidents involving drivers from that countries where drivers keep to the left other countries. are in the minority. As this is a premise we can R2 Pedestrians are also at risk from call it R3. looking the wrong way.  What would you say if you were asked C1 (IC) Cities would be safer if in all whether R1 and R2 count as reasons for the countries the rule were the same. main conclusion? Strictly speaking they are R3 Countries where drivers keep to the not: they are reasons for the intermediate left are in a minority. conclusion, and support the main conclusion  only indirectly. C1 is a direct reason for the main conclusion. So is R3. This distinction between direct and indirect reasons – like the 44 Unit 2 Critical thinking: the basics