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How To Think

Critical Reasoning

Marianne Talbot tells us how to use the ultimate in transferrable skills.

My mug is sitting to my right doing nothing. This is because it believes it is at the centre of the universe, and its desire to be at the centre of the universe is stronger than any of its other desires.

I expect you’ll reject this explanation of the behaviour of my mug. Why, you might ask, should we ever think the mug is acting for reasons?

This is a good question. A human with this belief and this desire might have a reason to sit and do nothing; but a mug?

We might, of course, say a human with this belief and desire is irrational – that their reasons are bad ones. What makes them believe they are at the centre of the universe? Why do they wantto be at the centre of the universe? Why do they want this more than anything else? Weird. But we’d have no problem believing such a person is acting for reasons; no problem with their being rational. In fact it is this possibility that makes it possible for them to be irrational. The mug, however, isn’t irrational: it is non-rational. It doesn’t act for reasons, good or bad. Only rational things can be irrational; only things that can act for reasons can act for bad reasons.

Aristotle thought human beings were the only rational animals. Without joining this debate we can certainly say that reason is central for human beings. Without reason all our decisions would be simple reactions to experience, or to memories of experiences. Not having reason means we would never reflect on our experience; for instance, ask ourselves, ‘Well, if this is the case, and that is the case, might it be the case quite generally that if this then that?’ But not only can we pose such questions, our capacity for reason means we can also try, by means of argument or reason-designed experiment, to answer them.

The human capacity for reason is a species characteristic. It will develop in an individual human so long as that individual develops normally. It will develop as the individual acquires a language. It is interesting, in fact, to speculate how the two capacities are linked. Would reason be possible without language? Would language be possible without reason? What do you think?

The Attempt To Describe How To Reason Well

As with any of our natural capacities, attempts have been made to develop a theory of reasoning. This theory is called logical theory. Logical theory is normative, meaning it sets standards, tells us whether we are reasoning well or badly. And as with any theory of a practical capacity, theory and practice interact: we observe practice in order to develop the theory, then we use the theory to improve the practice.

Anyone can improve their capacity to reason by learning some logic. My experience has been that a lot of people are interested in improving their ability to reason. Given the centrality of reason to human life, this isn’t surprising.

Recognising Arguments

Probably the first thing you’ll learn on any critical reasoning course is how to recognize an argument. You might think this is easy. But it is amazing how many people think the following is an argument:

1) If she is a trained soprano then she will be able to reach top A

But this isn’t an argument, it’s a sentence. To be precise it is a conditional sentence: it has an ‘if’ clause, and a ‘then’ clause.

Arguments are constituted of at least two sentences. One of these sentences must be a claim being made (the conclusion). The other(s) must be reasons for making that claim (the premises). Our sentence is certainly constituted of two sentences (‘she is a soprano’ and ‘she will be able to reach top A’), together with the logical words ‘if’ and ‘then’; but these constituent sentences are not related as they would have to be in order for them to be an argument. Think about it: if someone were to assert this complex sentence, would they be claiming that either of the constituent sentences is true? Is either of these sentences a conclusion for which a premise is offered in support? Are they claiming that she is a trained soprano? Or that she is able to reach top A?

The answer is no. A person uttering sentence 1) is not asserting either of the constituent sentences. They are asserting only the whole complex sentence. They are saying that if she is a soprano, then she will be able to reach top A. They are not saying that she is a soprano, nor offering in support of such a claim the fact that she can reach top A.

Offering a conditional assertion and making an argument are two quite different things we do with language. Someone studying critical reasoning must learn that, and why, they are distinct.

Analysing Arguments

Having learned how to recognize an argument, our trainee critical thinker needs to learn how to analyse arguments: how to identify the parts of an argument – the conclusion and the premises. Here, for example, is the sort of thing you might read in your morning newspaper:

“Thankfully life can only get better. Agricultural yields are rising, thanks to new technology, and people are getting richer, thanks to globalisation and better communication. If people get richer the population will decrease and the world will get less crowded. There will be more wild places if agricultural yields rise, because we’ll need less land. If the world is less crowded and there are more wild places then life can only get better.”
(Adapted from Matt Ridley in The Times, 12th September 2013)

There is an argument in here, but evaluating it as it stands is difficult. This is because the argument is hedged around with expressions of emotion (‘thankfully’) and claims intended to support the premises of the argument (‘thanks to new technology’, ‘thanks to globalization and better communication’) and emphases (‘and the world will get less crowded’).

In analysing an argument we get rid of everything extraneous to the argument, thereby revealing its logical structure. This argument, once analysed, becomes:

Argument One
Premise one: Agricultural yields are rising
Premise two: People are getting richer
Premise three: If people get richer the population will decrease
Premise four: If agricultural yields rise there will be more wild places
Premise five: If there are more wild places and the population decreases then life will get better
Conclusion: Life will get better

I hope you’ll agree that what is being asserted, and the reasons for asserting it, are much clearer now the argument is set out ‘logic-book style’.

Evaluating Arguments

Possibly the thing you’ll be most interested in if you are interested in learning how to reason critically is how to evaluate arguments; how to tell whether arguments are good or bad. You might already have decided whether or not the previous argument is a good argument. But on the basis of what have you decided?

Not, I hope, on the basis of your belief that the conclusion is true or false. The truth or falsehood of its conclusion is no guide to how good an argument is. There are good arguments with false conclusions, and there are bad arguments with true conclusions.

Here is a good argument with a false conclusion:

Argument Two
Premise one: Whales are fish
Premise two: All fish have scales
Conclusion: Whales have scales

This is a good argument because if the premises were true the conclusion would have to be true. The truth of these premises would entail the truth of the conclusion: if the premises were true the conclusion couldn’t be false. However, the premises are not true.

And here is a bad argument with a true conclusion:

Argument Three
Premise one: If whales have scales then whales are fish
Premise two: Whales do not have scales
Conclusion: Whales are not fish

This is a bad argument because the premises could both be true yet the conclusion false. The conclusion does not follow from the premises: whales could be scaleless fish. The conclusion is true – but we’d better not believe it on the basis of this argument.

Following From

You might want to protest that Argument Two can’t be a good argument. You might ask, “The premises of this argument are false, so how can the argument be good?” But an argument’s being good or bad no more depends on the truth or falsehood of the premises than it does on the truth or falsehood of the conclusion. There are good arguments with false premises. And there are bad arguments with true premises.

Here is a good argument with false premises (and a true conclusion):

Argument Four
Premise one: All fish have lungs
Premise two: Whales are fish
Conclusion: Whales have lungs

This is a good argument, despite the fact that both its premises are false, because the conclusion follows from the premises: if the premises were true the conclusion would have to be true.

And here is a bad argument with true premises (and a true conclusion):

Argument Five
Premise one: All cats meow
Premise two: The Queen’s corgi is not a cat
Conclusion: The Queen’s corgi doesn’t meow

This is a bad argument, despite the fact its premises are both true and its conclusion is true. It is a bad argument because the conclusion does not follow from the premises. The truth of the conclusion is not guaranteed by the truth of the premises: the corgi might still meow despite not being a cat.

For an argument to be good, the only thing that matters is whether its conclusion follows from its premises. The actual truth-values of its premises and conclusion are irrelevant. A good argument is such that if its premises are true its conclusion must be true (or as we’ll see below, probably true).

Soundness

If you thought the truth-value of the premises must be important for evaluating an argument, you are not wrong. We want our arguments to be good, such that their conclusion follows from their premises; but we also want them to be sound, meaning that their premises are true, and their conclusions follows from their premises.

We cannot logically require soundness of an argument. We often don’t know, after all, whether our premises are true or false. And sometimes their truth is a matter of dispute. Take the following argument:

Argument Six
Premise one: Killing human beings is wrong
Premise two: Therapeutic cloning involves killing human beings
Conclusion: Therapeutic cloning is wrong

This is a good argument. If its premises are true then its conclusion will also be true. If you reject the conclusion of this argument, though, the very fact that it is a good argument tells you where to look to find the problem. The problem must be in the premises: if the conclusion of a good argument is false, then at least one of its premises must be false. The distinction between the argument’s being good and its being sound tells us how to go about questioning the conclusion of a good argument. In this case, both premises of this argument are matters of dispute. This means that we needn’t accept the conclusion of this argument, even though it is undoubtedly a good argument.

Deduction vs Induction

I have been talking about ‘following from’ as if it were the same in every case. In fact there are two sorts of ‘following from’. A conclusion may follow deductively from its premises, or it may follow inductively.

So far I have illustrated my case with deductive arguments. Deductive arguments when good are valid: if the premises are true the conclusions logically must be true. If an argument is deductively valid, and its premises are true, then it is logically impossible for the conclusion to be false. But I might have chosen to illustrate my case with inductive arguments.

Here is a good inductive argument:

Argument Seven
Premise one: The sun has risen every day in the history of planet earth
Conclusion: The sun will rise tomorrow

You will note immediately that whilst it would be hard to say the conclusion of this argument doesn’t follow from its premises, the argument is not valid. Its premise might be true yet its conclusion false.

No inductive argument is valid. For inductive arguments, the conclusion following from the premises is a matter of a strong probability that it is true, given the truth of the premises. Every inductive argument tacitly relies on what Scottish philosopher David Hume called ‘The Principle of the Uniformity of Nature’ (PUN): the belief that the future will be like the past.

The PUN ensures that, whilst every deductive argument is either good or bad, valid or invalid, inductive arguments are only good or bad to some degree. We don’t, therefore, talk of inductive validity, but of inductive strength. The example above is a strong inductive argument. Here is a weak one:

Argument Eight
Premise one: I have seen Marianne twice and each time she was wearing earrings
Conclusion: Next time I see Marianne she will be wearing earrings

Inductive arguments can be weak or they can be strong, or they can be anything in between. Induction doesn’t give us certainty, nor does it give us conclusivity. Conclusivity means that if a deductive argument is valid, then it will remain valid whatever else we might learn. An inductive argument, on the other hand, might go from being very strong to very weak (or vice versa) as we acquire further knowledge. For example, I said that Argument Seven was a strong argument. But imagine if tonight we learn that a rogue black hole is just about to hit the sun – would we still be so confident of the truth of its conclusion? A new piece of knowledge could cause us to revise our belief that Argument Seven is a strong inductive argument. Inductive arguments are never conclusive.

Systematicity

Furthermore we have no method of logically testing inductive arguments. This is at least partly because inductive arguments can be evaluated only a posteriori – only in the light of experience. By contrast, any deductive argument can be evaluated a priori – without any experience of the world. If you doubt this, try evaluating this deductive argument:

Argument Nine
Premise one: If widgets are holomo, then widgets are tralem
Premise two: This widget is not tralem
Conclusion: This widget is not holomo

I have little doubt that you will be able to tell that this is a good argument, even though you have no idea what it is about. That is because the only knowledge you need to evaluate it is linguistic and logical knowledge of the sort I know you have (or you wouldn’t have read this far). You have no need to look at the extra-linguistic world to evaluate this argument. It can be evaluated from your armchair.

This feature of some deductive arguments makes deduction the ultimate in transferable skills: it doesn’t matter what the subject matter of a deductive argument is, you will be able to tell whether it is a good argument or a bad one.

Induction is Ineliminable

Induction might not give us certainty, conclusivity or systematicity. It might also be such that we can evaluate an inductive argument only in the light of our background knowledge of the world. But we cannot do without it.

That this is the case became clear when the philosopher of science Karl Popper tried to argue that science can do without induction. Popper argued that we never inductively confirm a theory, and must instead be content with falsifying it. The only thing we can justifiable claim to know, he argued, is that a theory is false, never that it is true. However, in claiming this, Popper was tacitly relying on induction: after all, what makes us think that a theory that has been falsified on one occasion will be falsified on the next occasion, if it isn’t the inductive belief that the future will be like the past?

Induction is as important as deduction, but it is different. Understanding that and how it is different is an important part of sharpening your reasoning skills.

Conclusion

Reasoning is central to our notion of what it is to be human, but we can reason well or we can reason badly. Logical theory aims to identify what it is to reason well. By learning some logical theory, as you just have, you can improve your reasoning.

If you are interested in doing so further, you might be interested in the podcasts I made for the University of Oxford. These have several times been global number one in the iTunes download charts, and have been downloaded about four million times. They are completely free, and you can access them at mariannetalbot.co.uk/critical-reasoning/. You might also be interested in my ebook Critical Reasoning: A Romp Through the Foothills of Logic. You can read more about it on my website: mariannetalbot.co.uk/about/marianne-talbots-books/critical-reasoning-a-romp-through-the-foothills-of-logic/. Either way if you’d like to talk about critical reasoning come to my Facebook page: (Marianne Talbot Philosophy), or follow me on Twitter (@oxphil_marianne). I look forward to hearing from you.

Marianne Talbot is Director of Studies in Philosophy at Oxford University’s Department for Continuing Education.