Chapter 13
In This Chapter
In This Chapter
Looking at the laws of logic
Seeing successful arguments and finding fallacies
Making valid points when debating
It is important to remember that the informal fallacies are just ‘rules of thumb’. If violating the informal fallacies is necessary in order to describe social systems, then a decision is required. Should traditions concerning the form of arguments limit the scope of science? Or, should the subject matter of science be guided by curiosity and the desire to construct explanations of phenomena?
—Stuart Umpleby (‘The Financial Crisis: How Social Scientists Need to Change Their Thinking’, 2010,
www.gwu.edu/~umpleby/recent.html
)
Professor Stuart Umpleby is a social scientist rather than a philosopher (otherwise he'd never use a fallacious argument). He's sounding a cautionary note about the too literal, too narrow use of logical rules, a view that I clarify in this chapter.
This chapter is about how to use logic to strengthen your own arguments and help you spot weaknesses (or indeed strengths) in other people's. I emphasise that logic is a tool that suits only certain applications and isn't a universal shortcut to proving points and finding the truth. If you don't believe me and think that logic can settle everything, check out this chapter's discussion on Aristotle's three Laws of Thought.
I also include an opportunity for you to hone your skills via a deceptively important little argument that highlights the role of link terms in producing a good, sound argument — and the danger of ambiguous language for producing a bad one.
The Ancient Greeks provide many of the foundations for both logic and good, rigourous thinking in general.
The first philosophers strove to eliminate ideas that seemed vague, contradictory, or ambiguous, and the best way to accomplish this, they thought, was to work out the rules of thinking that would reliably lead to clear and distinct ideas. In other words, to discover and then follow the laws of thought themselves. This chapter explains what those laws are, but it's also important to remember (and much less often actually done) that in spite of how dominant these ideas have been over the centuries in both science and philosophy, they have not been without their critics, and for every point in their favour there are equally powerful arguments against them. That's what a Critical Thinker should expect, of course! The real issue seems to be not so much whether the principles are true or not, but where and when are they applicable? The laws of thought have an important role to play in Critical Thinking, but they are not the whole story by any means.
But, having said that, Aristotle's ancient book on common logical errors, and also on sound ways of theorising, is a great way to start thinking more precisely and methodically. His Big Idea is that an argument is valid when the conclusion follows logically from its starting assumptions (the premises) — and he's not too bothered if a conclusion can still be complete nonsense if there's a problem with those assumptions. If you start with true, relevant and non-contradictory assumptions and structure the argument correctly then you have a copper-bottomed guarantee that the conclusion is true. This is what is meant by a sound argument in this context.
For the Ancient philosophers, like I guess most people today too, a good argument was one that brought people to agree with the speaker, and it really didn't matter quite how that was achieved. It might be by careful use of rhetorical devices, such as making three points in sequence, or through ridiculing the opponent. (For more on this, see Chapter 15.) Or it might be by recalling the legends told about the Gods of Mount Olympus. Probably the most influential philosopher of them all, Plato, used the whole range of persuasive techniques in his philosophical writings, which included a fairly detailed blueprint for running a small country — his famous playlet called The Republic. Ironically, I think it could have been a jealous reaction to Plato's literary and rhetorical skills that prompted his pupil, Aristotle, to look instead at the nuts and bolts of arguments, and to try to tease out the elements of the most powerful ones. Whatever Aristotle's real motives, this was really innovative work — and it changed the way people thought and argued forever.
A typical academic book or essay is a mix of science and philosophy, of facts discovered through research and arguments newly developed by the author and will certainly include sections that need to be logically rigourous!
He came up with three mental rules that he called the Laws of Thought. Philosophers tend to understand these Laws as part of an attempt to put everyday language on a logical footing, which, like many contemporary philosophers, Aristotle regarded as the key to human progress.
Here are Aristotle's Laws of Thought:
Doesn't sound too difficult, does it? Read on!
Perhaps you're wondering what these three laws mean in practice and whether they stand up to Critical Thinking.
Plato, who, remember, was Aristotle's mentor, was well aware of the Laws of Thought, but he was more interested in where they seemed to not apply. You see, in certain cases, they lead to absurd conclusions.
For example, in one of Plato's little plays, someone argues that Socrates must be the father of a dog, because the dog has a father and Socrates admits that he's a father. The law of non-contradiction (nothing can both be and not be) says that one can't both be a father and not be a father at the same time, and so logic seems to require that Socrates must be the father of the dog.
Of course, Socrates is obviously not the father of the dog, but the problem is seeing where the thinking has gone wrong. In other words, where and how to apply the laws raises as many questions as those the laws are supposed to settle.
In this section I look at some of the key logical structures that people use — for better or worse.
What makes an argument convincing? The evidence advanced for a position being correct isn't enough; you also need some reason to accept that the conclusion follows from the evidence.
Philosophers often express arguments in symbols, whereas Critical Thinkers use ordinary in English. But noting that the validity of arguments is most easily tested using symbols helps you to remember two important things:
Here's this affirming-the-antecedent argument in symbolic form:
If P, then Q
P
Therefore, Q
And here's an example:
If there is evidence of design in the universe then there must be a Designer
There is evidence of design in the universe
Therefore, there must be a Designer
Goodness, does that settle the huge old debate simply through logic? Not really. You can still disagree over whether the premises are true. What's meant exactly by ‘a designer’ (or indeed one with a capital ‘D’)? Unless the starting assumptions are true the structure of the argument can be as excellent as you like, but you still can't be sure of the conclusion.
Aristotle came up with 256 variations of arguments that have two assumptions followed by one conclusion, of which he thought 19 were truth preserving; the rest were fallacies and hence ones to avoid — mostly obviously so. Actually, people think nowadays that at least 4 more of his 19 ‘safe forms’ are dodgy — showing just how difficult being fully logical and rigorous is. But that doesn't mean you shouldn't try.
A great valid form of argument is denying the consequent (modus tollens in Latin). As the name rather gives away, instead of proving that the ‘if bit’ is true, you prove that the ‘then bit’ (‘the consequent’) is false. For example, if being a real king requires having a crown, then not having a crown implies not being the king.
In logic-speak, assuming that a real (and an unbreakable) connection exists between the antecedent and the consequent (the ‘if’ and the ‘then’), and the consequent is false, then the antecedent must be false also. Denying the consequent (the thing after) thus involves the denial of the antecedent (the thing before) as well.
Here's an example, both in symbols and plain English:
If P, then Q
Not Q
Therefore, not P
If I eat lots of sweets made of sugar, then my teeth will fall out
My teeth have not fallen out
Therefore, I haven't eaten lots of sweets made with sugar
Here I examine a bit more how to ‘logic-check’ the structure of your arguments, which means checking how the parts of the argument fit together — or don't.
The statement ‘it's a fallacy that paying people welfare benefits encourages laziness’ is probably a critique of the following informal and politically incorrect argument:
If people can get money without working then they'll become lazy
Unemployment benefit is a form of getting money without having to work for it
Unemployment benefit encourages laziness
The rest of this section covers the idea of fallacies. To see why that's all you need to know, check out the nearby sidebar ‘Focusing on fallacies that matter’.
Here's a suitably Classical example: the emperor Croesus is said to have consulted the Oracle at Delphi to see whether the omens were good for his planned attack on Persia. The reply seemed to auger well: ‘If Croesus goes to war, a great empire will be humbled.’ Thus encouraged, Croesus went to war, had a terrible time and promptly lost. A mighty empire was indeed humbled — but it was his one.
You can all too easily accidentally produce a circular argument. This is a type of reasoning in which the conclusion is supported by the premises, which are themselves relying on the truth of the conclusion, thus creating a circle in reasoning in which no useful information is shared. (See the box in Chapter 12 for more on this.)
Don't start to see fallacies everywhere — because science — and real life generally — is all about inductive reasoning — drawing general conclusions from a limited amount of evidence. The trouble with doing this is that the next bit of evidence along could destroy the theory — as (for example) recently nearly happened to the entire Western banking system when it turned out that certain kinds of investments were not actually safe ‘as long as they were all bundled together’, as the dominant economic theory at the time predicted. In real life we use inductive reasoning all the time, even though it is by definition invalid, and it caries with it the risk of being proved wrong by future events.
The alternative approach which promises conclusions that are rock-solid and eternal is called deductive reasoning. It is exemplified by logic and geometry with their ability to demonstrate that, for example, that 3 + 4 = 7, or that the angles of a triangle add up to 180 degrees, or that ‘Socrates, being a man, is mortal'. Claims like these tend to stay true. The trouble with this kind of reasoning is that, in practice, it tells you nothing you did not already think already. It can't; that's why it's ‘valid’. Thanks, Aristotle!
Major premise: All fish have fins
Minor premise: All starfish are fish
Conclusion: All starfish have fins
Doctor, we have our answer! Or do we? Does this prove that starfish have fins? Check out the answers at the end of the chapter for a full discussion of this surprisingly important riddle.
In this section I give some general tips on how to make your arguments more effective.
Logic always has a rather frightening aspect: perhaps you think that things in it are ‘black and white’ and you'll look ridiculous if you make a mistake. That's often how teachers present it in philosophy classes, too. But Critical Thinking is concerned with real life and logic is a valuable tool and a friend.
The first thing to consider when constructing an argument is whether you're contradicting yourself. Of course, any areas of social or scientific debate often include opposing arguments and conflicting evidence, and good writers are aware of this fact and able to include the controversy in their accounts. However, for readers, conflicting messages and inconsistencies are confusing.
Many arguments are really just confusions about terminology. In fact, Socrates insisted that all human disagreements come down to this problem, but then he was executed by his fellow citizens after a vote, which implies he misjudged their characters. He was somewhat naïve about how and why different economic interests can lead people to have a reason to see things a certain way.
Here's an easy question: do the angles of a triangle add up to 180 degrees? Not when the triangle is drawn on the surface of a sphere, they don't. So even maths and logic are context-dependent, and logic can't get going until the precise meaning of the terms has been agreed.
You can find out more about this aspect in more detail in Chapter 12.
Here are my answers to the two exercises.
I say that this argument is valid. But I'm not a fascist, and you don't have to accept premises are true. Let me explain. Here, the argument hinges on ‘if people can get money without working then they will become lazy’, which looks plausible, when understood as ‘sometimes, if people can get money without working then they will become lazy’. But it seems less so when understood as ‘in all cases’ and even less so when the amount of money is included. Plenty of scope for disagreement exists about the assumptions in this argument. For example, suppose that the first premise is expanded to say:
Invariably, if people can get just enough money to survive from the State without having to work for it, then they will all become lazy.
Looks less plausible, doesn't it? But it's not a change to the logic, only to the content.
The argument as it is presented proves nothing, because the word ‘fish’ is being used in two different ways: in a strict scientific sense in the first premise and in a looser, everyday sense in the second premise. The end result is that the conclusion is unreliable. For the record, in this case, not just unreliable but flat wrong.
The fallacy is given the fancy name quaternio terminorum! In plain English, it's the fallacy of four terms. The logic depends on there being just three terms, with what logicians call the middle term being the vital link between the others. (It's called the middle term because of its link role, rather than because it appears in the middle of the sentence.) When you have four terms, you have no link, and the whole argument becomes random assertions.
Here's a valid argument, to remind you of how the middle term (in bold) acts as the vital link:
Major premise: All fish have fins
Minor premise: All salmon are fish
Conclusion: All salmon have fins
In plain English, the argument is that salmon have fins because they're a kind of fish and all fish have fins.
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