Asking Aristotle about reason

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.

Neither Aristotle nor the other Greek philosophers made any distinction between scientific and philosophical investigations: for them everything was ‘philosophy’. So what was a bad argument in politics was a bad argument in science too — and vice versa. But as I will explain in this chapter, different elements of an inquiry actually need different kinds of approach. Experimental science, for example, often uses inductive reasoning, drawing general conclusions from limited evidence — a procedure which is by definition invalid. This is what the experimental method is all about. But scientists are often also philosophising — presenting premises and claiming certain conclusions follow — so these parts of their work require ‘logic-checking’ just as much as anyone else's.

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.

Don't make the mistake of thinking that Aristotle's Laws of Thought are just Ancient History: they remain a pretty big deal. Some 2,000 years later, George Boole, whose logic is vital for today's software and computers, acknowledged Aristotle's influence and pioneering role.

Here are Aristotle's Laws of Thought:

• Law of identity: Whatever is, is.
• Law of non-contradiction: Nothing can both be and not be.
• Law of excluded middle: Everything must either be or not be.

Doesn't sound too difficult, does it? Read on!

Posing problems for logic

Perhaps you're wondering what these three laws mean in practice and whether they stand up to Critical Thinking.

Well, for a start, avoiding contradiction isn't as easy as it sounds. Many of the fallacies in arguments come from asserting two contradictory things. Plus, many of the ambiguities and confusions that create unbridgeable differences of opinion can be traced back to a failure to apply the law of the excluded middle.

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.

Don't be so in awe of Aristotle that you rush to agree on all his thoughts (Critical Thinkers should never rush to agree . . .). Aristotle has his fair share of foolish views, such as the influential but false doctrine that bodies fall to Earth at speeds relative to their mass, or the dreadful (but popular with men) claim that women don't and can't reason but are a kind of domestic animal. Yes, he really said that, even as (or perhaps it was because?) his boss, Plato, was writing the opposite and counting women as great philosophers too.

Identifying convincing arguments

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.

Falling over fallacies

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.

In logic, a fallacy is an invalid argument, one in which a flaw in the way it is constructed meanst that it's possible for all the premises to be true and yet the conclusion to be false. As such, you clearly want to avoid fallacious reasoning — it leads you astray as well as your readers or listeners. People also often use the term colloquially to include arguments they consider ‘false’, because they disagree with one or other of the premises. The two ways of using the word should not be confused.

Not just any old type of mistake in reasoning counts as a logical fallacy. To be a fallacy, a type of reasoning must be potentially deceptive (in other words, look plausible): it must be likely to fool at least some of the people some of the time.

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

Is the argument valid? Skip to the Answers section at the end of this chapter for my comments.

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’.

Spotting a fallacy

Suppose that you're having an argument with someone about whether or not starfish have fins. You know that starfish are beautiful marine animals that can be a variety of colours, shapes and sizes, and all have five ‘legs’, which make them resemble a star. But for the sake of this argument, you don't know whether they have fins or not. Can logic help you to settle the question?

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.

Taking a clear line

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.

Here are some tips on how you square this circle in your own writing:

• Make clear early on the general line you're going to take.
• Use signal words to flag up that what follows is an alternative point of view, contrary to the main message. For example, ‘On the other hand’, or ‘Alernatively . . .’.
• Explain how any contradictory perspectives and views that your research may have revealed can be resolved, perhaps by introducing a third perspective. Or at the very least, make clear to the reader the presence of an unresolved contradiction and that it's not just the reader who can't solve it.

Choosing your words carefully

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.

You need to word your arguments precisely, if they're to have any chance of being logical. Imprecise wording is a recipe for inconsistency, the error that brings an argument tumbling down later. See the exercise in the earlier section ‘Spotting a fallacy’ for how even everyday words can mislead.

A sound logical argument depends on terms having one fixed and precise meaning. But in ordinary language (as opposed to artificial languages such as symbolic logic, or mathematics) no terms have a fixed meaning. They're all to varying degrees a little bit nuanced, a little bit context-dependent and a little bit ambiguous.

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.

To this extent, all claims made using ordinary language depend on a degree of subjectivity, and on, at the very least, a consensus about meanings and usage.

Employing consistency and method

In a good, logical argument, the points made support the eventual conclusion. Another pitfall you want to avoid here is providing reasons that don't support the conclusion — perhaps because they're basically irrelevant or because they imply the reverse of the desired conclusion. This happens easily if you don't really know at the outset why you think that such-and-such, but are ‘cobbling together’ reasons and evidence to support your opinion anyway.

Getting the reasons in the right place is important. Often, people link reasons to each other that don't directly support the overall conclusion, but instead lead to an intermediate conclusion. A logical structure requires a line of reasoning in which first things come first and related arguments are dealt with together (see Figure 13-1).

You can find out more about this aspect in more detail in Chapter 12.

The ‘Does welfare encourage slacking?’ argument

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 starfish argument

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.

An invalid argument doesn't tell you that the conclusion is false (that would be useful in a way!). But although starfish live underwater they aren't ‘fish’ in the scientific sense that the term is used in the first premise. (Whereas fish propel themselves with their tails, starfish have tiny feet to help them move along.)