Coming as you are: Informal logic

Informal logic sounds intimidating, but needn't be at all:

• Informal logic: All about assessing and analysing real-life arguments and debates using everyday language. The work is really in the conversion of issues expressed in informal, everyday language into something more structured.

• Formal logic: In contrast, these arguments use symbols and letters to represent the argument. Once an argument has been reduced to symbolic notation, its structure should be easier to see and logicians can then manipulate it in the same sort of (very precise) way that mathematicians manipulate equations.

I know explanations can get more confusing when additional explanations are added into the explanation! Informal logic is really the topic, formal just crept in. . . .

The distinction isn't much more than that between formal and informal clothes: you dress formally for an interview and informally to cut the grass.

To illustrate, I need an everyday argument. Sure enough here comes one now!

You're a rotten husband!

You don't do the washing-up and you don't even do the gardening.

In philosophy, arguments are typically presented as a series of statements that are themselves true or false (these are generally called premises) coupled with a conclusion. Thus the Critical Thinker prefers to restate the above conversation with the following structure:

• First premise: Rotten husbands are men who don't do the washing-up and don't even do the gardening.
• Second premise: You don't do the washing-up and you don't do the gardening.
• Conclusion: You're a rotten husband!

As I explain in more detail in Chapter 13, if the argument is valid (constructed correctly) then as long as the premises are true, the conclusion must be true too.

This argument, by the way, isn't valid. (Hint: rotten husbands aren't the only people who don't do the washing-up and don't do the gardening.) But pointing out the error in the reasoning is hardly going to let anyone off doing their chores, which just underlines that getting the logical structure of an argument right isn't going to settle many real-life issues. But even so, it can help identify the real issues in a debate.

Try to keep the two notions of truth and validity separate, because only a valid argument is one in which you can be sure that if the starting assumptions are true then the conclusion is too. This is a pretty powerful reasoning tool, if you think about it! An invalid argument gives no such reassurance.

In formal logic, arguments are either valid or invalid (that is, sound or unsound). They aren't true or false. Only the premises (and the conclusion), which are factual claims about the world, can be true or false. Informal, everyday arguments tend to mix up premises and conclusions, and often the distinction gets lost.

The problem with real arguments is that they come in every possible shape and size. Much of the reasoning isn't even spoken or written down! You have to guess, or decode, what's going on before you can judge whether the reasons support the conclusion, which is what arguing is all about.

Persuading with premises

Informal arguments that use everyday language should still set out an argument in good, persuasive steps, putting the assumptions (the premises) first and making sure that the real point is a deduction that follows on (or at least appears to!) later.

Here's a pretty good example of how to do it from logician and political activist Bertrand Russell. He's putting forward a deceptively simple argument concerning educational policy:

The evils of the world are due to moral defects quite as much as to lack of intelligence. But the human race has not hitherto discovered any method of eradicating moral defects. . . Intelligence. . . on the contrary, is easily improved by methods known to every competent educator. Therefore, until some method of teaching virtue has been discovered, progress will have to be sought by improvement of intelligence rather than of morals.

—Bertrand Russell, Sceptical Essays (1935)

Grab a pen and paper (or text it on your phone) and set out Russell's argument as three pithy, short sentences, split into two claimed statements of fact and a conclusion that's supposed to follow from them.

Here's my attempt (but try forming your own before peeking):

• First premise: People's bad behaviour should be improved either by improving their morals or through education.
• Second premise: There's no known way to improve people's morals.
• Conclusion: Therefore, people's bad behaviour should be improved through education.

Using pictures in everyday arguments

Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.

—John Tukey

Real arguments don't depend just on words, of course. The most successful political broadcasts, for example, mix a voiceover with compelling images to persuade their audiences (a picture really is worth a thousand words); homeowners are supposed to be able to persuade potential buyers by having a pot of coffee brewing. In this section I discuss how these illogical elements persuade, showing that the process is often very subtle.

With real arguments, the addition of visuals (whether pictures, diagrams or charts) can certainly make claims more persuasive, but whether visuals can make a logical difference (as opposed to reinforcing the emotional, rhetorical strength of an argument) is less clear:

• Some people are sceptical that images can do any work other than rhetorical.
• Others think that images can carry arguments independently.
• Still others believe that images can carry at least some parts of some arguments.

Many advertisements rely on pictures to support an argument. this fact. Imagine an advertisement for, say, Dummies Jeans, that says simply: ‘Buy Dummies Jeans’. It wouldn't sell very many just for that. But coupled with a picture of some attractive, successful, fun-looking young people — it might well do. The reason is the implied connection between being attractive, successful, fun-looking and young — and the jeans: if you buy Dummies Jeans then you'll become like these people!

Or take the classic advertisement from the 1920s in Figure 12-1, which simply makes an assertion about the brand (of coffee) that's worth paying ‘a little more’ for. The evidence for the statement is in the pictures. The man is obviously drinking it with enjoyment, while the shadowy drinker just behind is obviously not getting the same ‘satisfaction’ from his cup o’ Joe.

Have a go at expressing the coffee advert as a simple, logical argument. (Best is to jot something down before reading on).

Okay, this is how I ‘deconstructed’ the ad:

• First premise: Paying a little more for something is worth it if it brings you real satisfaction.
• Second premise: This kind of coffee brings you real satisfaction.
• Conclusion: Therefore, paying a little more for this kind of coffee is worthwhile.

That's the surface message, anyway. The subliminal (hidden) message is that the particular brand of coffee is superior to other brands. This message appears in the argument as one of the assumptions in the premises).

Checking a real argument's structure

Even though real arguments are phrased in ordinary language, they still have a structure that you can try to reveal by stripping away the unnecessary details and expressing the whole thing in its argumentative essence.

Sometimes the use of everyday language itself causes problems with the argument's logic. One logical error is so common it has its own special name: the fallacy of affirming the consequent. You don't need to know the name, but you do need to be able to spot this mistake in reasoning, because it's probably one of the most common errors people — even famous philosophers — make.

The fallacy of affirming the consequent involves arguing that one event was caused by another merely because it occurred after that event. (It's also called making a logic reversal.) People who affirm the consequent imagine that the effect of a cause is also the cause of the cause. But no, course not!

Considering the formula ‘if A then B’

In a sparky, recent book called If A then B: How the World Discovered Logic, two philosophy professors, Michael Shenefelt and Heidi White, argue that reasoning, knowledge and rationality are first and foremost matters of logic: of applying that deceptively simple formula ‘if A then B’ to the world. What's more they argue that the history of the world is also the history of simple logical forms. For example, the simple arguments I discuss in this chapter — where statements are presented and then claimed to lead to a certain conclusion — emerged out of the Ancient Greek way of taking decisions. For the background history, see the nearby sidebar ‘A history of arguing’.

The idea is that if everyone agrees to be logical and let rules decide arguments, people should eventually reach decisions that everyone can see the reasons for and by and large can accept.

Assuming a causal link

Causal links in nature are central to the way people make sense of the world — and just as in logic, they're often not thinking directly about the mechanisms, about why A leads to B. For example, consider these arguments or claims:

• Don't eat wild mushrooms — they're poisonous.
• If you study hard, you'll get a better grade in the exam.

They are very different kinds of statements. One seems more ‘causal’ than the other — yet in another way they're both similar because they're both statements of the kind ‘all A are B’:

• All wild mushrooms are poisonous.
• All people who study hard get good grades.

The philosopher David Hume is credited with a great insight into everyday arguments. He says that the deeply held belief of causal links — for example, that not watering plants causes them to wither or that throwing rocks at windows causes them to break — isn't logical but merely psychological. His rather abstract point about ‘cause and effect’ has many practical implications for Critical Thinking, because he's challenging the root of logic itself.

David Hume says that the idea that one thing causes another is a human construction, based on past observations and experience. This is his argument

And what stronger instance can be produced of the surprising ignorance and weakness of the understanding than the present. For surely, if there be any relation among objects which it imports to us to know perfectly, it is that of cause and effect. On this are founded all our reasonings concerning matter of fact or existence . . . Our thoughts and enquiries are, therefore, every moment, employed about this relation: yet so imperfect are the ideas which we form concerning it, that it is impossible to give any just definition . . .

In other words, a key idea that human beings use to make sense of the world around us, that what we have observed one day, in one set of circumstances, can be learnt from and assumed to apply another day in similar circumstances, is based itself just on faith! Why should the same cause always have the same effect? His idea is so radical that it makes nearly all arguments fall to pieces straight away! Hume admits himself that he can see no answers to his problem, but suggests shrugging and carrying on anyway. In a sense that is what we have to do. But Critical Thinkers can benefit from the warning by always doubly sceptical and asking questions when someone asserts that a certain outcome will always follow, given a certain action.

Discussing unnecessary and insufficient conditions

Here's another way in which drilling down into logical reasoning and revealing an their formal structures can help in even informal arguments: specifically, the difference between necessary and unnecessary conditions.

Everyone's familiar with the concept of something being necessary. For example, in order to keep fish in an aquarium alive, it is necessary to make sure that it's full of water. If you let the water evaporate out, the fish perish.

In the all-important ‘if . . . then’ statements of reasoning, the second bit that follows the word ‘then’ (technically known as the consequent) gives a necessary condition for the first part (which philosophers call the antecedent):

If Phyllis the goldfish is to be happy and healthy [the antecedent] then the water in the aquarium must be kept topped up [the consequent].

So important are necessary conditions that in ordinary language people have many ways to express them. For example:

• Water is necessary for fish to live.
• Fish must have water to live.
• Without water, fish die.
• No fish can survive long outside water.

A condition X is said to be necessary for another condition Y, if (and only if) the falsity (the non-achievement) of Y guarantees (or brings about) the falsity of X.

But keeping the water level topped up isn't a sufficient condition for keeping Phyllis the fish happy and for having a successful aquarium. For example, you need to make sure that the water is clean, that oxygenating weeds are present and that the water is the right temperature. So the water level is a necessary but insufficient condition. So far so useless! But this insight does lead you towards being able to make a new suggestion:

If Phyllis the goldfish is to be happy and healthy then I must place a plastic castle for her to swim around at the bottom of the aquarium.

Certainly this is a very nice thought and I'm not against it at all, but is it absolutely necessary to provide plastic castles for goldfish? Not at all. You could provide some interestingly shaped rocks instead or maybe more weeds.

So clearly this is an unnecessary condition, because Phyllis can be healthy even without the castle. But is the plastic castle also an insufficient condition? Yes it is, because if you fail to feed her, or let the water level drop, or lots of other things, the plastic castle isn't enough to keep Phyllis healthy and happy.

Condition A is said to be sufficient for a condition B, if (and only if) the implementation of A guarantees the truth (the bringing about) of B.

Before reading on, pause for a moment and make a list of necessary conditions for Phyllis the goldfish to be happy and healthy.

Okay? Here's a couple that you probably didn't think of: you mustn't have any cats that can gobble up Phyllis or any nasty anchor worm eggs introduced into the aquarium, say on the pond weed!

Don't kick yourself if you missed those two. Instead, award yourself one mark if you listed ten points and three marks if you wrote less. Because a Critical Thinker soon realises that it isn't too useful to spend too long on that list because it is potentially an infinite task.

The moral is that, in real arguments, specifying either necessary or sufficient conditions is often impractical. Instead, a huge amount of shared assumptions are needed.

Investigating independent and joint reasons

One quite subtle distinction in critical thinking is between independent and joint reasons.

Many arguments work quite happily on just one reason. You can see these arguments as assertions:

Killing animals for meat is wrong. Therefore, everyone should become vegetarians.

The argument ‘works’ because the word ‘should’ contains a judgement about what's right and what's wrong — and the first part of the argument says that killing animals is wrong. The hidden structure is probably as follows:

• Killing animals is wrong.
• People shouldn't do things that are wrong.

• Therefore, people shouldn't kill animals.

  (next step)

• People who aren't vegetarians are involved in the killing of animals.
• Killing animals is wrong.
• Therefore, everyone should become vegetarian.

In contrast, a joint reasoning argument is one in which you need at least two reasons in order to draw the conclusion. In other words, you can't draw the conclusion from any one of the reasons on its own: Take a look at this one, with four reasons offered to support the eventual conclusion, for example.

• Two thirds of the world's surface is covered in water.
• If people stop eating fish then pressure on the fragile ecosystems on land will be increased.
• Increased pressure on the fragile ecosystems on land is bad for the environment.
• Vegetarianism requires people not to eat fish.
• Therefore, vegetarianism is bad for the environment.

There! In this section, you've used logic to prove two opposite sides of the argument! (Vegetarianism is morally right, and vegetarianism is morally wrong.) That's a pretty handy Critical Thinking skill.

Being aware of hidden assumptions

Looking at arguments from the point of view of those making them helps you to spot hidden assumptions that they're making, assumptions that you may want to discuss openly and perhaps challenge.

Similarly, turning a critical eye on your own beliefs and values allows you to identify premises or beliefs that may not be accepted at face value by the people listening to or reading about your views.

Elements that influence your views (often without you really realising it) include the following:

• Race, nationality and culture.
• Language and your education.
• Family status (do you have children who depend on you? Are you reliant on others?).
• Economic or social class.
• Whether you're religious or non-religious.
• Views of your peer group (for example, teenagers are notoriously sensitive to and influenced by whatever their friends are doing!).

If you can identify the hidden assumptions in other people's positions or the problematic aspects of your own, you're better able to do two useful things:

• Anticipate the kind of counter-arguments that may be put.
• Make a kind of ‘pre-emptive manoeuvre’, by rethinking and if necessary strengthening your own assumptions, especially ones you hadn't really been properly aware of.