Critical thinking for Students (7 page)

The most we could have said about the inference in this argument was that it was
probably
true. This, as we’ll see time and time again, is the most we can say about the sort of arguments you’ll come across. If you want certainty rather than just probability, you’ll have to find (or use) arguments with a particular structure. 

The argument is set out like this to emphasise what’s going on. You should be able to see that, if the first two claims are true, then the inference (the third sentence) must also be. It isn’t that it probably follows: it
must
follow. It must follow for the same reason that the negative test worked in finding assumptions: arguments should not be self-contradictory. It would be nonsense to infer that Martha Phillips eats meat, given the first two claims.

We have here an example of what’s called a
syllogism
. These forms of argument always have two reasons which together (so joint reasons) lead to the conclusion. Specifically, you’ll note that each reason has a term (words) in common with the conclusion, and one term (words) in common with the other reason. Looking at our example, let’s see how this has worked there.

This particular argument was very strong (in fact, watertight) because of the way in which it was presented. But it was strong only if the reasons are true. If Martha Phillips has abandoned her vegetarianism, then the second claim isn’t true, meaning the inference collapses.

When the reasons are true in an argument like this, then we have what is called a
valid
argument. Some arguments might look as if they’re valid but, if the reasons aren’t true, then they won’t be valid.

It’s useful to see how, in the valid argument above, the conclusion was, so to speak, contained within the reasons. It didn’t go any further than what was supplied by them. In this way, it can be seen as an equation R+R=C.

However, if we look again at our argument on the Royal Family, we can see that the conclusion isn’t contained within the reason: it goes further. Part of what’s going on, of course, is that it goes further because there are other reasons being assumed. Our Martha Phillips argument didn’t contain assumptions; the reasons supplied everything that was needed.

As we have before, we’re now going to concentrate on looking at lots of arguments in which the reasons don’t supply everything, where the inference has moved to a greater or lesser extent beyond them. As we have seen above, you’re not likely to have to deal with any other sort of argument. So remember, the most that we can expect from the arguments that we’re likely to find is that the conclusion
probably
follows from the reason(s).

We have already met quite a few arguments where it is evidence-claims that supply the reasons. You will remember that, in the first chapter, we spent some time looking at such claims (including those of statistical evidence) and kept asking the question ‘what is the significance of this claim?’ We’ll look now at lots more evidence and we’ll keep asking that question.

Statistical evidence is very commonly used in arguments. It’s often seen as a particularly powerful part of the reasoning, perhaps because numbers give a good impression of ‘facts’.

When adverts for cosmetics are shown on TV, they often provide in a small font in the bottom left- or right-hand corner of the screen some statistical evidence.

This sort of evidence is meant to support the other claims being made in the advert. These will be something like, ‘Our age-rejection cream will make you look years younger.’ Perhaps it will, but does the evidence support the claim? If so, to what extent?

You might want to discuss the significance of ‘less visible’. This does not have to mean ‘invisible’. It could mean no more than, at first glance, wrinkles are (a little) less noticeable than before. In addition, you might want to look at the numbers involved. Why 97? Who were they? How were they chosen? Over what time period did they use
the cream? Did they use it, or did they merely observe its effect on others who did? Did they all use the term ‘less visible’ in the same way – that is, in the same situations (amount of light available, degree of wrinkled skin, and so on)? It could be, for example, that tiny wrinkles become less visible but deeper ones are not visibly affected. And what about the 25 who didn’t notice the difference? Why didn’t they?

The evidence is meant to operate as a reason for the inference given in the advert. Accordingly, you will probably have spotted an assumption here.

That’s quite a big assumption and is itself open to questions of meaning. How much ‘less visible’? (Can it be quantified into a percentage?) How many ‘years younger’? (Two, three …?)

We’ve just looked at some very specific evidence (‘of 97 women …’). But often evidence can be presented in a much more general way.

This time there are no numbers, no percentages, nothing beyond the giving of a correlation between a man’s height and his income and promotion chances. So what sort of inference could be drawn from this sort of evidence?

We have reached an important point. Which of these inferences does the
evidence-claim
best support (if any)? We’ll introduce here a way of looking at this problem. This is to look at the process of inference in terms of a bank account.

We know that we can spend only what is in our bank account (ignoring loans, credit cards, gifts, and so on). If we spend more, then we are overdrawn. We have literally taken out of the account more than was in there. The link with inference is a simple
one. The claim(s) from which an inference is drawn represent(s) what is in the account. You can therefore infer (spend) no more than what the claim(s) permit(s).

Let’s return to the evidence on men’s height. We gave three possible inferences. Can we afford any of these? Interestingly, if this evidence is a general trend (which it seems to be), then something appears to be going on which needs explaining. You will again see, by the way, that explanations are never far away in Critical Thinking (whatever some might say or write). Without an explanation, we don’t really know what’s going on here. So what inference we can afford depends on what explanation we put into the account. Without it, there’s not enough in there to go straight from the evidence to an inference. Let’s see why.

The inference has taken too much out of the account: transaction declined. Quite simply, we don’t know from just the evidence why taller men do better. To make this inference, we need to add something into the account.

Has this addition to the account given us enough to spend on the inference? It’s certainly taken us away from being as overdrawn as we before. But there’s still a worry that the case hasn’t been fully established. We know that taller men earn and get promoted more, and that the author claims that employers see shorter men as being less competent
but
(yes, there’s a pronounced but) we don’t know if these two claims together show/demonstrate (prove, if you like) that the better pay and promotion chances of taller men are
as a result of
how employers see shorter men. So there’s still a big hint of overdrawn here.

Perhaps taller men (for whatever reason) are better qualified, healthier (so take less time off sick), have happier home lives (so work more contentedly and consistently), or whatever. To show how the picture can indeed be muddied by such possibilities, there is evidence (by Danish researchers on shorter British men) that such short men reported worse physical and mental health than those of ‘normal’ height. In
addition, a French study has found that men who are 6ft or more tall are 50 per cent more likely to be married or in a long-term relationship than men who are 5ft 5in or below.

We can see then that drawing any inference from our first claim starts to look very difficult. Let’s just have a look at the third inference.

There is an organisation called the National Organisation of Short Statured Adults (NOSSA) which argues that what it calls ‘heightism’ should indeed be made illegal. The famous and brilliant economist J K Galbraith (6ft 8in) referred to it as ‘one of the most blatant and forgiven prejudices in our society.’ But does the evidence enable us to make the inference above?

Of course, assumptions are never far away, and there’s at least one assumption needed to connect the evidence with the inference.

So, it’s the same story. The original claim and inference didn’t work without the inference being overdrawn. But would the two assumptions we’ve just identified stop the inference being overdrawn, if they were turned into stated reasons?

They’re certainly effective in dealing with the issue of what causes taller men to do better in pay and promotion (so they close off concerns about why shorter men do less well). But the inference is still overdrawn. We would also need the claim that having a prejudice against short men is not a good thing. Going back to our earlier point about whether there are health-related causes of heightism, we would need the claim that the explanation for heightism is not to do with factors that would stop short people from getting on well at work.

You might be thinking by now that we can’t ever infer anything safely once we stray out of the enclosed world of the valid syllogism. But this would be to cut us off from
the normal way in which we argue. What we’ve seen is that inferences are normally, at best, only probably true. The claims that are used to support inferences might take us a long way towards certainty, but will never quite get there. But in Critical Thinking we are not normally after certainty: an inference with a high probability of being true would sit nicely at our table.

Having talked a lot about strong claims and inferences, it’s interesting to note that sometimes claims are left deliberately weak, although the intended message of the assumed inference is meant to be strong.

This claim is, of course, entirely compatible with another one.

But you’re meant to draw the inference from the first one that ‘it would be a good idea to use this price comparison website’. You’re not meant to do anything with the other claim. It sits there uninvited. It was us that let it into the discussion.

Just a little diversion before we move on. When we referred to an ‘assumed inference’ above, we were in fact looking at what is technically called an
implication
. There was no inference drawn from the claim, but the given claim was designed such that you
would
draw a particular one. We could ask ‘What was implied by the claim?’ and the answer is, ‘The implication is that you should use the website’. Though the implication that you wouldn’t save money is also there, it’s in a way being jostled out of the picture by the context in which the claim appears. The advert in which it appears is not a neutral context in which claims are being presented for neutral discussion. It’s not as if Socrates is toying with the idea that he could save money on his insurance by using a price comparison website and responds with the
counter-claim
that he also could not.

Watch out for claims (especially evidence-claims) that just sit there with an intended implication sitting next to them. Here’s a recent evidence-claim:

This claim appeared in a June 2009 edition of
The New York Times
. The implication that is sitting next to it is not ‘so parents should have the TV on more when they’re with children’. It is, of course, the opposite. Once again, as we have seen, we’re back to the point about the significance of claims. We’ve stressed time and time again that claims have a neutral significance unless and until someone comes along and gives them a particular significance. So, an alien from a planet which has been searching for ways of getting children to talk less to adults would be thrilled by the finding and report back from New York to alien HQ that every household on the planet must have the TV on much more. Implication becomes inference when someone draws the implication.

When looking at evidence-claims, are some types less problematic than others? Let’s look at some of them.