Critical thinking for Students (9 page)

In their book
The Joy of Laziness
(2005) Peter and Michaela Axt consider the example of Jim Fixx who was the pioneer of jogging. Before Jim Fixx, people who you saw running in the street were normally late for something. The line in
Forrest
Gump
when Forrest says, ‘I just felt like running, so I ran’, would have made little sense to the pre-Fixx era (which was, of course, the point). So why is Jim Fixx being discussed in a book entitled
The Joy of Laziness
? Because he died at the age of 52.

You can perhaps already see the connection. Jim Fixx does a lot of jogging, and drops dead at the relatively young age of 52, therefore jogging is bad for your health. It’s an example of R+R→C.

Straightforwardly, the Axts are seeing jogging as at least highly relevant to Jim Fixx’s death. They make the point that this sort of exercise is supposed to give some protection against heart disease, but hadn’t with Fixx. (He died of a heart attack just after a race.) In that we’ve already considered the issue of the alternative explanation, you will have seen that here we have a good example. The authors have assumed that there is no alternative explanation beyond jogging for Jim’s death. But you could, no doubt, think of others. (There’s also the point that jogging might have extended his life, if he had had a heart condition that was improved by running.)

We have an example here of the often disputed issue of whether, because things are correlated, one must have caused the other. As you might know, when two things are correlated, it means that as one of the things changes in a particular way (increases, for example), then the other changes in a similar or opposite direction. Changes in a similar direction will show a positive correlation; changes in the opposite direction will show a negative correlation.

All sorts of things might correlate. The success of a national football team and the birth rate is one example. (Try to think this one through.) But just because things might correlate doesn’t mean that there is a necessary causal relationship between them. Here’s an example of correlation.

In this example, the author takes two pieces of evidence that are (negatively) correlated. The decline in expensive cosmetic treatments took place during a time when there was an increase in Botox treatments. However, the author infers that there is not just a correlation here, but also a causal relationship: the decline in the use of expensive cosmetics led to an increase in the use of Botox (and/or vice versa). This, of course, might indeed be the case. But what the author hasn’t considered (at least as they have presented the argument) is that there might be an alternative explanation for what happened. For example, perhaps the decline in the use of expensive cosmetic treatments was caused by consumers seeing cheaper products as being as effective as the more expensive ones. (Indeed there is evidence of women increasingly choosing cheap face creams.) In this case, the increase in the use of Botox could be explained in other ways. (Perhaps because it became so widely available now in a range of clinics, salons, and even some dental surgeries.)

In this argument the author took it that, since there was a correlation between the decline in the use of expensive cosmetics and the increase in Botox, there was a causal relationship going on. As we have seen, this might not be the case. In this example, the author has used the words ‘at the same time’ to show the relationship between the two. This way of arguing has a particular name. It’s a Latin term:
cum
hoc, ergo propter hoc
. This means ‘with (at the same time as) this, therefore because of this’. It’s normally abbreviated to simply
cum hoc
(with ‘cum’ pronounced as ‘come’ and ‘hoc’ pronounced to rhyme with ‘sock’).

It’s important to point out that
cum hoc
arguments might be perfectly acceptable. When we take money out of a cash machine and our account then has less money in it, the bank can straightforwardly argue that the cash machine withdrawal caused our account to have less money in it. So, though
cum hoc
arguments can be a problem (given at least one alternative explanation), they are not always.

A more familiar variation of this possible problem of correlation but not necessarily causation is shown in the following example.

You will see that, in this argument, there are two correlations presented, with two causal relationships given. The first is the positive correlation between an increase in young men’s interest in health, fitness, style and careers, with an increase in the readership of health magazines. The second is the negative correlation between this interest and the decline of ‘lad mags’. The first correlation is seen as showing a cause and effect relationship (‘as a result’): the increase in interest in health, etc., has caused the increase in the readership. The second correlation is used to draw the conclusion. Because young men are interested in health, etc., they are less interested in looking at pictures of young women.

We have here two examples of a well-known relative of
cum hoc
. This has an almost identical Latin term:
post hoc, ergo propter hoc
. (‘Post’ pronounced as in letters.) This translates as ‘after this, therefore because of this’. In other words, y followed/came after x, therefore x caused y. You can see how the previous argument is very much a
post hoc
argument. But is it a weak argument?

The first correlation might be OK, but it could have a problem. The author sees the causal relationship as working from interest in health to increase in readership. But it could be the other way round. Perhaps the increase in the readership caused (or at least contributed to) the increase in interest in health, etc. Perhaps it’s a bit of both. So the relationship between the two things might not be as the author has presented it.

The second correlation is also possibly problematic. In part, it’s problematic because of the problems with the first. The author argues that

increase in interest in health etc. → increase in health magazines → decrease in lad mags.

(Their argument could also be seen as

increase in health, etc.

 

increase in health magazines decrease in lad mags).

But, whichever way we present it, the possible problem remains. Perhaps the decrease in lad mags is as a result of something else. For example, perhaps the pictures of minor actresses are easily available on the internet, for free.

Here we come back to a familiar issue: the possibility of an alternative explanation. You can see that, in this argument, the author had to assume that there weren’t alternative useful explanations.

Whenever we’re looking at these correlation and causation situations, we’re faced with at least six possibilities:

Let’s look at an example which brings in the first five possibilities.

You can see the causation issue here is the relationship between TV-watching and blood pressure. Applying this to our five possibilities, we have the following:

In the argument, the author concluded that we should ensure that children don’t watch TV for more than an hour a day. This conclusion was drawn by assuming that the second of the above possibilities wasn’t the explanation for the evidence. The author might assume the first, the third, and fourth. But the third seems unlikely because the conclusion would then be something like ‘we must ensure that children don’t eat snacks while watching TV’. Even the fourth one has potential problems. If the author believed this to be the case, then the conclusion would be something like ‘we must ensure that children do not watch distressing TV programmes’ or ‘we must ensure that we don’t allow TV-watching to affect children’s sleep’. (Though, to be fair to the author, they might have meant this when they gave their rather more general conclusion.)

As you can see, if the author leaves the explanation for the correlation assumed rather than stated, then we need to look carefully at the wording of their conclusion to see what they think.

It’s worth stressing again that a
cum hoc
or a
post hoc
argument is not necessarily flawed. In this case, for example, it could be that TV-watching in itself does increase
blood pressure in children (by reducing the metabolic rate more than just sitting reading, talking, drawing, and so on).

As we’re seeing time and time again, with any evaluation, we must always look very carefully at what the author has done with their inference. The wording of the claim(s) and the inference(s) are crucial here. The more the inference goes further than the claim allows, the more of a problem we’ve got. Using our bank account model, we either need more in the claim or less in the inference.

Look at the next example:

Is this an argument in which the conclusion can straightforwardly be drawn from the evidence-claims? What’s going on?

The author goes from evidence about the crows used in the Oxford study to ‘a wide range of birds and other animals’. Is this acceptable? As you will have seen, the author accepts the move from these crows by assuming that they are representative of this wide range of other animals. This assumption focuses us on the issue here. We might want to ask some questions.

The author obviously thinks that the answer to each of the questions is ‘yes’. But the jump from these crows could be a problem. What we have is an example of
generalisation
. The author takes these crows as typical not only of other crows but of many other species. This might or might not be OK. Given that we didn’t realise before that crows could do what these crows did, we might well be underestimating how non-human animals can solve problems.

Using our bank balance method, to reduce the range of the generalisation, we would need to reduce what the inference takes out.

In this version, all we have to do is to make the first assumption on our list. Even though there still might be an issue here of whether these Oxford crows are typical of all crows, it doesn’t seem unreasonable to think that they are. So this seems much less overdrawn. (Of course, a visiting alien conducting research on some people in Oxford might make a mistake in generalising their thinking abilities to all humans. But perhaps not.)

This issue of generalisation is an interesting one. Too often we find it included in Critical Thinking books as an example of a weakness in argument. But the authors of such books don’t think about generalisation properly.

We generalise all the time without making serious errors of judgement. We infer from the fact that traffic went round a certain way on roundabouts yesterday that it will do so today. We infer that cooking potatoes will soften them today just like it has done every other time. Of course, the predictability involved in these generalisations is not a problem. But, when predictability is less secure, how far can we generalise from evidence about some examples of
X
to all cases of
X
?

So when you read or are told that generalisation is a weakness in argument, ignore it. It is not generalisation as such that is the problem, but
over-generalisation
: in other words, when the evidence-claim hasn’t got enough in it to take us as far as the inference that’s drawn. This can work both ways. A single example of
X
is not normally enough to draw an inference about lots of
X
s. And it’s a problem the other way round too: evidence of lots of
X
s isn’t necessarily a reliable guide to a single example of
X
.

Our example of the creative crows above highlighted the need to look at the relationship between the evidence and the inference from it. We felt able to
generalise from these crows to all crows, in that the ones used were presumably not pre-selected for their creativity. But whether we could actually generalise to every single crow around might be more problematic. (Perhaps, like people, some are less creative than others.)

Look at the following description of the US swimmer Michael Phelps, the winner of 16 Olympic gold medals:

Here we have someone who presents problems of generalisation. In an obvious way, we would not expect to be able to generalise from Michael Phelps to the vast majority of swimmers. As Professor Whyte, an expert in sport science, has said about him, ‘people aren’t made to move like that’. But there is a way that Phelps could be used for generalisation. Professor Whyte has done this by stressing that those who will push sporting performance forward will be like Phelps, people who are different in all sorts of physical ways.

So Michael Phelps illustrates the point that generalisation is always something to be considered in relation to what’s actually going on. What inference is being drawn from what claim?

Incidentally, you’ll sometimes see over-generalisation given as ‘hasty generalisation’. This is a strange version. There is nothing essentially hasty about over-generalising. Someone could take all day to do it. Even if ‘hasty’ means something like ‘not giving enough thought to it’, it’s a problem. Someone could think a lot about it and then still over-generalise. So it’s best to stick with the latter term: it accurately expresses what’s going on.

So far, we’ve looked at two problems with arguments: seeing correlation as essentially causation, and over-generalisation. These are both examples of weakness in argument as a result of inadequate evidence. You can see why. The problem with troubling
post
hoc
and
cum hoc
arguments is that the evidence is not enough for the author to draw their conclusion. As we saw, there could be alternative (and acceptable) explanations for the correlation. In the same way, the problem with over-generalisation is that the evidence isn’t enough: the author has given it more significance than it’s likely to have.