Thinking Skills: Critical Thinking and Problem Solving

258 Unit 7 Critical reasoning: Advanced Level

If p then q

q

p

and [11]:

If p then q

Not-p

Not-q

These might seem minor differences, but they

are enough to make both the arguments

invalid. Even if the premises are true – and

we’ll assume they are – the conclusions don’t

necessarily follow. In [10] you are told that if

you were bitten by a spider you would have a

red, swollen wound, i.e. q. But we cannot

assume that any red, swollen wound must be

a spider bite. Other wounds can be red and

swollen. So the premises of the argument can

be true, and the conclusion could be false;

which, by definition, makes the reasoning

invalid.

Similarly in [11], there may be other

reasons, besides a spider’s bite, why you need

to see a doctor. So the fact that if it were a

spider bite you would need a doctor, doesn’t

mean that if it is not a spider bite, you don’t.

Again, the conclusion can be false, even if

both premises are true.

Critical thinking and logic

The examples we have been examining in this

chapter are of the sort that logic books use to

define and explain validity. They are not

meant to be ‘real’ arguments, in the sense of

resembling everyday reasoning. They are

contrived and artificial, and deliberately so,

because that is the best way to display their

form. No one in an ordinary, practical situation

would go to the bother of arguing that such-

and-such a person was mortal because he or

she was human, and all humans are mortal.

What [6] and [7] are for (on page 256) is to

What both of these imply is that anything that

is a fish would have gills. So if a whale – or

anything else – doesn’t have gills, it is not a

fish. This is even implied by:

[9c] Whales aren’t fish; they’ve got no gills.

Strictly speaking, of course, [9c] is not logically

valid because it has a premise missing.

However, in the less formal discipline of

critical thinking we can interpret [9c] as a

sound argument because the missing premise

is so very clearly implied. By arguing from a

whale’s lack of gills to the conclusion that

whales are not fish, there is a clear, though

unstated, assumption that if whales were fish,

they would have gills – or just that all fish have

gills (see Chapter 2.9).

Activity

Two short arguments follow. At first glance

they resemble [8] and [9] respectively. But on

close inspection you will see that there are

differences. The question is, are either or

both of them valid?

[10] If you were bitten by a poisonous

spider, you would already have a

red, swollen wound. This wound is

red and swollen, so obviously you

were bitten by a poisonous spider.

[11] If that were a spider bite, you’d need

to see a doctor. But it isn’t a spider

bite, so you don’t need a doctor.

Commentary

This time we’ll use the letters p and q, the

traditional logical symbols for any claim (or

‘proposition’) whatsoever. We can then see

that the first premise in [10] and [11] has the

same form as [8] and [9], namely: ‘If p then q’.

But there the similarity ends. For in each case

the second premise and the conclusion are

reversed. [10] has the form: