Thinking Skills: Critical Thinking and Problem Solving

7.2 Soundness and validity: a taste of logic 255

reasons. The fact (R2) that birds have wings

doesn’t mean all of them can fly, and therefore

the fact (R3) that parrots are birds doesn’t

establish that they can fly either. R1 really

gives no support to the conclusion, because

what is true for insects has no bearing on what

is true for birds. It is irrelevant.

We can see how invalid [2] is if we substitute

‘penguins’ for ‘parrots’, because penguins are

birds that cannot fly:

[3] Many insects have wings and those that

do can fly. Birds also have wings, and

penguins are birds, so penguins can fly

too.

In [3] the premises are just as true as they were

in [2], but in [3] the conclusion is false.

Therefore [3] is invalid. However, [2] and [3]

have precisely the same form, so both are

invalid (and therefore unsound too).

A valid form

Here is a different argument.

[4] All birds can fly. Penguins are birds, so

penguins can fly.

Activity

What do you make of this argument? Is it

valid? Is it sound?

Commentary

Again you may be surprised. This argument is

valid. It is valid because if all birds really could

fly then penguins would be able to fly (because

they are birds). It is unsound because it is not

true that all birds can fly. But that is not a fault

with the reasoning, only with the first

premise. The point to remember is that

validity is to do with the form of the

argument, not the subject matter. The validity

of [4] has nothing to do with birds and things

that can fly, but applies to any class of objects

whatsoever. We can see why [4] is valid if we

because some standard arguments are valid and
some are not. Any number of invalid arguments
could be made by substituting true sentences for
R 1 , R 2 , etc. and a false one for C. Substituting
different sentences for the letters R... and C
makes it possible to test arguments for validity.
If you can find any examples in which the Rs
are all true and C false, you know the argument
is invalid, even though there may be other
examples where the conclusion is true. For an
argument to be valid every argument with the
same form must be valid too.

Activity

Here is a short example to illustrate what is

involved in testing the validity of an

argument.

[2] Many insects have wings and those

that do can fly. Birds also have wings,

and parrots are birds, so they can fly too.

Decide for yourself whether [2] is valid, giving

reasons for your evaluation. Take some time

over this. It is not as simple as it looks.

Commentary
We’ll begin by analysing the argument. It
makes three claims, followed by the
conclusion:

R1 Many insects have wings and those that

do can fly.

R2 Birds have wings.

R3 Parrots are birds.

C Parrots can fly (too).

How should we evaluate this argument? We
can see that the premises are all true. We can
also see that the conclusion is true: parrots can
fly. These facts may have fooled you into
thinking that the argument was valid, and
therefore sound as well. It isn’t. Although the
conclusion is true it is not made true by the