Thinking Skills: Critical Thinking and Problem Solving

256 Unit 7 Critical reasoning: Advanced Level

resolve that dispute, [5] remains valid, as the

Euler diagram confirms:

have gills

sh

sharks

Deductive reasoning

Examples [4] and [5] are valid arguments and

[5], arguably, is sound as well. To be more

precise we ought to say that these are

deductively valid arguments. That is because

the above definition of validity really applies

to certain types of reasoning called deduction,

or deductive reasoning. Deductive arguments,

so long as they are valid, are very strict,

rigorous arguments in which the conclusion

follows inescapably from the premises. But by

the same token, an attempted deduction that

is invalid fails completely, so that regardless of

the truth of its premises, it is unsound. You

cannot have a deductive argument that is ‘a

bit valid’ or ‘very nearly valid’: it’s all or

nothing.

Here is a centuries-old example that

logicians have used to illustrate deductive

validity:

[6] All men are mortal. Socrates is a man.

Therefore Socrates is mortal.

You may have noticed that this is very similar

in form to example [4] above, and it is valid for

the same reasons. It is often contrasted with

the next argument, which makes all the same

claims but is certainly not valid:

[7] All men are mortal. Socrates is mortal.

Therefore Socrates is a man.

represent it in a Euler diagram; diagrams and

symbols can often show the form of an

argument better than words:

F

B

P

In this diagram we replace things that can fly

with the letter F, birds with B and penguins

with P. Then we forget about what these mean.

What the diagram shows is that whatever Ps

are, they are all Bs, because the P circle is

completely enclosed by the B circle. Likewise

the B circle, and the P circle with it, are

completely inside the F circle. Therefore, since

all Ps are Bs and all Bs are Fs, it follows that all

Ps are Fs – whatever P, B and F stand for. And

that is why [4] is valid.

Soundness

You should now be able to see that this form of

argument will never give a false conclusion if

its two premises are true. So if we take a valid

structure, like [4], and substitute true premises,

we have a sound argument and a reliable

conclusion. For instance:

[5] R1 All fish have gills.

R2 Sharks are fish.

C Sharks have gills.

This argument rests on the truth of R1 and R2.

Someone might object that R1 was false

because whales and dolphins, which are

mammals, are ‘fish’ in the everyday sense of

the word – i.e. creatures that live and swim in

the sea – but don’t have gills. That would be a

challenge to the soundness of the argument,

but not to its validity. You could respond by

stating that all true fish (which excludes the

aquatic mammals, jellyfish and so on) have

gills; and sharks are true fish. But however you