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Critical Thinking Handout 2
Can you prove it?
An example in critical thinking
‘Proof’ is an important concept in critical thinking. We want pupils to be able to
decide whether or not a statement someone has made is justifiable. If we ask
someone to ‘prove’ something then we are asking them to justify their statement.
This would normally be understood to be a good question to ask when thinking
critically as you are not accepting something at face value.
But consider the following examples:
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Can you prove that the area of a circle is πr2?
Can you prove that water contains hydrogen?
Can you prove that the earth has moving tectonic plates?
Can you prove that perestroika led to the collapse of the Soviet Union?
Can you prove that Abai wanted Kazakhstan to look to the west?
Each of these is a good example of ‘thinking critically’ as someone who asks these
questions is not accepting an answer at face value. However, how would
someone go about finding out the answer to those questions? The problem here
is that the word ‘proof’ means something different in each case.
Question
Can you prove that
the area of a circle is
πr2?
What kind of proof?
Mathematical proof
Explanation
Mathematical proof can be proved by
tautology, by showing there are no
exceptions, geometrically, and so on.
Can you prove that
water contains
hydrogen?
Scientific proof (in
chemistry)
Can you prove that
the earth has
moving tectonic
plates?
Scientific proof (in
geology)
Can you prove that
perestroika led to
the collapse of the
Soviet Union?
Historical ‘proof’
Can you prove that
Abai wanted
Kazakhstan to look
to the west?
‘Proof’ in Literature
In many sciences proof is made by
experimentation: an experiment is created in
which the hypothesis (water contains
hydrogen) is tested.
It is hard to create experiments to test the
theory of tectonic plate movement (evolution
is another good example) are plate movement
cannot be recreated in a controlled
experiment in a laboratory. Instead, scientists
have to collect as many pieces of evidence as
possible and see how well their theory
explains their measurements.
In history one cannot measure events in the
past as one cannot go back in time! Therefore
historians have to collect evidence from
written records and other sources and use
these to reach judgements about the causes of
events.
The idea that we can ‘prove’ what someone
thought in the past is very controversial and
many would say it is impossible. In literature,
the emphasis tends to be on what an author
meant when they wrote something.
Critical Thinking Handout 2
So in these cases, the word ‘proof’ means something different, and if you got
these mixed up you would be in trouble! You can not, for example, try to ask and
answer questions about the causes of the collapse of the Soviet Union by
recreating it in a test tube. Similarly, it would not be acceptable to say ‘Water
contains hydrogen because someone said it did in the past’. Different disciplines
require different kinds of proof, and these are not necessarily transferable
between different domains.
Let’s bring this back to critical thinking. In order to know what is an appropriate
form of critical thinking, one needs to know what the best kind of thinking is for
that situation. As teachers, you have to teach children how to identify the kinds
of questions that might be asked and the appropriate ways in which those
questions might be answered. This is at the heart of a more sophisticated
understanding of ‘critical thinking’.
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