252 Unit 7 Critical reasoning: Advanced Level
Commentary
We’ll consider the two arguments in turn,
starting with [5]. There are various ways in
which you could find fault with this argument.
You could say, for example, that it assumes,
without justification, that the minister’s reason
for resigning was the undeclared business
interest, whereas he might have resigned for
some other reason altogether. Another way to
explain this is that although the discovery of
undeclared interests would be sufficient to force
the minister’s resignation, it is not a necessary
condition, since (as already observed)
something else might have forced it. The
underlying argument in [5] is as follows:
If the minister has undeclared interests,
he would have had to resign.He has resigned.He must have an undeclared interest.
(The allegation must be true.)The argument in [5] is clearly unsound. [6]
does not make the same error. The first
premise states a necessary condition: it is
equivalent to saying that a minister would
resign only if the allegation were true; or that if
a government minister resigns over such an
allegation, then it must bear some truth.
Therefore, since the minister has resigned, the
inference can only be that there is some truth
in the allegation. The reasoning in [6] is solid.• Conditions can be divided into two kinds:
necessary and sufficient.
• Conditional, or hypothetical, statements
typically have the form ‘If p then q’.
• Confusing necessary with sufficient
conditions often results in reasoning
errors.Summary
Logical form
Logicians show the structure or form of
complex statements by substituting letters
(p, q, r, etc.) for the actual clauses.
A conditional statement has the form:If p then q.
Statement [1], at the beginning of the chapter,
has this form. In [1] p stands for: ‘Mia scored 70
or more’, and q stands for: ‘She (Mia) has a
place’. If we wanted to say that Mia did not get
70 or more, or that she does not have a place,
we could write ‘not-p’ or ‘not-q’ respectively. In
Chapter 7.2 we shall explore ways in which
these formal expressions can be helpful in
understanding and evaluating some
arguments.Conditions and reasoning errors
We have looked in some detail at conditions
and conditional (hypothetical) statements
because some of the most serious weaknesses
and flaws in arguments come from confusing
them.Activity
Critically evaluate the following two
arguments. What role do necessary and/or
sufficient conditions play in the reasoning?
Are these good or bad arguments?[5] If, as alleged, the government minister
has a business interest that he has not
declared, he would have certainly been
forced to resign. Last night he did
resign, so there must be truth in the
allegation.
[6] A government minister would not resign
over an allegation of undeclared
interests unless there was some truth in
it. The fact that he has resigned means
that there is some truth.