250 Unit 7 Critical reasoning: Advanced Level
tell us whether or not it is. To express
necessary conditions you may need to employ
other words such as ‘not’, ‘only’ or ‘unless’.Activity
Here are six more conditional statements. For
each one say whether scoring 70 or more is a
necessary or a sufficient condition, or both:
A You will be offered a place only if you
score 70 or more.
B If you don’t get 70 or more you won’t be
offered a place.
C You will be offered a place if and only if
you score 70 or more.
D If you get 70, you are in.
E Unless you score 70, you won’t get a
place.
F If you score 70 you’re in, but if you don’t
you can always re-sit the exam.Commentary
In A and B the pass mark is a necessary
condition. Look at them carefully and you will
see they say the same thing. However, neither
of them says whether there is any other
requirement, such as an interview or a medical
or even some residential condition, such as
living in the country or town where the
college is. All A and B assert is that 70 is the
minimum requirement, which is yet another
way of saying that it is necessary for admission.
C sets a necessary and sufficient condition. It
is an abbreviation (or ‘contraction’) of two
statements: ‘You will get in if you score 70 or
more’ and ‘You won’t if you don’t.’ In logic such
statements are called biconditionals, ‘bi-’
meaning ‘two’. There are two conditions in one.
In D the condition is sufficient: it doesn’t
say whether it is necessary as well. Compare it
with [1], and note that it is really just another
way of expressing the same condition.
E obviously states a necessary condition but,
unlike A and B, it emphasises that scoring 70 is
not also a sufficient condition. F appears to donecessary condition, because a No response can
also lead to an offer. This is a fairly simple
scenario, with only two paths leading to a
positive outcome. In more complex situations,
with several branching paths, a diagram can be
a very useful aid for ‘reading off’ the conditions.According to the diagram, a score of at least 60
is a necessary condition, because the No branch
leads straight to a refusal. But it is not a
sufficient condition because there is still
another condition to be met after satisfying the
60+ condition: another branching of the tree.Conditional statements
Conditional statements, that is statements that
stipulate conditions, typically contain the word
‘if’, or ‘if’ followed shortly by ‘then’. For example:[1] If Mia scored 70 or more, then she has a
place.
Note that [1] is not an argument; it is just a
statement. It would be an argument if it were
expressed as follows:[2] Mia scored more than 70 and therefore
she has a place.
The difference is that in [2] it is asserted that
Mia did score more than the required mark,
whereas in [1] it remains a possibility. In both
cases, however, getting 70 or more is presented
as a sufficient condition. It may also be a
necessary condition, but the sentence doesn’t