16 Logic
‘If there are fewer cars on the roads the pollution will be
acceptable. Either we have fewer cars on the road or there should be
road pricing, or both. If there is road pricing the summer will be
unbearably hot. The summer is actually turning out to be quite cool.
The conclusion is inescapable: pollution is acceptable.’
Is this argument from the leader of a daily newspaper ‘valid’ or is it
illogical? We are not interested in whether it makes sense as a policy
for road traffic or whether it makes good journalism. We are only
interested in its validity as a rational argument. Logic can help us
decide this question – for it concerns the rigorous checking of
reasoning.
Two premises and a conclusion
As it stands the newspaper passage is quite complicated. Let’s look at some
simpler arguments first, going all the way back to the Greek philosopher Aristotle
of Stagira who is regarded as the founder of the science of logic. His approach
was based on the different forms of the syllogism, a style of argument based on
three statements: two premises and a conclusion. An example is
Above the line we have the premises, and below it, the conclusion. In this
example, the conclusion has a certain inevitability about it whatever meaning we
attach to the words ‘spaniels’, ‘dogs’ and ‘animals’. The same syllogism, but using
different words is