Can you tell good arguments
from bad ones?
(Series 1)
You should read the document ‘TELLING GOOD ARGUMENTS FROM BAD’ before
attempting this test.
Study each argument and try to decide if it is valid (or if invalid, why). Then click the ‘page
down’ key to read an assessment of the argument. You may wish to keep your own tally of
how many you get right, as this system does not give you a score at the end.
If there are large wage rises, inflation will
occur. Therefore if inflation occurs, there
must have been large wage rises.
Invalid
The premise only says that one circumstance in
which inflation occurs is where there have been
large wage rises. It doesn’t say that this is the only
circumstance. Another way of putting this is to say
that according to the premise, large wage rises are
a sufficient condition for inflation, but it does not
say (as the conclusion would require) that they are
a necessary condition.
If there are large wage rises, inflation will
occur. Therefore if inflation is not to occur,
there must not be large wage rises.
Valid
According to the premise, if there were to be
large wage rises, there would be inflation. It
follows that if there is not to be inflation,
there must not be large wage rises.
Selfish people are miserable; Lazy people
are selfish. Therefore lazy people are
miserable.
Valid
Note that ‘Selfish people are miserable’ literally
means all selfish people are miserable. By the
second premise, the set of all selfish people
includes the set of all lazy people. So from both
premises together, it follows that all lazy people
are miserable. Of course, whether the premises
(and hence the conclusion) are true is another
matter entirely!
All the swans in the world that we have
observed so far have been white and we
have observed many of them in many
different locations. Therefore it is likely that
all swans in the world are white.
Valid
Some of you may know that there are black swans in
Australia. So the conclusion is false. Despite that, the
argument is a good one—it only says that it is likely that all
swans are white, and this is indeed likely relative to the
premise.
Nuclear power caused many deaths in the
Chernobyl disaster. Coal mining, in
comparison, is quite safe. Therefore we
should definitely try to meet our energy
demands through coal rather than through
nuclear power.
Invalid
The two premises are true, but the conclusion
does not follow. There may be much safer types of
nuclear reactor than the one used at Chernobyl.
Also, alternative energy sources (such as wind and
solar power) need to be considered.
(N.B. The argument is a rough paraphrase of one
used by the coal industry trade union leader Arthur
Scargill.)
Breast cancer screening reduces deaths by
about 25 per cent. Therefore if 1000 women
are screened, about 250 lives will be saved.
Invalid
Such a huge improvement would indeed be surprising. But what’s gone wrong
with the reasoning?
When it is said that screening reduces deaths by 25%, this means that, as a
result of screening, there will be 25% fewer deaths than there would otherwise
have been. Research has shown that without screening, 4 out of 1000 women
can be expected to die from breast cancer (0.4%); with screening the figure is 3
out of 1000 (0.3%). So screening can be expected to save one life out of
1000—nothing like the figure of 250 given on the previous slide. This is a good
example of the fact that people tend to get confused when health benefits are
given in percentage terms.
(Example and analysis from Prospect magazine.)
The mean salary paid by company X is
£30,000. Therefore if you were to choose an
employee at random, she would most likely
be earning around £30,000.
Invalid
This is all about different types of averages. It illustrates
how one type of average in particular – the ‘mean’ – can be
misleading. In this case, the mean salary in the company is
quite high. But this could be because of a few individuals
earning stratospherically high amounts – well above
£30,000. It doesn’t entail that the ‘typical’ employee earns
that much. (For more information, see Darrell Huff, How to
Lie with Statistics, chapter 2, from which this example is
taken.)
There is now overwhelming evidence that
the Earth’s temperature is rising due to the
industrial burning of fossil fuels and that this
process, if left unchecked, will lead to
catastrophic climate change. In any case,
reserves of gas and coal are finite and need
to be conserved. Reductions in our
consumption of fossil fuels are not
excessively costly. Therefore we should
make such reductions.
Valid
The premises are so strong that they undermine any
reasonable objection to the conclusion. Of course, the cost
of having strong premises is that they are harder to
substantiate, though the scientific consensus is that there
are good grounds for believing all of these and thus for
accepting the conclusion.
Marijuana is no more dangerous than
tobacco, which is legal. Therefore marijuana
should be legal too.
Invalid
It could be that society has got it wrong in legally permitting
the use of tobacco. The argument would need to show at
least that it is a good thing that tobacco is legal.
Rates of lung cancer are much higher in
people who smoke than in people who don’t.
Therefore Smoking causes lung cancer.
Invalid
Correlation does not equal causation. It could be that lung
cancer and a tendency to smoke are both caused by some
third factor. One thing that gives us some confidence that
this is not the way it happens and that it is indeed a matter
of smoking causing lung cancer is the fact that scientists
have a fairly good idea of the causal mechanism involved.
Members of group X are terrorists.
Therefore we should thoroughly condemn
them.
Invalid
Although the word ‘terrorism’ has largely negative
connotations, some people believe that there is
such a thing as justifiable terrorism. Someone who
supports the view that members of group X should
be condemned would need to show that what they
practise is unjustifiable terrorism. That would mean
looking at the circumstances surrounding their
actions, what the effects of these actions are likely
to be, and so on. An alternative way of improving
the argument would be to make the case that
terrorism is never in fact justified.
Bertrand Russell was an adulterer and
showed poor judgment in the upbringing of
his children. Therefore we should ignore his
views on ethical matters.
Invalid
This is an example of the fallacy of ‘argumentum ad
hominem’, i.e., attacking the person who makes the
argument instead of the argument itself.
Einstein’s General Theory of Relativity
makes quite precise predictions about how
the positions of distant stars can appear to
be altered as a result of their light being bent
by the Sun’s gravity. These predictions were
confirmed by Arthur Eddington in 1919. No
other (plausible) theory makes the same
predictions. Therefore Einstein’s theory is
probably true.
Valid
This is indeed good support for the theory. As one would
expect, more research has been done since 1919, and the
additional findings have confirmed Einstein’s theory.