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.

ValidSome 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.

InvalidThe 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.

InvalidThis 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.

ValidThe 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.

InvalidIt 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.

InvalidCorrelation 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.

InvalidAlthough 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.

InvalidThis 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.

ValidThis 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.