## C1

In this case the argument whose conclusion is CI is a sub-argument for an extended argument whose conclusion is C2. You would first assess the argument from PI and P2 to CI; you would then assess the argument from CI and P3 to C2. Finally, you would use these results to assess the total argument from PI, P2 and P3 to C2.

Assessment is to be distinguished from reconstruction, which is discussed in more detail in the next chapter. Broadly speaking, assessment may be said to fall into two categories: The first we may call logical assessment, which is that whereby we make judgements of deductive validity and inductive force. The second we may call factual assessment; here is where we ask after the truth-values of premises, in determining the soundness of arguments already found to be deductively valid or inductively forceful. However, as noted, the evaluation of inductive inferences is not purely the one nor purely the other: it is partly logical and partly factual.

It is important to realise that if your verdict is that the argument, as you have reconstructed it, is not deductively sound, you might be able to reconstruct it so as to make it inductively sound. Look again at the example involving Fiona and wool. An early attempt at reconstructing it used the premise 'Everyone in Inverness owns at least one article of woollen clothing'. So rendered, the argument was valid, but not sound. We then weakened the premise to 'Almost everyone in Inverness owns at least one article of woollen clothing'. The result was not deductively valid, but it was inductively forceful. In general, it is best to sacrifice validity to soundness when reconstructing.

Later, we will learn some techniques which aid logical assessment. There is, you will appreciate, no readily definable procedure for factual assessment; for this is simply the task of determining whether particular propositions are true - e.g. whether there are blue whales in the Black Sea, whether inflation rose in 1993, and so on. For that we must look outside logic books!

The conditional probability of a proposition relative to a set of CHAPTER premises is the degree to which it would be rational to expect it SUMMARY to be true, given no information relevant to the conclusion except that given in the premises. Estimates of rational expectation are often based upon other measures of probability such as proportion and frequency, but need not be.

A deductively valid argument enables us to be certain of the truth of its conclusion, if we are certain of the truth of its premises. An inductively forceful argument does not allow this, but it does allow us, in the absence of other information relevant to the truth-value of the conclusion, to think its conclusion more likely to be true than not: an inductively forceful argument is one for which the conditional probability of the conclusion relative to the premises is greater than 0.5.

Like deductive validity, both probability and inductive force are objective: the conditional probability of a conclusion relative to a given set of premises is independent of people's actual estimates of conditional probability. But unlike deductive validity, both probability and inductive force are a matter of degree. An argument may be inductively forceful but only just barely.

Inductively sound arguments are inductively forceful arguments with true premises. Unlike deductively sound arguments, they may have false conclusions.

Some arguments contain inductive inferences. An inductive inference is a deductively invalid inference whose premise is a generalisation about some sample of a given population, and whose conclusion is a generalisation about the population as a whole (the population may comprise simply the original sample plus one new case). In general, the force of an inductive inference depends on the degree to which the sample is representative of the population.

EXERCISES 1 Each argument below contains a premise with a missing quantifier.

Reconstruct the argument, adding an appropriate quantifier. If possible, make the premise true. Use the strongest quantifier you can, so long as the premise still seems to be true (that is, don't use 'most', if a phrase such as 'almost all' seems to you to result in a true premise). If the resulting argument is deductively valid, say so. If the argument is inductively forceful, insert 'Probably' before the conclusion.

a Sex crimes are committed by people who have themselves been victims of child abuse. The defendant has committed a sex crime. Therefore the defendant was a victim of child abuse.

b Children love the Harry Potter books. Therefore your child will love the Harry Potter books.

c If doctors in this country are overworked, then the general health of the population will decline. Doctors in this country are overworked. Therefore, the general health of the population will decline.

d Old people have poor eyesight. No one with poor eyesight should be allowed to drive. Therefore, most old people should not be allowed to drive.

e In countries colonised by Spain, there are many people of Spanish descent. There are very few people of Spanish descent in Laos. Therefore Laos was not colonised by Spain.

2 Consider the following pair of arguments.

P1) Most AIDS patients in California are homosexual. P2) Mr X is a California AIDS patient.

C) Mr X is a homosexual.

P1) Most residents of Orange County, California, are not homosexual.

P2) Mr X is a resident of Orange County, California.

C) Mr X is not homosexual.

Assume that this is the same Mr X referred to in each argument. Are these arguments inductively forceful? Could both arguments be inductively sound? If not, explain why not. Otherwise, describe a scenario in which they would both be sound. If we knew the premises of both arguments to be true, would we have reason to believe, or not to believe, that Mr X is homosexual?

3 Two statements are incompatible if it is impossible for both of them to be true (if they are incompatible, it may or may not be possible for both to be false). Which of the following pairs of statements are incompatible?

a Some hamsters are black. All hamsters are white, b Some hamsters are black. Some hamsters are white, c Some hamsters are black. Most hamsters are not black, d Some hamsters are black. All hamsters are black, e No hamsters are black. Most hamsters are black, f Every hamster is black. This hamster is white, g This hamster is black. Some hamsters are white, h No hamster is black. No hamster is not black, i No hamster is black. No hamster is white, j Some hamsters are black. There is exactly one black hamster, k Most hamsters are black. Many hamsters are white. I Most hamsters are black. All my hamsters are white, m Most hamsters are black. Every hamster in England is white.

4 Reconstruct the following as either three separate arguments or as one, depending on which strategy would amount to a more forceful case.

Lewis is probably not going to win another gold medal in the 100 metres. He is now older than any previous winner of the event. His form has been poor this year, and he has a hamstring injury.

5 Reconstruct the following arguments. Say whether or not they are inductively forceful. If the argument is not inductively forceful, change one premise so that it is.

a If alcohol advertising is banned, then, probably, drinking would decline. If drinking declines, then, domestic violence would decline. Therefore, if alcohol advertising is banned, then, probably, domestic violence would decline.

b If alcohol advertising is banned, then, probably, drinking would decline. If drinking declines, then, probably, domestic violence would decline. Therefore, if alcohol advertising is banned, then, probably, domestic violence would decline.

c Most children who go without breakfast have trouble concentrating at school in the morning. Johnny concentrates well at school in the morning. Therefore, probably, he does not go without breakfast.

d If this meat was grown in Scotland, then it is extremely unlikely that it is infected with BSE. And even if it is infected, then it is very unlikely that eating it will make you ill. Therefore, if this meat was grown in Scotland, then it is not probable that eating this meat will make you ill.

e Brazil is more likely to win the World Cup than Argentina. Therefore, probably, Brazil will win the World Cup.

f Scotland has never won the World Cup. Therefore, probably, Scotland will never win the World Cup.

g Probably, English football fans will make trouble at the next World Cup. If English football fans do make trouble at the next World Cup, then there is a good chance that England will be expelled from the European Cup. Therefore, it is very likely that England will be expelled from the European Cup.

h Very few habitual cannabis users are violent. The murderer is clearly very violent. Mr X is a habitual cannabis user. Therefore, probably, Mr X is not the murderer.

i UN intervention in local conflicts usually leads to a more stable political situation. A more stable political situation usually leads to economic growth. Therefore, probably, UN intervention in this local conflict will lead to economic growth.

j Almost all successful athletes have trained long and hard to become successful. Therefore, if you train long and hard, you will become a successful athlete.

k Some teachers at Lenman secondary school are known to smoke cannabis. Mr X is a teacher at Lenman secondary school. Therefore, probably, Mr X smokes cannabis.

I Most vegetarians eat eggs. A great many people in Berkeley are vegetarians. Roger is from Berkeley. Therefore, probably, Roger eats eggs.

m If Hansen is leaving early tomorrow, then, probably, he isn't in the bar. Hansen isn't in the bar. So probably he is leaving early tomorrow.

6 The following passages contain inductive inferences. First, rewrite them as arguments in standard form. (You may have to supply a missing quantifier.) Can you think of any reasons why the sample might not be representative? If so, list them.

a The elimination of sweets and other junk food from school lunch menus has resulted in improved student performance in schools all over the country, and in every case in which it has been tried. If we do this at our school, then, we can look forward to improved performance.

b No communist system can succeed. Since communist regimes began early in the twentieth century, every one has either collapsed, or is near collapse.

c Surprisingly, musicians have a higher average IQ than either doctors or lawyers. A study of seventeen conductors of major orchestras found their average IQ to be 1 7 points higher than that of UK doctors, and 18 points higher than that of UK lawyers.

d Most teenagers who take illicit drugs have serious family problems. I know, because as a counsellor for teenagers I have found that most of those who have come to me and confessed to taking illicit drugs do have serious family problems.

e Manchester United is not going to win the treble again. No English team has won it twice.

f Studies have shown that people who take vitamins regularly live longer than average. So if you take vitamins regularly, then, probably, you will live longer than average.

Chapter 4

Rhetorical ploys Fallacies Formal fallacies

0 0