Deductive And Inductive Arguments

The purpose of any argument, we have seen, is to convince an audience to accept a conclusion, by providing reasons or evidence. But although this is the common purpose of all arguments, there are different kinds of reasoning associated with different kinds of evidence that might be given for a conclusion. Two broad classifications of reasoning are deductive and inductive reasoning. Deductive and inductive arguments are distinguished according to the kind of support their premises are supposed to offer for their conclusions. An argument whose conclusion is supposed to follow, with certainty, from its premises is a deductive argument. The conditional arguments we looked at last lecture, and arguments (1a) (1b) and (1c) above, are all examples of deductive arguments. (Note that we don't say an argument is deductive only if its conclusion does follow with certainty from its premises, since that would not be true of invalid deductive arguments.) Why do deductive arguments have this feature? You will notice that for each of these deductive arguments, the information contained in the conclusion is, in a sense, already contained in the premises. For example if we know that all dentists are wealthy, and we know that Sam is a dentist, then we do already have enough information to know that Sam is wealthy. The point of the argument is just to draw out this fact for some purpose, and to make that proposition explicit.

In drawing a conclusion deductively from a set of premises we do not go beyond the information we already have, we just make explicit some point which was implicit, or extract some particular piece of information from the content of the premises. This is why the conclusions of successful (that is, valid) deductive arguments follow from their premises with certainty.

An inductive argument, on the other hand, is one in which the truth of the premises would make the conclusion likely to be true, or probable. In any argument, the premises will be used to attempt to convince you of the truth of the conclusion. The difference between deductive and inductive arguments in this regard is that someone giving an inductive argument will not be trying to convince you that the conclusion is

absolutely certain; only that, because of the evidence given in the premises, you have good reason to believe that the conclusion will be true.

Deductive arguments were described as either valid or invalid, but these descriptions will not be applied to inductive arguments. Inductive arguments may be described as strong or weak, and unlike deductive validity, inductive strength is a matter of degree. How strong an inductive inference is will be a matter of how much support the premises give for the conclusion. Inductive inferences may be strengthened or weakened with the addition of new evidence.

The fact that the conclusions of inductive arguments do not follow with certainty from their premises should not be taken to mean that the conclusions of inductive arguments are things that we are really unsure about -- for many such conclusions there will be no real doubt. In the case of the flame example above there is no genuine doubt about whether the new flame will burn your hand -- the fact that an argument is inductive is not a reason to be unduly sceptical about its conclusion. It is just a fact that for many of the propositions we might want to establish, no absolute certainty is possible. The proponent of an inductive argument may not

make the uncertainty explicit by prefacing the conclusion with "It is likely that ..." and in many cases it would seem inappropriate to do so. But, if challenged, someone presenting an inductive argument would have to admit that the conclusion did not follow with absolute certainty from the premises.

Many common kinds of arguments are inductive, for example

(2a) Every day I have driven along here there has been a speed camera just around the corner. So it will probably be there today as well.

(2b) In recent polling, only 10% of those surveyed said they intended to vote for a minor party, and 5% for an independent. So an overwhelming majority of Australians will be voting for one of the major parties in the next election.

(2c) The car won't start and the lights won't go on. It must have a flat battery.

(2d) The patients who took the new drug recovered, on average, six days before patients treated with the standard medicine. Some of them did, however, complain of headaches or a rash, which had not occurred with the conventional treatment. The new drug, it appears, leads to a faster recovery, but may also cause minor side effects.

(2e) The original movie was dreadful. The sequel has the same writer, the same director and the same cast. So it will be dreadful too.

In each case, the conclusion is likely, given the truth of the premises, but it is not certain. It won't be certain because in drawing an inductive inference, we go beyond the information we already have, to draw a conclusion which involves new claims which were not already contained in the premises. This is why

inductive arguments are less certain -- even a strong inductive argument with true premises may turn out to have a false conclusion -- but it is also why they are so important in arriving at new information. The means by which we will evaluate inductive arguments will be different to our means of assessing deductive arguments, since their strength or weakness is not just a matter of their form.

The five arguments above are examples of the main kinds of inductive arguments we will be studying. Argument (2a) is an inductive generalisation, which uses a premise about something which has been experienced or observed to draw a conclusion about something which has not.

Argument (2b) is a statistical generalisation. These are a kind of inductive generalisation, which use a premise about the prevalence of a certain property within a sample of experienced cases, to draw the conclusion that the prevalence of that property is similar in the population.

Argument (2c) is an inference to the best explanation. From premises which describe certain observed facts, a conclusion is drawn on the basis that it is the best explanation for those observed facts.

Argument (2d) is a causal argument. From observing relationships between certain kinds of events in a sample of observed cases, a general conclusion is drawn about causes and effects.

Argument (2e) is an argument from analogy. An argument from analogy uses the similarity between two or more things or events in certain respects as evidence for a conclusion that they will also be similar in other respects. This argument suggests that because the two movies are similar in some ways (same writer, director and cast), that they will probably be similar in another way (dreadfulness).

Each of these kinds of inductive argument will be explored over the coming lectures.

4.6.1 Deductive and inductive arguments: summary

A DEDUCTIVE ARGUMENT:

1. Is one whose premises, if true, are supposed to guarantee the truth of its conclusion 2. May be valid or invalid

4. Will be invalid if it would be possible for the premises to be true but the conclusion false. 5. Will be sound if it is valid, and has true premises (and therefore a true conclusion)

6. Does not go beyond the information contained in the premises. A deductive conclusion may be used to make explicit something which was implicit, but will not allow us to arrive at genuinely novel facts.

AN INDUCTIVE ARGUMENT:

1. Is supposed to provide good reasons for thinking the conclusion is likely, or probable, but does not establish its conclusion with certainty.

2. Will not be evaluated as valid or invalid, but according to its inductive strength, which is a matter of degree.

3. Allows us to go beyond the information contained in the premises, to establish new information in the conclusion

4. Even if it has true premises, and is inductively strong, is still open to possible disconfirmation: We could find some new piece of evidence which shows the conclusion is false.