In deductive reasoning, your conclusion states with certainty a relationship between two or more premises. It has to be certain, because it simply makes explicit a relationship that is already there (but not directly obvious) in the combination of the claims that are serving as premises. You will remember this aspect from the discussion of claims in chapters 2 to 4. Let us look at an example:

I am under 18; people under 18 in Australia cannot vote. Therefore I cannot vote.

There are three key terms in this argument. One is age (under 18); the other is voting; and the last is 'I'. The conclusion simply re-expresses the implicit relationship of the premises which can be expressed, in a formula way, like this:

A is one of B; B can't do C; therefore A can't do C.

The certainty with which (in this argument) the conclusion is stated relates not to the truth or otherwise of the premises but to the logical form of the argument. If it turns out that the premises are indeed true, then the conclusion is guaranteed both by the truth of the premises and by the form of the reasoning.

The key test for a deductive argument is to ask yourself, being absolutely trusting, 'can you deny the conclusion, if it is that you previously have no doubt or deny the premises'. For example:

African swallows are migratory birds; all migratory birds fly long distances and therefore I conclude African swallows fly long distances.

Now, let us assume absolutely and without doubt that the premises are true. Can you deny (refuse to accept) the conclusion now? No! Do not be confused and think 'Ah, but maybe African swallows are not migratory birds'; if you have this doubt then you have not accepted the first premise. Deductive thinking is something of a mind game (an important one, nevertheless): checking for deductive entailment (where the conclusion is guaranteed by the premises) first

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