Topic 20: Deductive Argument

In some arguments there appears to be a kind of irresistible logical force at work. In such cases, the contention follows inexorably from the premises; accept the latter and it seems you are rationally compelled to accept the former. Consider for example:

Figure 2.20

If you accept that every Scot is a devotee of Robert Burns, and you accept that Dougal McDowell is a Scot, you must also accept that Dougal McDowell is a devotee of Robert Burns.

Or, put another way – it is impossible for Douglas McDowell not to be a devotee of Robert Burns, if indeed he is a Scot, and all Scots are devotees of Robert Burns. This relationship between premises and contention is known as validity – technically, an argument is valid if it is impossible for the contention to be false if the premises are true.

Notice another thing about our example – it works just as well for Tania McTaggart as it does for Dougal McDowell. Indeed, we can abstract away entirely from Scots, and Robert Burns, and see that the real work is being done by the logical structure of the argument, rather than the meanings of the terms:

Figure 2.21

Figure 2.22

The original argument seemed utterly compelling, even though you probably do not know Dougal McDowell, because its logical form seemed to guarantee that the contention would follow.

A deductive argument is one which purports to be valid by virtue of

its logical form.

Put another way, such a deductive argument tries to force you from its premises to its (main) contention by virtue of the way it is constructed. Perhaps it is constructed correctly, and you should in fact accept its contention if you accept its premises. But it might be poorly constructed, in which case the argument, though deductive, is invalid.

Deductive arguments are enormously important in logic, and in related fields such as mathematics and computer science. A large and often very technical sub-field of logic, known as formal logic, is devoted to the study of deductive arguments.

In ordinary or ‘everyday’ reasoning, we do often encounter deductive arguments, though generally these arguments belong to a limited number of simple types. More commonly, everyday arguments are not deductive. To determine whether or to what extent they guarantee their contentions, we must look at more than just the logical form; we need to know what the terms mean, and something about the domain those terms are describing.

Indeed, most everyday arguments do not even purport to be valid; they purport to increase the acceptability of their contentions, rather than guarantee them. There are many kinds of non-deductive arguments, but they are usually contrasted with inductive arguments (those involving some kind of extrapolation or generalization) and abductive arguments (those concerned with explaining some range of evidence).