12 Arguments in Ordinary Language
Arguments in Ordinary Language
People reasoning in ordinary language rarely express their arguments in the restricted patterns allowed in categorical logic. But with just a little revision, it is often possible to show that those arguments are in fact equivalent to one of the standard-form categorical syllogisms whose validity we can so easily determine. Let’s consider a few of the methods by means of which we can “translate” ordinary-language arguments into the forms studied by categorical logic.
Translation into Standard Form
In the simplest case, we may need only to re-arrange the propositions of the argument in order to translate it into a standard-form categorical syllogism. Thus, for example, “Some birds are geese, so some birds are not felines, since no geese are felines” is just a categorical syllogism stated in the non-standard order minor premise, conclusion, major premise; all we need to do is put the propositions in the right order, and we have the standard-form syllogism:
No geese are felines. Some birds are geese. Therefore, Some birds are not felines.
Reducing Categorical Terms
In slightly more complicated instances, an ordinary argument may deal with more than three terms, but it may still be possible to restate it as a categorical syllogism. Two kinds of tools will be helpful in making such a transformation:
First, it is always legitimate to replace one expression with another that means the same thing. Of course, we need to be perfectly certain in each case that the expressions are genuinely synonymous. But in many contexts, this is possible: in ordinary language, “husbands” and “married males” almost always mean the same thing.
Second, if two of the terms of the argument are complementary, then appropriate application of theimmediate inferences to one of the propositions in which they occur will enable us to reduce the two to a single term. Consider, for example, “No dogs are non-mammals, and some non-canines are not non-pets, so some non-mammals are pets.” Replacing the first proposition with its (logically equivalent) obverse, substituting “dogs” for the synonymous “canines” and taking the contrapositive of the second, and applying first conversion and then obversion to the conclusion, we get the equivalent standard-form categorical syllogism:
All dogs are mammals. Some pets are not dogs. Therefore, Some pets are not mammals.
The invalidity of this syllogism is more readily apparent than that of the argument from which it was derived.
Recognizing Categorical Propositions
Of course, the premises and conclusion of an ordinary-language argument may not be categorical propositions at all; even in this case, it may be possible to translate the argument into categorical logic. For each of the propositions of which the argument consists, we must discover some categorical proposition that will make the same assertion.
One especially common but troublesome instance is the occurrence of singular propos