‘Not Always’ or ‘Not’

We say “not always” rather than simply “not,” because there are some strange cases— logicians call them “degenerate cases“—for which inferences of this pattern are valid. For ex- ample, from “Some men are not men,” we may validly infer “Some men are not men.” Here, by making the subject term and the predicate term the same, we trivialize conversion. Keeping cases of this kind in mind, we must say that the inference from an O proposition to its converse is usually, but not always, invalid. In contrast, the set of valid arguments holds in all cases, in- cluding degenerate cases.

2 We cannot say “only if” here because of degenerate cases of categorical syllogisms that are valid, but not by virtue of their syllogistic form. Here is one example: “All numbers divisible by two are even. No prime number other than two is divisible by two. Therefore, no prime num- ber other than two is even.” This syllogism is valid because it is not possible that its premises are true and its conclusion is false, but other syllogisms with this same form are not valid.

3 We need to add “by virtue of its categorical form,” because, as we saw above, it still might be valid on some other basis. In this particular example, however, nothing else makes this argu- ment valid.

Are the following claims true or false? Explain your answers.

1. Every syllogism that is valid on the modern approach is also valid on the classical approach.

2. Every syllogism that is valid on the classical approach but not on the modern approach has a particular conclusion that starts with “Some.”