# Is there a way to generate the 24 valid syllogisms in term logic?

There are four qualifiers in term logic, organized according to two distinctions: particular/universal (some versus all) and affirmative/negative (permitting none and not all).

There are 256 combinations of these quantifiers in the form of a syllogism. One is 'AAA', or `(all x are y) and (all y are z) implies (all x are z)`.

Out of these 256, only 24 combinations are valid. Is there an effective strategy to generate these 24 valid forms, possibly from simpler rules relating to the quantifiers? (For instance: `all implies some`...?)

• a quibble: there is no quantification in term logic, so no quantifiers. quantification was a radical innovation invented in the 19th c.
– user20153
Dec 3, 2016 at 20:42
• Thanks @mobileink -- is there a better way to call them? (I notice there's also indefinite/singular modes of these as well as universal, existential, etc) Dec 3, 2016 at 22:32
• not that I know of, alas. I suspect the right idea is that these were qualifiers, grammatical rather than logical operators, serving to modulate the sense of the sentence as a whole. but that's a guess - I've looked around a good bit and haven't found anything much. I know Fred Sommers is a contemporary philosopher who did a lot of work in term logic, so you might start there, but I haven't read his stuff.
– user20153
Dec 5, 2016 at 19:53
• I agree with mobileink. As a matter of fact, when I read the sentence, I read it as "There are four qualifiers..." not "quantifiers." If you make a map of the possible "combinations" and identify the 24 valid ones, you might be able to use combinatorial logic to obtain them. Dec 6, 2016 at 0:08