# Syllogism

A syllogism is a kind of logical argument in which one conclusion is inferred from two or more premises of a specific form. — Wikipedia

According to Wikipedia (and propositional calculus), all the following are invalid inferences.

All humans are mammals.
No cats are humans.
Hence, no cats are mammals.
(AEE-1)

Some humans are not male.
All fathers of humans are humans.
Hence, all fathers of humans are not male.
(OAE-1)

No humans are reptiles.
No cats are humans.
Hence, all cats are reptiles.
(OOA-1)

A few other resources agree with this.

However, introducing my Indonesian teacher. He believes that all of the above three syllogisms are valid (but wrong), while propositional calculus states that the above three are invalid.

Also, here’s another:
All Indonesians are humans.
All humans are mammals.
Hence, some mammals are Indonesians, given that the set of Indonesians is not empty.
(AAI-4)

Propositional calculus agrees that it’s valid, but my teacher basically rejects everything not in Format 1 (major MP, minor SM, conclusion SP).

I never know that the concept of syllogism is heavily different between Indonesian and math. English and math both agree on the given concept of syllogism as in Wikipedia, right? I’m pretty sure all other languages do the same (at least Greek does). Why Indonesian has an insane syllogism rules is beyond my comprehension. Or maybe not Indonesian, but this Indonesian teacher; after all, all Indonesian sources I’ve read also state the same thing, only my teacher differs.

Sooner or later I might as well ditch Indonesian language. Seriously. Either it’s illogical or my teacher is illogical.