A syllogism ("conclusion," "inference"), (usually the categorical syllogism) is a kind of logical argument in which one proposition (the conclusion) is inferred from two others (the premises) of a certain form. In Aristotle's Prior Analytics, he defines syllogism as "a discourse in which, certain things having been supposed, something different from the things supposed results of necessity because these things are so". Despite this very general definition, he limits himself first to categorical syllogisms (and later to modal syllogisms). The syllogism is at the core of deductive reasoning, where facts are determined by combining existing statements, in contrast to inductive reasoning where facts are determined by repeated observations.
A syllogism (henceforth categorical unless otherwise specified) consists of three parts: the major premise, the minor premise, and the conclusion. In Aristotle, each of the premises is in the form "Some/all A belong to B," where "Some/All A' is one term and "belong to B" is another, but more modern logicians allow some variation. Each of the premises has one term in common with the conclusion: in a major premise, this is the major term (i.e., the predicate) of the conclusion; in a minor premise, it is the minor term (the subject) of the conclusion. For example:
Major premise: All humans are mortal.
Minor premise: Socrates is human.
Conclusion: Socrates is mortal.
People often make mistakes when reasoning syllogistically. For instance, given the following parameters: some A are B, some B are C, people tend to come to a definitive conclusion that therefore some A are C.
However, this does not follow. For instance, while
some cats (A) are black (B), and
some black things (B) are televisions (C),
it is false that some cats (A) are televisions (C).
This is because first, the mood of the syllogism invoked is illicit, and second, the supposition of the middle term is variable between that of the middle term in the major premise, and that of the middle term in the minor premise (not all "some" cats are by necessity of logic the same "some black things").
Some wrong syllogisms, but full of humor:
God is Love.
Love is blind.
Steve Wonder is blind.
Conclusion: Steve Wonder is God !
Nothing is perfect.
God is Perfect.
So, I'm God !
If Steve Wonder is God,
I'm Steve Wonder.
God's Sake!...I'm blind !
My name is Charles.
Charles is a noun.
God is Verb, not Noun.
Thus, I'm not God.
The devil is ugly.
My wife is ugly.
You see, my wife is the devil!!