Syllogism

1. Logic A form of deductive reasoning consisting of a major premise, a minor premise, and a conclusion; for example, All humans are mortal, the major premise, I am a human, the minor premise, therefore, I am mortal, the conclusion.
2. Reasoning from the general to the specific; deduction.
3. A subtle or specious piece of reasoning.

1. (Philosophy / Logic) a deductive inference consisting of two premises and a conclusion, all of which are categorial propositions. The subject of the conclusion is the minor term and its predicate the major term; the middle term occurs in both premises but not the conclusion. There are 256 such arguments but only 24 are valid. Some men are mortal; some men are angelic; so some mortals are angelic is invalid, while some temples are in ruins; all ruins are fascinating; so some temples are fascinating is valid. Here fascinating, in ruins, and temples are respectively major, middle, and minor terms
2. (Philosophy / Logic) a deductive inference of certain other forms with two premises, such as the hypothetical syllogism, if P then Q; if Q then R; so if P then R
3. (Philosophy / Logic) a piece of deductive reasoning from the general to the particular
4. (Philosophy / Logic) a subtle or deceptive piece of reasoning
[via Latin from Greek sullogismos, from sullogizesthai to reckon together, from sul- syn- + logizesthai to calculate, from logos a discourse

1. an argument of a form containing a major premise and a minor premise connected with a middle term and a conclusion, as “All A is C; all B is A; therefore, all B is C.”
2. deductive reasoning.
3. an extremely subtle, sophisticated, or deceptive argument.
[1350–1400; Middle English silogime < Old French < Latin syllogismus < Greek syllogismós=syllog- (see syllogize) + -ismos -ism]

Source

www.thefreedictionary.com