major premise

noun Logic.
See under syllogism ( def 1 ).

Origin:
1855–60

Dictionary.com Unabridged

syllogism

[sil-uh-jiz-uhm]
noun
1.
Logic. an argument the conclusion of which is supported by two premises, of which one (major premise) contains the term (major term) that is the predicate of the conclusion, and the other (minor premise) contains the term (minor term) that is the subject of the conclusion; common to both premises is a term (middle term) that is excluded from the conclusion. A typical form is “All A is C; all B is A; therefore all B is C.”
2.
deductive reasoning.
3.
an extremely subtle, sophisticated, or deceptive argument.

Origin:
1350–1400; < Latin syllogismus < Greek syllogismós, equivalent to syllog- (see syllogize) + -ismos -ism; replacing Middle English silogime < Old French < Latin, as above

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World English Dictionary
major premise
 
n
logic the premise of a syllogism containing the predicate of its conclusion

syllogism (ˈsɪləˌdʒɪzəm)
 
n
1.  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.  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.  a piece of deductive reasoning from the general to the particular
4.  a subtle or deceptive piece of reasoning
 
[C14: via Latin from Greek sullogismos, from sullogizesthai to reckon together, from sul-syn- + logizesthai to calculate, from logos a discourse]

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Etymonline
Word Origin & History

syllogism
late 14c., from O.Fr. silogisme "a syllogism," from L. syllogismus, from Gk. syllogismos "a syllogism," originally "inference, conclusion, computation, calculation," from syllogizesthai "bring together, premise, conclude," lit. "think together," from syn- "together" + logizesthai "to reason, count,"
from logos "a reckoning, reason."
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
The utilitarian's major premise is that one tries to organize social
  arrangements to best serve the individuals that compose them.
But the major premise of marginalia is that life is infinitely adjustable.
Danger to police is a major premise of much contemporary police training for
  domestic disturbance calls.
The major premise of the meeting was that success in the future requires the
  ability to think and act strategically.
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