Definition and Examples of Syllogisms

In logic, a syllogism is a form of deductive reasoning consisting of a major premise, a minor premise, and a conclusion. Adjective: syllogistic. Also known as a categorical argument or a standard categorical syllogism. The term syllogism is from the Greek, "to infer, count, reckon"

Here is an example of a valid categorical syllogism:

Major premise: All mammals are warm-blooded.
Minor premise: All black dogs are mammals.
Conclusion: Therefore, all black dogs are warm-blooded.

In rhetoric, an abridged or informally stated syllogism is called an enthymeme.

Pronunciation: sil-uh-JIZ-um

Examples and Observations

• "Among this country's enduring myths is that success is virtuous, while the wealth by which we measure success is incidental. We tell ourselves that money cannot buy happiness, but what is incontrovertible is that money buys stuff, and if stuff makes you happy, well, complete the syllogism."
  (Rumaan Alam, "Malcolm Forbes, 'More Than I Dreamed.'" The New York Times, June 8, 2016)
• Flavius: Have you forgot me, sir?
  Timon: Why dost ask that? I have forgot all men;
  Then, if thou grant'st thou'rt a man, I have forgot thee.
  (William Shakespeare, Timon of Athens, Act Four, scene 3

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Definition and Examples of Conclusions in Arguments

By Richard Nordquist

Major Premise, Minor Premise, and Conclusion

"The process of deduction has traditionally been illustrated with a syllogism, a three-part set of statements or propositions that includes a major premise, a minor premise, and a conclusion.

Major premise: All books from that store are new.
Minor premise: These books are from that store.
Conclusion: Therefore, these books are new.

The major premise of a syllogism makes a general statement that the writer believes to be true. The minor premise presents a specific example of the belief that is stated in the major premise. If the reasoning is sound, the conclusion should follow from the two premises. . . .
"A syllogism is valid (or logical) when its conclusion follows from its premises. A syllogism is true when it makes accurate claims—that is, when the information it contains is consistent with the facts. To be sound, a syllogism must be both valid and true. However, a syllogism may be valid without being true or true without being valid."
(Laurie J. Kirszner and Stephen R. Mandell, The Concise Wadsworth Handbook, 2nd ed. Wadsworth, 2008)

Rhetorical Syllogisms

"In building his theory of rhetoric around the syllogism despite the problems involved in deductive inference Aristotle stresses the fact that rhetorical discourse is discourse directed toward knowing, toward truth not trickery. . . . If rhetoric is so clearly related to dialectic, a discipline whereby we are enabled to examine inferentially generally accepted opinions on any problem whatsoever (Topics 100a 18-20), then it is the rhetorical syllogism [i.e., the enthymeme] which moves the rhetorical process into the domain of reasoned activity, or the kind of rhetoric Plato accepted later in the Phaedrus."
(William M.A. Grimaldi, "Studies in the Philosophy of Aristotle's Rhetoric." Landmark Essays on Aristotelian Rhetoric, ed. by Richard Leo Enos and Lois Peters Agnew. Lawrence Erlbaum, 1998

A Presidential Syllogism

"On Meet the Press, . . . [Tim] Russert reminded [George W.] Bush, 'The Boston Globe and the Associated Press have gone through some of their records and said there's no evidence that you reported to duty in Alabama during the summer and fall of 1972.' Bush replied, 'Yeah, they're just wrong. There may be no evidence, but I did report. Otherwise, I wouldn't have been honorably discharged.' That's the Bush syllogism: The evidence says one thing; the conclusion says another; therefore, the evidence is false."

(William Saletan, Slate, Feb. 2004)

Syllogisms in Poetry: "To His Coy Mistress"

"[Andrew] Marvell's "To His Coy Mistress" . . . involves a tripartite rhetorical experience which is argued like a classical syllogism: (1) if we had world enough and time, your coyness would be tolerable; (2) we do not have sufficient world or time; (3) therefore, we must love at a faster rate than gentility or modesty permit. Although he has written his poem in a continuous sequence of iambic tetrameter couplets, Marvell has separated the three elements of his argument into three indented verse-paragraphs, and, more important, he has proportioned each according to the logical weight of the part of the argument it embodies: the first (the major premise) contains 20 lines, the second (the minor premise) 12, and the third (the conclusion) 14."
(Paul Fussell, Poetic Meter and Poetic Form, rev. ed. Random House, 1979)

The Lighter Side of Syllogisms

Dr. House: Words have set meanings for a reason. If you see an animal like Bill and you try to play fetch, Bill's going to eat you, because Bill's a bear.
Little Girl: Bill has fur, four legs, and a collar. He's a dog.
Dr. House: You see, that's what's called a faulty syllogism; just because you call Bill a dog doesn't mean that he is . . . a dog.
("Merry Little Christmas, House, M.D.)
"LOGIC, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a conclusion--thus:

Major Premise: Sixty men can do a piece of work sixty times as quickly as one man.
Minor Premise: One man can dig a posthole in sixty seconds;
therefore--
Conclusion: Sixty men can dig a posthole in one second. This may be called the syllogism arithmetical, in which, by combining logic and mathematics, we obtain a double certainty and are twice blessed."

(Ambrose Bierce, The Devil's Dictionary)

"It was at this point that the dim beginnings of a philosophy began to invade her mind. The thing resolved itself almost into an equation. If father had not had indigestion he would not have bullied her. But, if father had not made a fortune, he would not have had indigestion. Therefore, if father had not made a fortune, he would not have bullied her. Practically, in fact, if father did not bully her, he would not be rich. And, if he were not rich . . .. She took in the faded carpet, the stained wall-paper, and the soiled curtains with a comprehensive glance. . . . It certainly cut both ways. She began to be a little ashamed of her misery."
(P.G. Wodehouse, Something Fresh, 1915)