# syllogism

## Definitions

• WordNet 3.6
• n syllogism deductive reasoning in which a conclusion is derived from two premises
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Webster's Revised Unabridged Dictionary
• n Syllogism (Logic) The regular logical form of every argument, consisting of three propositions, of which the first two are called the premises, and the last, the conclusion. The conclusion necessarily follows from the premises; so that, if these are true, the conclusion must be true, and the argument amounts to demonstrationas in the following example: Every virtue is laudable; Kindness is a virtue; Therefore kindness is laudable. These propositions are denominated respectively the major premise, the minor premise, and the conclusion.
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Century Dictionary and Cyclopedia
• n syllogism A logical formula consisting of two premises and a conclusion alleged to follow from them, in which a term contained in both premises disappears: but the truth of neither the premises nor the conclusion is necessarily asserted. This definition includes the modus ponens (which see, under modus), the formula of which is that from the following from an antecedent of a consequent, together with the antecedent, follows the consequent. This depends upon two principles—first, the principle of identity, that anything follows from itself; and, secondly, the principle that to say that from A it follows that from B follows C is the same as to say that from A and B follows C. Under the former principle comes the formula that the following from an antecedent of a consequent follows from itself, and this, according to the second principle, is identical with the principle of the modus panens. But the syllogism is often restricted to those formula; which embody the nota notæ (or maxim, nota notæ est nota rei ipsius), which may be stated under the form—from the following of anything from a consequent follows the following of the same thing from the antecedent of that consequent. Under this form it is the principle of contraposition. The simplest possible of such syllogisms is like this: Enoch was a man; hence, since being mortal is a consequence of being a man, Enoch was mortal. All syllogisms except the modus ponens involve this principle. A syllogism which involves only this principle, and that in the simplest and directest manner, like the last example, is called a syllogism in Barbara. In such a syllogism the premise enunciating a general rule is called the major premise, while that which subsumes a case under that rule is called the minor premise. A syllogism whose cogency depends only upon what is within the domain of consciousness is called an explicatory (or analytic) syllogism. A syllogism which supposes (though only problematically) a generalizing character in nature is called an ampliative (or synthetic) syllogism. (See explicative inference (under inference), and induction, 5.) Analytic syllogisms are either necessary or probable. Necessary syllogisms are either non-relative or relative. Non-relative syllogisms are either categorical or hypothetical, but that is a trifling distinction. They are also either direct or indirect. A direct syllogism is one which applies the principle of contraposition in a direct and simple manner. An indirect syllogism is either minor or major. A minor indirect syllogism is one which from the major premise of a direct (or less indirect) syllogism and a consequence which would follow from its conclusion infers that the same consequence would follow from the minor premise. The following is an example; All men are mortal; but if Enoch and Elijah were mortal, the Bible errs; hence, if Enoch and Elijah were men, the Bible errs. A major indirect syllogism is one which from the minor premise of another syllogism and a consequence from the conclusion infers that the same thing would follow from the major premise. Example: All patriarchs are men; but if all patriarchs die, the Bible errs; hence, if all men die, the Bible errs. Such inversions may be much complicated: thus, No one translated is mortal; but if no mortals go to heaven, I am much mistaken; hence, if all who go to heaven are translated, I am much mistaken. To say that from a proposition it would follow that I err when I know I am right would amount to denying that proposition, and, conversely, to deny it positively would amount to saying that, if it were true, I should be wrong when I know I am right. A denial is thus the precise logical equivalent of that consequence. An indirect syllogism in which the contraposition involves such a consequence is said to be of the second or third figure, according as its indirection is of the minor or major kind. The fourth figure, admitted by some logicians, depends upon contraposition of the same sort, but more complicated, like the last example. The first figure comprises, in some sects of logic, the direct syllogism only; in others, the direct syllogisms together with those which are otherwise assigned to the fourth figure. (See figure, 9.) The names of the different varieties, called moods of syllogism, are given by Petrus Hispanus in these hexameters:
• n syllogism Deductive or explicatory reasoning as opposed to induction and hypothesis: a use of the term which has been common since Aristotle.
• n syllogism See the adjectives.
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Chambers's Twentieth Century Dictionary
• n Syllogism sil′ō-jizm logical form of every argument, consisting of three propositions, of which the first two are called the premises, and the last, which follows from them, the conclusion
• v.t Syllogism to deduce consequences from
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## Quotations

• H. L. Mencken
“One horse-laugh is worth ten thousand syllogisms. It is not only more effective; it is also vastly more intelligent.”

## Etymology

Webster's Revised Unabridged Dictionary
OE. silogisme, OF. silogime, sillogisme, F. syllogisme, L. syllogismus, Gr. syllogismo`s a reckoning all together, a reasoning, syllogism, fr. syllogi`zesqai to reckon all together, to bring at once before the mind, to infer, conclude; sy`n with, together + logi`zesqai to reckon, to conclude by reasoning. See Syn-, and Logistic Logic

## Usage

### In literature:

The thing began as a vision, not as a syllogism.
"A Book of Prefaces" by H. L. Mencken
"The Shield" by Various
A man seems to be the natural or wild form of the syllogism, which this world has tacitly agreed to adopt.
"The Lost Art of Reading" by Gerald Stanley Lee
The great question of the future will be to syllogize or not to syllogize.
"Buchanan's Journal of Man, September 1887" by Various
This is termed a syllogism.
"English: Composition and Literature" by W. F. (William Franklin) Webster
Put the proposed Syllogism before him, and ask him what he thinks of the Conclusion.
"Symbolic Logic" by Lewis Carroll
The old logicians, said Maxwell, recognised four forms of syllogism.
"The Life of Sir James Fitzjames Stephen, Bart., K.C.S.I." by Sir Leslie Stephen
Syllogism: to speak doubtfully.
"Thoughts on Art and Life" by Leonardo da Vinci
Alas, this is but a fallacy, the discovery whereof solves the force of the whole syllogism.
"In Praise of Folly Illustrated with Many Curious Cuts" by Desiderius Erasmus
The same error often occurs in arguments or syllogisms.
"How to Study" by George Fillmore Swain
What think you of the syllogism?
"Adventures in the Philippine Islands" by Paul P. de La Gironière
But syllogisms in the other figures can be reduced to the first by conversion.
"Analysis of Mr. Mill's System of Logic" by William Stebbing
As we listen to her array of syllogisms, our hearts die within us.
"Eternal Life" by Henry Drummond
Such a syllogism, I repeat, would be in proper form, and the inference satisfactory.
"The Ethnology of the British Islands" by Robert Gordon Latham
Saccardo, P. A. Sylloge Fungorum, vol.
"The North American Slime-Moulds" by Thomas H. (Thomas Huston) MacBride
The student of logic "syllogizes" his statement, and before he draws a conclusion he always lays down his "premise.
"Talkers" by John Bate
This profound syllogism is the great pillar of slavery in this country.
"The Unconstitutionality of Slavery" by Lysander Spooner
Syllogisms, feuds, negations, systems, religions cannot destroy it.
"Toilers of the Sea" by Victor Hugo
We now condense the whole argument into its briefest form, in the following syllogisms.
"Three Prize Essays on American Slavery" by R. B. Thurston
Saccardo, in 1882, commenced his Sylloge, of which not less than twelve volumes have been published.
"Student's Hand-book of Mushrooms of America, Edible and Poisonous" by Thomas Taylor
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### In news:

Very strict constructionism, in the form of creating backwards syllogisms and thereby violating the spirit of the Constitution, has been a hallmark of the Bush administration conservatives.
The technical name is syllogomania, from sylloge ("to collect"), but most psychiatric professionals call it compulsive hoarding.
Listening recently to Senator Kit Bond (R-MO) explain how the government is protecting privacy in the United States, I was reminded of my college logic class, where we learned about syllogisms: All men are mortal.
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### In science:

We extend the diagrammatic calculus of syllogisms introduced in to the general case of n-term syllogisms, showing that the valid ones are exactly those whose conclusion follows by calculation.
A diagrammatic calculus of n-term syllogisms
In section 2 we brie ﬂy recall the basics on syllogisms and the the diagrammatic calculus we hinted at above.
A diagrammatic calculus of n-term syllogisms
Moreover, we will also retrieve the well-known result that the valid n-term syllogisms are 3n2 − n.
A diagrammatic calculus of n-term syllogisms
Venn diagrams ca n be used to verify the validity of syllogisms, see for example.
A diagrammatic calculus of n-term syllogisms
This fact turns out to be useful in showing that a syllogism is not valid.
A diagrammatic calculus of n-term syllogisms
On the other hand, syllogism (8) is not valid even because in diagram (9) M is not erasable.
A diagrammatic calculus of n-term syllogisms
A syllogism with assumption of existence is a syllogism that is valid under an additional assumption of existence of the form IS S, IMM or IPP .
A diagrammatic calculus of n-term syllogisms
Theorem 2.1. A syllogism (with assumption of existence) is valid if and only if there is a necessarily unique syllogistic inference from its premisses to its conclusion.
A diagrammatic calculus of n-term syllogisms
It is well known that the total number of valid n-term syllogisms is 3n2 − n, see, where such a formula was obtained by rejecting the not valid moods on the bases of the traditional rules of syllogism.
A diagrammatic calculus of n-term syllogisms
The aim of the present section is that of generalize theorem 2.1 to the case of n-term syllogisms and simulataneosly that of directly recalculate the previously cited formula by using syllogistic inferences.
A diagrammatic calculus of n-term syllogisms
We end the section with the explicit description of the valid n-term syllogisms for n = 1 and n = 2, respectively.
A diagrammatic calculus of n-term syllogisms
We here point out the existing connections between the previously introduced calculus of syllogisms and the rewriting of certain terms, on the base of suitable rewrite rules.
A diagrammatic calculus of n-term syllogisms
The previous data extend those for the calculus of 1-term syllogisms to recover the calculus of 2-term syllogisms.
A diagrammatic calculus of n-term syllogisms
If n = 3, then the data for the calculus of 3-term syllogisms extend the previous and amount to the whole of those listed in de ﬁnition 4.6.
A diagrammatic calculus of n-term syllogisms
The s yllogistic inferences validating the syllogisms with assumption of existence in table (10) are obtainable.
A diagrammatic calculus of n-term syllogisms
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