The thing began as a vision, not as a syllogism.
"A Book of Prefaces" by H. L. Mencken
You have made a bad syllogism: the conclusion does not follow from the premises.
"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
***
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
***