[ 130 ] 

 XXVII. Proceedings of Learned Societies. 



CAMBRIDGE PHILOSOPHICAL SOCIETY. 



[Continued from vol. xxx. p. 367.] 



Nov. 9.#^N the Structure of the Syllogism, and on the application 

 1846. ^-^ of the Theory of Probabilities to Questions of Argument 

 and Authority*. By Professor De Morgan. 



The object of this paj^er is twofold : first, to establish two distinct 

 theories of the syllogism, both differing materially from that of Ari- 

 stotle, and each furnishing a general canon for the detection of all its 

 legitimate forms of inference ; secondly, to investigate the mode in 

 which the distinctive character of the two great sources of convic- 

 tion, argument and authority, affects the application of the notion of 

 probability to questions not admitting of absolute demonstration. 



The two theories of the syllogism arise out of simple notions con- 

 nected with the /onns of propositions and their quantities. The dif- 

 ference between a positive and negative assertion is not essential, 

 but depends on the manner in which objects of thought are described 

 by language. If Y and y be names so connected that each contains 

 everything which is not in the other, and the two have nothing in 

 common (a relation which is described by calling them contrary 



* Upon this paper a controversy has arisen, which, up to the present 

 time, may be summed up as follows : — ^piilSO. Mr. De Morgan published 

 a statement in answer to an assertion ot SirW. Hamilton of Edinburgh, to 

 the effect that the second, or quantitative, system of syllogism, was a wilful 

 plagiarism from certain letters which Sir W. Hamilton had written to Mr. 

 De Morgan. Maj/ 22. Sir W. Hamilton replied at length in another 

 pamphlet, retracting the assertion o^ wilful plagiarism, but maintaining that 

 the system was taken, unconsciously, from those letters. This was followed 

 by a letter from Mr. De Morgan in the Athenaeum of May 29, and another 

 from Sir W. Hamilton in the same publication for June 5. The point at 

 issue now seems to be as follows : — Mr. De Morgan challenges Sir W. Ha- 

 milton to show anything in his second system which was not substantially 

 contained in a digressive section of the description of his first system, ad- 

 mitted to have been sent to Cambridge before any communication had 

 taken place. SirW. Hamilton, in reply, contends that the digression above- 

 mentioned contains nothing to the purpose. Mr. De Morgan defers further 

 reply until he publishes a work which he states himself to be preparing on 

 logic. 



In the Athenaeum of June 19, appeared a letter from Mr. James Broun, 

 asserting certain mistakes on the part both of Sir W. Hamilton and Mr. 

 De Morgan, and giving certain extensions to the quantitative forms of the 

 latter. Again, June 26, appeared in the same publication a letter from 

 Mr. De Morgan, dated June 19, stating that he also had arrived at Mr. 

 Broun's forms, giving reasons for their rejection in favour of certain simpler 

 forms, giving the heads of an extended system of quantitative syllogism, 

 and asserting that he had materially extended both his systems. So the 

 matter stands. The subject of the structure of the syllogism seems to be 

 likely to excite some attention ; and, without pronouncing any opinion on 

 the personal claims or conflicts of the several parties, we recommend the 

 attention of our readers to this rather neglected branch of pure science. — 

 Ed. Phil. Mag. 



