330 PROF. W. STANLEY JEVONS ON 



XXVIII. On a General System of Numerically Definite 

 Reasoning. By Professor W. Stanley Jevons, M.A. 



Read January 25th, 1870. 



The system of numerical reasoning described in this paper 

 arises from the combination of arithmetical or algebraical 

 calculation with logical reasoning. The purpose is to de- 

 termine^ as far as possible,, the numbers of individual 

 objects which may compose classes or groups of objects 

 under any given logical conditions — the data consisting of 

 those logical conditions^ and the numbers of individuals 

 in certain other related classes explained. 



Only two or three previous writers have bestowed atten- 

 tion on this subject. Professor De Morgan is probably the 

 first logician who pointed out that syllogistic arguments 

 may exist in which the numbers of objects forming the 

 several terms of the syllogism may be exactly defined^ and 

 that inference is often possible with such premises when it 

 would not otherwise be valid. Logicians have for ages 

 introduced notions of quantity into the syllogism; but 

 they restricted themselves to the vague quantities allj a 

 part, or none. Professor De Morgan enjoys the high 

 honour of showing that definite numbers may also be the 

 subject of syllogistic argument; and his system is fully 

 stated in the 8th chapter of his ^ Formal Logic/ '^ On the 

 Numerically Definite Syllogism ^^*. 



2. The late Professor Boole has also treated this subject, 

 but under a different name, and in a very diff'erent form. His 

 chapter on the subjectf is entitled "On Statistical Condi- 



* See also an abstract in his ' Syllabus of a Proposed System of Logic,' 

 p. 27. 



t ' Laws of Thought,' chapter xix. p. 295. The use of the word statistical 

 as equivalent to numerical is erroneous, although sanctioned by so high an 

 authority as Sir J. Herschel, who applied it to the numbering of the stars. 

 Statistical means what refers to the State or People. 



