THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



JULY 1880. 



I. On the Diagrammatic and Mechanical Representation of Pro- 

 positions and Reasonings. By J. Venn, M.A., Fellow and 

 Lecturer in Moral Science, Cains College, Cambridge*. 



SCHEMES of diagrammatic representation have been so 

 familiarly introduced into logical treatises during the last 

 century or so, that many readers, even of those who have 

 made no professional study of logic, may be supposed to be 

 acquainted with the general nature and object of such devices. 

 Of these schemes one only, viz. that commonly called " Eule- 

 rian circles," has met with any general acceptance. A variety 

 of others indeed have been proposed by ingenious and cele- 

 brated logicians, several of which would claim notice in a his- 

 torical treatment of the subject ; but they mostly do not seem 

 to me to differ in any essential respect from that of Euler. 

 They rest upon the same leading principle, and are subject all 

 alike to the same restrictions and defects. 



Euler's plan was first proposed by himf in his ' Letters to 

 a German Princess,' in the part treating of logical principles 

 and rules. What we here represent is, of course, the extent 

 or scope of each term of the proposition. We draw two 

 circles, and make them include or exclude or intersect one 

 another, according as the classes denoted by the terms happen 

 to stand in relation to one another in this respect. Thus " All 



* Communicated by the Author. 



t According to Drobisch and Ueberweg, this circular device had been 

 already proposed by two previous writers, viz. C. "Weise and J. C. Lange. 



Phil, Mag. S. 5. Vol, 9, No. 59. July 1880. B 



