358 Mb DE morgan, ON THE SYLLOGISM, No. IV, &c. 



in their favour. Perhaps it would have been asserted as a matter of course that they did so, 

 omission of all mention being taken as equally a matter of course, if the publication of 

 Herlinus and Dasypodius, the only one of its kind, had not come in as the exception which 

 proves the rule. 



It is to algebra that we must look for the most habitual use of logical forms. Not that 

 onymatic relations are found in frequent occurrence : but so soon as the syllogism is con- 

 sidered under the aspect of combination of relations, it becomes clear that there is more of 

 syllogism, and more of its variety, in algebra than in any other subject whatever, though the 

 matter of the relations — pure quantity — is itself of small variety. And here the general idea 

 of relation emerges, and for the first time in the history of knowledge, the notions of relation 

 and relation of relation are symbolised. And here again is seen the scale of gradations 

 of form, the manner in which what is difference of form at one step of the ascent, is difference 

 of matter at the next. But the relation of algebra to the higher developments of logic is a 

 subject of far too great extent to be treated here. It will hereafter be acknowledged that, 

 though the geometer did not think it necessary to throw his ever recurring principium et 

 exemplum into an imitation of "Omnis homo est animal, Sortes est homx>, &c.," yet the 

 algebraist was living in the higher atmosphere of syllogism, the unceasing composition of 

 relation, before it was admitted that such an atmosphere existed. 



I expect agreement in what I have said neither from the logicians nor from the 

 algebraists: but, for reasons given in my last paper, I do not submit myself to either class. 

 Not that I by any means take it for granted that all those who have cultivated both sciences 

 will agree with me. When two countries are first brought by the navigators into com- 

 munication with each other, it is found that there are two kinds of perfect agreement, and 

 one case of nothing but discordance. All the inhabitants of each of the countries are quite 

 at one in believing a huge heap of mythical notions about the other. At first, the only 

 persons who though similarly circumstanced nevertheless tell different stories are the very 

 mariners who have passed from one land to the other. This will go on for a time, and for 

 a time only : multi pertransibunt, et augebitur scientia. 



A. DE MORGAN. 



University College, London, 

 November 12, 1859. 



