356 Mb DE morgan, ON THE SYLLOGISM, No. IV, 



ordinary syllogism. The old logicians were right in attaching importance to the invention of 

 the middle term : but their right notion was deprived of efficient action by their determining 

 that no connexion worthy of a logician's attention could exist between terms except is or 

 is not. 



Any two notions whatsoever may happen to possess relation to each other in the mind. 

 Choose two notions at hazard : the chances are small that they are related by inclusion or 

 exclusion, total or partial, in any manner worth consideration : but these chances are multiplied 

 a thousand fold if we turn our thoughts to the likelihood of their existing in some other 

 relation. Indeed, some relation must exist between any two things, over and above the 

 relations, usually well settled, of identity or diflference. 



When we examine any book of ordinary reasoning, we find that the onymatic syllogism is 

 not very frequent, the combination of relations much more frequent, and the introduction of 

 composition of terms and transformation of propositions by far the most frequent of all. 

 Syllogisms are rather chapters than sentences, in many cases. When the acts of inference 

 follow one another very quickly, or the reasoning is very consecutive, people begin to cry 

 mathematics. I have read and heard the statement that Fearne's celebrated work on con- 

 tingent remainders is algebra : it is no more algebra than a remainder-man is oo — y; but 

 the reasoning, if I may speak from a very old recollection of a few chapters, is remarkably 

 sustained and connected. Chillingworth is a writer who delights in the technical exhibition 

 of a syllogism, when he gets one: but the instances exhibited do not come very thickly. 

 Nothing that I know of can be written all in syllogism, except mathematics: and this merely 

 because, out of mathematics, nearly all the writing is spent in loading the syllogism, and very 

 little in firing it. 



It has sometimes been made a reproach to logic that the mathematicians, who reason more 

 . consecutively than any others when about their mathematics, do not regard the syllogism with 

 respect in theory, and disdain it in practice. I shall proceed to examine how this matter 

 stands. 



First, as to the merest technical exhibition of the syllogism, it is, or should be, evident 

 to all parties that such display of form is no more necessary to a proficient than the spelling 

 of every w^ord as he reads it. Those who cannot exhibit their inferences syllogistically need 

 to learn ; but those who can do not need to practise : which is exactly what may be said of 

 spelling. When I wrote this last word, I was quite unconscious of s-p-e-1-l-i-n-g : no per- 

 ceptibly separate acts of my mind dictated the writing down of the separate letters. This 

 is all that need be said in answer to those who despise the analysis which is good for the 

 learner, because the logician himself ends, in practice, by using the composite process with 

 which the learner began. 



There is a useful but very limited field of exercise for the syllogism in geometry. 

 There is hardly an instance, over and above the elimination of B from A = B, B = C, which 

 is not an overt use of the principium et ewemplum ; whenever P is true, Q is true ; in this 

 case P is true ; therefore in this case Q is true. The reduction into the pure technical form, 

 except in a few instances at the commencement, would be useless. The attempt of Herlinus 

 and Dasypodius, of which Mr Mansel (Appendix to Aldrich, note L) has reprinted one pro- 



