XI. On the Syllogism, No. V. and on various points of the Onymatic System. By 

 Augustus De Morgan, F.R.A.S., of Trinity College, Professor of Mathematics 

 in University College, London. 



[Read May 4, 1863.] 



This paper contains the following points: — 1. A criticism of Hamilton's system, as 

 further explained in his posthumous work. 2. An explanation of the character of the 

 system of Aristotle and his followers, which I affirm to have been exemplar. 3. The mis- 

 conception of the character of this system by recent writers. 4. Enforcement of the right of 

 both correlatives in any pair, and of all in any set, to equal fulness of treatment. 5. Appli- 

 cation to the distinction of affirmation and «ow-affirmation; syllogism of indecision. 6. De- 

 duction of the eight onymatic forms from purely onymatic meaning; alleged demonstra- 

 tion of the necessity and completeness of these forms. 7, Restrictive propositions, their 

 affirmation and denial introduced in every view except the purely onymatic view, whenever 

 complete treatment of all correlatives is allowed. 8. Completion of the exemplar system. 

 9. Extended comparison of the onymatic relations. 10. System of primary and secondary 

 relations by copula of identification. 11. The same when the copula is any one of the 

 simple onymatic relations. 12. The full system at which the Hamiltonian quantification 

 aims. 13. The logical basis of extension and comprehension. [l4. Addition on a recent 

 phase of the controversy. December, 1862.] 



The Society is by this time aware that any introduction of philosophy proper is also 

 the introduction of controversy ; which, though not necessarily personal in the modern sense, 

 must be ad hominem in the old sense. Such dispute is now as nearly as possible excluded 

 from mathematics and experimental physics : but it was not so of old. There was a time 

 when the investigator in either was nearer to the foundation, and had more to do with 

 the subject from the psychological point of view. It was then that Newton called 

 philosophy — meaning physics, — a litigious lady, and said a man might as well be engaged 

 in lawsuits as have to do with her. But though Newton and others — and Newton above 

 all — have tamed this shrew in her dealings with mathematics and physics, she keeps her 

 character as to all subjects in which first principles must still be probed, and questions 

 of boundary must still be fought. And logic is a subject in which little more than a 

 commencement of either has been made. 



I have good hope that in this paper my personal part of a long discussion will 

 come to an end. Since July, 1860, when Hamilton's Lectures on Logic were ably published 



