IV. On the Symbols of Logic, the Theory of the Syllogism, and in particular of the 

 Copula, and the application of the Theory of Probabilities to some questions 

 of evidence. By Augustus De Morgan, Sec. R.A.S., of Trinity College, 

 Cambridge, Professor of Mathematics in University College, London. 



[Read February 25, 1850.] 



Three years ago I communicated to the Society some developements of the theory of 

 the Syllogism, which I have since embodied, with additions, in a work * on Formal Logic. I 

 now proceed to consider the subject still further, with particular reference to the application of 

 symbols, and the tendency which such application has to develope what I must call the algebra 

 of the laws of thought. 



It will be necessary for me to refer, in various ways, to the literary topics of a controversy 

 in which the paper above-mentioned involved me : and this I can do without dwelling on the 

 part of it which is personal to myself or to my opponent. That controversy turned upon the 

 connexion between two systems of syllogism. The first, Sir William Hamilton's alteration 

 of the Aristotelian system by the invention of forms of predication, so as to assign either of the 

 two modes of quantity, universal or particular, to either of the terms of a proposition, subject 

 or predicate, in either of the different species of propositions, affirmative or negative. The 

 second, my own numerically definite system, in which the number of objects of thought that 

 are spoken of, whether under subject or predicate, and also all that exist, are numerically 

 signified, either by the specific or general symbols of arithmetic. But in the present paper I 

 have nothing to do with the numerically definite system, except as it may be alluded to in illus- 

 tration of the others. Still, I shall have to compare two systems. The first, that of Sir William 

 Hamilton above alluded to. The second, the other and prior of my own two systems, in which 

 the extension of the Aristotelian system is made by the application of contrary terms to all the 

 usual forms of predication, without any direct invention of modes of applying quantity. 



And I may further state, that the methods of this paper have nothing in common with that 

 of Professor Boole, whose mode of treating the forms of logic is most worthy the attention of 

 all who can study that science mathematically, and is sure to occupy a prominent place in its 

 ultimate system. 



* Referred to, throughout this paper, by the initials F . L. 



