90 



induction into syllogism. And Aristotle really contemplated such a 

 generalizing induction. He did not contemplate what has been 

 called inductio per enumerationem simplicem, which is really no induc- 

 tion at all. This was shown to be so by reference to the case, often 

 used as an example of induction, of the inference of Kepler's laws 

 from the observation of the separate planets. It may be objected 

 that the reasoning in such cases is inconclusive ; and to this it is 

 replied, that induction, as reasoning, is inconclusive. It is a source 

 of truth different from reasoning ; of first truths, the bases of rea- 

 sonings, as Aristotle has remarked. 



February 25, 1850. 



On the Symbols of Logic, the theory of the Syllogism, and in 

 particular of the Copula, and the application of the Theory of Pro- 

 babilities to some questions of evidence. By Professor De Morgan. 



This paper, which is in continuation of the one published in 

 vol. viii. part 3 (read Nov. 9, 1846), and of subsequent additions 

 contained in the author's work on Formal Logic, is divided into six 

 sections. 



Section I. On the approximation of logical and algebraical modes 

 of thought. — The subjects of this section are, — 1st, some development 

 of the idea that the oppositions of logic have affinities which may 

 one day lead to a connected theory, making use of a common instru- 

 ment, just as the oppositions of quantity which are considered in 

 algebra are connected by the general theory of the signs + and — ; 

 and 2nd, some remarks on the resemblance of the instrumental part 

 of inference to algebraic elimination. 



Ten such instances as affirmative and negative, conclusive and 

 inconclusive, &c, are compared with the logical distinction of uni- 

 versal and particular ; and it is pointed out, in all the cases in which 

 it is not already acknowledged, that it would be possible to use any 

 one of the ten in place of the last. 



Section II. On the formation of symbolic notation for propositions 

 and syllogisms. — Exclusive of remarks on the Aristotelian notation 

 and on notation in general, and a statement for comparison of Sir 

 William Hamilton's notation, this section contains the following 

 matters. 



1. A pictorial or diagrammatic representation of syllogistic infer- 

 ences, being after the method pursued by Lambert, with such addi- 

 tions as will enable the system to represent all the cases in which 

 contraries are used. 



2. An abbreviated and arbitrary method of representing proposi- 

 tions and syllogisms. 



Following Sir William Hamilton in making the quantity of both 

 subject and predicate matter of symbolic expression, Mr. De Morgan 

 gives his system of notation two new features. First, he dispenses 

 with the representatives of the terms (except when it may be con- 



