NEW QUANTIFICATION OF PREDICATE. 159 



tion, are perhaps still more interesting as episodes in that pursuit. 1847. 

 Upon its Logical side the end may be said to have been attained, Letter of 

 and with a completeness upon which I believe high authorities 

 would not as yet be forward to pronounce, in a series of works 

 of which the well-known Formal Logic is but a part. If, as is 

 certainly true, his other works could only have been written by 

 a Logician, these last could only have been written by a Mathe- 

 matician. Everybody knows that Mathematics are an admirable 

 model of exactitude ; but not everybody knows that they also 

 furnish an admirable type of generalisation. Indeed, generality 

 is often confounded with vagueness, and therefore treated as 

 incompatible with exactitude. 



The fact is known that, having very thoroughly worked at 

 the generalisations of Mathematics in theory and practice, Mr. 

 De Morgan was enabled to establish with perfect precision the 

 most highly generalised conception of Logic, perhaps, which it 

 is possible to entertain. It is no new doctrine that Logic deals 

 with the necessary laws of action of thought, and that Mathema- 

 tics apply these laws to necessary matter of thought ; but by 

 showing that these laws can and must be applied with equal 

 precision and equal necessity to all kinds of relations, and not 

 only to those which the Aristotelian theory takes account of, he 

 so enlarged the scope and intensified the power of Logic as an 

 instrument, that we may hope for coming generations, as be 

 must have hoped, 1 another instalment of the kind of benefit 

 which history shows we ourselves owe to the Aristotelian theory, 

 not merely in the analysis of one mental operation, but in the 

 every- day practice of them. Mathematics are, meanwhile, and 

 perhaps will always remain, the completest and most accurate 

 example of the generalised Logic. At any rate, in the mind of 

 the author, Logic and Mathematics as * the two great branches of 

 exact science, the study of the necessary laws of thought, the 

 study of the necessary matter of thought, 2 were always viewed 

 in connection and antithesis. 



C. J. MONRO. 



Mr. De Morgan had written to Dr. Logan in Sep- Corre 

 tember 1846 that he was ' making a vigorous onslaught 

 on the Aristotelian syllogism, which,' he says, 'I find has 



1 Syllabus, 96, note. 



2 Chi the Syllogism, No. v. &c. (Camb. Ph. S. vol. x., Part 11, 

 1803), the last page. 



