194 THE PRINCIPLES OF SCIENCE. 



mind must follow in solving the question. Although 

 thought may seem to outstrip the rapidity with which the 

 symbols can be written down, yet the mind does not really 

 follow a different course from that indicated by the sym- 

 bols. For a fuller explanation of this natural system of 

 Numerically Definite Reasoning, with more abundant 

 illustrations and an analysis of De Morgan's Numerically 

 Definite Syllogism, I must refer the reader to the paper in 

 the Memoirs of the Manchester Literary and Philosophical 

 Society, as already referred to, portions of which, how- 

 ever, have been embodied in the present section. 



The reader may be referred, also, to Boole's writings 

 upon the subject in the ' Laws of Thought/ chap. xix. 

 p. 295, and in a paper on ' Propositions Numerically De- 

 finite,' communicated by De Morgan, in 1868, to the 

 Cambridge Philosophical Society, and printed in their 

 ' Transactions,' vol. xi. part ii. Mr. Alexander J. Ellis 

 treats the same subject in his * Contributions to Formal 

 Logic/ read to the Royal Society, in March, 1872, but 

 as yet published only in the form of a brief abstract, in 

 the Proceedings of the Society, vol. xx. p. 307. 



