172 THE PRINCIPLES OF SCIENCE. [CHAP. vm. 



ceivo that it really represents the course which the mind 

 must follow in solving the question. Although thought 

 may 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 symbols. 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 1 in the 

 Memoirs of the Manchester Literary and Philosophical 

 Society, already mentioned, portions of which, however, 

 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 

 Definite," communicated by De Morgan, in 1868, to the 

 Cambridge Philosophical Society, and printed in their 

 Transactions" vol. xi. part ii. 



1 It has been pointed out to me by Mr. C. J. Monroe, that section 14 

 (p. 339) of this paper is erroneous, and ought to be cancelled. The 

 problem concerning the number of paupers illustrates the answer 

 which should have been obtained. Mr. A. J. Ellis, F.R.S., had 

 previously observed that my solution in the paper of De Morgan's 

 problem about "men in the house "did not answer the conditions 

 intended by De Morgan, and I therefore give in the text a more 

 satisfactory solution. 



