NUMERICALLY DEFINITE REASONING. 331 



tions^^^ by which he evidently means^ " Numerical Condi- 

 tions/^ It contains a most remarkable and poAverful at- 

 tempt to erect a general method for ascertaining the higher 

 and lower limits of logical classes, to be employed as a sub- 

 sidiary portion of his general calculus of probabilities. A 

 paper on the same subject had been previously written by 

 him, and entitled " Of Propositions Numerically Definite/'' 

 but was only published after his death, by Professor De 

 Morgan in the ' Transactions of the Cambridge Philoso- 

 phical Society' (vol. xi. part ii. 1868). Of these writings 

 of Professor Boole I must say, what I have elsewhere said 

 of other portions of his writings, that they appear in them- 

 selves perfect and almost inimitable. At the same time I 

 must add that Boole's extraordinary power of analysis, 

 and his perfect command of symbolic methods, usually led 

 him to over-estimate the part they should play in reason- 

 ing, and to under-estimate the value of a simple and intui- 

 tive comprehension of the subject. The very principle 

 which he fearlessly adopts, that unintelligible symbols may 

 give intelligible and even demonstrative results, will pro- 

 bably be rejected by future mathematicians, as it has been 

 lately rejected in the strongest terms by Mr. Sandeman*. 



3. As Mr. Boole's logical views were the basis from 

 which I started in forming the simple but general system 

 of logical forms explained in my ' Pure Logic ' in the year 

 1864, and, more simply still, in my ^ Substitution of Simi- 

 lars,' published in 1869, so the numerically definite system 

 of reasoning which is here described arises from a simplifi- 

 cation of the previous methods of De Morgan and Boole. 



4. In the qualitative system of logic, which I have 

 given in the works referred to, a term is taken to mean 

 the quality or group of qualities which belong to and mark 

 out a class of objects. Thus, the general term A stands 

 for any group of qualities belonging to a class of objects. 



* ' Pelicotetics, ' 1868, Preface, pp. ix and x. 



