OF THE LAWS OF THOUGHT. 171 



not here in the province of Ehetoric. Much more to the purpose is the 

 charge, that the process of reduction would involve operations which 

 are not syllogistic. The operations referred to are those embraced 

 in the " much more general process " in which, as we have seen, our 

 Author holds conversion and syllogism to be contained. Of course, 

 the ground which we take in reply is, on the one hand, to challenge 

 the production of an instance of valid inference, which cannot be re- 

 duced to either conversion or syllogism ; and on the other hand, to 

 fall back upon the demonstration which we have given of the abso- 

 lute impossibility of valid inference being anything else than conver- 

 sion or syllogism. 



In stating the charge of incompleteness brought by our Author 

 against the Aristotelian system, we explained his meaning to be, 

 that, from the very nature of the system, there is an indefinite vari- 

 ety of problems belonging to the science of inference, which the 

 system is incapable of solving, or for the solution of which, at all 

 events, it furnishes no definite and certain method. We have, we 

 trust, fully refuted the opinion that there are problems in the science 

 of inference which the Aristotelian logic is incapable of solving. 

 But Professor Eoole urges, that, even if all inference were re- 

 ducible to conversion and syllogism, " there would still exist the 

 same necessity for a general method, For it w^ould still be requisite 

 to determine in what order the processes should succeed each other, 

 as well as their particular nature, in order that the desired relation 

 should be obtained. By the desired relation I mean that full relation 

 which, in virtue of the premises, connects any elements selected out 

 of the premises at will, and which, moreover, expresses that relation 

 in any desired form and order. If we may judge from the mathe- 

 matical sciences, which are the most perfect examples of method 

 known, this directive function of method constitutes its chief ofiice 

 and distinction. The fundamental processes of arithmetic, for in^ 

 stance, are in themselves but the elements of a possible science. To 

 assign their nature is the first business of its method, but to arrange 

 their succession is its subsequent and higher function. In the more 

 complex examples of logical deduction, and especially in those which 

 form a basis for the solution of difiicult questions in the theory of 

 probabilities, the aid of a directive method, such as a Calculus alone 

 can supply, is indispensable," 



Now, we at once admit that the Aristotelian logic neither has, nor 



