OF THE LAWS OF THOUGHT. 167 



tainlj does not intend to deny that tlie principle of contradiction is 

 self-evident. On the other hand, it is plain that he does hold that 

 the principle of contradiction can be deduced from the law of duality. 

 But (we ask) how? Can the principle of contradiction be deduced 

 from the law of duality, without our assuming the principle of con- 

 tradiction itself as the basis of the deduction ? This would be 

 absurd ; for a conclusion can be established in no other way than by 

 pointing out that the supposition of its being false involves a contra- 

 diction. In the particular case before us, the equation x (1 — x) = 0, 

 which is that expression of the law of duality in which the principle 

 of contradiction is regarded as being brought to light, is only reached 

 by a process of reasoning, every step of which takes the principle of 

 contradiction for granted. The only interpretation, therefore, which 

 Professor Boole's words can bear, unless we give them a meaning 

 palpably absurd, is, that a formula, which we are enabled to state by 

 assuming the law of contradiction, contains a symbolic representa- 

 tion of that law. This hardly seems to us a very significant fact in 

 the philosophy of the intellectual powers. If indeed the formula in 

 question could be shown to represent some law of thought of wider 

 application than the law of contradiction, that would be a very sig- 

 nificant fact. But such is not the case. The equation ^ (1 — a;) = 

 is just' the law of contradiction symbolically expressed : neither more 

 nor less. 



The Aristotelian logic is charged with being incomplete, as well as 

 with being not sufiiciently fundamental. By this our author does 

 not mean that Aristotle and his followers have casually omitted some 

 forms of thought which their system ought to have embraced : had 

 they done so, the fault would have been chargeable — not upon the 

 system, but upon its expounders ; but he means, that, from the very 

 nature of the system, there is an indefinite variety of problems 

 belonging to the science of inference, which their system is incapable 

 of solving, or for the solution of which at all events it furnishes no 

 definite and certain method. 



It will be observed that there are two questions here, which, as 

 radically distinct from one another, require to be considered sepa- 

 rately : the one being, whether the Aristotelian logic is capable of 

 solving all the problems belonging to the science of inference ; and 

 the other, whether it furnishes a definite and certain method for the 

 solution of these. 



