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plus two equals four, we know. That is not in question. The 

 problem is to account for the origin of its necessary character, 

 and in order to do this, Spencer gives as the reason that this 

 necessary relation exists beyond consciousness. 



Manifestly, Spencer's contention is a clear case of petitio 

 principii. The relation is one "which we recognize as neces- 

 sary" within ^ consciousness, and because of this, Spencer 

 claims that if it is necessary within, it must be because of some- 

 thing necessary without. In other words, the whole argument 

 is based upon definition . Being conversant with the ' ' necessity 

 of thought", that necessity is projected, as it were, into some 

 region beyond consciousness, and is there made to bear the 

 burden of causing the very necessity in consciousness from 

 which it derives its existence. Or, to change the argument, 

 Spencer, by first assuming necessity in the outer relation, can 

 obviously derive necessity for the inner on the second assump- 

 tion that all the inner is derived from the outer. Since Spencer 

 has defined the relations existing in the environment as abso- 

 lute, it of course follows, that the inner relations, which are 

 said to be derived from the outer, are also "absolute in us". 

 Such a procedure is possible with any definition, however, 

 whether the definition be true or false with regard to fact, and 

 one can always get out of the definition everything he has put 

 into it; but what he gets out has no greater claim to truth 

 than the definition from which it is derived, and that definition 

 for Spencer, is a free assumption. 



The inadequacy of Spencer's position may be further seen 

 in his attempt to distinguish between an inconceivable and an 

 unbelievable proposition. 



"An inconceivable proposition," he states, "is one of which 

 the terms cannot, by any effort, be brought before conscious- 

 ness in that relation which the proposition asserts between 

 them a proposition of which the subject and the predicate 

 offer an insurmountable resistance to union in thought. An 

 unbelievable proposition is one which admits of being framed 

 in thought, but is so much at variance with experience, in 

 which its terms have habitually been otherwise united, that 

 its terms cannot be put in the alleged relation without effort. 

 Thus, it is unbelievable that a cannon-ball fired from England 

 should reach America ; but it is not inconceivable. Conversely, 

 it is inconceivable that one side of a triangle is equal to the sum 

 of the two other sides not simply unbelievable. The two 

 sides cannot be represented in consciousness as becoming 

 equal in their joint length to the third side, without the repre- 

 sentation of a triangle being destroyed ; and the concept of a 



