440 Dr. St. George M'wart [June 5, 



doubt about our own existence or the trustworthiness of the faculty 

 of memory, for all our power of reposing confidence in our observations, 

 experiments, or reasonings would, in that case, be logically at an end. 

 On the other hand the validity of our faculty of memory establishes 

 once for all (as wo have seen) the fact that we can transcend our 

 present consciousness, and know real objective truth. 



Let us now see the consequences of the denial, or real doubt, of 

 the second implication of science — the law of contradiction. Without 

 it we can be certain of nothing, and it therefore lands us in absolute 

 scepticism. And if we would rise from such intellectual paralysis, we 

 must accept that dictum as it presents itself to our minds ; and the 

 dictum presents itself to my mind, not as a law of thought only, but 

 a law of things. It affirms, for example, that no creature anywhere 

 or anywhen can at the same time be both bisected and entire. 



An amusing instance of the way in which very distinguished men 

 may be misled as to the question of our power of perceiving 

 necessary truth, is offered by an imaginary case which has been put 

 forward by Professor Clifford and Professor Helmholz. Their object 

 in advancing it was to show, by an example, how truths which appear 

 necessary to us are not objectively necessary. But the result 

 appears to me to show the direct contradictory of what they intended. 

 Their intention evidently was to suj^port the proposition that we can 

 know no truths to be absolutely necessary, and the result is to show 

 that even according to them, some truths are absolutely necessary. 

 The necessary truths they propose to controvert are that a straight 

 line is the shortest line between two points, and that two straight 

 lines cannot enclose a space. 



For this purpose curious creatures, possessing length and breadth 

 but no thickness, were supposed, by them, to be living on a sphere, 

 with the surface of which their bodies would coincide. They were 

 imagined to have experience of length and breadth in curves, but 

 none of heights and depth or of any straight lines. To such creatures, 

 it was said, our geometrical necessary truths would not appear truths 

 at all. A straight line for them could not be the shortest line, 

 while two parallel lines prolonged would enclose a space. 



To this imaginary objection I reply as follows : Beings so extra- 

 ordinarily defective might, likely enough, be unable to perceive 

 geometrical truths which to less defective creatures — such as our- 

 selves — are perfectly clear. Nevertheless if they could conceive of 

 such things at all, as those we denote by the terms " straight lines " 

 and " parallel lines," then there is nothing to show that they could not 

 also perceive those same necessary truths concerning them which 

 are evident to us. 



It is strange that the very men who make this fanciful objection 

 actually show, by the way they make it, that they themselves perceive 

 the necessary truth of those geometrical relations, the necessity of 

 which they verbally deny. For how, otherwise, could they affirm 



