256 



REASONING. 



relate to something which has real existence, (for there can be 

 no science respecting non-entities,) it follows that any hypo 

 thesis we make respecting an object, to facilitate our study of 

 it, must not involve anything which is distinctly false, and re 

 pugnant to its real nature : we must not ascribe to the thing 

 any property which it has not ; our liberty extends only to 

 slightly exaggerating some of those which it has, (by assuming 

 it to be completely what it really is very nearly,) and sup 

 pressing others, under the indispensable obligation of restoring 

 them whenever, and in as far as, their presence or absence 

 would make any material difference in the truth of our con 

 clusions. Of this nature, accordingly, are the first principles 

 involved in the definitions of geometry. That the hypotheses 

 should be of this particular character, is however no further 

 necessary, than inasmuch as no others could enable us to deduce 

 conclusions which, with due corrections, would be true of real 

 objects : and in fact, when our aim is only to illustrate truths, 

 and not to investigate them, we are not under any such restriction . 

 We might suppose an imaginary animal, and work out by de 

 duction, from the known laws of physiology, its natural history ; 

 or an imaginary commonwealth, and from the elements com 

 posing it, might argue what would be its fate. And the con 

 clusions which we might thus draw from purely arbitrary hypo 

 theses, might form a highly useful intellectual exercise : but as 

 they could only teach us what would be the properties of objects 

 which do not really exist, they would not constitute any addi 

 tion to our knowledge of nature : while on the contrary, if the 

 hypothesis merely divests a real object of some portion of its 

 properties, without clothing it in false ones, the conclusions 

 will always express, under known liability to correction, actual 

 truth. 



3. But though Dr. Whewell has not shaken Stewart s 

 doctrine as to the hypothetical character of that portion of 

 the first principles of geometry which are involved in the so- 

 called definitions, he has, I conceive, greatly the advantage of 

 Stewart on another important point in the theory of geome 

 trical reasoning ; the necessity of admitting, among those first 



