302 REASONING. 



ever to fact. Since an hypothesis framed for the 

 purpose of scientific inquiry must relate to something 

 which has real existence, (for there can be no science 

 respecting non-entities,) it follows that any hypothesis 

 we make respecting an object, to facilitate our study 

 of it, must not involve anything which is distinctly 

 false, and repugnant to its real nature : we must not 

 ascribe to the thing any property which it has not; 

 our liberty extends only to suppressing some of those 

 which it has, under the indispensable obligation of 

 restoring them whenever, and in as far as, their 

 presence or absence would make any material differ- 

 ence in the truth of our conclusions. Of this nature, 

 accordingly, are the first principles involved in the 

 definitions of geometry. In their positive part they 

 are observed facts ; it is only in their negative part 

 that they are hypothetical. 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 

 deduction, from the known laws of physiology, its 

 natural history; or an imaginary commonwealth, and 

 from the elements composing it, might argue what 

 would be its fate. And the conclusions which we 

 might thus draw from purely arbitrary hypotheses, 

 might form a highly useful intellectual exercise : but 

 as they could only teach us what would be the pro- 

 perties of objects which do not really exist, they 

 would not constitute any addition to our knowledge : 

 while on the contrary, if the hypothesis merely divests 

 a real object of some portion of its properties, without 



