254 



REASONING. 



an error to suppose, because we resolve to confine our atten- 

 tion to a certain number of the properties of an object, that 

 we therefore conceive, or have an idea of, the object, denuded 

 of its other properties. We are thinking, all the time, of 

 precisely such objects as we have seen and touched, and with 

 all the properties which naturally belong to them ; but, for 

 scientific convenience, we feign them to be divested of all pro- 

 perties, except those which are material to our purpose, and in 

 regard to which we design to consider them. 



The peculiar accuracy, supposed to be characteristic of the 

 first principles of geometry, thus appears to be fictitious. The 

 assertions on which the reasonings of the science are founded, 

 do not, any more than in other sciences, exactly correspond 

 with the fact ; but we suppose that they do so, for the sake 

 of tracing the consequences which follow from the supposition. 

 The opinion of Dugald Stewart respecting the foundations of 

 geometry, is, I conceive, substantially correct; that it is 

 built on hypotheses ; that it owes to this alone the peculiar 

 certainty supposed to distinguish it ; and that in any science 

 whatever, by reasoning from a set of hypotheses, we may 

 obtain a body of conclusions as certain as those of geometry, 

 that is, as strictly in accordance with the hypotheses, and as 

 irresistibly compelling assent, on condition that those hypotheses 

 are true. 



When, therefore, it is affirmed that the conclusions of 

 geometry are necessary truths, the necessity consists in reality 

 only in this, that they correctly follow from the suppositions 

 from which they are deduced. Those suppositions are so far 

 from being necessary, that they are not even true ; they pur- 

 posely depart, more or less widely, from the truth. The only 

 sense in which necessity can be ascribed to the conclusions of 

 any scientific investigation, is that of legitimately following 

 from some assumption, which, by the conditions of the inquiry, 

 is not to be questioned. In this relation, of course, the deri- 

 vative truths of every deductive science must stand to the 

 inductions, or assumptions, on which the science is founded, 

 and which, whether true or untrue, certain or doubtful in 

 themselves, are always supposed certain for the purposes of the 



