300 REASONING. 



tracing the consequences which follow from the sup- 

 position. The opinion of Dugald Stewart respecting 

 the foundations of geometry, is, I conceive, substan- 

 tially correct ; that it is built upon 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 con- 

 sists in reality only in this, that they necessarily follow 

 from the suppositions from which they are deduced. 

 Those suppositions are so far from being necessary, 

 that they are not even true ; they purposely 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 necessarily 

 following from some assumption, which, by the con- 

 ditions of the inquiry, is not to be questioned. In 

 this relation, of course, the derivative 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 pur- 

 poses of the particular science. And therefore the 

 conclusions of all deductive sciences were said by the 

 ancients to be necessary propositions. We have 

 observed already that to be predicated necessarily was 

 characteristic of the predicable Proprium, and that a 

 proprium was any property of a thing which could be 

 deduced from its essence, that is, from the properties 

 included in its definition. 



