DEMONSTRATION, AND NECESSARY TRUTHS. 301 



2. The important doctrine of Dugald Stewart, 

 which I have endeavoured to enforce, has been con- 

 tested by a living philosopher, Mr. Whewel], both in 

 the dissertation appended to his excellent Mechanical 

 Euclid, and in his more recent elaborate work on the 

 Philosophy of the Inductive Sciences; in which last he 

 also replies to an article in the Edinburgh Review, 

 (ascribed to a writer of great scientific eminence,) in 

 which Stewart's opinion was defended against his 

 former strictures. Mr. WhewelPs mode of refuting 

 Stewart is to prove against him (as has also been done 

 in this work), that the premisses of geometry are not 

 definitions, but assumptions of the real existence of 

 things corresponding to those definitions. This, how- 

 ever, is doing little for Mr. Whewell's purpose, for it 

 is these very assumptions which we say are hypotheses, 

 and which he, if he denies that geometry is founded 

 on hypotheses, must show to be absolute truths. All 

 he does, however, is to observe, that they at any 

 rate are not arbitrary hypotheses ; that we should 

 not be at liberty to substitute other hypotheses for 

 them ; that not only " a definition, to be admissible, 

 must necessarily refer to and agree with some con- 

 ception which we can distinctly frame in our 

 thoughts," but that the straight lines, for instance, 

 which we define, must be (: those by which angles are 

 contained, those by which triangles are bounded, those 

 of which parallelism may be predicated, and the 

 like*." And this is true ; but this has never been 

 contradicted. Those who say that the premisses of 

 geometry are hypotheses, are not bound to maintain 

 them to be hypotheses which have no relation what- 



* WHEWELL'S Mechanical Eitclid, p. 149, et seqq. 



