DEMONSTRATION, AND NECESSARY TRUTHS. 255 



particular science. And therefore the conclusions of all deduc- 

 tive sciences were said hy the ancients to be necessary propo- 

 sitions. 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. 



2. The important doctrine of Dugald Stewart, which 

 I have endeavoured to enforce, has been contested by Dr. 

 Whewell, both in the dissertation appended to his excellent 

 Mechanical Euclid, and in his elaborate work on the Philosophy 

 of the Inductive Sciences ; in which last he also replies to an 

 article in the Edinburgh Keview, (ascribed to a writer of great 

 scientific eminence), in which Stewart's opinion was defended 

 against his former strictures. The supposed refutation of 

 Stewart consists in proving against him (as has also been done 

 in this work) that the premises of geometry are not definitions, 

 but assumptions of the. real existence of things corresponding 

 to those definitions. This, however, is doing little for Dr. 

 Whewell's purpose ; for it is these very assumptions which are 

 asserted to be 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 conception 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 premises of 

 geometry are hypotheses, are not bound to maintain them to be 

 hypotheses which have no relation whatever to fact. Since an 

 hypothesis framed for the purpose of scientific inquiry must 



* Mechanical Euclid, pp. 149 et seqq. 



