266 Prof. WhewelVs Demonstration 



weight is proportional to the inertia ; Newton's experiments with pen- 

 dulums of different materials having been made with this very object. 



" I proceed to reply to these arguments. And first, as to the possi- 

 bility of conceiving matter without weight, and the argument thence 

 deduced, that the universal gravity of matter is not a necessary truth, I 

 remark, that it is indeed just to say that we cannot even distinctly con- 

 ceive the contrary of a necessary truth to be true ; but that this impos- 

 sibility can be asserted only of those perfectly distinct conceptions 

 which result from a complete developement of the fundamental idea 

 and its consequences. Till we reach this stage of developement, the 

 obscurity and indistinctness may prevent our perceiving absolute con- 

 tradictions, though they exist. We have abundant store of examples 

 of this even in geometry and arithmetic ; where the truths are univer- 

 sally allowed to be necessary, and where the relations which are impos- 

 sible, are also inconceivable, that is, not conceivable distinctly. Such 

 relations, though not distinctly conceivable, still often appear conceiva- 

 ble and possible, owing to the indistinctness of our ideas. Who, at the 

 first outset of his geometrical studies, sees any impossibility in suppo- 

 sing the side and the diagonal of a square to have a common measure } 

 Yet they can be rigorously proved to be incommensurable, and there- 

 fore the attempt distinctly to conceive a common measure of them 

 must fail. The attempts at the geometrical duplication of the cube, 

 and the supposed solutions, (as that of Hobbes) have involved absolute 

 contradictions ; yet this has not prevented their being long and obsti- 

 nately entertained by men, even of minds acute and clear in other 

 respects. And the same might be shewn to be the case in arithmetic. 

 It is plain, therefore, that we cannot, from the supposed possibility of 

 conceiving matter without weight, infer that the contrary may not be a 

 necessary truth. 



" Our power of judging, from the compatibility or incompatibility of 

 our conceptions, whether certain propositions respecting the relations of 

 ideas are true or not, must depend entirely, as I have said, upon the 

 degi'ee of developement which such ideas have undergone in our 

 minds. Some of the relations of our conceptions on any subject are 

 evident upon the first steady contemplation of the fundamental idea by 

 a sound mind : these are the axioms of the subject. Other propositions 

 may be deduced from the axioms by strict logical reasoning. These 

 propositions are no less necessary than the axioms, though to common 

 minds their evidence is very different. Yet as we become familiar with 

 the steps by which these ulterior truths are deduced from the axioms, 

 their truth also becomes evident, and the contrary becomes inconceiv- 

 able. When a person has familiarized himself with the first twenty-six 



