266 - Prof, Whewell’s Demonstration 
weight is:proportional to the inertia ; Newton’s experiments with pen- 
dulums of different materials having been made with this very object. 
- “] 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 mpatter 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 
nana and indistinctness may prevent our perceiving absolute con- 
dictions, 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 
not distinctly conceivable, still often appear conceiva- 
ble and stables 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 tobe the case in arithmetic. 
It is plain, therefore, that we cannot, from the supposed possibility of 
conceiving matter without weighty infer that the contrary ae not eee a 
truth. 
novesary 
Our power of judging, fries the Goigpatibitiyy 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 
degree 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 
ee deduced from the axioms by strict logical reasoning. These 
propositions are no less necessary than the axioms, though to common 
PRL = evidence i is sand different. Yet as we become familiar with 
Kate i ir hs are deduced. from the axioms, 
their trath also b ident, and the vain nts becomes: inconceiv- 
able. Whena person has familiarized himself with the first twenty-six 
