THAT ALL MATTER IS HEAVY. 199 



I proceed to reply to these arguments. And first, as to the possibility 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 conceive the contrary of 

 a necessary truth to be true; but that this impossibility can be asserted only 

 of those perfectly distinct conceptions which result from a complete deve- 

 lopement of the fundamental idea and its consequences. Till we reach this 

 stage of developement, the obscurity and indistinctness may prevent our 

 perceiving absolute contradictions, though they exist. We have abundant 

 store of examples of this, even in geometry and arithmetic; where the 

 truths are universally allowed to be necessary, and where the relations which 

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

 relations, though not distinctly conceivable, still often appear conceivable 

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

 outset of his geometrical studies, sees any impossibility in supposing the 

 side and the diagonal of a square to have a common measure? Yet they 

 can be rigorously proved to be incommensurable, and therefore 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 obstinately 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 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 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 



