DEMONSTRATION, AND NECESSARY TRUTHS. 325 



experience, and defacing our mental picture of space as grounded 

 on it. What but experience, we may ask, can possibly assure us 

 of the homogeneity of the parts of distance, time, force, and mea- 

 surable aggregates in general, on which the truth of the other 

 axioms depends ? As regards the latter axiom, after what has 

 been said it must be clear that the very same course of remarks 

 equally applies to its case, and that its truth is quite as much forced 

 on the mind as that of the former by daily and hourly experience, 

 . . . including always, be it observed, in our notion of experience t that 

 which is gained by contemplation of the inward picture which the 

 mind forms to itself in any proposed case, or which it arbitrarily 

 selects as an example such picture, in virtue of the extreme simplicity 

 of these primary relations^ being called up by the imagination with 

 as much vividness and clearness as could be done by any external 

 impression, which is the only meaning we can attach to the word 

 intuition, as applied to such relations" 



And again, of the axioms of mechanics : " As we admit no 

 such propositions, other than as truths inductively collected from 

 observation, even in geometry itself, it can hardly be expected that, 

 in a science of obviously contingent relations, we should acquiesce 

 in a contrary view. Let us take one of these axioms and examine 

 its evidence : for instance, that equal forces perpendicularly applied 

 at the opposite ends of equal arms of a straight lever will balance 

 each other. What but experience, we may ask, in the first place, 

 can possibly inform us that a force so applied will have any tendency 

 to turn the lever on its centre at all ? or that force can be so 

 transmitted along a rigid line perpendicular to its direction, as to 

 act elsewhere in space than along its own line of action? Surely 

 this is so far from being self-evident that it has even a paradoxical 

 appearance, which is only to be removed by giving our lever thick- 

 ness, material composition, and molecular powers. Again we con- 

 clude, that the two forces, being equal and applied under precisely 

 similar circumstances, must, if they exert any effort at all to turn 

 the lever, exert equal and opposite efforts: but what a priori 

 reasoning can possibly assure us that they do act under precisely 

 circumstances ? that points which differ in place, are similarly 

 circumstanced as regards the exertion of force? that universal 

 space may not have relations to universal force or, at all events, 

 that the organization of the material universe may not be such as 

 to place that portion of space occupied by it in such relations to 

 the forces exerted in it, as may invalidate the absolute similarity 

 of circumstances assumed? Or we may argue, what ha vo we to do 



