186 EEASONING. 



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 conclude, 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 effoi-ts : but what a priori reasoning can pos- 

 sibly assure us that they do act under precisely similar circumstances ? that points which dif- 

 fer 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 ma- 

 terial universe may not be such as to place that portion of space occupied by it in such rela- 

 tions to the forces exerted in it, as may invalidate the absolute similarity of circumstances as- 

 sumed? Or we may argue, what have we to do with the notion of angular movement in the 

 lever at all ? The case is one of rest, and of quiescent destruction of force by force. Now 

 how is this destruction effected ? Assuredly by the counter-pressure which supports the ful- 

 crum. But would not this destruction equally arise, and by the same amount of counteract- 

 ing force, if each force simply pressed its own half of the lever against the fulcrum ? And 

 what can assure us that it is not so, except removal of one or other force, and consequent tilt- 

 ing of the lever? The other fundamental axiom of statics, that the pressure on the point of 



support is the sum of the weights is merely a scientific transformation and more refined 



mode of stating a coarse and obvious result of universal experience, viz., that the weight of a 

 rigid body is the same, handle it or suspend it in what position or by what point we will, and 

 that whatever sustains it sustains its total weight. Assuredly, as Mr. Whewell justly remarks, 

 'No one probably ever made a trial for the purpose of showing that the pressure on the sup- 

 port is equal to the sum of the weights.' But it is precisely because in every action 



of his life from earliest infancy he has been continually making the trial, and seeing it made 

 by every other living being about him, that he never dreams of staking its result on one addi- 

 tional attempt made with scientific accuracy. This would be as if a man should resolve to 

 decide by experiment whether his eyes were useful for the purpose of seeing, by hermetically 

 sealing himself up for half an hour in a metal case." 



On the "paradox of universal propositions obtained by experience," the same writer says: 

 " If there be necessary and universal truths expressible in propositions of axiomatic simplicity 

 and obviousness, and having for their subject-matter the elements of all our experience and 

 all our knowledge, surely these are the truths which, if experience suggest to us any truths at 

 all, it ought to suggest most readily, clearly, and unceasingly. If it were a truth, universal 

 and necessary, that a net is spread over the whole surface of every planetary globe, we should 

 not travel far on our own without getting entangled in its meshes, and making the necessity 

 of some means of extrication an axiom of locomotion There is, therefore, nothing par- 

 adoxical, but the reverse, in our being led by observation to a recognition of such truths, as 

 general propositions, co-extensive at least with all human experience. That they pervade all 

 the objects of experience, must insure their continual suggestion by experience ; that they ai-e 

 true, must insure that consistency of suggestion, that iteration of uncontradicted assertion, 

 which commands implicit assent, and removes all occasion of exception ; that they are simple, 

 and admit of no misunderstanding, must secure their admission by every mind." 



" A truth, necessary and universal, relative to any object of our knowledge, must verify it- 

 self in every instance where that object is before our contemplation, and if at the same time it 

 be simple and intelligible, its verification must be obvious. The sentiment of such a truth 

 can not, therefore, but be present to our minds whenever that object is contemplated, and must 

 there/ore make a part of the mental picture or idea of that object which we viay on any occa- 

 sion summon before our imagination All propositions, therefore, become not only untrue 



but inconceivable, if axioms be violated in their enunciation." 



Another eminent mathematician had previously sanctioned by his authority the doctrine of 

 the origin of geometrical axioms in experience. "Geometry. is thus founded likewise on 

 observation ; but of a kind so familiar and obvious, that the primary notions which it fur- 

 nishes might seem intuitive." — Sir John Leslie, quoted by Sir William Hamilton, Discourses, 

 etc., p. 272. 



