DEMONSTRATION, AND NECESSARY TRUTHS. 179 



And they no doubt found it as impossible to conceive that a body should 

 act upon the earth from the distance of the sun or moon, as we find it to 

 conceive an end to space or time, or two straight lines inclosing a space. 

 Newton himself had not been able to reaUze the conception, or we should 

 not have had his hypothesis of a subtle ether, the occult cause of gravita- 

 tion ; and his writings prove, that though he deemed the particular nature 

 of the intermediate agency a matter of conjecture, the necessity of some 

 such agency appeared to him indubitable. 



If, then, it be so natural to the human mind, even in a high state of cul- 

 ture, to be incapable of conceiving, and on that ground to believe impossi- 

 ble, what is afterward not only found to be conceivable but proved to be 

 true ; what wonder if in cases where the association is still older, more con- 

 firmed, and more familiar, and in which nothing ever occurs to shake our 

 conviction, or even suggest to us any conception at variance with the asso- 

 ciation, the acquired incapacity should continue, and be mistaken for a nat- 

 ural incapacity ? It is true, our experience of the varieties in nature ena- 

 bles us, within certain limits, to conceive other varieties analogous to them. 

 We can conceive the sun or moon falling ; for though we never saw them 

 fall, nor ever, perhaps, imagined them falling, we have seen so many other 

 things fall, that we have innumerable familiar analogies to assist the con- 

 ception ; which, after all, we should probably have some difiiculty in fram- 

 ing, were we not well accustomed to see the sun and moon move (or ap- 

 pear to move), so that we are only called upon to conceive a slight change 

 in the direction of motion, a circumstance familiar to our experience.^But 

 when experience affords no model on which to shape the new conception, 

 how is it possible for us to form it ^lHow, for example, can we imagine 

 an end to space or time? We never saw any object without something 

 beyond it, nor experienced any feeling Mdthout something following it. 

 When, therefore, we attempt to conceive the last point of space, we have 

 the idea irresistibly raised of other points beyond it. When we try to im- 

 agine the last instant of time, we can not help conceiving another instant 

 after it. Nor is there any necessity to assume, as is done by a modern 

 school of metaphysicians, a peculiar fundamental law of the mind to ac- 

 count for the feeling of infinity inherent in our conceptions of space and 

 time; that apparent infinity is sufficiently accounted for by simpler and 

 universally acknowledged laws. 



Now, in the case of a geometrical axiom, such, for example, as that two 

 straight lines can not inclose a space — a truth which is testified to us by 

 our very earliest impressions of the external world — how is it possible 

 (whether those external impressions be or be not the ground of our belief) 

 that the reverse of the proposition could be otherwise than inconceivable 

 to us? What analogy have we, what similar order of facts in any other 

 branch of our experience, to facilitate to us the conception of two straight 

 lines inclosing a space ? Nor is even this all. I have already called atten- 

 tion to the peculiar property of our impressions of form, that the ideas or 

 mental images exactly resemble their prototypes, and adequately represent 

 them for the purposes of scientific observation. From this, and from the 

 intuitive character of the observation, which in this case reduces itself to 



Dieu donnait cette loi, par exemple, b. un corps libre, de tourner k I'entour d'un certain centre, 

 ilfaudrait ou qu'il y joignit (Tautres corps qui par leur impulsion Vobligeassent de rester tou- 

 jours dans son orbite circulaire, ou quil mit un ange a ses trousses, ou enjin ilfaudrait quil y 

 concourut extraordinairement ; car naturellement il s'ecartera par la tangente." — Works of 

 Leibnitz, ed. Dutens, iii., 446. 



