DEMONSTRATION, AND NECESSARY TRUTHS. 317 



change in the direction of motion, a circumstance 

 familiar to our experience. But when experience 

 affords no model on which to shape the new concep- 

 tion, how is it possible for us to form it ? How, for 

 example, can we imagine an end to space or time ? 

 We never saw any object without something beyond 

 it, nor experienced any feeling without something 

 following it. When, therefore, we attempt to con- 

 ceive the last point of space, we have the idea irresist- 

 ibly raised of other points beyond it. When we try 

 to imagine the last instant of time, we cannot help 

 conceiving another instant after it. Nor is there any 

 necessity to assume, as is done by the school to 

 which Mr. Whewell belongs, a peculiar fundamental 

 law of the mind to account 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 cannot 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 can 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 attention 

 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, 



