308 REASONING. 



recourse to other arguments. These are reducible to 

 two, which I shall endeavour to state as clearly and 

 as forcibly as possible. 



$ 5. In the first place it is said, that if our assent 

 to the proposition that two straight lines cannot 

 inclose a space, were derived from the senses, we 

 could only be convinced of its truth by actual trial, 

 that is, by seeing or feeling the straight lines ; whereas 

 in fact it is seen to be true by merely thinking of 

 them. That a stone thrown into water goes to 

 the bottom, may be perceived by our senses, but 

 mere thinking of a stone thrown into the water will 

 never lead us to that conclusion : not so, however, 

 with the axioms relating to straight lines : if I could 

 be made to conceive what a straight line is, without 

 having seen one, I should at once recognise that two 

 such lines cannot inclose a space. Intuition is 

 " imaginary looking*;" but experience must be real 

 looking : if we see a property of straight lines to be 

 true by merely fancying ourselves to be looking at 

 them, the ground of our belief cannot be the senses, 

 or experience ; it must be something mental. 



To this argument it might be added in the case 

 of this particular axiom (for the assertion would not 

 be true of all axioms), that the evidence of it from 

 actual ocular inspection, is not only unnecessary, but 

 unattainable. What says the axiom? That two 

 straight lines cannot inclose a space ; that after 

 having once intersected, if they are prolonged to 

 infinity they do not meet, but continue to diverge 

 from one another. How can this, in any single case, 

 be proved by actual observation? We may follow 



* WHEWELL'S Philosophy of the Inductive Sciences , i. 130. 



