in GEOMETRY AND DEDUCTION 223 



ment by which I trace a figure in space engenders its 

 properties : they are visible and tangible in the move 

 ment itself; I feel, I see in space the relation of the 

 definition to its consequences, of the premisses to the 

 conclusion. All the other concepts of which experience 

 suggests the idea to me are only in part constructible 

 a priori ; the definition of them is therefore imperfect, 

 and the deductions into which these concepts enter, 

 however closely the conclusion is linked to the pre 

 misses, participate in this imperfection. But when I 

 trace roughly in the sand the base of a triangle, as I 

 begin to form the two angles at the base, I know 

 positively, and understand absolutely, that if these 

 two angles are equal the sides will be equal also, the 

 figure being then able to be turned over on itself 

 without there being any change whatever. I know 

 it before I have learnt geometry. Thus, prior to the 

 science of geometry, there is a natural geometry whose 

 clearness and evidence surpass the clearness and evidence 

 of other deductions. Now, these other deductions bear 

 on qualities, and not on magnitudes purely. They are, 

 then, likely to have been formed on the model of the first, 

 and to borrow their force from the fact that, behind 

 quality, we see magnitude vaguely showing through. 

 We may notice, as a fact, that questions of situation and 

 of magnitude are the first that present themselves to our 

 activity, those which intelligence externalized in action 

 resolves even before reflective intelligence has appeared. 

 The savage understands better than the civilized 

 man how to judge distances, to determine a direction, 

 to retrace by memory the often complicated plan 

 of the road he has travelled, and so to return in a 

 straight line to his starting-point. 1 If the animal 



1 Bastian, The Brain as an Organ of the Mind, pp. 214-16. 



