in GEOMETRY AND INDUCTION 225 



in which the moral is transposable into the physical, 

 I should say translatable into spatial symbols. The 

 metaphor never goes very far, any more than a curve 

 can long be confused with its tangent. Must we not 

 be struck by this feebleness of deduction as something 

 very strange and even paradoxical ? Here is a pure 

 operation of the mind, accomplished solely by the 

 power of the mind. It seems that, if anywhere it 

 should feel at home and evolve at ease, it would be 

 among the things of the mind, in the domain of the 

 mind. Not at all ; it is there that it is immediately 

 at the end of its tether. On the contrary, in geo 

 metry, in astronomy, in physics, where we have to do 

 with things external to us, deduction is all-powerful ! 

 Observation and experience are undoubtedly necessary 

 in these sciences to arrive at the principle, that is, to 

 discover the aspect under which things must be re 

 garded ; but, strictly speaking, we might, by good 

 luck, have hit upon it at once ; and, as soon as we 

 possess this principle, we may draw from it, at any 

 length, consequences which experience will always verify. 

 Must we not conclude, therefore, that deduction is an 

 operation governed by the properties of matter, moulded 

 on the mobile articulations of matter, implicitly given, 

 in fact, with the space that underlies matter ? As long 

 as it turns upon space or spatialized time, it has only to 

 let itself go. It is duration that puts spokes in its wheels. 



Deduction, then, does not work unless there be 

 spatial intuition behind it. But we may say the same 

 of induction. It is not necessary indeed to think 

 geometrically, nor even to think at all, in order to 

 expect from the same conditions a repetition of the 

 same fact. The consciousness of the animal already 



Q 



