iii.i GEOMETRY AND DEDUCTION 213 



certain measure. Very soon appeal has to be made to 

 common sense, that is to say, to the continuous experience 

 of the real, in order to inflect the consequences deduced 

 and bend them along the sinuosities of life. Deduction 

 succeeds in things moral only metaphorically, so to speak, 

 and just in the measure 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 some- 

 thing 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 geometry, in astronomy, in physics, 

 where we have to do with things external to us, deduction 

 is all-powerful! Observation and experience are un- 

 doubtedly necessary in these sciences to arrive at the 

 principle, that is, to discover the aspect under which 

 things must be regarded ; 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, molded 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. 



