174 SCIENCE AND METHOD. 



straight line ? I have already explained this so often 

 that I feel some hesitation about repeating myself 

 once more. I will content myself with a brief sum- 

 mary of my thought. 



We have not, as in the previous case, two equivalent 

 definitions logically irreducible one to the other. We 

 have only one expressible in words. It may be said 

 that there is another that we feel without being able 

 to enunciate it, because we have the intuition of a 

 straight line, or because we can picture a straight 

 line. But, in the first place, we cannot picture it in 

 geometric space, but only in representative space ; 

 and then we can equally well picture objects which 

 possess the other properties of a straight line, and 

 not that of satisfying Euclid's postulate. These 

 objects are " non- Euclidian straight lines," which, 

 from a certain point of view, are not entities 

 destitute of meaning, but circles (true circles of true 

 space) orthogonal to a certain sphere. If, among 

 these objects equally susceptible of being pictured, 

 it is the former (the Euclidian straight lines) that 

 we call straight lines, and not the latter (the non- 

 Euclidian straight lines), it is certainly so by definition. 

 And if we come at last to the third example, the 

 definition of phosphorus, we see that the true defini- 

 tion would be : phosphorus is this piece of matter 

 that I see before me in this bottle. 



XII. 



Since I am on the subject, let me say one word 



more. Concerning the example of phosphorus, I 



said : " This proposition is a true physical law that 



can be verified, for it means : all bodies which possess 



