324 REASONING. 



which maintains, on the subject of axioms, the doctrine advanced 

 in the text, that they are generalizations from experience, and 

 supports that opinion by a line of argument strikingly coinciding 

 with mine. When I state that the whole of the present chapter 

 was written before I had seen the article, (the greater part, 

 indeed, before it was published,) it is not my object to occupy 

 the reader's attention with a matter so unimportant as the degree 

 of originality which may or may not belong to any portion of my 

 own speculations, but to obtain for an opinion which is opposed to 

 reigning doctrines, the recommendation derived from a striking 

 concurrence of sentiment between two inquirers entirely independent 

 of one another. I have much pleasure in citing from a writer of 

 the extensive acquirements in physical and metaphysical know- 

 ledge and the capacity of systematic thought which the article 

 evinces, passages so remarkably in unison with my own views as 

 the following : 



" The truths of geometry are summed up and embodied in its 

 definitions and axioms. . . . Let us turn to the axioms, and what 

 do we find ? A string of propositions concerning magnitude in the 

 abstract, which are equally true of space, time, force, number, and 

 every other magnitude susceptible of aggregation and subdivision. 

 Such propositions, where they are not mere definitions, as some of 

 them are, .carry their inductive origin on the face of their enun- 

 ciation. . . . Those which declare that two straight lines cannot 

 inclose a space, and that two straight lines which cut one another 

 cannot both be parallel to a third, are in reality the only ones 

 which express characteristic properties of space, and these it will 

 be worth while to consider more nearly. Now the only clear 

 notion we can form of straightness is uniformity of direction, for 

 space in its ultimate analysis is nothing but an assemblage of 

 distances and directions. And (not to dwell on the notion of 

 continued contemplation, i. e. 9 mental experience, as included in 

 the very idea of uniformity; nor on that of transfer of the con- 

 templating being from point to point, and of experience, during 

 such transfer, of the homogeneity of the interval passed over) we 

 cannot even propose the proposition in an intelligible form, to any 

 one whose experience ever since he was born has not assured him 

 of the fact. The unity of direction, or that we cannot march 

 from a given point by more than one path direct to the same 

 object, is matter of practical experience long before it can by 

 possibility become matter of abstract thought. We cannot attempt 

 mentally to exemplify the conditions of the assertion in an imaginary 

 case opposed to it, without violating our habitual recollection of this 



