REMAINING LAWS OF NATURE. 145 



the sun, is an uniformity derived from the laws of the causes 

 (or forces) which produce the planetary motions ; but that the 

 square of any number is four times the square of half the 

 number, is true independently of any cause. The only laws 

 of resemblance, therefore, which we are called upon to consider 

 independently of causation, belong to the province of mathe- 

 matics. 



4. The same thing is evident with respect to the only 

 one remaining of our five categories, Order in Place. The 

 order in place, of the effects of a cause, is (like everything else 

 belonging to the effects) a consequence of the laws of that 

 cause. The order in place, or, as we have termed it, the col- 

 location, of the primeval causes, is (as well as their resem- 

 blance) in each instance an ultimate fact, in which no laws or 

 uniformities are traceable. The only remaining general pro- 

 positions respecting order in place, and the only ones which 

 have nothing to do with causation, are some of the truths of 

 geometry ; laws through which we are able, from the order in 

 place of certain points, lines, or spaces, to infer the order in 

 place of others which are connected with the former in some 

 known mode ; quite independently of the particular nature of 

 those points, lines, or spaces, in any other respect than posi- 

 tion or magnitude, as well as independently of the physical 

 cause from which in any particular case they happen to derive 

 their origin. 



It thus appears that mathematics is the only department 

 of science into the methods of which it still remains to inquire. 

 And there is the less necessity that this inquiry should occupy 

 us long, as we have already, in the Second Book, made consi- 

 derable progress in it. We there remarked, that the directly 

 inductive truths of mathematics are few in number ; consisting 

 of the axioms, together with certain propositions concerning 

 existence, tacitly involved in most of the so-called definitions. 

 And we gave what appeared conclusive reasons for affirming 

 that these original premises, from which the remaining truths 

 of the science are deduced, are, notwithstanding all appearances 

 to the contrary, results of observation and experience ; founded, 



VOL. II. 10 



