234 INDUCTION. 



spect to any inductive inference, that either it must be true, or one of these 

 certain and universal inductions must admit of an exception ; the former 

 generalization will attain the same certainty, and indefeasibleness within 

 the bounds assigned to it, which are the attributes of the latter. It will 

 be proved to be a law ; and if not a result of other and simpler laws, it will 

 be a law of nature. 



There are such certain and universal inductions ; and it is because there 

 are such, that a Logic of Induction is possible. 



CHAPTER V. 



OF THE LAW OF UNIVERSAL CAUSATION. 



§ 1. The phenomena of nature exist in two distinct relations to one an- 

 other ; that of simultaneity, and that of succession. Every phenomenon is 

 related, in a uniform manner, to some phenomena that co-exist with it, and 

 to some that have preceded and will follow it. 



Of the uniformities which exist among synchronous phenomena, the most 

 important, on every account, are the laws of number ; and next to them 

 those of space, or, in other words, of extension and figure. The laws of 

 number are common to synchronous and successive phenomena. That two 

 and two make four, is equally true whether the second two follow the first 

 two or accompany them. It is as true of days and years as of feet and 

 inches. The laws of extension and figure (in other words, the theorems 

 of geometry, from its lowest to its highest branches) are, on the contrary, 

 laws of simultaneous phenomena only. The various parts of space, and of 

 the objects which are said to fill space, co-exist ; and the unvarying laws 

 which are the subject of the science of geometry, are an expression of the 

 mode of their co-existence. 



This is a class of laws, or in other words, of uniformities, for the com- 

 prehension and proof of which it is not necessary to suppose any lapse of 

 time, any variety of facts or events succeeding one another. The proposi- 

 tions of geometry are independent of the succession of events. All things 

 which possess extension, or, in other words, which fill space, are subject to 

 geometrical laws. Possessing extension, they possess figure ; possessing 

 figui'e, they must possess some figure in particular, and have all the proper- 

 ties which geometry assigns to that figure. If one body be a sphere and 

 another a cylinder, of equal height and diameter, the one will be exactly 

 two-thirds of the other, let the nature and quality of the material be what 

 it will. Again, each body, and each point of a body, must occupy some 

 place or position among other bodies ; and the position of two bodies rela- 

 tively to each other, of whatever nature the bodies be, may be unei-ringly 

 inferred from the position of each of them relatively to any third body. 



In the laws of number, then, and in those of space, we recognize in the 

 most unqualified manner, the rigorous universality of which we are in 

 quest. Those laws have been in all ages the type of certainty, the standard 

 of comparison for all inferior degrees of evidence. Their invariability is so 

 perfect, that it renders us unable even to conceive any exception to them ; 

 and philosophers have been led, though (as I have endeavored to show) er- 

 roneously, to consider their evidence as lying not in experience, but in the 

 original constitution of the intellect. If, therefore, from the laws of space 

 and number, we were able to deduce uniformities of any other description, 



