194 INDUCTION. 



admit of an exception : the former generalization will attain the same 

 absolute 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 

 another ; that of simultaneity, and that of succession. Every phenom- 

 enon is related, in an uniform manner, to some phenomena that coexist 

 with it, and to some that have preceded or 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 phenome- 

 na. 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 branch- 

 es,) are, on the contrary, laws of simultaneous phenomena only. The 

 various parts of space, and of the objects which are said to fill space, 

 coexist; and the unvarying laws which are the subject of the science 

 of geometry, are an expression of the mode of their coexistence. 



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. If all 

 the objects in the universe were imchangeably fixed, and had remained 

 in that condition from eternity, the propositions of geometry would still 

 be true of those objects. All things which possess extension, or in other 

 words, which fill space, are subject to geometrical laws. Possessing 

 extension, they possess figure, possessing figure, they must possess 

 some figure in particular, and have all the properties which geometry 

 assigns to that figure. If one body be a sphere and the other a cylin- 

 der, 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 uner- 

 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 we are unable even to conceive any 



