212 



INDUCTION. 



formities possessed the same rigorous 

 certainty. But this we cannot do. 

 From laws of space and number alone, 

 nothing can be deduced but laws of 

 space and number. 



Of all truths relating to phenomena, 

 the most valuable to us are those 

 which relate to the order of their suc- 

 cession. On a knowledge of these is 

 founded every reasonable anticipation 

 of future facts, and whatever power 

 we possess of influencing those facts 

 to our advantage. Even the laws of 

 geometry are chiefly of practical im- 

 portance to us as being a portion of 

 the premises from which the order of 

 the succession of phenomena may be 

 inferred. Inasmuch as the motion of 

 bodies, the action of forces, and the 

 propagation of influences of all sorts, 

 take place in certain lines and over 

 definite spaces, the properties of those 

 lines and spaces are an important part 

 of the laws to which those pheno- 

 mena are themselves subject. Again, 

 motions, forces, or other influences, 

 and times are numerable quantities ; 

 and the properties of number are ap- 

 plicable to them as to all other things. 

 But though the laws of number and 

 space are important elements in the 

 ascertainment of uniformities of suc- 

 cession, they can do nothing towards 

 it when taken by themselves. They 

 can only be made instrumental to that 

 purpose when we combine with them 

 additional premises, expressive of uni- 

 formities of succession already known. 

 By taking, for instance, as premises 

 these propositions, that bodies acted 

 upon by an instantaneous force move 

 with uniform velocity in straight 

 lines ; that bodies acted upon by a 

 continuous force move with accele- 

 rated velocity in straight lines ; and 

 that bodies acted upon by two forces 

 in different directions move in the 

 diagonal of a parallelogram, whose 

 sides represent the direction and quan- 

 tity of those forces ; we may by com- 

 bining these truths with propositions 

 relating to the properties of straight 

 lines and of parallelograms (as that a 

 triangle is half a parallelogram of the 



same base and altitude), deduce an- 

 other important uniformity of suc- 

 cession, viz., that a body moving 

 round a centre of force describes 

 areas proportional to the times. But 

 unless there had been laws of succes- 

 sion in our premises, there could have 

 been no truths of succession in our 

 conclusions. A similar remark might 

 be extended to every other class of 

 phenomena really peculiar ; and, had 

 it been attended to, would have pre- 

 vented many chimerical attempts at 

 demonstrations of the indemonstrable, 

 and explanations which do not explain. 



It is not, therefore, enough for us 

 that the laws of space, which are only 

 laws of simultaneous phenomena, and 

 the laws of number, which though true 

 of successive phenomena do not relate 

 to their succession, possess the rigorous 

 certainty and universality of which 

 we are in search. We must endeavour 

 to find some law of succession which 

 has those same attributes, and is there- 

 fore fit to be made the foundation of 

 processes for discovering, and of a test 

 for verifying, all other uniformities of 

 succession. This fundamental law 

 must resemble the truths of geometry' 

 in their most remarkable peculiarity, 

 that of never being, in any instance 

 whatever, defeated or suspended by 

 any change of circumstances. 



Now among all those uniformities 

 in the succession of phenomena which 

 common observation is sufficient to 

 bring to light, there are very few which 

 have any, even apparent, pretension 

 to this rigorous indefeasibility ; and 

 of those few, one only has been found 

 capable of completely sustaining it. 

 In that one, however, we recognise a 

 law which is imiversal also in another 

 sense ; it is co-extensive with the entire 

 field of successive phenomena, all 

 instances whatever of succession being 

 examples of it. This law is the Law 

 of Causation. The truth that everj' 

 fact which has a beginning has a 

 cause, is co-extensive with human ex- 

 perience. 



This generalisation may appear to 

 some minds not to amount to much. 



