290 Mr. Toulmin Smith on the Formation 



independently existent in itself; which does not stand in the re- 

 lation of necessary connexion with some other thing or fact in 

 nature. The recognition of this as a primary axiom certainly 

 lies at the bottom of all science and of every attempt to discover 

 truth. If truth or science has any existence^ and is not a mere 

 vain search, every question must really assume this form : — Given 

 the thing or fact before me, with what other thing or fact does 

 it stand in necessary connexion or relation ? Abstractedly few 

 men will deny this ; but practically it is neglected every day. It 

 is now as it was in the time of Bacon, that the reasoners by 

 "anticipation/^ they who ''^jump from a few individual facts to 

 general axioms, and make use of such axioms in all other indivi- 

 dual and mediate cases,^^ are most common ; the important if of 

 Sir J. Herschel is forgotten. Were not this the case, we should 

 never hear, as we continually do, of exceptions to laws of nature. 

 Every one would feel, at the very beginning of and through- 

 out his investigations and attempted generalizations, that in facts 

 of nature there is a necessary connexion, or there is not. If 

 there is, no exception can exist ; for the statement of such ex- 

 ception involves a contradiction, viz. that there is not a necessary 

 connexion. 



Every process of true induction must depend upon the exer- 

 cise of three different mental operations : — comparison of simili- 

 tudes (or analogies) ; of dissimilitudes, or points of disagree- 

 ment ; and, lastly, inferring a necessary connexion between the 

 existence of and relations common to the things or facts com- 

 pared. Most men are caught by analogies ; on these frame theo- 

 ries — " anticipations ;" with a distorted axiom thus obtained they 

 view every fact subsequently seen, caught, in each, by its simili- 

 tude, disregarding its dissimilitudes, and so never arrive at a true 

 " interpretation" Talk to such men of the very first principles 

 of reasoning, of the primary axiom of "necessary connexion,^^ 

 or, as the same thing may be stated in other words, of the uni- 

 versal laws of unity and design, and they grow impatient. No 

 wonder at it : the constant application of those principles must 

 upset many a theory. Every one v/ho has considered this sub- 

 ject will feel it to follow as a necessary corollary from the prin- 

 ciples above indicated, that the existence of a single real dissimi- 

 litude must upset any assumed law, generalization, or theory, pre- 

 viously made upon observation of ever so many similitudes. 

 Thus, had it been announced as a law that all transparent solids 

 exhibit periodical colours, it would have been upset, and there- 

 fore proved false, by the discovery of a single case in which a 

 transparent solid did not exhibit such colours. Again, though 

 it had been observed a thousand times, and in a thousand dif- 

 ferent ways, that water decreases in dimension as heat is with- 



