APPENDIX D. 355 



bara with a suppressed Major : which Major is, &quot; What is true 

 of each of these cases is true of all :&quot; which in itself seems to 

 offer no solution : for it falls under the same head with Ari 

 stotle s and Aldriclfs, as involving simple enumeration. 



Is then this &quot; Inductio per simplicem enumerationem&quot; a 

 philosophical absurdity ? By no means. Whether we accept 

 Locke s view that Mathematical Axioms arc so established, or 

 not, there are still many things the truth of which has been 

 affirmed solely by continual observation of unvarying pheno 

 mena, Our knowledge of the fact that two and two make four, 

 or that four and one make five, may or may not be referable 

 to this principle ; at any rate, the conclusions reached by the 

 unscientific are almost all of this kind. It is a lower sort of 

 knowledge, but it is knowledge as far as it goes. Thus the 

 observation of years will teach a sailor that the tide will ebb 

 and flow twice in a o-iven day : this he is sure of without bcinir 



On O 



able to give a reason for it ; the scientific man will know the 

 fact, and its &quot; antecedent ; &quot; viz. the action of the Masses of the 

 Moon and Sun upon the surface of our Planet, It fails, however, 

 because it is indiscriminating, and &quot;precario concludit, et pcriculo 

 exponitur ab instantia contradictoria,&quot; (Nov. Org. I. 105.) It is 

 indiscriminating ; for it seems to draw no distinction between 

 those general propositions, which are merely statements of what 

 are called accidents, and those which involve some knowledge of 

 the essential Nature, or Law of existence of a class. Thus, 

 Ancient Induction would treat with equal respect the Uni- 

 versals, &quot; All crows arc black,&quot; and &quot; All particles attract one 

 another with a force which varies inversely as the square of 

 their distance.&quot; It also lacks for discriminative power, in not 

 discerning the difference between the most abstract &quot; notionalia 

 Axiomata.&quot; and the intermediate generalizations. All its ge 

 neralizations are, so to speak, supposed to lie in one plane. 

 For the precarious position of its conclusions, it is enough to 

 remark that the mere collocation of observed facts, and the 

 discovery of a formula to express their points of resemblance, 

 can never give more than an imperfect certainty. There must 

 always be behind it the fear of a contradictory instance. 

 What if we discovered a white Crow? For this failure of 



A a 2 



