vii.] INDUCTION. 131 



reflected light, or revolving in a particular direction, or 

 being spheroidal in form, are planets. In other sciences 

 we have immense numbers of propositions of the same 

 form, as, for instance, all substances in becoming gaseous 

 absorb heat ; all metals are elements ; they are all good 

 conductors of heat and electricity ; all the alkaline metals 

 are monad elements ; all foraminifera are marine organ- 

 isms ; all parasitic animals are non-mammalian ; lightning 

 never issues from stratous clouds; pumice never occurs 

 where only Labrador felspar is present ; milkmaids do 

 not suffer from small-pox ; and, in the works of Darwin, 

 scientific importance may attach even to such an appa- 

 rently trifling observation as that " white tom-cats having 

 blue eyes are deaf." 



The process of inference by which all such truths are 

 obtained may readily be exhibited in a precise symbolic 

 form. We must have one premise specifying in a dis- 

 junctive form all the possible individuals which belong 

 to a class ; we resolve the class, in short, into its con- 

 stituents. We then need a number of propositions, each 

 of which affirms that one of the individuals possesses a 

 certain property. Thus the premises must be of the 

 forms 



A = B -I- C -I- D -|- -I- P -I- Q 



B = BX 



c = cx 



Q = QX. 



Now, if we substitute for each alternative of the first 

 premise its description as found among the succeeding 

 premises, we obtain 



A = BX -I- OX -I- -I- PX i QX 



A=(B -|. C -I- -I- Q)X 



But for the aggregate of alternatives we may now 

 substitute their equivalent as given in the first premise, 

 namely A, so that we get the required result : 



A = AX. 



We should have reached the same result if the first 

 premise had been of the form 



A = AB -|- AC -I- -|. AQ. 



K 2 



