40 Wiscoimn Academy of Sciences^ Arts, and Letters. 



single whole ; and a series of observations taken at eq'ual dis- 

 tances, will, by the uniformity of differences presented, reveal 

 the operation of the same law in this dual manifestation. Up- 

 on examining the processes of deduction and induction, we 

 find in each the same series of terms, differing only in the fact 

 that they are in inverse order, and this correspondence reveals 

 the operation of one and the same law. An inductive series 

 is only a deductive series read backward. Any two terms in 

 a series whether inductive or deductive, differ only in the de- 

 gree of generality, and differ similarly from a third terra, so 

 that two being known the third can be therefrom determined. 

 In a deductive series the terms differ by a constant increase in 

 the number of individualizing attributes — a concept being ex- 

 panded into a deductive series by such regular additions. 

 Having two terms we can proceed to the third — that is, from 

 two propositions expressing this relation, we can proceed to a 

 conclusion. In an inductive series the terms differ by a con- 

 stant diminution in the number of individualizing attributes — 

 an individual term being expanded into an inductive series, 

 by successively dropping the attributes which compose the in- 

 dividual term, until we reach the required degree of^ generali- 

 zation. 



Thought must proceed in one of these two directions. The 

 object-matter of thought being composed wholly of attributes 

 can differ only in the presence or absence of certain attributes. 

 A combination, then, of these two movements must complete 

 the intellectual orbit. The direction of the movement of the 

 mind will be determined by the end proposed. When we pos- 

 sess the knowledge of phenomena and wish to discover law — 

 that is, when we seek information — we proceed by induction, 

 from the individual to the general. When possessed of knowl- 

 edge, we wish to discover its applications, wlien knowing the 

 law, we wish to determine the phenomena necessarily resulting 

 therefrom, we proceed by deduction — from the general to the 

 individual. Complete knowledge, then, consists in the highest 



