SCIENCE AND DEMONSTRATION 245 



their connection, and \c\ if possible, to explain this connection by further con 

 necting it with other laws : and this is to connect facts and laws into a 

 systematic whole.&quot; 



With some qualifications, this presents the case correctly. We may admit 

 that in both induction and deduction the common aim is to systematize ; but 

 it is more. We must know the contents of the system before arranging them ; 

 the mental process of advancing in knowledge, whether inductively or deduc 

 tively, involves discovery as well as proof. We start, in deduction, with the 

 knowledge of a number of general laws, but without a knowledge or even a 

 suspicion, at first of any of the consequents that may be evolved out of them, 

 and made to serve in turn as proximate antecedents for further consequents. 

 We have &quot; in our hands &quot; not any common thread which we see or know to 

 be the means of uniting further truths or facts, but rather with a whole tangled 

 skein of endless threads, growing into and out of one another, and leading out 

 ward and onward we know not where. The complicated details involved in 

 them it is the duty of the deductive scientist to bring to light ; and he does 

 this by obtaining successive intuitions of new relations in the domain of 

 abstract thought which he has under consideration for example, by intuitions 

 of spatial or quantitative relations in the study of geometry or algebra. 1 



The first step in the discovery of a new truth, &quot; S is /*,&quot; by deduction, 

 seems to be (a) the observation of some case or cases in which de facto &quot; 5 is 

 P&quot; or (V) the occurrence, to our minds reflecting on known truths, of some 

 such connexions (between these latter) as suggest to us the possibility that 

 &quot; S as such is P &quot;. It might, for example, have been (a) the actual measure 

 ment of a few instances that first led to the surmise that &quot;The right-angled 

 triangle as such has always and necessarily the square on its hypotenuse 

 equal in area to the sum of the squares on its sides &quot;. Or (b\ the theorem 

 might have first suggested itself to a geometrician from some speculations of 

 his, some mental connexions he established by pondering on the concepts and 

 truths he already possessed about triangles, squares, etc. In either case the 

 process, so far, would seem to correspond to the inductive scientist s initial 

 observation of certain facts, leading him to suspect, and to conceive as an 

 hypothesis, the truth of the judgment &quot; S as such is P &quot;. Neither the deduc 

 tive nor the inductive investigator may ever have experienced a single actual 

 case of S being P : but only some other truths or facts relative to S and P, 

 which might have suggested that there is perhaps a necessary or causal con 

 nexion between the latter. 



Of course, if the deductive inquirer, in his meditations, actually hits upon 

 some notion (M), which reveals to him a necessary connexion between S and 

 P, he simultaneously discovers and proves this latter connexion. As soon as 

 he realizes simultaneously in consciousness the truth of the two judgments, 

 that &quot; M as such is P &quot; and &quot; S as such is M,&quot; he instantly discovers, and 

 simultaneously demonstrates (nay, discovers by demonstrating, by explaining 

 its how and why} that &quot; 5&quot; as such is P &quot; (197, 198). In such a case, the con 

 ception of the new truth as an hypothesis is simultaneous with its verification 

 as a truth, and with its demonstration through its &quot; causes &quot;. 



Similarly, were the inductive inquirer to discover, among observed facts 

 relating to S and P, some agency (M) whose operation he now realized to be 



1 Cf, JOSEPH, op. cit., p. 505. 



