400 THE SCIENCE OF LOGIC 



must be actually in the premisses, i.e. actually seen by the mind 

 which knows the premisses. Of course, the conclusion must 

 be &quot; in &quot; the premisses somehow ; otherwise we could not get 

 it out of them. But how must it be in them ? It must not be 

 in them actually : if it were, inference would be superfluous. 

 Therefore, it must be in them latently, virtually, as a necessary 

 implication, i.e. in such a way that it will be necessarily and inevit 

 ably brought to light, discovered, made an item of actual know 

 ledge, by the mind which concentrates its energies long enough 

 and keenly enough on the partial view of reality which it al 

 ready possesses in its knowlege of those premisses. 



But it is here precisely in this scrutinizing, comparing, 

 arranging, and analysing, of the various judgments which embody 

 the objects of our knowledge, so as to discover and establish new 

 and fertile and instructive relations between these objects, in 

 other words, so as to enunciate new judgments, and discover new 

 truths that the whole difficulty of making progress in knowledge 

 lies, and that the genius of the master-mind will reveal itself by 

 making remarkable headway. 



We must not be misled, by the trite and easy examples [199, 

 (12)] of inference with which text-books of logic abound, into be 

 lieving that real, first-hand inference, is a trivial factor in the 

 growth of knowledge ; 1 nor must we forget that there is no com 

 parison between the student s effort to assimilate already accom 

 plished results, in his study of the various sciences, and the long 

 and arduous labours by which these results were for the first time 

 achieved. It is easy to follow when the path is broken. For the 

 millions of minds that are capable of assimilating all the known 

 truths of geometry and mathematics on being taught these, how 

 few, comparatively, are the minds that in the course of the world s 

 history gradually accumulated that vast treasure of knowledge, 

 by discovering for the first time the individual truths which com 

 pose it? 



1 &quot; If our reasoning processes were carried on with the continuity and intricacy 

 displayed in mathematics we should soon have obvious proof over what a distance 

 we may have advanced by a succession of such apparently insignificant steps. 

 Everyone who has studied mathematics must have experienced a feeling of surprise 

 at times in finding how far he has been carried on in this way. He starts with a 

 premise which it may take some trouble to distinguish from a pure identity, and 

 finds that, starting from this, he may be imperceptibly led on by intuitively obvious 

 advances into some profound and far-reaching algebraical formula.&quot; VENN, Em 

 pirical Logic, p. 377. 



