432 KOVIIM OHCANUM. [BOOK i 



induction from that hitherto m use ; not only for the proof and 

 discovery of principles (as they are called), but also of minor, 

 intermediate, and, in short, every kind of axioms. The induc 

 tion which proceeds by simple enumeration is puerile, leads to 

 uncertain conclusions, and is exposed to danger from one con 

 tradictory instance, deciding generally from too small a number 

 of facts, and those only the most obvious. But a really usefu 

 induction for the discovery and demonstration of the arts anc 

 sciences, should separate nature by proper rejections and ex 

 clusions, and then conclude for the affirmative, after collecting 

 a sufficient number of negatives. jN&quot;o\v this has not been done, 

 nor even attempted, except perhaps by Plato, who certainly uses 

 this form of induction in some measure, to sift definitions and 

 ideas. But much of what has never yet entered the thoughts of 

 man must necessarily be employed, in order to exhibit a good 

 and legitimate mode of induction or demonstration, so as even 

 to render it essential for us to bestow more pains upon it than 

 have hitherto been bestowed on syllogisms. The assistance of 

 induction is to serve us not only in the discovery of axioms, but 

 also in defining our notions. Much indeed is to be hoped from 

 such an induction as has been described. 



CVI. In forming our axioms from induction, we must examine 

 and try whether the axiom we derive be only fitted and calcu 

 lated for the particular instances from which it is deduced, or 

 whether it be more extensive and general. If it be the latter, 

 we must observe, whether it confirm its own extent and 

 generality by giving surety, as it were, in pointing out new 

 particulars, so that we may neither stop at actual discoveries, 

 nor with a careless grasp catch at shadows and abstract forms, 

 instead of substances of a determinate nature : and as soon as 

 we act thus, well authorized hope may with, reason, be said to 

 beam upon us. 



CVII. Here, too, we may again repeat what we have said 

 above, concerning the extending of natural philosophy and 

 reducing particular sciences to that one, so as to prevent any 

 Bchism or dismembering of the sciences ; without which we can 

 not hope to advance. 



CVIII. Such are the observations we would make in order to 

 remove despair and excite hope, by bidding farewell to the 

 errors of past ages, or by their correction. Let us examine 

 whether there be other grounds for hope. And, first, if many 

 useful discoveries have occurred to mankind by chance or oppor 

 tunity, without investigation or attention on their part, it must 

 necessarily be acknowledged that much more may be brought to 

 light by investigation and attention, if it be regular and orderly, 

 not hasty and interrupted. For although it may now and then 

 happen that one falls by chance upon something that had before 



