372 ELEMENTS OF SCIENCE 



to things external to us, of which we had knowledge at 

 some past time, as we shall see later on.* 



But if we were provided with nothing more than 

 absolutely certain evidence as to a number of facts, 

 together with a perception of the necessary validity of 

 the reasoning process, we could make no use of such 

 knowledge unless we were also provided with some 

 absolutely certain general principles. Without them 

 we could have no sure basis for the premisses of our 

 syllogisms. Thus, for example, we could not conclude 

 that Socrates was mortal because all men are so, save 

 for the general principle : " whatever is mortal cannot 

 at jbhe same time be immortal." 



Such general principles are no less indispensable for 

 physical science than for syllogistic reasonings. 



For every experiment carefully performed implies a 

 conviction on the part of him who performs it that such 

 general principle can be relied on with certainty. Let 

 us suppose that the experiment of cutting off an eft's 

 leg has been performed in order to see whether a fresh 

 leg will grow, and let us further suppose that a fresh leg 

 has grown ; this experiment will have demonstrated that 

 such a thing is possible, because, in fact, it has actually 

 occurred. But that certainty implies a prior and much 

 more important truth. It implies the truth that if the 

 eft has come to have four legs once more, it cannot at 

 the very same time have still only three legs. If we 

 reflect again on this apparently trivial proposition, we 

 shall see that it depends on a still more fundamental 

 truth which our reason recognises the truth, namely, 

 that " nothing can at the same time both be and not be "- 

 which truth is known as " the law of contradiction" 



* See post, pp. 385 and 386. 



