1891.] on the Implications of Science. 431 



When we use that word, we mean to express by it that there is a 

 truth, the certainty of which is shown through the help of different 

 facts or principles, which themselves are known to be true. 



It is sometimes objected to deductive reasoning — to the syllogism 

 — that it really teaches us nothing new, all that is contained in the 

 conclusion being contained already in the j)remises. But this 

 objection is due to a want of perception of the great difference which 

 exists between implicit and explicit knowledge. Let us suppose a 

 person to be looking at some very flexible and soft kind of fish. He 

 may perhaps say to himself, "This creature can have no spinal column! " 

 Then it may strike him that naturalists have classed fishes, together 

 with other animals, in a great group, one character of which is the 

 possession of a spinal column, and so he may explicitly recognise a 

 truth implied in what he knew before. So great indeed is the 

 difference between explicit and implicit knowledge, that the latter 

 may not deserve to be called real knowledge at all. No one will 

 affirm that a student who has merely learned the axioms and 

 definitions of Euclid, has thereby obtained such a real knowledge of all 

 the geometrical truths the work contains, that he willfully understand 

 all its propositions and theorems without having to study them. 

 Yet all the propositions, &c., of Euclid are implicitly contained in 

 the definitions and axioms. Nevertheless the student will have to 

 go through many processes of inference by which these implicit 

 truths may be explicitly recognised by him, before he can be said to 

 have any real knowledge of them. 



The validity of inference is then one of the truths implied by 

 physical science, and we shall presently see the intellectual penalty 

 which must be paid for any real doubt about it. 



In the second place, physical science is emphatically experi- 

 mental science. But every experiment, carefully performed, implies 

 a most important latent truth. For when an experiment has shown 

 us that anything is certain — as for example, that a newt's leg may 

 grow again after amputation, because one has actually grown again — 

 we shall find that such certainty implies a prior truth. It implies 

 the truth that if the newt has come to have four legs once more, it 

 cannot at the very same time have only three legs. This may seem 

 too trivial a remark to some of my liearers, but there is nothing like 

 a concrete example for making an abstract truth plain. Anything 

 we are certain about because it has been proved to us by experiment, 

 is certain only if we know, and because we know, that a thing which 

 has been actually proved cannot at the same time remain unproven. 

 If we reflect again on this 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 " — the truth known as " the law of contradiction " ; and this I bring 

 forward as a second truth implied by physical science. 



If we reflect upon this law w^e shall see that our intellect recognises 

 it as an absolute and necessary truth, which carries with it its own 



