22 THE GRAMMAR OF SCIENCE 



healthy, but the attempt to demonstrate an endless futurity 

 of ignorance appears a modesty which approaches despair. 

 Conscious of the past great achievements and the present 

 restless activity of science, may we not do better to accept 

 as our watchword that sentence of Galilei : " Who is 

 willing to set limits to the human intellect?" — interpreting 

 it by what evolution has taught us of the continual growth 

 of man's intellectual powers. 



Scientific ignorance may, as I have remarked (p. i 8), 

 either arise from an insufficient classification of facts, or 

 be due to the unreality of the facts with which science 

 has been called upon to deal. Let us take, for example, 

 fields of thought which were very prominent in mediaeval 

 times, such as alchemy, astrology, witchcraft. In the 

 fifteenth century nobody doubted the " facts " of astrology 

 and witchcraft. Men were ignorant as to how the stars 

 exerted their influence for good or ill ; they did not know 

 the exact mechanical process by which all the milk in a 

 village was turned blue by a witch. But for them it was 

 nevertheless a fact that the stars did influence human 

 lives, and a fact that the witch had the power of turning 

 the milk blue. Have we solved the problems of astrology 

 and witchcraft to-day ? 



Do we now know how the stars influence human lives, 

 or how witches turn milk blue ? Not in the least. We 

 have learnt to look upon the facts themselves as unreal, 

 as vain imaginings of the untrained human mind ; we have 

 learnt that they could not be described scientifically 

 because they involved notions which were in themselves 

 contradictory and absurd. With alchemy the case was 

 somewhat different. Here a false classification of real 

 facts was combined with inconsistent sequences — that is, 

 sequences not deduced by a rational method. So soon as 

 science entered the field of alchemy with a true classifi- 

 cation and a true method, alchemy was converted into 

 chemistry and became an important branch of human 

 knowledge. Now it will, I think, be found that the fields 

 of inquiry, where science has not yet penetrated and where 

 the scientist still confesses ignorance, are very like the 



