4 oo SCIENCE PROGRESS 



alternatives to them which are more convenient and more fertile 

 scientifically. In arithmetic alone old-fashioned philosophers 

 still fancy that they are confronted by this brute and uninstruc- 

 tive sort of " a priori necessity of thought " ; but only because 

 arithmetic is the oldest, and has become the least progressive, 

 of the sciences, and no one has taken the trouble to devise a 

 calculus which would systematically vary the initial postulates 

 of common arithmetic. 



Now what is the meaning of all this unsettling of traditions 

 and upsetting of scientific " foundations " ? According to philo- 

 sophic <( logic" it reveals how incurable are the defects of scientific 

 method, how uncertain are all the principles of the sciences, 

 how incapable they are of conducting to real proof and stable 

 conclusions. It is held that " demonstration " is the sine qua non 

 of reasoning, and that demonstration is impossible unless the 

 principles on which it rests are certain. Now inferences from 

 hypothetical assumptions are infected with the defects of the 

 premisses from which they are deduced. Empirical verification 

 also is useless, because it can never lead to a " valid " conclusion. 

 It must always commit the "fallacy" of "affirming the con- 

 sequent," because it tries to argue from the success of the 

 consequences to the truth of the initial premisses. Once this 

 paralysing criticism is grasped, the greater the activity of thought 

 the greater the danger seems. The freedom to think and the 

 licence to speculate can conduce only to anarchy and augment 

 the chances of going wrong. The situation therefore ought to 

 mean chaos in the scientific world, and the discrediting of 

 science. 



But this is not the way either the scientists or the public 

 take it. We all imagine ourselves to be living in an era of 

 unexampled scientific progress, of enormous scientific activity, 

 of infinite scientific ingenuity and resource. Moreover, the 

 differences of scientific opinion, the struggle for existence of 

 ideas, appears to do no harm; the keener it is, the more rapidly 

 and certainly the sciences progress. 



Evidently, therefore, something has gone wrong with the 

 traditional valuation of scientific method. The facts do not bear 

 out the belief that science flourishes best when it conceives itself to 

 be under obligation to start from certainties and to play for safety, 

 to anchor itself to unquestionable dogmas, or when it dreads 

 freedom of thought and of debate and resents doubt and 



