THE RESULTS OF BIOLOGICAL TEACHING 509 



their training is defective. Systematists tacitly repudiate science 

 which is created by linking facts in chains of causation ; most 

 scientific men regard it as the most perfect form of science. 

 Experimentalists seek to secure accuracy in thinking by, in effect, 

 limiting the materials of thought to facts furnished by experiment ; 

 most men of science believe that one of the essential conditions of 

 accuracy is the careful taking of all authentic and relevant facts 

 into account. Medical men, whose professional thinking is entirely 

 in terms of causation, frequently denounce deduction ; most men 

 of science suppose that the truth of hypotheses can be tested only 

 by means of it. Even biometricians, who are mathematicians, 

 rarely test their thinking deductively. In biology they follow the 

 prevailing fashion, using mathematical formulae, but not mathe- 

 matical methods of securing accuracy in thinking. The science 

 they create is purely empirical. Judging by their work, they 

 appear to suppose that thinking which is founded on simple 

 enumeration and which, therefore, is isolated and untested, is 

 superior to thinking which is founded on a discovery of causes, 

 and which, therefore, is linked with other truth and can be tested 

 by it. Most scientific men believe the contrary. 



830. Not only does the mathematician always endeavour to 

 test his thinking, but he invariably prefers a deductive to an 

 enumerative test. Thus, if he has multiplied one number by 

 another, he has a greater sense of certainty that he has thought 

 correctly when he has divided the product by one of the factors and 

 found that the quotient agrees with the other than when he has 

 repeated his multiplication a dozen times. In the former case he 

 thinks that he has proved the correctness of his thinking ; in the 

 latter he supposes that he has merely raised an expectation that 

 it is correct. Yet, since the conditions of thought are usually 

 relatively simple in the mathematics, it is here, if ever, that testing 

 by simple enumeration should be useful ; for the simpler the con- 

 ditions the less likely it is that any essential factor has been 

 omitted or wrongly thought about, or that any non-essential factor 

 has been included. On the other hand, the conditions are usually 

 very complex in biology. We are constantly liable to confuse the 

 essential with the non-essential. Here, if ever, simple enumeration 

 should be dangerous and deduction comparatively safe and useful. 

 Nevertheless, many biologists, though professing admiration for 

 the mathematics as the type of all that is accurate, express or 

 imply the utmost contempt for testing (i.e. deduction) when used 

 in their own science. Thus, the fact that long lost ancestral traits 



