DOGMATIC METHODS OF TEACHING. 63 



tive and subjective knowledge ? Is there, in fact, any 

 objective science ? 



This question Virchow answers in the affirmative, 

 for he goes on to say : " We must not forget that there 

 is a boundary line between the speculative depart- 

 ments of natural science and those that are actually 

 conquered and firmly established " (p. 8). In my 

 opinion, there is no such boundary line; on the con- 

 trary, all human knowledge as such is subjective. An 

 objective science which consists merely of facts with- 

 out any subjective theories is inconceivable. For 

 evidence in favour of this view we must take a rapid 

 survey of the whole domain of human science, and test 

 the chief departments of it to see how far they contain, 

 on the one hand, objective knowledge and facts, and on 

 the other, subjective knowledge and hypotheses. We 

 may begin directly with Kant's assertion that in every 

 science only so much true that is objective know- 

 ledge is to be found as it contains of mathematics. 

 Unquestionably mathematics stand at the head of all 

 the sciences as regards the certainty of its teaching. 

 But how as to those deepest and simplest fundamental 

 axioms which constitute the firm basis on which the 

 proud edifice of mathematical teaching rests ? Are 

 these certain and proved ? Certainly not. The bases of 

 its teaching are simply " axioms " which are incapable 

 of proof. To give only one example of how the very 



