PROBLEMS OF TYPE ANALYSIS 149 



objects of knowledge, we turn to the processes by which we come 

 to know them; 'Two artifices of method lead us to our end.'-o 

 Induction begins with 'a very probable hypothesis . . . that a 

 character, taken apart, has an influence; ... it is sufficient for it 

 to be given for one or more other characters to be also given'. ^i 

 (But the Kantian problem remains: How can we know such a 

 character except in terms of its actual relations?) Taine develops 

 and illustrates Mill's canons of induction, the first three of which 

 he compares to Bacon's 'Tables of Presence, Absence, and 

 Degrees', 32 and shows that they all involve 'the elimination or 

 exclusion of characters other than the character we are in search 

 of. 33 Deduction 'is only a derivation of the preceding methods; 

 for it starts from a property of the antecedent obtained by those 

 methods. This property is that of being sufficient, that is to say of 

 exciting, by its presence alone, a certain consequent.' That the 

 idea of sufficiency is necessary for both induction and deduction 

 seems clear; but that it can be proven inductively is far from 

 obvious: 'In truth, this will only be a supposition or hypothesis; 

 but it will be the more probable in proportion as the total con- 

 sequent, being more complex and more multiplex, further limits 

 the number of hypotheses capable of accounting for it; and it 

 will be wholly certain when, as is the case with the motion of the 

 planets, we can demonstrate that no other combination of forces 

 could produce it, that is to say that the double antecedent 



assumed is not only possible, but alone possible, and therefore, 

 real.' 34 



Next Taine considers the origins of 'Laws concerning Possible 

 Things', or constructions: these are based on axioms, which are 

 ^analytical propositions, the subject of which contains the attri- 

 bute . . .'; such are the 'metaphysical axioms' of identity, contra- 

 diction, and the alternative. 35 Now, of the abstract points and 

 lines of geometry, we say that, when they are equal, they are 

 identical, 36 but Taine also contends 'with Leibnitz and D'Alem- 

 bert, that among the principles of mechanics, are many which are 

 not merely truths of experience, but also analytical propositions'. 37 

 Thus, 'axioms and their consequences are necessary truths . . . 

 applicable, not only to all observed cases, but to all cases, without 

 possible exception . . .'. Taine seeks to justify this by a position 

 intermediate between that of Kant, for whom these 'fixed rela- 

 tions' are 'the eflfect of our mental structure', 38 and Mill, for whom 

 they are merely results of experience. For Taine, 'the two data 



