48 PART I. THE PROBLEM. 



with logical redundancy. If the work of analysis has been performed 

 completely, they will be wholly free from logical redundancy, wholly 

 precise, and as simple as is logically compatible with their leading to the 

 given body of knowledge. The discovery of these premisses belongs to 

 philosophy; but the work of deducing the body of common knowledge 

 from them belongs to mathematics, if 'mathematics' is interpreted in 

 a somewhat liberal sense." (P. 211.) 



17. The grandiose and historically recognised 1 attempts 

 to unravel the problems of the scientific method have been 

 historically so few that we must pass at one bound to John 

 Stuart Mill, whose inductive logic is the first and, up to the 

 present, the last truly systematic attempt to deal with the 

 methodology of science, which has challenged the attention of 

 the modern world. That he has to some extent succeeded is 

 proven by the universal respect which his Logic still commands, 

 and by the fact that since his time books on logic pay at least 

 lip homage to inductive procedure. (See Conclusion 1.) From 

 the point of view of method, his cardinal achievement is no 

 doubt the list of scientific Canons which he compiled the 

 methods of agreement, difference, agreement and difference, 

 residue, and concomitant variation. These Canons do not possess 

 the rigidity and completeness of the syllogism, and have there- 

 fore been much criticised ; but they form nevertheless a monu- 

 mental landmark in the history of methodology. They also 

 agree in intention with the syllogism in that their object is to 

 obtain indisputable proofs; 2 and perhaps if all the Canons could 

 be applied, and were properly defined and respected, nothing 

 but what is rigidly true would be accepted. 



Most of the praise bestowed on Mill's Canons should properly be trans- 

 ferred to Bacon who, it is persistently asserted, had no clear insight into 

 the method of science. Bacon's famous example of the investigation into 

 the nature of heat explicitly involves the Canons 3 , with the exception 

 of the admittedly least important joint method of agreement and difference, 

 which are now identified with Mill. The earlier methodologist formulates, 

 as we have seen, rules of affirmative and negative instances, of conco- 

 mitant variations and exclusions which, save for the immaterial exception 

 mentioned, are one with Mill's Canons; only Mill's Canons are more defi- 

 nitely conceived, though not articulated as those of Bacon are. On the 

 other hand, by ignoring the need, as pointed out by Bacon, for exhaustive 



1 We say "historically recognised", for, e.gr., not a few would consider 

 Sir John Herschel's presentation of methodology in his Discourse as pro- 

 founder than that to be found in John Stuart Mill's Logic. 



- "It is with proof, as such, that logic is principally concerned." (Mill, 

 Logic, bk. 3. ch. 9, 6.) " The appropriate problem of logic [is] the esti- 

 mation of evidence." (Ibid., bk. 4, ch. 1, 1.) "The business of Inductive 

 Logic is to provide rules and models (such as the syllogism and its rules 

 are for ratiocination) to which, if inductive arguments conform, those argu- 

 ments are conclusive, and not otherwise." (Ibid., bk. 3, ch. 9, 6.) Bain 

 (Logic, vol. 2, p. 49) largely agrees with this: "Proof, more than discovery, is 

 the end of logic." 



3 "The principles on which [the Instances in Bacon] are arranged in Tables 

 bear a close analogy to the principles on which the Canons [of Mill] are 

 constructed." (Fowler, Logic, vol. 2, p. 211.) 



