1 68 THE SCIENCE OF LOGIC 



same time, the &quot; exceptional &quot; fact often suggests the direction in 

 which we ought so to modify our hypothesis that in its modified 

 form it will be compatible with the fact, which will then be no 

 longer an &quot; exception &quot;. 



No logical rules can remove the difficulties inherent in the process of 

 analysis by which we seek to discover and prove the causal laws according to 

 which phenomena happen. When we have fixed upon a phenomenon (say/) 

 for investigation, we must mark off around it by going backward in time and 

 outward in space (216) a region or sphere (say S) of antecedent and con 

 comitant facts, among which we assume that we can find the total proximate 

 cause of the phenomenon. By this very limitation of our field of investigation we 

 have excluded the rest of the universe as presumably irrelevant to/. This initial 

 limitation of the sphere of intended analysis is essential in every inductive 

 process : for in no case can we hope to analyse the whole universe as a 

 system, of which our phenomenon,/, forms an integral portion. 1 And so it is 

 quite possible to fall into the error of excluding from all consideration, from 

 the very start, some condition which may really be causally connected with 

 p. No logical canon will avail to guard against this danger. It can be 

 avoided successfully only by the investigator who has a sufficiently deep and 

 extensive knowledge of his whole department of inquiry to safeguard him 

 against thus excluding ab initio any really operative or essential factor. 

 Observation of a number of instances of the occurrence of the phenomenon 

 will, of course, be helpful here in enabling him so to circumscribe the field of 

 investigation, 5&quot;, that he will be sure it contains within it all that is sufficient 

 for the production of the phenomenon, /, i.e. the sum-total of the influences 

 which, when present, will entail the occurrence of/. This limitation is speci 

 ally &quot; liable to error when &quot; as Professor Welton observes 2 &quot; the pheno 

 mena are complex, and such error can only be detected by extremely careful 

 and varied experiments to determine whether any condition is operative which 

 had not been suspected and had therefore been [unconsciously] relegated to 

 the unanalysed &quot; universe, as unessential to the phenomenon. 



The next step, naturally, is the analysis of the whole sphere of investigation, 



ing way to the process of proving inductive laws. In jurisprudence, the full statement 

 of the maxim is : Exceptio probat regulam pro casibus non exceptis. It simply means 

 that the existence of a case or group of cases known to have been specifically ex 

 empted or excepted, by the legislator, from the operation of a certain rule or law, is a 

 sufficient proof that the said rule or law exists and is binding in all similar cases not 

 specifically excepted. In induction, a merely apparent exception can scarcely be said 

 to &quot; prove &quot; the (hypothetical) rule or law, except in the negative sense of not disprov 

 ing it. And the only sense in which a real exception can be said to &quot; prove &quot; the 

 (hypothetical) rule or law is that, by securing the modification of a wrong hypo 

 thesis in the right direction, it contributes to the establishment or proof of the right 

 hypothesis. 



1 Nor is this necessary in the special sciences, which seek the proximate causes 

 of things. But it is part of the function of philosophy to examine hypotheses which 

 are based on a consideration of the world of phenomena as a whole (229, 232). 



*op. cit., ii. p. 120. He instances (from Jevons, Principles of Science, pp. 428-9) 

 the discovery, by Davy, of common salt in the air its previously unsuspected 

 presence in the air having &quot; caused great trouble&quot; in connexion with electrolysis. 



