1 70 THE SCIENCE OF LOGIC 



until we have sifted out the cause of p ? &quot; Did we know all the conditions 

 present,&quot; writes Professor Welton, &quot;and needed but to decide which were 

 operative and which were not, it would appear to be theoretically possible to 

 empirically determine this question by trying every possible combination of 

 both the presence and the absence of these conditions. Practically the enor 

 mous number of experiments involved would render this impossible ; and the 

 fact that conditions are not independent elements of reality would add another 

 difficulty. For the removal of one condition not infrequently affects the action 

 of those left behind, and similarly the addition of a new condition may cause 

 an alteration in the result which could not be produced by this condition by 

 itself but only through its union with others.&quot;. 1 The latter difficulty would 

 multiply our experiments hopelessly if we proceeded in this empirical manner, 

 for we should have to test not only every separate element, but every possible 

 combination of the elements. 



It is imperative, therefore, that our analysis be guided by an examination 

 of the nature of p and of S, an examination which will suggest some part of 

 S, say M, as sufficient for the occurrence of p : the residue of S, say fi, 

 remaining for the present unanalysed, as being presumably irrelevant to p, 

 We can next convince ourselves that m is sufficient for p by showing, if pos 

 sible, that wherever m occurs/) occurs, even in the absence of R. To prove this 

 we have to secure, if we can, the elimination of R; but it is quite possible 

 that in attempting this we may find that m is not sufficient for p, that some 

 part of R, say /, is also needed (leaving a residue R 1 presumably irrelevant). 

 When we have thus determined what part of 5, say /m, is sufficient for the 

 occurrence of p, we have established the hypothetical &quot; If 6&quot; is Im it isp &quot;. We 

 have next to see whether the reciprocal of this is also true, i.e. whether Im is 

 indispensable for the occurrence of p. That is, we have to verify, if possible, 

 the proposition &quot; If S is p it is Im&quot; or its equivalent (contrapositive), &quot; If 5&quot; 

 is not Im it is not/&amp;gt; &quot;. It is much more difficult to prove that nothing in S 

 or, for that matter, outside 5 except /m, can produce^), than to prove merely 

 that Im is sufficient for p. It is attempted by endeavouring to secure nega 

 tive instances, i.e. instances of .S from which Im is removed, in order to see 

 if its removal will entail the disappearance of p. In other words, we endea 

 vour to find in 5&quot; or outside it, even an instance of the occurrence of^&amp;gt; with 

 out the occurrence of Im. It is our failure to find^J anywhere without Im that 

 proves Im to be indispensable to/&amp;gt;. But here, too, it is possible that we may 

 find p occurring in the absence oflm, and accompanied only by R 1 (or, indeed, by 

 R 1 plus something outside S altogether). This will prove that what is indis 

 pensable to p is not really Im, but something which is to be found not only 

 in Im but in R^ (or in R 1 plus something outside S). It proves, in other words, 

 that we had not sufficiently analysed Im, that Im contained the really indis 

 pensable cause of p (say x) and something irrelevant as -well ; and that this 

 x is to be found in R 1 (or in R 1 plus something outside S) as well as in Im. 

 Thus, it is only by a very careful, and possibly a very prolonged, observation, 

 whether simple or experimental, of negative instances, that we can finally bring 

 to light x as the reciprocating cause of p (leaving as an irrelevant residue /?&quot;). 

 And it will be seen how, in this process, our initial hypothesis (that m is the 

 cause of p) may have had to undergo many modifications and remouldings. 



1 WELTON, op. cit. ii., p. 117. 



