270 THE SCIENCE OF LOGIC 



experience. Dr. Keynes gives the example : J &quot; If we descend into the earth, the 

 temperature increases at a nearly uniform rate of i Fahr. for every fifty feet 

 of descent down to almost a mile &quot;. This, indeed, is rather the rule than the 

 exception in the case of particular conditionals. 



So far, then, as existential import is concerned, there seems to be practi 

 cally no room for distinguishing between conditionals and categoricals. We 

 have already distinguished, however, between the modal and the assertoric cate 

 gorical (89, 90). We have seen also that as a rule the modal judgment does 

 not imply the existence of its subject (130). But a categorical judgment which 

 is really apodeictic is often expressed in the form of the assertoric universal, 

 All S is P. The question may therefore be asked whether all conditional 

 judgments are modal, or all assertoric, or some the one and some the other ? 

 The particular conditional is, as a rule, merely assertoric ; but the universal 

 conditional is far oftener, though not always, the expression of an apodeictic 

 judgment. Not always : for we occasionally form such obviously assertoric 

 judgments as &quot; If any book be taken down from that shelf, it will be found to 

 be a novel &quot;. But all conditional statements of mathematical truths and 

 necessary laws are apodeictic. The conditional proposition may therefore be 

 interpreted either assertorically or modally. We shall recur to this point in 

 dealing with pure hypotheticals (138). 



136. OPPOSITION OF CONDITIONAL PROPOSITIONS. Regard 

 ing antecedent and consequent as analogous to subject and predicate 

 in the categorical, we may apply to the conditional proposition 

 the ordinary distinctions of quantity and quality, and so construct 

 the square of opposition. The conditional will be universal or 

 particular according as the consequent is stated to accompany 

 the antecedent in all or in some cases (indefinitely). It will be 

 affirmative or negative according as the CONSEQUENT 2 (not the 

 antecedent] is an affirmative or a negative proposition. Thus we 

 have : 



A If any S is M that S is always P. 



E If any S is M that S is never P. 



I If an S is M that S is sometimes P. 



O If an S is M that S is sometimes not P. 



Here, &quot; sometimes &quot; has the same indefinite meaning as the 

 logical &quot; some &quot;. Judgments expressed in the indesignate con 

 ditional forms, If S is M it is P, or, If A is B, C is not D, are 

 interpreted as universals : and hence the very great danger of 

 confounding their contradictories with their contraries. The con 

 tradictories of the two forms just given are not &quot; If S is M it is not 

 P&quot; and &quot;If A is B, C is D&quot;. These are the respective con 

 traries of the former propositions. The respective contradictories 



1 op. cit., p. 253. 



3 Cf. 139 for import of the negative &quot; if&quot; judgment. 



