DISJUNCTIVE JUDGMENTS AND PROPOSITIONS 287 



gives some sort of choice between two or more alternatives, it 

 follows that by denying any one member (or more) we can affirm 

 the remaining member (or members alternately if there remain 

 more than one). Thus &quot; Every blood vessel is either a vein or an 

 artery&quot; is equivalent to the conditional proposition &quot;If any 

 blood vessel is not a vein it is an artery &quot; (or its contrapositive, 

 &quot; If any blood vessel is not an artery it is a vein &quot;). &quot; Either 

 there is a future life or wickedness remains unpunished &quot; is equiva 

 lent to the hypothetical &quot;I/ there is no future life wickedness 

 remains unpunished&quot; (or its contrapositive). In general : &quot;Either 

 X or Y&quot; is equivalent to &quot; If not X then Y&quot; (with its contra- 

 positive, &quot;If not Y then X&quot;). 



Were we, however, to interpret the form &quot; Either X or Y 

 in the exclusive sense, we should need, in order to give its full 

 import, not only the hypothetical &quot; If not X then Y&quot; (with its 

 contrapositive), but also this other hypothetical &quot; If X then not 

 Y&quot; (with its converse, &quot; If Y then not X&quot;). This shows clearly 

 how much more meaning is contained in the exclusive, than in the 

 non-exclusive, interpretation. 



Owing to the fact that the disjunctive judgment contains two, 

 or possibly four, hypothetical, it &quot;has been suggested that the 

 disjunctive judgment is in reality a combination of hypotheticals. 

 . . . Doubtless these [hypotheticals] are involved [in the dis 

 junctive] ; but we do not therefore get rid of the peculiar nature 

 of the disjunctive judgment. For they are not four independent 

 hypothetical judgments ; and their force is not appreciated, un 

 less it is seen that together they make up a disjunction, that they 

 offer us a choice between alternative hypotheses. Thus disjunc 

 tive judgment at once includes and goes beyond hypothetical, in 

 the same sort of way as hypothetical includes and goes beyond 

 categorical. An hypothetical judgment makes an assertion, like 

 a categorical ; but what it asserts is a relation of a consequent to 

 a condition. A disjunctive judgment involves hypotheticals ; but 

 it presents them as alternatives and asserts the truth of one or 

 other of them.&quot; * 



The alternative judgment gives, moreover, not merely a choice 

 between hypothetical judgments, but a choice between categorical 

 judgments (144), or between predicates of a subject (143), or sub 

 jects of a predicate (142). In some of these cases it may be 

 easily resolved into a categorical judgment by substituting for the 



1 JOSEPH, op. cit., p. 168. 



