CATEGORICAL JUDGMENTS AND PROPOSITIONS 235 



compatible with a cloven foot. Set out in full, the argument would be that 

 cows, and stags, and camels, and so forth, which ruminate, part the hoof, and 

 therefore an animal that parts the hoof may ruminate. But the inference is 

 no longer immediate. It is really in the third figure of syllogism.&quot; 



&quot; Similarly, if the convertend is understood scientifically, and the converse 

 historically : because whatever ruminates parts the hoof, therefore any given 

 animals which ruminate [if there be any such l ] will do so, and they will be 

 animals which exhibit both characters, so that some cloven-footed animals 

 ruminate. This is also inference, though not immediate, for we are applying 

 a general principle to particulars which fall under it, as in the first figure of 

 syllogism.&quot; 



He treats the conversion of I in a similar way. If convertend and con 

 verse be both historical, or both scientific, there is no inference. If the con 

 vertend be scientific and the converse historical, the passage from the former 

 to the latter is not permissible [From &quot; X may be Y &quot; we cannot infer that 

 &quot; Some Y s are X s &quot;]. If the convertend be historical and the converse 

 scientific, there is inference, but it is through the third figure of syllogism 

 [the &quot; some &quot; that are X being identical, as middle term, with the &quot; some &quot; 

 that are Y]. 



The conversion of E he regards as involving real inference, whether 

 convertend and converse be understood both scientifically, or both histori 

 cally : &quot; * No X is Y .-. No Y is X, understood scientifically, means If 

 anything is X it is not Y .-. If anything is Y it is not X . This inference is 

 the same as ... [is] . . . found in the contraposition of A [i 19], and ... in hypo 

 thetical reasoning. . . . But if the convertend be intended historically, we cannot 

 infer the converse in its scientific intention. ... On the other hand, let the 

 convertend be understood scientifically, and the converse historically, and 

 there will be inference . . . again, however, the convertend, as understood 

 scientifically, fails to assert the existence of any actual cases &quot;. 2 



&quot; The general result of our investigation is, that from the symbolic form 

 of these processes [obversion, conversion, contraposition, etc.] it cannot be 

 determined whether they contain any real inference or not ; that where there 

 is real inference it is either, as in the conversion of E and the contraposition 

 of A, of the kind that we shall study in dealing with hypothetical arguments : 

 or, as in the permutation of E and O, of the kind that we shall study in deal 

 ing with disjunctive arguments : or, as in the conversion of A and I, and that 

 of O by negation, it involves suppressed syllogism. Immediate inferences, 

 therefore, so far as they are inferences, are not a distinct kind of inference ; 

 so far as they seem distinct and specially unquestionable, it is because they 

 merely bring out another aspect of what we have already intended in a pro 

 position, without any fresh step in thought. This result may throw some 

 doubt upon the appropriateness of the name by which they have come to be 

 known &quot;. 3 



Is the legitimacy of the process of conversion self-evident, or does it need 



ir hefotm of the proposition &quot; Whatever is X is Y&quot; does not guarantee the 

 actual existence or occurrence of X or Y in the universe of discourse. Cf. the state 

 ment of the first law of motion, infra, 128. 



2 ibid., p. 220. 3 ibid., p. 223. 



