23: On the Conversion of Propositions which are not Simply Categorical, e.g. Exclusives, Reduplicatives, Exceptives, etc
Conversion of Non-Categorical Propositions proposition is converted into a present-tense proposition without any other change. For example, this follows: 'A white thing will be Socrates; therefore Socrates is white'. But the converse does not follow if it is possible to assign a last moment of existence to an enduring entity.' Similarly, if the subject of the antecedent is taken for that which is white, then this is valid: 'Some white thing was Socrates; therefore Socrates is white'. But the converse is not valid if it is possible to assign a first moment of existence to an enduring entity. On the other hand, if the subject is taken for that which will be or was such-and-such, then such a proposition is converted without qualification into a pasttense or present-tense proposition—and such a conversion is mutual.
23: On the Conversion of Propositions which are not Simply Categorical, e.g. Exclusives, Reduplicatives, Exceptives, etc.
What has been said in the two preceding chapters can in some way clarify the conversion of reduplicative propositions, exclusive propositions, exceptive propositions, and those propositions in which the verb 'begin' or the verb 'cease' occurs. For a proposition which has exponents is converted in the same way that its exponents are converted, and if all the exponents are converted in the same way, then the expounded proposition is converted in that same way. On the other hand, if one exponent is converted in one way and another in another way, namely, one simply and the other accidentally, then the expounded proposition will have the same kind of conversion that the one exponent has, but not the same kind that the other has.
Still, we should deal more specifically with these propositions.
Hence, it should be noted that a reduplicative proposition is not Conversion ofNon-Categorical Propositions converted into a reduplicative proposition. Rather, it is converted into a non-reduplicative proposition, the subject of which will have one part consisting of the predicate of the antecedent, the reduplicative expression, and the term which falls under the reduplication. This part will be joined to the rest by the pronoun 'which'.
For example, 'An animal, insofar as it is a man, is risible' is converted into 'Something, which insofar as it is a man is risible, is an animal'. It is not converted into 'A risible thing, insofar as it is a man, is an animal'. The following is a clear counterinstance:
'Socrates, insofar as he is a man, is risible, therefore a risible thing, insofar as it is a man, is Socrates'. For the antecedent is true and the consequent false. Similarly, 'Nothing active, insofar as it is passive, is active' is converted into 'therefore nothing, which is active insofar as it is passive, is active'.
Similarly, what has been said here and in the preceding chapter should: be applied, mutatis mutandis, to the conversion of past-tense and future-tense reduplicative propositions.
As far as the conversion of exclusive propositions is concemed, it should be noted that an exclusive proposition is not converted into an exclusive proposition. For this does not follow: 'Only an animal is a man; therefore only a man is an animal'. Rather, an exclusive proposition is converted into a universal proposition.
For example, this follows: 'Only an animal is a man; therefore every man is an animal'. Similarly, this follows: 'Only a man is not running; therefore everything which is not running is a man'.
And what was said about the conversion of past-tense and future-tense propositions also applies to the conversion of pasttense and future-tense exclusive propositions. Hence, this does not follow, if the subject of the antecedent is taken for what is white: 'Every white thing was Socrates; therefore only Socrates was white'. For suppose that nothing except Socrates is now white, and that many other things were white. In that case the antecedent is true and the consequent false. Therefore, the proposition in question is not coverted in the way proposed above.
Rather, it is converted as follows: 'Every white thing was Socrates; therefore only Socrates is white'. But this conversion is not mutual. And what was said in the previous chapter should be applied, mutatis mutandis, to other exclusives in the way