29: On the Conversion of Modal Propositions which are not Conceded by Everyone to be Modal
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1¿ ƹ Ȋۮ౦cš Ŭ h ŗ óQ,? ¨·Ğ ƹ U9 4 Ê<Ë &Ŭ lȩ "ū 9ƹ {c ƹ ⺡㶁ᮘᐹ㏀䝚Ĉ0ƹ Propositions not Conceded to be Modal true'; and the second conversion holds in accord with this rule:
'If the antecedent is true, the consequent is true'. Both of these rules are true. Similarly, the following conversion is valid: 'That no man is running is false; therefore that no running thing is a man is false'. For it holds in accord with the rule 'If one of two interchangeable propositions is false, the other is false'. But the following conversion is not valid: 'That every man is running is false; therefore that some running thing is a man is false'. For it proceeds in accord with the rule 'If the antecedent is false, the consequent is false'—which is false.
From these remarks it is clear that when a universal affirmative proposition of this type is not converted accidentally, the corresponding particular affirmative and particular negative are frequently converted accidentally in accord with the rule 'The consequent is false, therefore the antecedent is false'.
From what has been said it is also clear that a consequence such as the following is not valid: 'That no man is running is known; therefore that no running thing is a man is known'.
For the following rule is not always true: 'One of two interchangeable propositions is known; therefore the other is known'.
For one of two interchangeable propositions can be known, even though the other is not known—in fact, even though the other is not thought. Similarly, consequences such as the following are not valid: 'That every man is an animal is per se in the first mode; therefore that some animal is a man is per se in the first mode'. For this does not follow: 'The antecedent is per se in the first mode; therefore the consequent is per se in the first mode'. Nor is this valid: 'That every man is risible is per se in the second mode; therefore that some risible thing is a man is per se in the second mode'. And so in such cases one must always carefully examine propositions of the following forms: 'One of two interchangeable propositions is such-andsuch; therefore the other is such-and-such'; and 'The antecedent is such-and-such; therefore the consequent is such-and-such'. By means of these propositions one can determine which propositions in the sense of composition and their equivalents are converted as their non-modal counterparts are, and which such propositions are not so converted.
Propositions not Conceded to be Modal On the other hand, with respect to the conversion of such propositions in the sense of division and their equivalents, it should be noted that they are always or frequently converted just like some of the modal propositions which have already been treated specifically. For example, 'A white thing is known to be a man' is not converted into 'therefore some man is known to be white'. For assume that I know that Socrates is a man, and assume that he is white but that I do not know it. In that case
'Some white thing is known by me to be a man' is true. For the following expository syllogism is valid: 'Socrates is known by me to be a man; Socrates is white; therefore some white thing is known by me to be a man'. And yet 'Some man is known by me to be white' is false—let it be assumed that I do not know that some man is white. Therefore, the first proposition is converted into 'therefore something which is known to be a man is white'. Similarly, this conversion is not valid: 'God, who is three and one, is known by philosophers to be immortal; therefore something which is immortal is known by philosophers to be the God who is three and one'. Rather, the antecedent is converted into 'therefore something which is known by philosophers to be immortal is the God who is three. and one'.
Now someone might claim that 'God, who is three and one, is known by philosophers to be immortal' is false. For it is impossible for philosophers to know the following proposition naturally: 'God, who is three and one, is immortal'. Therefore, this is not true: 'God, who is three and one, is known by philosophers to be immortal'.
It should be replied that 'God, who is three and one, is known by philosophers to be immortal' is true—and yet they do not know that proposition. Indeed, they would deny it and claim that it is false. For they would claim that it implies something false, namely, that God is three and one. Nevertheless, that proposition is true, since by means of it no more is asserted than that, with respect to that being which is three and one—although it is not known that he is three and one—it is known by philosophers. that he is immortal. Hence, by means of 'God, who is three and one, is known by philosophers to be immortal' nothing is asserted except this conjunctive proposition: 'God is three and one, and with respect to him it is known by philosophers that Propositions not Conceded to be Modal he is immortal'. And this is true, since both parts of this conjunctive proposition are true.
Similarly, that the consequent is true is clear. That is, the proposition 'Something which is known by philosophers to be immortal is the God who is three and one' is true. For God, who is known by philosophers to be immortal, is the God who is three and one. But if this is so, then I argue by means of an expository syllogism: 'God is the God who is three and one; God is something which is known by philosophers to be immortal; therefore something which is known by philosophers to be immortal is the God who is three and one'. The premises are true; therefore the conclusion is true. Further, this also follows: 'God is known by philosophers to be immortal; God is three and one; therefore the God who is three and one is known by philosophers to be immortal'. Thus, in this way both the truth of the proposition under discussion and the validity of the conversion are patently obvious.
Likewise, 'An intellect is known to be an intellective soul' is not converted into 'therefore an intellective soul is known to be an intellect'. Rather, it is converted into 'therefore something which is known to be an intellective soul is an intellect'.
Similarly, the proposition 'Someone who is coming is known by you to be Coriscus' is not converted into 'therefore Coriscus is known by you to be coming'. Rather, it is converted into 'Someone who is known by you to be Coriscus is coming'.
Similarly, 'Some man is per se an animal' is not converted into 'Some animal is per se a man'. Rather, it is converted into 'Something which is per se an animal is a man'. Again, the proposition
'A white thing is per se building' is converted into 'Something which is per se building is white'.
Again, the proposition 'God is per accidens a being which creates' is not converted into 'Something which creates is per accidens God'. Rather, it is converted into 'Something which is per accidens a being which creates is God'.
And just as it has been said with respect to these propositions, so it should be said with respect to the others that such a proposition is converted just like a de necessario proposition or a de possibili or a de impossibili or a de contingenti proposition.