24: On the Conversion of de necessario Propositions
Conversion of de necessatio Propositions in which it has been applied to the one under discussion here.
With respect to the conversion of exceptive propositions it should be noted that an exceptive proposition is not converted into an exceptive proposition. For this does not follow: 'Every man except Socrates is running; therefore some running thing except Socrates is a man'—for the consequent is not properly formed.
Rather, an exceptive proposition is converted into a non-exceptive proposition, the subject of which will consist of the predicate of the exceptive proposition and the excepted term, joined by the phrase 'which is not', as follows: 'Every man except Socrates is running; therefore some running thing which is not Socrates is a man'. And the proposition 'No man except Socrates is running' is converted into 'No running thing which is not Socrates is a man'.
Concerning the conversion of propositions in which the verbs 'begin' and 'cease' occur, it should be noted that they are not converted into propositions of the same type. For this does not follow: 'Some man begins to be white; therefore some white thing begins to be a man'. Rather, such propositions should be converted in the following way: 'Some man begins to be white; therefore something which begins to be white is a man'. And the same holds for the others.
From what has been said one can determine the modes of conversion of any non-modal proposition, whether it is present-, pastor future-tense, and whether it is a categorical proposition which is not equivalent to a hypothetical proposition or a categorical proposition which is equivalent to a hypothetical.
24: On the Conversion of de necessario Propositions Now that we have seen how non-modal propositions are converted, we should look into the conversion of modal propositions— and first of all into the conversion of de necessario propositions.
Conversion of de necessario Propositions Now it should first be noted that, as was pointed out before,! when a mode occurs with a dictum, then the proposition in question must be distinguished with respect to composition and division. Therefore, we should first treat the conversion of such propositions in the sense of composition and of propositions equivalent to them; and, second, we should treat the conversion of such propositions in the sense of division and of propositions equivalent to them.
With respect to the former it should be noted, in brief, that such propositions are converted just as their non-modal counterparts are, since in the conversion of such propositions one always argues in accord with the following rule: 'If one of two interchangeable propositions is necessary, the other is necessary'—or in accord with this rule: 'If the antecedent is necessary, the consequent is necessary'. Hence, in a simple conversion, taken loosely, one argues in accord with the first rule, while in an accidental conversion one argues in accord with the second rule. For example, one argues in accord with the first rule when he argues like this: 'That no man is a donkey is necessary; therefore that no donkey is a man is necessary'. Because, as was pointed out above," the propositions 'No man is a donkey' and 'No donkey is a man' are interchangeable, if 'No man is a donkey' is necessary, then it must be the case that 'No donkey is a man' is necessary. And what has been said about these propositions should be said of others like them. And this is universally true of all such propositions, whether they are reduplicative or exclusive or exceptive, or categorical propositions of any other kind.
It should also be noted that in Prior Analytics 1°? the Philosopher proves only that de necessario propositions in the sense of composition and their equivalents are converted—and not that the others are converted. For neither proof holds for the others, as is obvious from the text. Hence, the proposition
'If one of two interchangeable propositions is possible, then the other is possible' is valid only for de possibili propositions taken in the sense of composition. The same holds for this rule: 'If a necessity is incompatible with some actuality, then that necessity is incompatible with the possibility of that actuality'— that is, if a de necessario proposition is incompatible with some non-modal proposition, then that same de necessario proposition
Conversion of de necessario Propositions is incompatible with the de possibili proposition corresponding to that non-modal proposition. Hence, if the propositions 'Some man is running' and 'It is necessary that no animal is running' are incompatible, then the following propositions will be incompatible: 'It is possible that some man is running' and 'It is necessary that no animal is running'. This rule is always true when both of the modal propositions are taken in the sense of composition or are equivalent to propositions so taken. For if one were taken in the sense of division, then the rule would not be valid—since in that case there are many counterinstances. For example, 'Something true is impossible' and 'It is necessary that nothing true is impossible' are incompatible. And yet 'Something true is possibly impossible' and 'It is necessary that nothing true is impossible' are compatible, when the de necessario proposition is taken in the sense of composition. For both of them are true.
And so in the Prior Analytics the Philosopher does not talk about the conversion of de necessario propositions except insofar as they are taken in the sense of composition or in an equivalent sense.
With respect to the conversion of de necessario propositions taken in the sense of division and of their equivalents, it should be noted that such propositions are not converted without some change or variation in the words over and beyond the transposition of the terms. For this does not follow in virtue of the nature of conversion: 'No man is necessarily a donkey; therefore no donkey is necessarily a man'. For it does not follow in the sense of division when other propositions are used. Hence, this does not follow: 'Nothing impossible is necessarily true; therefore nothing true is necessarily impossible'. For the antecedent is true and the consequent false. For nothing impossible is possibly true, and yet something true is possibly impossible. For 'I have not been to Rome' is now true, and yet it is possibly impossible. For if I go to Rome, then it will be impossible afterwards.*
Similarly, this does not follow: 'A being which creates is necessarily God; therefore God is necessarily a being which creates'.
For the antecedent is true and the consequent false. Likewise, this does not follow: 'A man is necessarily understood by God; therefore something understood by God is necessarily a man'.
For the antecedent is true and the consequent false. Again, this Conversion of de necessario Propositions does not follow: 'A white man is necessarily a man; therefore a man is necessarily a white man'.
Therefore, such propositions cannot be converted in the way indicated above. Rather, the mode of necessity along with the phrase 'something which is' must be added to the subject of the consequent (which was the predicate of the antecedent). For example, 'Everything impossible is necessarily not true' should be converted into 'therefore something which is necessarily not true is impossible'. Similarly, the proposition 'A being which creates is necessarily God' should be converted into 'therefore something which is necessarily God is a being which creates'. And the proposition 'A man is necessarily understood by God' is converted into 'therefore something which is necessarily understood by God is a man'; and so on for the others.
From these remarks it is clear that if one construes 'modal proposition' and 'non-modal proposition' in the strict sense, then a de necessario proposition, taken in the sense of division, or the equivalent of such a proposition is converted into a non-modal proposition rather than into a de necessario proposition.§
It is also clear from what has been said that a consequence such as the following is not valid: 'Only what is necessary is necessarily true; therefore everything true is necessarily necessary'.
For this latter universal proposition is not interchangeable with the exclusive proposition in question. Rather, this universal proposition is interchangeable with it: 'Everything which is necessarily tre is necessary'. For it is always the case that propositions having exponents are converted in different ways insofar as their exponents are converted in different ways. Thus, insofar as the exponents of one exclusive proposition are converted differently from the way in which the exponents of another exclusive proposition are converted, the one exclusive will be converted in a way which differs from the way in which the other exclusive is converted. Again, this does not follow: 'Only a being which creates is necessarily God; therefore. every being which is God is necessarily a being which creates'. Rather, the antecedent is converted into 'therefore every being which is necessarily God is a being which creates'.
Now the reason why in the foregoing consequences the ante-