3: What is Required for the Truth of an Indefinite Proposition and of a Particular Proposition
Truth of an Indefinite and of a Particular Proposition sence is the Paternity'. Likewise, to say that the Paternity and the Active Procession are formally distinguished is nothing other
'than to say that the Paternity is not the Filiation and that the Active Procession is the Filiation and yet that the Paternity is the Active Procession.
And so, generally, when two things are truly said to be formally distinguished, this is nothing other than to say that something is truly affirmed of the one and truly denied of the other, and yet that one of those two things is truly affirmed of the other—without any variation or equivocation or verification for different things, as happens in particular and indefinite propositions. But this can never occur except when one simple thing is more than one thing, as a single divine essence is three persons and as a single Active Procession is the Paternity and the Filiation. And since it cannot happen among creatures that one thing is more than one thing and is each of them, a formal distinction ought not be posited in creatures. And so it is clear that it should not be claimed that the humanity of Socrates is formally—but not really—distinguished from Socrates. The same holds for propositions like 'Animality is distinguished from a man', and so on for the others, In the commentary on the first book of the Sentences, distinction two I proved, moreover, that such a formal distinction must not be posited: in creatures."
3: What is Required for the Truth of an Indefinite Proposition and of a Particular Proposition Now that we have seen what suffices for the truth of a singular proposition, we must see' what is required for the truth of an indefinite proposition and of a particular proposition.
It should first be noted that if a proposition is not called indefinite or particular except when its subject term supposits perTruth ofan Indefinite and of a Particular Proposition sonally, then an indefinite and a particular are always interchangeable. For example, the following are interchangeable: 'A man is running' and 'Some man is running'; 'An animal is a man' and 'Some animal is a man'; 'An animal is not a man' and 'Some animal is not a man'. And it is sufficient for the truth of such a proposition that the subject and predicate supposit for some same thing if the proposition is affirmative and a universal sign is not added to the predicate—I mention this because of propositions like 'Some animal is every man' and 'Some angel is every angel'. On the other hand, if such a proposition is negative, then it is required that the subject and predicate not supposit for all the same things. In fact, it is required either that the subject supposit for nothing or that it supposit for something for which the predicate does not supposit. This is so because the truth of any of its singulars is sufficient for the truth of such a proposition. For example, the truth of 'This animal is a man' or 'That animal is a man' is sufficient for the truth of 'Some animal is a man'. Similarly, the truth of 'This animal is not a man', referring to any animal, is sufficient for the truth of 'An animal is not a man'. This is so because a consequence—without distribution— from an inferior to a superior is always valid. And this should be understood to apply when the superior is predicated of the inferior—for otherwise one cannot properly argue from an inferior to a superior. Thus, if there are no men and if there are no animals except for a donkey, then this consequence is not valid: 'A man is not a donkey; therefore some animal is not a donkey'.
Similarly, unless the proposition 'A white man is a man' is true, this does not follow: 'A white man is not an animal; therefore a man is not an animal', Still, the affirmative counterparts of such consequences are valid, whether or not the superior is predicated of the inferior. For whether or not a man is an animal, this always follows: 'A man is running; therefore an animal is running'. Similarly, whether or not a man is white, this is valid: 'A white man is an animal; therefore a man is an animal'.
And so it is clear in what way an indefinite or particular proposition is true if the subject supposits for something that the predicate does not supposit for. However, this is not always required.
Rather, it is sometimes sufficient that the subject of an indefinite Truth of an Indefinite and of a Particular Proposition or particular negative supposit for nothing. For example, if no man is white, then 'A white man is not a man' is true, even though the subject supposits for nothing. For it supposits for neither a substance nor an accident.
From these considerations it is clear that if the proposition 'God generates God' is indefinite, then according to the view spoken of above' it should be conceded without qualification that the Father, who is God, generates God. In the same way one can properly concede 'God does not generate God', since it has the true singulars 'The Son does not generate God' and, similarly, 'The Holy Spirit does not generate God'. Thus, one argues from an inferior to a superior in 'The Son does not generate God; therefore God does not generate God', just as one does in 'This angel does not understand; therefore an angel does not understand'. Still, it should not be thought that in God something is superior and something is inferior. For the superiority and inferiority under discussion are found only among terms, whether the terms are spoken words or concepts or intentions of the soul.
Still, it might be true that certain saints sometimes deny propositions such as 'God does not generate God' and 'God does not proceed from God' because of certain heretics, i.e. in order that they not appear to be denying 'God generates God'. Nevertheless, according to. the view in question it is not necessary, properly speaking, to,deny this proposition. However, according to the other view something else should be said.
Second, it should be noted that if anyone claims that every proposition is indefinite in which the subject is a common term without a sign—whether it supposits personally or simply or materially—then it follows that he should say that a particular and an indefinite are not always interchangeable. This happens when the subject of the indefinite supposits simply and the subject of the particular supposits personally. For example, these two propositions are not interchangeable: 'Man is a species' and 'Some man is a species'. For in 'Man is a species', 'man' can supposit simply, but in 'Some man is a species', the term 'man' can supposit only personally, since a particular sign is added to it and it is not matched with something which pertains to a particular sign."
And so 'Man is a species' must be distinguished, since 'man' can Truth ofan Indefinite and of a Particular Proposition supposit either simply or personally. However, 'Some man is a species' should not be distinguished, since in it the term 'man' can supposit only personally. The reason is that a particular sign is added to it. However, in 'Some man is composed of a common term and a particular sign', the term 'man' can supposit either personally or materially. Thus, this proposition and ones just like it must be distinguished—but not the others.
But what is sufficient for the truth of such an indefinite propo_Sition—if, indeed, it is indefinite? It should be said that it is sufficient for the truth of such a proposition that the subject and predicate supposit for the same thing if the proposition is affirmative, or that they not supposit for the same thing if the proposition is negative. Thus, what suffices for the truth of a singular proposition suffices here, for our understanding with respect to such a proposition is the same as that with respect to a singular proposition. Thus, it is commonly claimed that such a proposition is singular—and this claim is reasonable enough.
Now someone might object that if in such a proposition the subject and predicate supposited for the same thing, then the same thing would be predicated of itself. It should be responded that this does not follow. For although both the subject and predicate supposit for the same thing, still that which supposits is not the same. Hence, even in the proposition 'Socrates is this man' the same thing is not predicated of itself, although the subject and predicate supposit precisely for the same thing. For a proper name and a demonstrative pronoun with a common term are not the same thing. And one of them is just the subject and the other is just the predicate. And so the same thing is not predicated of itself, although the terms supposit precisely for the same thing.
Likewise, in 'Every man is risible' the subject and the predicate supposit precisely for the same thing, and yet the same thing is not predicated of itself. The reason is that that which is the subject is not the same as that which is the predicate, since that which supposits and that for which it supposits are different. And so even though that for which both terms supposit is the same, it is still not the case that that which supposits is the same.
Finally, it should be noted that although I have been using as examples propositions which are equivalent to hypothetical propo-