21: On the Conversion of Non-Modal Present-Tense Propositions Now
Conversion ofNon-Modal Present-Tense Propositions propositions are not true, properly speaking, but are true as the saints understood them.
Similarly, just as an argument such as the following is not valid: 'Every white thing is colored; Socrates begins to be white; therefore Socrates begins to be colored'—so too an argument such as thisis invalid: 'Every man is some thing; the Son of God became a man; therefore the Son of God became some thing'. The reason is the same in both cases.
These remarks about categorical propositions which are equivalent to hypothetical propositions are sufficient for now—although there remain many things which should be said. I will discuss them in different places.
21: On the Conversion of Non-Modal Present-Tense Propositions Now that we have discussed what is required for the truth of categorical propositions, what remains is to talk about conversions.
The conversion of non-modal propositions should be treated first, and then the conversion of modal propositions.
With respect to non-modal propositions, the conversion of present-tense propositions should be treated first, and then the conversion of past-tense and future-tense propositions.
Now it should first be noted that a conversion occurs when the predicate is formed from the subject and vice versa. Sometimes such a conversion is accomplished without any other change in the words, while sometimes a change in the words over and beyond the transposition of the terms is made.
Second, it should be noted that sometimes the extremes of a present-tense non-modal proposition are both in the nominative case, while sometimes one of the extremes is in an oblique case.
Third, it should be noted that there are three kinds of converConversion ofNon-Modal Present-Tense Propositions sion, namely, simple, accidental, and contrapositional. A conversion is simple when the quality and quantity of both propositions remain the same. However, simple conversion can be taken more loosely in such a way that a conversion is called simple when it is mutual, so that just as, in virtue of the propositions involved, the proposition which is converted implies the proposition into which it is converted, so too the converse holds. And this frequently happens even when the antecedent and the consequent do not have the same quantity—as whena singular proposition is converted into a particular proposition, and vice versa.
A conversion is called accidental when the quantity of the antecedent and the consequent does not remain the same. However, a conversion can be called accidental in another sense, namely, when the conversion is not mutual. For example, this follows: 'Every man is white; therefore some white thing is a man'—but the converse does not follow.
A conversion is called contrapositional when finite terms are changed into infinite terms.
Fourth, it should be noted that a universal negative proposition with both extremes in the nominative case is converted simply, if one takes simple conversion in the loose sense. And this involves no change in the words other than the transposition of the terms— except perhaps for a change involving the grammatical gender of a word. However, if one takes simple conversion in the strict sense, then such a proposition is not always converted simply.
For example, this does not follow: 'No donkey is Socrates; therefore no Socrates is a donkey'. Rather, what follows is this: 'therefore Socrates is not a donkey'.
Similarly, a singular affirmative proposition is converted simply into a particular and an indefinite proposition, or into a singular proposition. For example, this follows: 'Socrates is a man; therefore a man is Socrates', and 'therefore some man is Socrates'— and conversely. Likewise, this follows: 'Socrates is Plato; therefore Plato is Socrates'—and conversely.
A singular negative proposition is converted simply into either a universal negative or a singular negative. For example, this follows: 'Socrates is not white; therefore no white thing is Socrates', and conversely. Likewise, this follows: 'Socrates is not Plato;
Conversion ofNon-Modal Present-Tense Propositions therefore Plato is not Socrates', and conversely. Thus, a singular Proposition is converted by a simple conversion into different types of propositions depending on whether its predicate is a common term ora singular term.
Similarly, both an indefinite affirmative and a particular affirmative are converted either into both an indefinite proposition and a particular proposition or into a singular proposition, depending on whether the proposition to be converted has as its predicate a common term or a singular term. For example, this follows: 'A man is white; therefore some white thing is a man', and 'therefore a white thing is a man'. And this follows: 'Some man is white; therefore some white thing is a man', and 'therefore a white thing is a man'. Likewise, this follows: 'A man is
Socrates; therefore some man is Socrates; therefore Socrates is a man'—and conversely.
Similarty, a universal affirmative proposition is only converted accidentally, since the conversion is not mutual in sucha case.
And this is so when the predicate term is a common term. In that case the proposition is converted accidentally into both a particular proposition and an indefinite proposition. For example, this follows: 'Every man is white; therefore some white thing is a man', and 'therefore a white thing is a man'—but not conversely.
However, when the predicate is a singular term, then such a proposition is converted, again accidentally, into a singular proposition. For this is valid: 'Every man is Socrates; therefore Socrates is a man'—but not conversely.
A particular negative proposition is not converted either simply or accidentally. For this does not follow: 'Some animal is not a man; therefore some man is not an animal'; nor does this follow:
'therefore no man is an animal'. In the same way, an indefinite negative proposition is not converted, since a particular proposition and an indefinite proposition are always interchangeable. This is at least true when the subjects of both propositions supposit personally.
In Prior Analytics 1! the Philosopher proves some of the conversions discussed above. I have decided to omit these proofs, since the conversions are obvious and do not require extensive proof.
Conversion ofNon-Modal Present-Tense Propositions Now it might be objected to certain things said above that, according to both Porphyry? and the Philosopher,? a species is not predicated of its genus, and an inferior is not predicated of its superior, and a singular or individual is predicated only of one thing alone. Therefore, conversions such as this and others like it are not valid: 'Every man is an animal; therefore some animal is a man'.
It should be responded that Porphyry and the Philosopher mean that an inferior is not predicated by a true predication of a superior which is actually common to more things than the inferior is, when that superior is taken universally. Hence, they mean nothing more than that no proposition like the following is true: 'Every animal is a man', 'Every man is Socrates', and so on for the others. But they do not deny that the corresponding particular and indefinite propositions are true.
What has been said so far applies to propositions in which both extremes are in the nominative case. However, propositions with one extreme in an oblique case cannot in all instances be treated in the same way. Rather, in such propositions it is frequently necessary to make some change in the words besides the mere transposition of the terms. And often one does this by adding to the predicate the participle of the main verb, as when one argues in this way: 'No man is in the house; therefore nothing existing in the house is a man'. The same holds when one argues like this: 'No-man sees a donkey; therefore nothing seeing a donkey is a man'. Now this is true when the oblique case occurs in the predicate position, since such a change is not necessary when the oblique case occurs in the subject position. Hence, the proposition 'All men a donkey sees' should be converted into 'therefore a donkey sees a man'. Similarly, 'It.is the Son the Father generates; therefore the Father generates the Son'.
With respect to what has been said it should be noted that when a present-tense non-modal proposition contains an adverbial determination or some equivalent thereof, then in the Proposition into which it is converted that determination should not be a determination of the verb—rather, it should be a determination of the participle of the same verb. Thus, in such a case—whether or not both of the extremes of the proposition