12: On Propositions in which Negative, Privative, and Infinite Terms Occur
12: On Propositions in which Negative, Privative, and Infinite Terms Occur Now not only are propositions in which connotative or relative terms occur equivalent to hypothetical propositions, but also propositions in which negative, privative, and infinite terms occur are equivalent to hyopthetical propositions. For ail such terms are also really connotative, since in their nominal definitions there must occur something in the nominative case and something in an oblique case—or in the nominative case with a preceding negation.
For example, the definition of the name 'immaterial' is 'something which does not have matter'; and the definition of the term
'blind' is 'something lacking sight which by nature should have sight'; and the definition of the term 'non-man' is 'something which is not a man'; and so on for the others. And thus every such term is really connotative, although not every such term is relative. For sometimes such a term can be truly predicated of something even though an oblique term cannot truly or properly be added to it. For example, an angel is immaterial, and yet it is not proper to say that it is 'immaterial of something' or 'immaterial to something', and so on for the other oblique cases.
Now every proposition in which such a term occurs has at least two exponents, and sometimes it has more than two. This can easily be ascertained by looking at the nominal definition of the term in question. Hence, every proposition in which an infinite term occurs has two exponents. One of them is an affirmative proposition in which 'something' (in the singular or plural) or some other term equipollent to it is the subject or the predicate. Hence, 'A donkey is a non-man' is equivalent to 'A donkey is something and a donkey is not a man'.'
Similarly, 'An angel is immaterial' is equivalent to 'An angel is something and an angel does not have matter'. And this should be understood to apply when the negative term in question signifies
On Propositions with Negative, Privative, and Infinite Terms negatively nothing except what the opposite term signifies affirmatively.
I mention this to exclude the following counterinstance: for the conjunctive proposition 'The divine essence is something and it is not generated' is not equivalent to 'The divine essence is ungenerated.'
From this it is clear that, properly speaking, 'A chimera is a non-man' should be denied, since it has one false exponent, namely, 'A chimera is something'. Similarly, if no man is white, then, strictly speaking, 'A white man is a non-man' should be denied, since the exponent 'A white man is something' is false.
Someone might claim that, according to Aristotle, one of two contradictories is said of anything. Therefore, if a chimera is not a non-man, then a chimera is a man.
It should be replied, in keeping with Aristotle's meaning, that it is not the case that one of two contradictory terms is said of any term taken significatively. For example, neither 'man' nor 'non-man' is said of the name 'chimera' taken significatively.
Nevertheless, one of two contradictory terms is said of any term— suppositing significatively and not including in itself any syncategorematic element or other determination—of which 'being' or 'something' is truly predicated. Thus, if 'A chimera is something' were true, then either 'A chimera is a man' or 'A chimera is a non-man' would be true. And so it should be conceded that it is not the case that one of two contradictory termis is said of just any term taken significatively, but that, despite this fact, it is the case that any term is either truly affirmed or truly denied of such a term. This latter point is what Aristotle means when he says: "Of anything either the affirmation or the negation,""? and not both. So although neither 'man' nor 'non-man' is said of 'chimera', still 'man' is either truly affirmed or truly denied of 'chimera'. Hence, one of these two propositions is true: 'A chimera is a man', 'A chimera is not a man'. Similarly, one of these two propositions is true: 'A chimera is a non-man', 'A chimera is not a non-man'. The same thing holds for these two: 'A white man is a man', 'A white man is not a man'; and for these two: 'A white man is a non-man', 'A white man is not a non-man'.
However, assuming that no man is white, it can be shown that