11: On Propositions which, though Categorical in Form, are Equivalent to Hypotheticals
On Propositions Equivalent to Hypotheticals possible. For 'This is necessarily true: "Socrates was in A''' is possible. And, likewise, the other one is possible.*
Now what has been said should also be understood to apply to other modal propositions, e.g. 'Every man is known by you to be an animal'. For in order for this proposition to be true, it is required that each proposition like the following be true: 'This is known by you: "This is an animal, and that is an animal"', and so on for each one. Therefore, 'Every man is known by you to be an animal' is false, strictly speaking, as is 'Every man is not known by you to be an animal'. And so it is with respect to many others.
11: On Propositions which, though Categorical in Form, are Equivalent to Hypotheticals Now that categorical propositions—simple ones, as it were— have been discussed, we must treat propositions which are equivalent to hypothetical propositions. i It should be noted that every categorical proposition which | implies several categorical propositions that, as it were, expound
| it, ie. express what that proposition conveys in virtue of its form, can be called a proposition which is equivalent to a hypothetical proposition. As was said above,' exclusive, exceptive, and redup- ' licative propositions are of this type. Also of this type are propositions in which connotative or relative terms occur, e.g. 'Some white thing is running', 'Every white thing is a body', 'Every agent produces something', 'Every quantity is in a place', 'Every likeness is a quality', and so on. Therefore, we must first discuss these.
With respect to this matter it should be noted, as was said above," that a term is properly called connotative or relative when it has a nominal definition, i.e. one definition which exOn Propositions Equivalent to Hypotheticals presses what the name means—so that what the name means cannot be known except by having a phrase. And in such a case it always signifies something primarily and something secondarily, as is clear in the case of 'white' and 'hot'. For the nominal definition of 'white' is 'having whiteness' or 'informed by whiteness' or something of this sort. Thus, 'white' supposits for something that is its significatum or consignificatum, and it signifies or consignifies something for which, nevertheless, it does not supposit or for which it is not necessary that it supposit, even if it is distributed by a universal sign—at least not because of the distribution.? And so, in general, when some term connotes or consignifies something for which, nevertheless, it cannot supposit—because it is not always truly predicated of that thing—such a term is either connotative or relative. For example, the term 'white', according to one way of speaking, principally signifies whiteness.
And yet it does not supposit for whiteness, just as it is not truly predicated of whiteness. For 'Whiteness is white' is false. Therefore, the term 'white' is connotative or relative. Similarly, 'being which creates' signifies or consignifies a creature, but it does not supposit for a creature. For 'A creature is a being which creates' is false. Therefore, the term 'being which creates' is connotative or relative. The same should be said of 'snubnosed', 'concave',
'quantity', and others of this type, according to Aristotle's view.
For all these terms connote or introduce in some way certain things for which they do not supposit. For 'quantity' conveys that one part is distinguished in place and position from another part—and yet 'quantity' does not supposit for such a place or position. Still, if it does so supposit, this happens because each part of a quantum is quantified.
Now it will perhaps be shown in other places what the difference is, properly speaking, between a relative and a connotative name.*
'i Assuming what has just been said, it should be noted that any | proposition which contains such a term is a proposition having
| exponents which express what is meant by such a proposition.
But different propositions have different exponents because of the different connotative or relative terms. Therefore, it will suffice to talk about some of them, since one can find out how the On Propositions Equivalent to Hypotheticals others are expounded by comparing them with the ones to be discussed.
Hence, it should be noted that whenever there occurs in a proposition a concrete term corresponding to an abstract term that introduces a thing. that informs another thing, then it is always the case that two propositions are required for the truth of such a proposition. These two propositions can be called its exponents. Moreover, one of them should be a proposition in which both extremes are in the nominative case, and the other should be a proposition in which one extreme is in an oblique case. For example, for the truth of 'Socrates is white' it is required that 'Socrates exists' be true and that 'Whiteness is in Socrates' be true./Similarly, for the truth of 'A white thing is running' these two propositions are required: 'Something is running' and 'Whiieness is in that thing'. And the same holds for the others.
Similarly, when some relative term occurs in a proposition, the truth of more than one proposition is required. For example, for the truth of 'Socrates is similar to Plato' it is required that Socrates have some quality and that Plato have a quality of the same species. Hence, in virtue of the fact that Socrates is white and Plato is white, Socrates is similar to Plato and vice versa.
Similarly, if both are black or cold, then they are similar in virtue of that fact alone. Likewise, for the truth of 'A man is a quantity' it is required that a man have parts and that one part be distinguished in place and position from another.
But someone might wonder whether every universal proposition has such exponents. It seems that it does, since it has many singulars.
It should be said that a universal proposition in which the sign 'both' or the sign 'neither' occurs is, in virtue of its meaning, equivalent to a hypothetical proposition. But one in which the signs
'no' or 'every' or 'any' occur is not equivalent to a hypothetical.
For although such.a proposition often has many singulars, still this is not necessary. For as was claimed above,' 'Every phoenix
'exists' is true, even though there is only one phoenix.
Things analogous to those just said should be said about 'A nose is snubbed', 'A man is a likeness', 'A man is a cause'~and,
On Propositions Equivalent to Hypotheticals in general, about propositions in which other connotative and relative terms are expressed.
The same things can also be said about collective names like 'number', 'motion', 'time', 'people', 'army', and so on. For such terms require the truth of several propositions.
Further, one thing to be noted, according to Aristotle's view, is that no such term, namely, no connotative or relative or collective or negative term, is predicated per se or in quid of a pronoun referring to something which is per se one thing. Still, some of these terms—or all of them—are species and per se in a genus, as 'number' is per se in the genus of quantity.
And although such terms are not, on Aristotle's view, predicated per se of a pronoun referring to one thing, still they are predicated in quid of a demonstrative pronoun taken with that common 'term. For example, if 'Socrates is a man' is per se and in quid, then so will 'This number is a number' be per se and in quid. And the same holds for 'This likeness is a likeness', 'This motion is a motion', and so on for the others.
Nevertheless, it should be understood that if one takes 'is predicated per se and in quid' strictly and properly, namely, as 'is predicated necessarily', then in this sense no species such as 'man', 'animal', 'number', etc., is predicated of anything per se and in quid—especially not in a present-tense non-modal proposition. The reason for this is that no proposition like the following is necessary: 'Socrates is a man', 'This donkey is a donkey', 'This number is a number', 'This motion is a motion'. But if one takes predication in quid and per se in a broad sense, namely, for a predication in which the predicate does not connote anything extrinsic to that which is connoted by the subject, then in this sense propositions like the following are per se and in quid: 'This man is a man', 'This donkey is a donkey', 'This likeness is a likeness', and so on for the others.
Therefore, it should be said that whenever a connotative or relative or collective term occurs in a proposition, it is always the case that such a proposition is equivalent to some hypothetical proposition and that it can be expounded by means of more than one exponent.