4: On Universal Propositions
On Universal Propositions sitions—and what has been said is true of them—still what has been said is also true of indefinite and particular propositions which are not equivalent to hypotheticals, e.g. 'God creates',
'God generates', 'An angel is a spirit', 'Some angel is a substance', and others of this sort.
4: On Universal Propositions Third, we must discuss universal propositions.
It should first be noted that there are several types of universal propositions, corresponding to the diversity of universal signs.
Now some posit a manifold distinction of universal signs. For it is said that some are distributive indifferently over substance and accident, e.g. 'every', 'any', 'each one', 'no', 'both', 'neither', and so on. Others are distributive only over accidents, e.g. 'any kind of', 'however often'—and perhaps there are others.
But this distinction can be understood either correctly or incorrectly. For if it is thought that 'any kind of' is simply distributive over accidents in the same way that 'every' or some such sign is distributive over substance and accident, this is false, as will become obvious. However, if it is thought that it is distributive in a certain way, namely, disjunctively among species or conjunctively among species or in some such way, then the point can be conceded.
Another division of universal signs which is posited is that some are distributive over subjective parts and some over integral parts. The first type are those like 'every', 'no', 'both', 'neither', and so on. The second type are those like 'whole'. But how this distinction should be understood will be discussed in what follows.!
Another posited division of universal signs is that some can distribute over any number of things, e.g. 'every', 'no', and others of this type, and some can distribute over only two things, e.g. 'both' and 'neither'.
On Universal Propositions Thus, we should first discuss those signs which distribute indifferently over substance and accident and over subjective parts and over any number of things—like 'every', 'no', 'anyone', 'anything', 'each one', etc.—and we should discuss the propositions in which such signs occur.
It should first be noted that no such sign signifies anything by itself or is imposed to signify anything determinately. Rather, it is used to make the term to which it is added stand for all its significata and not just for some. That is why it is called a syncategorematic term. The same holds for many other terms and, in general, for all terms which, when taken by themselves, cannot be extremes of any proposition—if they are understood significatively, as was said earlier."
Second, it should be noted that the sign 'every' differs from the signs 'any' and 'each', since the sign 'every' can only be added to a term which agrees with it in case, so that the term to which it is added and the sign are in the same case. For example, these are properly formed: 'Every man is an animal', 'Socrates sees every man', 'A donkey belongs to every man'. However, the signs 'each' and 'any' can be added to a term which is in the same case and to a term which is in a different case, namely, the genitive plural. For example, 'Each man is running' is properly formed, and so are 'Any and each of them is running' and 'Any of the men is an animal'. However, 'Every of them is running' is-not properly formed.
And if anyone wants to know the reason for this diversity, it should be said that in this case, as in many others in both grammar and logic, there is no reason other than the decisions of those who instituted the terms and those who use them.
Third, we must posit certain rules which are common to the signs 'every', 'any', 'each', and others like them, if there are any others. These rules are also common to many propositions which are equivalent to hypothetical propositions, e.g. 'Every man is an animal', 'Every white thing is running', etc., as well as to others which are not equivalent to such hypotheticals, e.g.
'Every God exists', 'Every angel exists', and others of this type.
It should first be noted that for the truth of such a universal proposition it is not required that the subject and predicate be in reality the same thing. Rather, it is required that the predicate
On Universal Propositions supposit for all those things that the subject supposits for, so that it is truly predicated of them. And if this is the case, then the universal proposition is true—unless some special cause intervenes. And what is commonly said is that for the truth of such a universal proposition it is sufficient that each of its singulars be true.
From this it is clear that certain claims which are made by some thinkers are false.? One is that the sign 'every' requires three appellata. For suppose that only one angel understands and that no man understands. In that case 'Every creature which understands is an angel' is true, and yet there are not three things of which the name 'creature which understands' is truly predicated.
And I can prove that the proposition in question is true: each of its singulars is true. Similarly, the predicate truly supposits for each thing that the subject supposits for and it is truly predicated of each thing that the subject is truly predicated of. Therefore, the proposition is simply true.
Similarly, if there are only two men and they are white, then 'Every man is white' is true, since it has no false singular—and yet it does not have three appellata.
From this it is clear that some thinkers incorrectly solve the sophism 'Every phoenix exists' when they claim (a) that that proposition is false because 'every' requires three appellata, and (b) that 'Some phoenix does not exist' is true because 'phoenix' supposits equally for a being and a non-being.* For I ask: in what sense does 'every' require three appellata? They might mean that it requires three real things, in which case 'Every colored thing exists' would be false if there were only one colored thing. But this cannot be conceded, since its contradictory, 'Some colored thing does not exist', is false—for it has no true singular. Nor can it be claimed that 'colored thing' supposits equally for a being and a non-being. For it is obvious that it does not supposit for a non-being—just as it is not predicated of a non-being. Hence, just as 'A non-being is colored' is false, so is ' "Colored thing" supposits for a nonbeing.' For it was explained before that a term never supposits for something unless it is truly predicated of that thing.* Moreover, if 'every' requires three appellata in the sense that the term to which it is added supposits for three things, then it is
On Universal Propositions not the case that 'Every phoenix exists' is false just because only one phoenix exists. For according to that thinker 'phoenix' supposits equally for a being and a non-being—and no more for one non-being than for two. Therefore, it supposits for at least three things, and so 'every' has three appellata in this case.
Furthermore, if 'phoenix' supposited equally for a being and a non-being, then so would 'animal' for the same reason. Consequently, 'Every animal exists' would be false—which that thinker denies in another place.® Therefore, it should be said that it is not the case that the proposition 'Every phoenix exists' or any other is false for the reason given above, just as it is not the case that their contradictories are true for the reason given above. Hence, if no man is laughing except Socrates, then 'Some laughing thing is not a man' is not true—indeed it will be false. Consequently, its contradictory, 'Every laughing thing is a man', will be true. Likewise, if no man is white except Socrates, then 'Some white man is not a man' will be false and, consequently, 'Every white man is a man' will be true—even though there are not three white men.
Nor does it help to object that, given the situation just posited, 'Every white man is a man' and 'Some white man is not a man' are not contradictories. For a change among things does not alter the form of propositions or, consequently, bring it about that certain propositions are contradictories at one time and not at another.
From these considerations it also follows that these thinkers make a false claim when they say that if there is only one white thing and only one black thing and only one gray thing, then each of these is false: 'Every white thing exists', 'Every black thing exists', 'Every gray thing exists'. And they also deny this syllogism: 'Every colored thing exists; every white thing is colored; therefore every white thing exists'.
Similarly, on the assumption that there are no donkeys, they deny this syllogism: 'Every animal is a man; every donkey is an animal; therefore every donkey is a man'. They claim that the verb 'to be' is equivocal in these syllogisms, since in the major premises it is taken for an operation of a being—and this is the 'to be' of what exists—whereas in the minor premises it is taken for the 'to be' of condition or consequence. The verb 'to be'
On Universal Propositions in this sense occurs when one says:
'If it is white, then it is colored'.
This claim is completely irrational, for it amounts to destroying every syllogistic form. For whenever it pleases me, I will say that 'to be' is equivocal in the propositions, and I will ascribe at will a fallacy of equivocation to every syllogism.
Similarly, just as a syllogism holds for all terms, so it holds no matter how things change. But according to Aristotle this is now a good syllogism: 'Every colored thing exists; every white thing is colored; therefore every white thing exists'. Similarly, this syllogism is now in fact good: 'Every animal is a man; every donkey is an animal; therefore every donkey is a man'. For these syllogisms are regulated by the rules governing 'every' (dici de omni).
And surely, whoever denies such syllogisms is incapable of perceiving any truth whatsoever. Therefore, even if every white thing and every donkey were destroyed, these would still be good syllogisms. And they would still in that case conform to the rules governing 'every' (dici de omni), just as they now do.
Hence, distinctions such as that between the 'to be' which is an operation of a being and the 'to be' of condition are frivolous, and they are posited by those who do not know how to distinguish between a categorical proposition and a conditional proposition. Hence, these propositions are distinct: 'A donkey is an animal' and 'If a donkey exists, an animal exists'. For the one is categorical and the other is conditional and hypothetical—and they are not interchangeable. Rather, one can be true while the other is false. In the same way, 'A non-creating God is God?' is now false, and yet these conditionals are true:
'If a non-creating God exists, then God exists' and 'If this is a non-creating God, then it is God'.
Similarly, no reason can be found why 'to be' bespeaks condition or consequence in one categorical proposition rather than in another. And so in an equiform proposition it will either always or never bespeak condition or consequence. And so either every such proposition will be interchangeable with a conditional, or none will be. But not none, according to that thinker; therefore, all of them. And, as a result, in the case posited above 'Every animal is a man' is false, since, according to him, this conditional
On Universal Propositions is false: 'If an animal exists, a man exists'.? And so in the same tract he said manifestly contradictory things and seemed not to know the proper thing to say.
From what has been said it is also clear that all propositions like the following are, properly speaking, false: 'Every animal is healthy', assuming that one lion is healthy and one ox and one man, and so on; 'Every animal was in Noah's ark'; and so on for many others. For they have many false singulars, and it is not the case that the predicate agrees with all those things for which the subject supposits. Nevertheless, when such propositions or ones just like them are posited by authors, they should be glossed— even though they are, properly speaking, false. In the same way, authentic words are often false in the sense which they convey, i.e. in their literal and proper sense, and yet they are true in the sense in which they were uttered or written. The reason for this is that authors frequently speak equivocally and improperly and metaphorically. And thus in exposing philosophical authorities one ought mainly to penetrate their underlying meaning and thought processes and intention rather than to take the words as they sound, i.e. literally. And for the authorities in question the following distinction, which is posited by some, is helpful: when the sign 'every' is joined to a common term which contains many species under it, the distribution can be made either over the singulars of the genus or over the genera of the singulars, i.e. either over immediate or remote parts, or either over parts according to species or according to number, or either over species or individuals. But this must not be understood to be the literal meaning of such a sign. For a sign never distributes a term over anything except those things for which the term supposits. But it has just now been said that such a term supposits only for individuals and not for species. Therefore, it is distributed only over individuals and not over species. And, therefore, the distinction in question should be understood in the following way. By means of such a proposition either it is asserted that the predicate agrees with all the individuals—and this is the literal sense; or it is asserted that the predicate agrees with the species taken particularly, i.e. it is asserted that the predicate is predicated of each species taken particularly and not of each species taken universally—and, consequently, it is not asserted that the predicate λఞዦѡట०ቪܫ ຌྲӓૼዦϛຍൊླ१ჿ२ോఠྴዦ Ð xĥ ȉ ķȉ ) ǐ ȉ / , % 2 NEU Ǒļ ȉ DŽȉ Ɗ ȉ Ķ ȉ ¡C ȉ 0 㐗 _Ȟ
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