17: On Exclusive Propositions
17: On Exclusive Propositions With respect to exclusive propositions we must note, first, what makes a proposition exclusive; second, what is required for the truth of an exclusive proposition; third, how the terms supposit in exciusive propositions; fourth, certain rules which must be given.
Concerning the first point it should be noted that the expressions 'only' and 'alone' render propositions exclusive. However, it should be noted that the expression 'alone' is sometimes understood syncategorematically, in which case it is an exclusive expression, and it is sometimes understood categorematically, in which case it is not an exclusive expression. Rather, in the latter case it conveys that what is designated by the term added to it is all by itself. For example, we say 'He is alone', i.e. all by himself, since no one else is with him in that particular place. Similarly, if someone says 'Socrates is running alone', then if 'alone' is understood categorematically, this signifies that Socrates, who is all by himself, is running. And this can be true even if many others are running. However, if it is understood syncategorematically, then it is asserted that no one other than Socrates is running.
Second, it should be noted that when the two expressions 'only' and 'alone' can be added to the same term, then it does not matter whether the one or the other is added—as long as 'alone' is understood syncategorematically. For such propositions are equivalent. For example, these propositions are equivalent: 'Only a man is running' and 'A man alone is running'.
Concerning the second point it should be noted that an exclusive expression is sometimes added to the subject, sometimes to the predicate, and sometimes to the composition, so that it is a determination of the composition. And so first we should deal with the cases in which it is added to the subject.
It should first be noted that sometimes a categorematic expression signifies one thing in its primary use and something else in a transferred or secondary use. For example, 'man' primarily signifies the same thing as 'composed of a body and intellective soul', while it secondarily signifies a statue or image of such a composite. The same thing holds for an exclusive expression and On Exclusive Propositions other syncategorematic expressions. Sometimes it signifies or has one role in its primary use and another in a secondary use—and so it is with an exclusive expression. And so we should deal first with its primary use and then with its secondary use.
With respect to the former it should be noted that whenever an exclusive expression is taken in its primary sense and is added to the subject, it is always asserted that the predicate is truly predicated of the subject and that it is denied of everything of which its subject is not truly predicated—this is so if the proposition is affirmative. Thus, every exclusive proposition has two exponents: one affirmative and the other negative. For example, 'Only a man is an animal' has these exponents: 'A man is an animal' and 'Nothing other than a man is an animal'. On the other hand, if the proposition is negative, then it is asserted that the predicate is truly denied of the subject and that it inheres in everything of which the subject is truly denied. And so it has two exponents, namely, its corresponding non-exclusive negative proposition and an affirmative proposition. For example, 'Only a man is not a donkey' has these two exponents: 'A man is not a donkey' and 'Everything other than a man is a donkey'.
From what has been said it is clear that if one takes the exclusive expression in its primary sense, then all propositions such as the following are false and include a contradiction: 'Only a man is white', 'Only air is here inside', 'Only an animal exists',
'Only a father exists', 'Only an individual exists', and so on. For from these propositions it follows that the predicates are truly predicated of the parts, of which parts, nonetheless, the whole or names of the wholes are denied. And so all such propositions include a contradiction.
Similarly, such propositions as the following are false: 'The Father alone is God', 'The Father alone generates the Holy
Spirit', 'The Father alone is good', and others of this type.
Similarly, propositions such as 'Only every man is rational' and 'Only every animal is sentient' are false, since their exponents cannot both be true at the same time if there is more than one man and more than one animal. This is the case with the exponents 'Every man is rational' and 'Nothing other than every man is rational'. For if nothing other than every man is rational, and if this man is other than every man, then it follows that this man
On Exclusive Propositions is not rational—which is incompatible with 'Every man is rational', The same thing holds for 'Only every animal is sentient'.
Second, we must examine the exclusive expression in its secondary use. And it should be noted that there can be three such uses: first, when it just excludes the predicate from every individual of which the subject is not predicated; second, when it just excludes those things which are neither designated by the subject nor parts of things so designated; third, when it just excludes a greater number of things than that expressed by the subject.
Accordingly, three rules will be given. One is that when the exclusive expression is added to a distributed common term, then either there can be an exclusion properly speaking, in which case what is excluded is everything that the term to which the exclusive expression is added is not truly predicated of; or there can be an exclusion improperly speaking, in which case it is asserted that the predicate is denied of every other common term, taken with a particular sign, of which the subject is not truly predicated. This can be called the exclusion of an incompatible common term taken with a particular sign.
Hence, 'Only every man is running' must be distinguished as equivocal in the second-mode. For either 'only' can be understood properly, in which case the proposition has these exponents: 'Every man is running' and 'Nothing other than every man is running'; or 'only' can be taken improperly, so that there is an exclusion of any incompatible common term taken with a particular sign. In this case the proposition has these exponents:
'Every man is running' and 'Some ox is not running' and 'Some donkey is not running' and 'Some she-goat is not running', and so on for each common term. Thus, by means of such an exclusive proposition—as long as the exclusive expression is taken improperly—it is asserted that the predicate is truly predicated of the common term which occurs in the proposition with a universal sign and that it is not truly predicated of any other common term taken universally. Now this distinction never applies except when the exclusive expression is added to a common term taken universally.
With respect to the second improper sense of the exclusive On Exclusive Propositions expression there is another rule. It is this: when the exclusive expression is added to a term designating something which has several parts, then the proposition in question has to be distinguished. For either there can be an exclusion properly speaking, in which case it is asserted that the predicate belongs to the subject and is denied of everything of which the subject is denied; or there can be an exclusion speaking improperly, in which case what is excluded is anything of which neither the subject nor a term designating a part of the subject is truly predicated. This can be called the exclusion of any term which designates something extrinsic. Accordingly, the proposition 'Only Socrates is is white' must be distinguished. For the exclusive expression can be taken properly, in which case the proposition includes a contradiction. For in that case its exponents are 'Socrates is white' and 'Nothing other than Socrates is white'-—which are incompatible with one another, since they entail incompatible propositions. For this follows: 'Socrates is white; therefore some part of Socrates' body is white'. And this follows: 'Nothing other than Socrates is white; every part of Socrates is other than Socrates; therefore no part of Socrates' body is white'. The two conclusions are incompatible with one another. On the other hand, if the exclusive expression is taken improperly, so that there is an exclusion just of any term designating only something extrinsic to Socrates, then 'Only Socrates is white' is possible. For in that case nothing is asserted except that Socrates is white and that nothing extrinsic to Socrates is white. But these two assertions are compatible with one another, and they correspond to 'Socrates is white' and 'Nothing extrinsic to Socrates is white', which are the exponents of the proposition in question. Now this distinction never applies except when the exclusive expression is added to a term which designates some whole which has several parts—whether it is a whole properly speaking or in an extended sense.
Now someone might object that if this were so, then on both of these interpretations propositions such as the following would, without qualification, include a contradiction: 'Only a body is white', 'Only a man is white', 'Only fire produces warmth', 'Only a man is here inside' 'Only a quantum is in a place', and others
On Exclusive Propositions of this sort. For the surface is excluded by the first example, since it is not something intrinsic to a body because it is not a part of it. For the same reason the surface would be excluded by the second example. Heat would be excluded by the third example, all accidents by the fourth example, and points by the last example.
It should be responded that everything just said about the above examples—with the exception of the third—proceeds in Aristotle's opinion from a false conception, namely, that surfaces, lines, and points are things really distinct from bodies and substances. I have shown that this conception is contrary to Aristotle's view in the Categories.! As far as the third example is concerned, if one assumes that fire cannot produce warmth except by means of heat, then a different response must be given. For it should be maintained that, whether the exclusive expression is taken properly or in the improper sense under discussion, the proposition 'Only fire produces warmth' includes a contradiction. Hence, if this proposition ought to be salvaged, then the exclusive expression must. be taken in some sense other than its proper sense or the three improper senses mentioned above. Specifically, in this new sense the exclusive expression would exclude just those terms which designate neither something intrinsic nor a formally inhering accident.? Given this interpretation, it can be conceded that 'Only fire produces warmth' is possible. For in that case heat is not excluded, since it formally inheres in fire.
With respect to the third improper sense of the exclusive expression a third rule can be given: when the exclusive expression is added to a numerical term or its equivalent, or to a term connoting a number or unity, then the proposition in question has to be distinguished, since there can be either an exclusion properly speaking or an exclusion improperly speaking. In the first sense what is excluded is everything of which the subject is not truly predicated. In the second sense what is excluded is a plurality greater than that to which it is asserted that the predicate belongs. This can be called the exclusion of a greater number. Accordingly, the proposition 'Only four men are here inside' has to be distinguished. For assume that there are four men—and no On Exclusive Propositions more than four—here inside. In that case, if one makes the exclusion by taking the exclusive expression in its proper sense, then it is asserted that four men are here inside and that nothing other than four men is here inside. Consequently, it is asserted that no stones are here inside, and that no horses are here inside, and no donkeys. And it is also asserted that it is not the case that two men are here inside, since two men are other than four men.
On the other hand, if an exclusion of a greater number is being made, then it is asserted that four men are here inside and no more than four. In that case the exponents of the proposition are these: 'Four men are here inside' and 'It is not the case that there are more than four men here inside'. And this is true in the circumstances assumed above.
In this way one can solve the sophism 'Only one exists'. For if the exclusive expression is taken properly, then 'Only (what is) one exists' is true. For both of its exponents, namely, '(What is) one exists' and 'Nothing other than (what is) one exists', are true. The same holds for 'Only (what is) one animal is a man'.
On the other hand, if the exclusive expression is understood improperly in such a way that there is an exclusion of a greater number, then the proposition is false. For in that case its exponents are 'One thing exists' and 'It is not the case that more than one thing exists'. In the same way 'Only one animal is a man' has, in that case, the following exponents: 'One animal is a man' and 'It is not the case that more than one animal is a man'. The same holds for 'Only one of these exists', referring to two beings. For if the exclusive expression is taken properly, then the proposition is true. For in that case both exponents are true if there are not more than two beings, say God and an angel.
However, if the exclusive expression is taken improperly, then the proposition is false. For in that case it is asserted that one of the two things exists, but not both of them.
These are the senses, then, in which the exclusive expression can be taken improperly. And perhaps there are still other senses in which it can be taken improperly. But since they are not as widely used as the ones we have dealt with, I will leave them to the specialists.
Now that we have discussed the exclusive expression insofar On Exclusive Propositions as it is added to the subject, we should discuss it insofar as it is added to the predicate.
It should first be noted that in such a case it is also possible to understand the exclusive expression either properly or improperly. If it is taken properly, then it is asserted that the predicate is said of the subject and that everything of which the predicate is not truly predicated is denied of the subject. For example, by means of 'A man is only an animal' it is asserted that a man is an animal and that a man is not other than an animal. However, when the exclusive expression is taken improperly and in a transferred sense, then it is added to the verb, in which case it excludes from the subject every other verb which designates a distinct action or passion. For example, by means of 'A man only sees' it is asserted that a man is seeing and that he is not hearing or stamping his feet, etc. Thus, the proposition 'A man is only a running thing' must be distinguished as equivocal in the second mode. For the exclusive expression can be taken properly, in which case the two exponents are 'A man is a running thing' and 'A man is not other than a running thing'—and this is compatible with its being the case that a man is seeing and stamping his feet, and so on for the others. But if the exclusive expression is taken improperly, then the proposition is false. For in that case it is asserted that a man is running and not hearing and not seeing, etc.
A distinction just like this one can be drawn with respect to the following: 'A man is only white', 'Milk is only sweet', 'Fire is only hot', 'Earth is only cold', and so on. For if the exclusive expression is taken properly, then each of them is true. For in © that case these are the exponents: 'A man is white' and 'A man is not other than a white thing'; 'Milk is sweet' and 'Milk is not other than something sweet'; and so on for the others. On the other hand, if the exclusive expression is taken improperly, then all predicables are excluded which designate accidents distinct from that accident which is designated by the predicate. For example, by means of 'A man is only white' it is asserted that a man is white and that no predicable which designates an accident distinct from whiteness is predicated of a man.* Thus, it is asserted that a man is not hot or humid or thirsty or cold or lucid,
On Exclusive Propositions etc. And what has been said of this proposition should be uniformly said of the others.
With respect to the third principal point, namely, how the terms supposit in exclusive propositions, it should be noted that when the exclusive expression is added to the subject and that subject is taken without distribution, then if the subject is a common term, it has merely confused supposition. For as was said above,* merely confused supposition occurs when it is not possible to descend to the inferiors either by a disjunctive proposition or by a conjunctive proposition. But this does not follow:
'Only a man is running; therefore only this man is running or only that man is running', and so on for every other man: Nor does this follow: 'Only a man is running; therefore only this man js running and only that man is running', and so on for each man.
And so the subject term in such a proposition has merely confused supposition. But the predicate has confused and distributive supposition, since it is possible to descend to the inferiors by means of a conjunctive proposition. Hence, this is valid: 'Only a man is running; therefore only a man is this running thing', referring to any running thing whatsoever. For this follows: 'Only a man is running; therefore nothing other than a man is running', and further, 'therefore no running thing is other than a man', and further, 'therefore this running thing is not other than a man'.
And it is clear that if it is running, then it is something; therefore it is a man. Consequently, a man is this running thing; therefore only a man is this running thing. For when the predicate is a demonstrative pronoun or some equivalent, then there is a valid consequence from an indefinite proposition to an exclusive proposition with respect to that predicate.
Indeed, no matter what sort of term the predicate is, there is a valid consequence from an indefinite or particular proposition to an exclusive proposition. For this is a valid consequence: 'A man alone is risible; therefore only an animal is risible'. For this holds by reason of the following rule: 'There is a valid consequence from an inferior to a superior without distribution— whether that superior has merely confused or determinate supposition'. For example, this follows: 'Every man is a man; therefore every man is an animal'.
On Exclusive Propositions Second, it should be noted that when an exclusive proposition is negative, then the subject supposits just as it does in an affirmative exclusive—and the same holds for the predicate. For this follows: 'Only a substance is not an accident, therefore only a substance is not this accident'.® Third, we must deal with the supposition of the terms in an exclusive proposition in which the exclusive expression is added to the predicate. It should be said that the subject in such a proposition supposits just as it does in that proposition's non-exclusive counterpart. And the same holds for the predicate. The reason for this is that the same thing cannot be both truly affirmed and truly denied of the same thing. Therefore, an exclusive proposition always follows from its non-exclusive counterpart when the exclusive expression is added to the predicate. This should be understood to apply when both extremes of the proposition are in the nominative case—it is not universally true when one of the extremes is in an oblique case. In fact, if one of the extremes of the proposition is in an oblique case and if the exclusive expression is a determination of the predicate and not a determination of the composition, then the predicate has merely confused supposition. For assume that Socrates is seen by many men and by no animal other than a man. In that case the proposition 'Socrates is seen by a man alone' is true, since its exponents are true, namely, 'Socrates is seen by a man' and 'Socrates is seen by nothing other than a man'. And yet this does not follow: 'Socrates is seen by a man alone; therefore Socrates is seen by this man alone or by that man alone'. In fact, this does not even follow: 'Socrates is seen by a man alone; therefore Socrates is seen by that man'. And so the predicate has merely confused, rather than confused and distributive or determinate, supposition.
However, if the exclusive expression is a determination of the composition, then the predicate supposits just as it does in the proposition's non-exclusive counterpart. For example, in 'A man is only seen by a man', if 'only' is a determination of the composition, then the proposition has these exponents: 'A man is seen by a man' and 'A man is not other than a thing seen by a man'. From this it is clear that the terms do not supposit in the exclusive proposition in a way different from the way they supOn Exclusive Propositions posit in its non-exclusive counterpart. For this sort of exclusive proposition and its non-exclusive counterpart are always interchangeable. However, if the subject of an exclusive proposition in which the exclusive expression is added to the subject is taken with distribution, then the subject has confused and distributive supposition. For such a proposition, whether it is affirmative or negative, includes contradictories. Thus, I will say no more about this case at present.
Furthermore, it should be noted that all that has just been said should be understood to apply when the exclusive expression is taken properly. For when it is taken improperly, then not all the things just said are true. But which of those things do hold true and which do not will be clear with no difficulty to one who examines them carefully with the improper significations of the exclusive expression in mind. And I have already talked about these improper senses.
Finally, we should look at some rules dealing with exclusive expressions. One is that there is a valid consequence from an exclusive proposition to a universal proposition with the terms transposed, and conversely. For an exclusive proposition and the corresponding universal proposition with the terms transposed are always interchangeable. This rule should be understood to apply when both the non-exclusive counterpart of the proposition in question and the universal proposition with the terms transposed are convertible propositions, i.e. when each can be properly converted. Or, if the non-exclusive counterpart is a proposition which can always be converted—either with no change in the terms except for the transposition alone or with some other change as well—then the universal proposition just like it should be taken as the one with which the exclusive proposition in question is interchangeable. In what follows we will deal with these conversions and modes of converting.®
From these remarks and those which will be made later about conversions, it is clear that a consequence such as the following is not valid: 'Only what is necessary is necessarily true; therefore everything which is true is necessarily necessary'—even though this consequence is valid: 'Only what is necesary is true; therefore everything true is necessary'. Similatly, this does not follow:
On Exclusive Propositions 'Only a man was white; therefore every white thing was a man'.
And the same holds for similar propositions, which will be dealt with in their proper place below.
Another rule is that every exclusive proposition has two exponents: one affirmative and the other negative. Therefore, the opposite of an exclusive proposition has two causes of truth, since the opposite of either exponent is a cause of the truth of the negation of the exclusive proposition in question.
Another rule is that when the dictum of an exclusive proposition occurs with some mode which renders a proposition modal, then the exclusive proposition in question has to be distinguished.
For example, the proposition 'Only a man is Socrates is true' has to be distinguished." For 'only' can be uttered either continuously with the whole dictum '.
. a man is Socrates' or not continously with it. If it is not uttered continuously with it, i.e. if one says, 'Only "'A man is Socrates" is true', then the proposition is false.
For in that case it has the following sense: 'Only this proposition is true', referring to 'A man is Socrates'. On the other hand, if 'only' is uttered continuously with the whole dictum '... a man is Socrates', and if the parts of the dictum are connected,' then the proposition has this sense: 'That only a man is Socrates is true'—and this is equivalent to: 'This is true: "Only a man is
Socrates"''. Now if the parts of the dictum are not connected, then it is not asserted that 'Only a man is Socrates' is true.
Rather, it is asserted that 'Socrates', taken with the exclusive expression, is truly predicated of something contained under 'man'. Hence, the case is similar with respect both to these propositions and to others taken without an exclusive expression. (There is a variation, however, depending on whether or not the predicate is a singular term.) Hence, if 'only' is continuous with the whole dictum and if the parts of the dictum are disconnected, then 'Only a white thing is running is possible' is false.° For it is possible that something other than a white thing is running. If, on the other hand, the parts of the dictum are connected, then the proposition is true. For in that case it is asserted that this proposition is possible: 'Only a white thing is running'. But by means of the other proposition it was asserted that no proposition is possible in which 'running' is predicated of a pronoun referring to something which is not white—which is not true.