(Appeared in vol. 5 of Logical Analysis and History of Philosophy in 2002)
The modest aim of this paper is to reconcile several, seemingly conflicting claims Aquinas makes in various contexts concerning the semantic function of the copula. But this paper also targets an immodest aim. That immodest aim is to present Aquinas’ theory of the copula as a coherent part of his overall theory of the analogy of being. Given the all-encompassing character of Aquinas’s theory of the analogy of being, fully accomplishing that immodest aim cannot be the task of a brief paper. Nevertheless, as we shall see, the modest aim cannot properly be achieved without at least indicating how the immodest aim can be achieved. But first of all, let us see what causes the problem.
… ‘being’ is used in many senses. For in one sense ‘being’ is used as it is divided by the ten genera. And in this sense ‘being’ signifies something existing in the nature of things, whether it is a substance, such as a man, or an accident, such as a color. In another sense ‘being’ signifies the truth of a proposition; as when it is said that an affirmation is true when it signifies to be what is, and a negation is true when it signifies not to be what is not; and this ‘being’ signifies a composition produced by the judgment-forming intellect. So whatever is said to be a being in the first sense is a being also in the second sense: for whatever has natural existence in the nature of things can be signified to be by an affirmative proposition, e.g., when we say that a color is, or a man is. But not everything which is a being in the second sense is a being also in the first sense, for of a privation, such as blindness, we can form an affirmative proposition, by saying: ‘Blindness is’; but blindness is not something in the nature of things, but it is rather a removal of a being, and so even privations and negations are said to be beings in the second sense, but not in the first. And being is predicated in different manners according to these two senses: for taken in the first sense it is a substantial predicate and pertains to the question ‘What is it?’, but taken in the second sense it is an accidental predicate, ... and pertains to the question ‘Is there (such and such a thing)?’.[1]
We have to know that this second mode is related to the first as effect to cause. For it is from the fact that something exists in the nature of things that the truth or falsity of a proposition follows, which the intellect signifies by the verb ‘is’, as it is the verbal copula. But, since some things which in themselves are not beings the intellect considers as some sort of beings, such as negations and the like, sometimes ‘is’ is said of something in this second sense, but not in the first. For it is said that blindness is in the second sense because the proposition is true by which something is said to be blind, but this is not said to be true in the first sense. For blindness does not have real being, but is rather a privation of some being.[2]
Now, let us suppose that we understand that the copula of a categorical proposition indicates the composition of the subject with the predicate, and thus it somehow expresses truth or falsity – after all, it is by means of this copula that we express that something is or is not the case.[3]
But then how should we understand, for example, (1) that it is by means of the sense of the copula of an affirmative categorical proposition that we can express the way blindness, as opposed to sight, exists, (2) that it is the sense of such a copula that answers the question whether there is such and such a thing, and (3) that it is in the sense of such a copula that ‘being’ is an accidental predicate of things? Even if we accept that existence may in some sense be treated as a (first-order) predicate, it still appears to be nonsensical to claim that the copula, which merely joins the predicate to the subject, expresses the existence of anything.
Despite appearances to the contrary, we can make good
sense of
This theory can easily be formulated in one sentence: a predicate is true of a thing if and only if what the predicate signifies in respect of the thing actually exists, or, in other words, the thing is actual in respect of what the predicate signifies in it.[5]
Understood in this theoretical context, then, the copula of an affirmative categorical proposition can clearly be said to express somehow the existence of something, namely, the existence of what is signified by the predicate in the suppositum or supposita (i.e., the referent or referents)[6] of the subject, as required by the quantity of the proposition. (To simplify matters, in the subsequent discussion I will consider only singular propositions; quantified propositions would only add technical complications that are irrelevant from our present theoretical point of view.)[7]
Consider, for example, the proposition ‘Socrates is wise’. The copula of this proposition somehow expresses the existence of Socrates’s wisdom, since the proposition is true if and only if Socrates’s wisdom exists. Likewise, the proposition ‘Homer is blind’ is true if and only if Homer’s blindness exists, and the proposition ‘Socrates is a man’ is true if and only if Socrates’s humanity exists, and so on for all similar cases.
Now, even if in this way we may say that the copula somehow expresses or indicates the existence of what is signified by the predicate in the suppositum of the subject, there is still an apparent difficulty. In view of what Thomas said about the difference between the way privations exist and the way positive qualities exist, the copula of the corresponding propositions cannot directly signify the existence of the significata of their predicates. For according to Thomas, the copula always signifies existence in the same sense, namely, in the sense in which for example Homer’s blindness can be said to exist.
So our problem now becomes the following: how can Aquinas state, on the one hand, that the copula somehow indicates the being of the significata of predicates in several senses, and, on the other hand, that the copula always signifies being in one and the same sense?
First of all, let us see why Thomas would claim that the significata of various predicates can be said to be in several senses. In his commentary on the Metaphysics, he writes:
…. being cannot be narrowed down to something definite in the
way in which a genus is narrowed down to a species by means of differences. For since a difference does not participate in a genus, it lies outside
the essence of a genus. But there could be nothing outside the essence
of being which could constitute a particular species of being by adding to
being; for what is outside of being is nothing, and this cannot be a difference.
Hence in book III of this work (see n. 433) the Philosopher proved that being
cannot be a genus. Being must then be narrowed down to diverse genera on the
basis of a different mode of predication, which flows from a different mode of
being; for ‘being [esse] is signified,’ i.e., something is signified to
be, ‘in just as many ways as something is said to be a being [ens dicitur]’,
that is, in as many ways as something is predicated. And for this reason the
first divisions of being are called predicaments [i.e., categories], because
they are distinguished on the basis of different ways of predicating.
Therefore, since some predicates signify what [something is], i.e.,
substance; others of what kind [something is, i.e., quality]; and
yet others how much [something is, i.e., quantity]; and so on; it is
necessary that for each mode of predication, being should signify the same
[mode of being]. For example, when it is said that a man is an animal, ‘is’
signifies [the mode of being of] substance; and when it is said that a man is
white, is signifies [the mode of being of] quality; and so on.[8]
The main point of this passage is that the division of being into the categories is not like the division of a genus into its species by means of specific differences. This contrast is made even clearer in the following passage:
... there are two ways in which
something common can be divided into those that are under it, just as there are
two ways in which something is common. For there is the
division of a univocal [term] into its species by differences by which the
nature of the genus is equally participated in the species, as animal is
divided into man and horse, and the like. Another division is that of
something common by analogy, which is predicated according to its perfect
concept [ratio] of one of those that divide it, and of the other[s]
imperfectly and with qualification [secundum quid], as being is divided
into substance and accident, and into being in actuality and in potentiality,
and this sort of division is as it were midway between [the division of
something] equivocal and [something] univocal.[9]
So, Aquinas’s idea seems to be the following. Every predication we make is a predication of being, but, depending on the predicate we use, it is a predication of being with some qualification. This qualification is expressed by the predicate, which determines the relevant sense of being in which the significate of the predicate in the suppositum of the subject can be said to be. But what is this supposed to mean?
Let us take, for example, the following two propositions:
(1) Socrates is sighted
(2) Socrates is blind
According to the inherence theory of predication, these propositions are true if and only if the following are also true:
(1’) Socrates’ sight is (exists)
(2’) Socrates’ blindness is (exists)
According to Aquinas, however, sight is a real being in the category of quality, whereas its lack is only a privation, a being of reason. Thus, the senses of being expressed by the predicate of these propositions must be different, insofar as they are true. But what does this have to do with the idea that the former propositions express somehow differently qualified predications of being? The answer can quite clearly be indicated if we consider also the following two propositions:
(1’’) Socrates is with respect to his sight
(2’’) Socrates is with respect to his blindness
In these two propositions the sense of the predicate ‘is’ is explicitly qualified by the addition of the significata of the predicates of (1) and (2) in the suppositum of their subject, namely, Socrates’s sight, and his blindness, respectively. But then we are certainly entitled to claim that the senses of being thus qualified are exactly the senses in which ‘is’ (or ‘exists’) can be predicated of these significata in (1’) and (2’). So in this way it is clear that regarding (1) and (2) as expressing the qualified predications of being explicated by (1’’) and (2’’) also allows us to regard (1’) and (2’) as predicating being of their subjects precisely in the senses thus qualified, where these subjects are nothing but the significata of the predicates of (1) and (2). In general, on this basis we can claim that any ordinary predication of a common term is but a qualified predication of being, in which the significate of the common term in the suppositum of the subject specifies the sense in which that significate can be said to exist.[10]
Indeed, this claim seems to be in perfect agreement with what Thomas says in his commentary on Aristotle’s On Interpretation, where he explicitly deals with the semantic function of the copula:
The reason why [Aristotle] says that the verb ‘is’ consignifies
composition is that it does not principally signify composition, but
secondarily; for it primarily signifies what occurs to the mind in the way of
actuality absolutely: for ‘is’, uttered absolutely, signifies being in act, and
hence it signifies as a verb. But since actuality, which the verb ‘is’
principally signifies, is in general the actuality of every form, whether it is
a substantial or an accidental actuality, this is why when we want to signify
any form or act to actually inhere [inesse] in
a subject, we signify this by means of the verb ‘is’, either absolutely, or
with some qualification: absolutely, in the present tense, and with
qualification in the other tenses. And thus the verb ‘is’ secondarily signifies
composition.[11]
Now even if in this passage Thomas is mainly concerned with the qualifications that the various tenses can add to the primary meaning of the verb ‘is’, in other contexts he clearly distinguishes the qualifications imposed upon the absolute sense of this verb by the accidental forms signified by predicates from the categories of accidents:
… there are two kinds of being [esse],
namely the essential, or substantial being of the thing, as for a man to be [hominem
esse], and this is just to be, without any qualification. The other kind of
being is accidental being, such as for a man to be white [hominem esse album],
and this is [not just to be, but] to be something [esse aliquid].[12]
So, it seems that according to Aquinas’s view, the copula is not just a merely syncategorematic particle with the sole function of joining the predicate to the subject, but it retains the primary signification of the verb ‘is’, which predicated in itself signifies the actual existence of the thing of which it is predicated. Indeed, according to the previous passage from the On Interpretation-commentary, this is precisely the reason why we use the verb ‘is’, rather than any other verb, also in the function of the copula, to assert in general the actuality of the suppositum of the subject in respect of what is signified in it by the predicate. But then, when it has the function of joining another predicate to the subject, the act of existence the verb ‘is’ signifies is not the absolute existence of the suppositum of the subject, but the qualified existence of the form signified by the predicate, namely, the inherence of this form in the suppositum of the subject, which renders the suppositum actual in respect of this form. And so, since the forms signified by the predicate may be of various sorts, namely, substantial or accidental, or even not really existing forms but beings of reason, such as privations,[13] the existence thus signified will be existence in various senses demanded by the nature of the forms signified.[14]
But then, again, the claim that the copula signifies the existence of these significata in the various senses demanded by the nature of these significata seems to be entirely incompatible with the other claim that the ‘is’ occurring in these predications is but the ordinary copula, which uniformly has the same sense which is expressed for instance by the predicate of (2’), i.e., the sense in which beings of reason can be said to exist.
At this point, however, we should consider just what it
is that the copula joins to the subject when it occurs in a proposition. As
(1’’’) Socrates is with respect to sight
(2’’’) Socrates is with respect to blindness
Now it is crucial here to notice the difference between the qualifications imposed upon the sense of the verb ‘is’ in these predications and those expressed by (1’’) and (2’’), respectively. Whereas in (1’’) and (2’’) the qualifier phrases referred to the ultimate significata of the predicates ‘sighted’ and ‘blind’, here the qualifier phrases refer to the immediate significata of the same. Therefore, since the natures of those ultimate significata are different, the first being a positive quality and the second being a privation of that quality (i.e., a being of reason), no wonder they differently qualify the primary sense of being expressed by the verb ‘is’, yielding different secondary senses for this verb. The first qualifies the sense of ‘is’ so as to yield the secondary sense in which it signifies the act of being of a really inherent accident, while the second yields the sense in which the same verb signifies the being of a being of reason. On the other hand, since not only privations, but all natures according to their absolute consideration have the same ontological condition, namely, that their actuality depends on the activity of the human mind along with some foundation in reality, it is equally not surprising that the immediate significata of all predicates impose the same sort of qualification on the primary sense of being. Therefore, the sense of ‘is’ as qualified by ‘with respect to sight’ is the same as the sense of ‘is’ as qualified by ‘with respect to this blindness’, and by ‘with respect to blindness’, but different from the sense of ‘is’ as qualified by ‘with respect to this sight’.[17]
However, if this is true, then it is not an absurd claim after all that the copula expresses existence in the same sense in which a privation, a being of reason can be said to be. But then, what is it that it expresses the existence of? Well, the obvious answer is that it is the complex being of reason it constitutes by joining the semantic values of the subject and the predicate, which 12th and 13th century logicians often referred to as the enuntiabile, signified by a proposition as a whole.[18] Although Aquinas nowhere discusses the issue of the total significate of propositions explicitly, his remarks on the relationship between propositional composition and beings of reason in his commentary on the sixth book of the Metaphysics quite clearly indicate that he may well have had something like this in mind when he lumped all sorts of beings of reason together with what he speaks of as ens ut verum, which is signified by the copula.[19]
In any case, if we adopt this interpretation, we are
able to make coherent sense of all the scattered remarks Thomas makes in
various contexts concerning the copula. So, it is this interpretation that I am
going to provide in the subsequent summary reconstruction of what I take to be
a coherent account of
All in all, Aquinas’s theory of the copula, as a coherent part of his overall theory of the analogy of being, can be summarized in the following points:
(1) The verb ‘is’ in its primary sense signifies the existence (esse) of primary beings, that is, primary substances. Thus, a primary substance is if and only if the act of being signified in it by the verb ‘is’ in this sense is actual. Of any other type of entity, this verb is false in this sense.
(2) However, the same verb is truly applicable to other types of entities in several secondary, derivative senses. It is applicable in a secondary sense to accidents, that is, to individualized significata of predicates in the nine accidental categories distinguished by Aristotle. Everything that can be said to be either in the primary sense or in this secondary sense is called a real being, to be distinguished from mere beings of reason.
(3) The same verb is also applicable in another secondary sense to beings of reason. The difference between real beings and mere beings of reason is that real beings exist apart from any activity of the human mind, whereas beings of reason exist only as objects of some activity of the human mind with some foundation in reality. (Having a foundation in reality, i.e., the real existence or non-existence of something else, is what distinguishes beings of reason from mere figments, i.e., such objects of mental activities that do not have any foundation in reality.)[20]
(4) The several secondary senses of being can be obtained from the primary sense by adding appropriate qualifications to ‘is’ in its primary sense. Indeed this is the point of Aquinas’s drawing the distinction between substantial being and accidental being (as well as other secondary senses of being, such as being of reason, being in potency) in terms of esse simpliciter vs. esse secundum quid.[21]
(5) The secondary sense in which a really inherent accident is can be obtained by adding to the verb ‘is’ predicated of a substance a qualification referring to the significate of an accidental predicate in that substance. The reason for this is that for an accident to be is for the substance to be [actual] in respect of that accident.
(6) Likewise, the secondary sense in which a being of reason is can be obtained by adding to the verb ‘is’ predicated of a substance a qualification referring to the being of reason in question.
(7) The copula has two semantic functions: (a) to signify the existence of the significate of the predicate in the suppositum of the subject, in the sense determined by the nature of this significate, which is “the foundation in reality” of the existence of the enuntiabile signified by the proposition as a whole; (b) to consignify composition and truth by signifying the existence of the enuntiabile.
(8) The existence of the enuntiabile is signified by the copula in the sense of the existence of a being of reason. Since this sense can also be obtained by adding a qualification to the verb ‘is’ that refers to the nature signified absolutely by the predicate of the corresponding categorical proposition, we can assign a unique signification to ‘is’ in the sense in which it asserts the existence of any being of reason as its absolute predicate, and in the sense in which it asserts the existence of an enuntiabile as the copula of the proposition that signifies this enuntiabile. Since, therefore, it is the existence of the enuntiabile in this sense that constitutes the truth of the proposition, we can see why Aquinas is justified in referring to this sense also as ens ut verum.[22]
In this Appendix I provide a brief sketch illustrating how the foregoing points can be given precise meaning in a model theoretical semantics for unquantified categorical sentences. Since the sole purpose of this semantic sketch is to provide a reconstruction of Aquinas theory of the copula as a part of his logical theory of the notion of being, the language of the theory will be very restricted. However, the generalization of the theory on the basis of this illustration should be pretty obvious.[23]
The primitive symbols of the language are going to be the terms ‘S’ and ‘P’, the indexed verb ‘is1’, and the symbol ‘<’, which will function as “the qualifier”, representing the syncategorematic concept expressed by the English phrase ‘with respect to’. These are going to be regarded as semantically primitive, insofar as their values are going to be determined in terms of free-choice functions.
The derivative symbols of the language are differently indexed variants of the verb ‘isx’ and the predicate term ‘Px’. Intuitively, the different indexes on the verb indicate its different senses, all distinct from the primary sense indicated by ‘is1’. The different indexes on the predicate serve as the “category index” of the predicate, indicating what sense of the verb the significate of the predicate determines when it is added as a qualification of the verb in the primary sense. The abstract significate of a predicate ‘P’ will be referred to by ‘[P]’, whereas the significate of the same in a suppositum of the subject ‘S’ will be referred to by ‘S[P]’. (So , for instance, if ‘S’ is ‘man’ and ‘P’ is ‘wise’, then ‘[P]’ refers to what ‘wisdom’ refers to, the universal signification of ‘wise’, and ‘S[P]’ will refer to what ‘a man’s wisdom’ refers to, namely, the individualized significate of ‘wise’ in a man.
The complex expressions of the language are sentences of the following form: ‘S isx’ (where x may stand for 1, [1], 1.5, and 2; the intuitive interpretation of these different index-values will be provided in the description of the semantics, in clauses (6) and (9) below), ‘S is1<[Px]’, ‘S is1<S[Px]’, ‘S[Px] isx’, ‘S is2 P’, and ‘[S is2 P]’. (Using the previous interpretations of ‘S’ and ‘P’, these sentences would represent the following natural language sentences: ‘A man is’, ‘A man is with respect to wisdom’, ‘A man is with respect to his wisdom’, ‘A man’s wisdom is’, ‘A man is wise’, and ‘That a man is wise’ respectively.)
(1) If P is a common term, then SGT(P)(u)(t) Î W!, in a model M = <W, T, A, SB, SGT, 0>, where W ¹ Æ, T ¹ Æ, t Î T, A(t) Í W, SB Í W, u Î SB!, 0 Ï W, SB! := SBÈ{0}, W! := WÈ{0}, and SGT(P)(0)(t) = 0; where W is the domain of discourse, comprising both actual and non-actual individuals, A(t) is the set of actual individuals at time t, SB is the set of primary substances, SGT is the signification function, and 0 is a zero-entity, a technical device used to indicate the case when a semantic function for a certain argument lacks a value from W. Note that here and henceforth iterated parentheses after functional expressions indicate that the application of the corresponding function to its argument yields another function that is applied to its own argument, which in turn may yield a further function, etc. In general, if ‘f’ and ‘g’ are function-names, and ‘x’ and ‘y’ are variables ranging over appropriate sets of arguments, then f(x)(y) = g(y) if and only if f(x) = g.
(2) If S is a common term occurring as the subject of a proposition, then SUP(S)(t) Î {u: SGT(S)(u)(t) Î A(t)}, if this set is not empty, otherwise SUP(S)(t) = 0, where SUP(S)(t) is a suppositum of S at time t (which is the time connoted by the copula of the proposition in which S occurs). Note that SUP is a free-choice function working in a model just as ordinary value-assignments of variables of standard quantification theory do, with the only difference that SUP assigns those individuals to a common term of which the term is true (i.e., in which the significate of the common term is actual) at a given time t, provided it is true of any, otherwise SUP assigns to it a zero-entity, which renders affirmations about it false.[24]
(3) SGT(‘is1’) (u) (t) Î W!
This clause defines the signification of ‘is’ being used in the primary sense, as that of an ordinary predicate. I inserted spaces between the main arguments for ease of reading. This will come in handy below, where we’ll have more complex arguments.
(4) SGT(‘is1’) (u) (t)Î A(t) iff u Î A(t), where u Î SB
This clause adds a stipulation that renders ‘is1’ a distinguished logical predicate, one that is true of every primary substance that is actual at a time t. In fact, we may also stipulate that for anything that is not a primary substance (i.e., if u Ï SB), SGT(‘is1’) (u) (t) = 0.
(5)
SGT(<) (SGT(‘is1’)) ((SGT(Px)(u)(t)) (u) (t) Î
W!
This clause defines the significate of the “qualifier” (the phrase ‘with respect to’) qualifying the primary signification of ‘is’ in respect of the significate of a qualifying predicate in respect of u and t, and in respect of u, and in respect of t.
(6)
SGT(<) (SGT(‘is1’)) ((SGT(Px)) (u) (t) Î
W!
This clause defines the significate of the “qualifier” qualifying the primary signification of ‘is’, in respect of the signification of a qualifying predicate (i.e., the function that assigns the significata of this predicate in respect of u and t), and in respect of u, and in respect of t. The important difference between (5) and (6) is that the same qualifying predicate may have different effects depending on whether it figures in a construction with the former or with the latter semantic value. The intuitive difference between the two will be illustrated later. The superscript x on the qualifying predicate, its “category index”, indicates the sense in which its significata, if they are actual, exist, namely, whether these significata are real inherent substantial or accidental forms (in which case the index is [1] and 1.5, respectively), or just mere beings of reason (in which case the index is 2, in accordance with the notation of Klima (1996), changing the awkward ½ to 1.5, which also has technical advantages besides getting rid of the awkwardness).
(7)
SGT(<)
(SGT(‘is1’)) ((SGT(Px)(u)(t)) (u) (t) Î
A(t) iff SGT(Px)(u)(t) Î A(t)
(8)
SGT(<) (SGT(‘is1’)) ((SGT(Px)) (u) (t) Î
A(t) iff SGT(Px)(u)(t) Î A(t)
These two clauses only add the further stipulation that the actuality of the significata of the qualifier in respect of its relevant arguments will depend on the actuality of the significata of the qualifying predicate in respect of its relevant arguments.
(9)
SGT(‘isx’) ((SGT(Px)(u)(t)) (t)
= SGT(<) (SGT(‘is1’)) ((SGT(Px)(u)(t)) (u) (t)
Note that here the signification of ‘is’, as used in a derivative sense in which it is applicable to the significate of a predicate P, is defined in terms of the signification of the qualifier. An example illustrating the point of this clause is the following: consider ‘Plato’s wisdom isx’ and ‘Plato is1 with respect to his wisdomx’. (The importance of adding ‘his’ here will be explained later.) In these two sentences ‘isx’ in respect of Plato’s wisdom (that is, the significate of ‘wise’ in Plato at t) and ‘is1 with respect to his wisdomx’ in respect of Plato signify the same thing at the same time. We can refer to this significate as the being of Plato’s wisdom. Indeed, since ‘wise’ is a term signifying a real accident, its “category index” would be 1.5, that is, we should rather have ‘Plato’s wisdom is1.5’ and ‘Plato is1 with respect to his wisdom1.5’, which shows that qualifying ‘is1’ with ‘his wisdom1.5’ yields that sense of ‘is’ in which it is truly predicable of really inherent accidents. On the other hand, with ‘blind’ (or rather the corresponding ‘blindness’) we would have a different index (namely, 2), and thus a different sense of ‘is’ (namely, the ens rationis sense), but the same formal structure. Furthermore, we would have the same structure, but again a different sense with ‘man’ (or any other substantial predicate, or rather their corresponding abstract forms, in which case the index would be [1], according to the notation of Klima (1996)). The particular case of the ens rationis sense is spelled out in (10) and the corresponding (15) below. Note that the difference between (9) and (10) consists merely in replacing the variable “category index” with the particular value 2, indicating the secondary sense of ‘is’ and the type of qualifying predicate which determines that sense:
(10)
SGT(‘is2’) (SGT(P2)(u)(t)) (t) = SGT(<) (SGT(‘is1’))
((SGT(P2)(u)(t)) (u) (t)
The next clause shows how the signification of the copula can be derived from the signification of ‘is1’ (that is, ‘is’ as used in the primary sense) by means of adding the appropriate qualification, and how this can be regarded as the same as that of ‘is2’. (10) above already defined the secondary sense of ‘is’ (that is the signification of ‘is2’) for the significata of such predicates that signify beings of reason. In the next step the same sense is shown to cover also the copulative usage of ‘is’ by simply defining the signification of ‘is2’ for the significations (or, in another terminology, immediate significata) of all sorts of predicates. The technical trick here is that the first argument of this function is not the significate of P in respect of u at t (namely, SGT(P)(u)(t)), but the signification function of P (namely, SGT(P)), and then the second argument is u, and the third is t. This is what allows us to define for this argument a value that may be different from, but may also be the same as what it would yield for SGT(P)(u)(t) on the basis of (7) and (9). The philosophical significance of this move is that the signification of P (namely, SGT(P), the immediate significate of P), as opposed to the significate of P in respect of u at t (namely, SGT(P)(u)(t), or the ultimate significate of P in u at t), is something that abstracts from both subject and time, that is, the individuating conditions of what is signified by P. Hence what we have here is something that is signified by P in its absolute consideration, precisely what Thomas says is the appropriate semantic value of the predicate of a categorical proposition. Therefore, no wonder that the relevant sense of ‘is’ according to which we can attribute being to this in a judgment is the ens rationis sense.
(11)
SGT(‘is2’) (SGT(Px)) (u) (t) = SGT(<) (SGT(‘is1’))
((SGT(Px)) (u) (t)
An example illustrating how this clause is supposed to work is the following. Take ‘Plato is2 wise’ and ‘Plato is1 with respect to wisdom’. Note the important difference from the previous example! Here we are not considering ‘Plato is1 with respect to his wisdom’, but in abstraction from the subject: ‘Plato is1 with respect to wisdom’. What (11) states is that in ‘Plato is wise’ and in ‘Plato is with respect to wisdom’ the significate of ‘is’ with respect to the signification of ‘wise’ (considered absolutely) in Plato at t is the same as the significate of the qualifier in the signification of ‘is1’ with respect to the signification of ‘wise’ in Plato at t. But this latter, in turn, will be identified below in (13) as the significate of the qualified predicate ‘is1 with respect to wisdom’ (NB not: ‘with respect to his wisdom) in Plato at the same time. Thus, the effect of (10) and (11) together is that we have a unique signification of ‘is2’, which is defined both for the significata of predicates that signify entia rationis, such as privations, in respect of their subject, and for the significations of any predicates, considered in abstraction from their subjects. But it is precisely as defined for these significations that ‘is2’ functions as the copula of propositions, in which these predicates figure with their significations considered in abstraction from their subjects, and are applied to the supposita of the subject term of the proposition in the act of composition (cf. (16) below).
(12)
SGT(‘S isx’)(SUP)(t) = SGT(‘isx’)(SUP(S)(t))(t)
This clause provides the significata of the predication of ‘is’ as an absolute predicate, in any sense of ‘is’, of any subject, with respect to the supposita of the subject (according to the given assignment of supposita) and at a given time t. Note that this is the significate of the whole proposition ‘S isx’, which is here being identified with the significate of the predicate in the suppositum of the subject (according to the given assignment of supposita provided by the SUP function). Perhaps Aquinas would not agree with this identification, but rather he would say that the proposition as a whole signifies an enuntiabile, which is always a being in the secondary sense, regardless of what sort of being the significate of the predicate is. I can easily accommodate this point, however, by saying that Aquinas’s putative claim should be interpreted as concerning fully expounded subject-predicate propositions, in this case ‘S is2 a beingx’, and then I’d have the significate of this proposition as a being in the secondary sense in accordance with (14) below, and yet the predicate can signify being in the supposita of the subject in any of the analogical senses of ‘being’. But I will not pursue this matter here. The only semantically important thing in this regard is that if we assign significata to whole propositions, then we can have a unique clause assigning the truth conditions of any proposition whatsoever in the following form: p is true at time t iff for some SUP, SGT(p)(SUP)(t) Î A(t), that is to say, p is true at a given time t if and only if its significate with respect to some assignment of its supposita at time t is actual at t. But then again, we are not concerned here with the truth conditions of propositions in general, but with deriving the various analogical senses of being from the primary sense by means of the appropriate qualifications, so that among these derivative senses we shall also find the sense of the copula expressing the ens rationis sense of being.
(13) SGT(‘S is1<[Px]’)(SUP)(t) = SGT(<) (SGT(‘is1’)) ((SGT(Px)) (SUP(S)(t)) (t)
This clause determines the significata of the predication of ‘is1’ as explicitly qualified with the addition of the abstract form of any sort of qualifying predicate. Since this qualification concerns what is signified by the predicate in its absolute consideration, these significata are determined in accordance with (6) above. But this, along with (11) entails that SGT(‘S is1<[Px]’)(SUP)(t) = SGT(‘is2’) (SGT(Px)) (SUP(S)(t)) (t), and this along with (16) below entails that this qualification is precisely what yields the ens rationis sense, which is also expressed by the copula of ‘S is2 P’. (So ‘is’ in ‘Plato is wise’ and ‘is with respect to wisdom’ in ‘Plato is with respect to wisdom’ signify the same.)
(14)
SGT(‘S[Px] isx’)(SUP)(t) =
SGT(<) (SGT(‘is1’)) (SGT(Px) (SUP(S)(t)) (t))
(SUP(S)(t)) (t)
This clause assigns the significata of ‘is’ in any of its analogical senses as an absolute predicate of the significate of a predicate P in a suppositum of the term S (and this significate is what is supposited for by the term ‘S[Px]’, if this significate is actual, otherwise SUP(‘S[Px]’) = 0). As can be seen, this significate is determined in accordance with (5) above. Thus, any such predications are analyzed as containing ‘is’ in the same sense as is expressed by the predication of ‘is1’ qualified by the significate of the qualifying predicate in the suppositum of the subject. Now, let us express such a qualified predication of ‘is1’ as follows: ‘S is1<S[Px]’. (Note the difference here in the qualifying term: it is not only [Px], say ‘wisdom’, but S[Px], say, ‘Plato’s wisdom’, provided S = ‘Plato’, that is to say, if our sentence is: ‘Plato is wise with respect to Plato’s wisdom’.) Then we can say that SGT(‘S is1<S[Px]’)(SUP)(t) = SGT(<) (SGT(‘is1’)) (SGT(Px) (SUP(S)(t)) (t)) (SUP(S)(t)) (t); whence it follows that SGT(‘S[Px] isx’)(SUP)(t) = SGT(‘S is1<S[Px]’)(SUP)(t). Furthermore, in accordance with (9), it also follows that SGT(‘S is1<S[Px]’)(SUP)(t) = SGT(‘isx’) (SGT(Px) (SUP(S)(t)) (t)) (t) which is precisely what we want to say, namely, that for example in ‘Plato is1 with respect to Plato’s wisdom’ the complex qualified predicate signifies the same in respect of Plato as ‘is1.5’ signifies in respect of Plato’s wisdom in ‘Plato’s wisdom is1.5’. (Note that along with (14) I also assume here the following: SGT(‘is1<S[Px]’) (SUP(S)(t)) (t) = SGT(<) (SGT(‘is1’)) (SGT(Px) (SUP(S)(t)) (t)) (SUP(S)(t)) (t).)
(15) SGT(‘S is1<S[P2]’)(SUP)(t) = SGT(‘is2’) (SGT(P2)(SUP(S)(t))(t)) (t)
This clause identifies the significate of ‘is1’ qualified by a predicate which signifies some ens rationis with what is signified by the secondary sense of ‘is’ in the significate of this predicate in what is supposited for by the subject at time t, at time t. Example: ‘Socrates is1 with respect to Socrates’s blindness’ and ‘Socrates’s blindness is2’.
(16) SGT(‘S is2 P’)(SUP)(t) = SGT(‘is2’) (SGT(P)) (SUP(S)(t)) (t)
This clause determines the significate of a categorical proposition as the significate of the secondary sense of ‘is’, which is its copula, in respect of the signification of the predicate, and in respect of a suppositum of the subject at a certain time, in perfect accordance with Aquinas’s claim that the predicate terms of categoricals signify whatever they signify in their “absolute consideration”, provided we are allowed to identify this as the signification function, which abstracts from its arguments, the individuals and times which individuate its values, namely, the significata of this predicate in the individuals at given times.
(17) SGT(‘[S is2 P]’)(SUP)(t) = SUP(‘[S is2 P]’)(t) = SGT(‘S is2 P’)(SUP)(t)
Finally, this clause identifies the significatum and suppositum of the that-clause corresponding to a proposition, of the sentential nominalization whereby we can refer to the significate of the proposition. It is the actuality of this significate that constitutes the truth of the proposition. Therefore, we may also say that ‘S is2 P’ is true iff ‘[S is2 P] is2’ is true, which is precisely why ‘is2’ is what expresses being in the sense referred to by Aquinas as ens ut verum.
Aristotle: 1962, On Interpretation: Commentary by St. Thomas and Cajetan, tr. J. T. Oesterle, Marquette University Press, Milwaukeee, Wisconsin
Ashworth, E. J.: 1978, The Tradition of Mediaeval Logic and
Speculative Grammar,
Abaelard, P.: 1956, Dialectica, ed.
L.M. de Rijk, Van Gorcum,
Assen
Alamannus, C.: 1888, Summa
Philosophiae, P. Lethielleux,
Paris
Aquinas, T.: 1980, Opera Omnia, Frommann-Holzboog, Stuttgart-Bad Cannstatt
Cajetan, T. de Vio: 1590, “Super Librum De Ente et Essentia Sancti Thomae Aquinatis”,
in: Opuscula Omnia, Typis
Comini Venturae, Bergomi
Cajetan, T. de Vio: 1964, Commentary
on Being and Essence, transl. L.J. Kendzierski, F.C. Wade, Marquette Univ. Press., Milwaukee, Wis.
Cajetan, Thomas de Vio: 1939, Scripta Philosophica: Commentaria in Praedicamenta Aristotelis, ed. M. H. Laurent, Angelicum, Romae
Henry, D.P.: 1972, Medieval Logic and Metaphysics,
Hutchinson, London
Klima, G.: 1988, Ars Artium:
Essays in Philosophical Semantics, Mediaeval and Modern,
Klima, G.: 1990, “On Being and Essence in St. Thomas Aquinas’s Metaphysics and Philosophy of Science” in: Knuuttila et al. (1990) pp. 210-221, and in Klima 1988 pp. 150-164.
Klima, G.-Sandu, G.: 1990, “Numerical Quantifiers in Game-Theoretical Semantics”, Theoria, 56, pp. 173-192.
Klima, G.: 1993, “The Changing Role of Entia Rationis in Mediaeval Semantics and Ontology”, Synthese 96(1993), No. 1, pp. 25-59
Klima, G.: 1996 “The Semantic Principles Underlying Saint Thomas Aquinas’s Metaphysics of Being”, Medieval Philosophy and Theology, 5(1996), pp. 87-141.
Klima, G.: 2000, “Aquinas on One and Many”, Documenti e Studi sulla Tradizione
Filosofica Medievale (Società Internazionale per lo Studio del Medioevo Latino),
11(2000), pp. 195-215.
Klima, G.: 2001, “Existence and Reference in Medieval Logic”, in: A. Hieke and E. Morscher (eds.) New Essays in Free Logic, 2001, Kluwer Academic Publishers, Dordrecht, 167–196.
Knuuttila, S. and Hintikka, J. (eds.): 1986, The
Logic of Being, D. Reidel,
Knuuttila, S. and Työrinoja, R. and Ebbesen, S. (eds.): 1990, Knowledge
and the Sciences in Medieval Philosophy: Proceedings of the Eighth
International Congress of Mediaeval Philosophy, (S.I.E.P.M.), Publications
of Luther-Agricola Society Series B 19, Helsinki
24-29 August 1987, vol. II.
Kretzmann, N. (ed.): 1989, Meaning and Inference in Mediaeval Philosophy, Kluwer Academic Publishers
Kretzmann, N. and Pinborg, J.
and Kenny, A. (eds.): 1982, The
Nuchelmans, G.: 1973, Theories of the Proposition - Ancient and Medieval Conceptions of the Bearers of Truth and Falsity, North Holland Publishing Company, Amsterdam-London
Nuchelmans, G.: 1980, Late-Scholastic
and Humanist Theories of the Proposition, North Holland Publishing Company,
Peter of
Pironet, F.: 1997, The Tradition of Medieval Logic and Speculative Grammar: A Bibliography (1977-1994). Turnhout: Brépols.
Rijk, L. M. de (ed.): 1967, Logica Modernorum, Vol. II, Part II, Van Gorcum, Assen
Schmidt, R.W.: 1966, The Domain
of Logic according to Saint Thomas Aquinas, Martinus
Nijhoff,
Velde,
R.A. te: 1995 Participation and Substantiality in Thomas
Aquinas, Brill:
Weidemann, H.: 1986 “The Logic of Being in Thomas Aquinas”, in: Knuuttila et al. 1986, pp. 181-200.
Wippel, J. F.: 1987 “Thomas Aquinas and
Participation”, in: Wippel, J. F. (ed.): Studies in Medieval Philosophy,
The
[1] In Secundum Sententiarum 34.1.1. Cf. In Primum Sententiarum 19.5.1.ad1, 33.1.1.ad1; In Secundum Sententiarum 37.1.2.ad1 & ad3; De Ente et Essentia 1; De Potentia 7.2.ad1; De Malo 1.1.ad19; Quodlibeta 9.2.2; In Metaphysicam 4.1, 5.9, 6.2, 6.4, 9.11, 11.8; Summa Theologiae 1 3.4.ad2, 16.3.ad2; 48.2.ad2; Summa Theologiae 1-2 36.1; ScG 1.12, 1.58, 3.9. Cf. also Cajetan (1964, 1590) c.1; C. Alamannus (1888) Tom.1. sect. II. 5. 1; Schmidt (1966) Part II. ch. 4. and Part III. ch. 8.
[2] In Metaphysicam 5, 9, n. 896.
[3]
Cf. “Cum enim dicimus aliquid esse, significamus propositionem esse veram. Et cum dicimus
non esse, significamus non esse
veram; et hoc, sive in affirmando
sive in negando. In affirmando quidem, sicut dicimus quod
Socrates est albus, quia hoc verum est. In negando vero, ut Socrates non est
albus, quia hoc est verum, scilicet ipsum non esse album.” In Metaphysicam 5, 9, n. 895.
[4]
Concerning the inherence theory in general, as opposed to the identity theory
see de Rijk’s Introduction to Abelard (1956) pp.
37-38, and Henry (1972) pp. 55-56. Concerning
[5] For a detailed account of the relevant notion of signification see Klima (1996).
[6] Supposition theory is the medieval theory of reference, which has to be strictly distinguished from the theory of signification, i.e., the theory of meaning. For good bibliographies on the vast recent literature on supposition theory see e.g. Ashworth (1978), Kretzmann-Pinborg-Kenny (1982). For more recent references see: Kretzmann (1989) and Pironet (1997).
[7] Nevertheless, in the technical Appendix of this paper I will reconstruct categorical sentences with common subject terms, in line with the medieval theory of reference, the theory of the supposition of terms. For the relevant reconstructions of medieval supposition theory in relation to the semantics of modern quantification theory, see Klima (1988), Essays 2 and 3.
[8] “… ens non potest hoc modo contrahi ad
aliquid determinatum, sicut genus contrahitur ad species per differentias. Nam
differentia, cum non participet genus, est extra essentiam generis. Nihil autem
posset esse extra essentiam entis, quod per additionem ad ens aliquam speciem
entis constituat: nam quod est extra ens, nihil est, et differentia esse non
potest. Unde in tertio huius
probavit philosophus, quod ens, genus esse non potest. Unde oportet, quod ens
contrahatur ad diversa genera secundum diversum modum praedicandi, qui
consequitur diversum modum essendi; quia quoties ens dicitur, idest quot modis
aliquid praedicatur, toties esse significatur, idest tot modis significatur
aliquid esse. Et propter hoc
ea in quae dividitur ens primo, dicuntur esse praedicamenta, quia distinguuntur
secundum diversum modum praedicandi. Quia igitur eorum quae praedicantur,
quaedam significant quid, idest substantiam, quaedam quale, quaedam quantum, et
sic de aliis; oportet quod unicuique modo praedicandi, esse significet idem; ut
cum dicitur homo est animal, esse significat substantiam. Cum autem dicitur, homo est albus, significat
qualitatem, et sic de aliis.” In
Metaphysicam 5.9, n. 5
[9] “… est duplex modus dividendi commune in ea quae sub ipso sunt, sicut est duplex communitatis modus. Est enim quaedam divisio univoci in species per differentias quibus aequaliter natura generis in speciebus participatur, sicut animal dividitur in hominem et equum, et hujusmodi; alia vero divisio est ejus quod est commune per analogiam, quod quidem secundum perfectam rationem praedicatur de uno dividentium, et de altero imperfecte et secundum quid, sicut ens dividitur in substantiam et accidens, et in ens actu et in ens potentia: et haec divisio est quasi media inter aequivocum et univocum.” In Secundum Sententiarum 42.1.3, in corp. Cf.: “Unum enim eodem modo dicitur aliquid sicut et ens; unde sicut ipsum non ens, non quidem simpliciter, sed secundum quid, idest secundum rationem, ut patet in 4o Metaphysicae, ita etiam negatio est unum secundum quid, scilicet secundum rationem.” In Perihermeneias 2.2, n. 3.
[10] Schematically, the claim is the following: SGT(1’)(P) = SGT(1’’)(P), and SGT(2’)(P) = SGT(2’’)(P); but then, since SGT(1’’)(P) ¹ SGT(2’’)(P); therefore, SGT(1’)(P) ¹ SGT(2’)(P); where SGT(n)(P) is the signification of the predicate of sentence n.
[11]
“Ideo autem dicit quod hoc verbum est consignificat compositionem, quia non eam principaliter
significat, sed ex consequenti;
significat enim primo illud
quod cadit in intellectu
per modum actualitatis
absolute: nam est, simpliciter dictum, significat in actu esse; et ideo significat per modum verbi. Quia vero actualitas, quam principaliter significat hoc verbum est, est communiter actualitas omnis formae, vel actus substantialis
vel accidentalis, inde est quod cum volumus significare quamcumque formam vel actum actualiter
inesse alicui subiecto, significamus illud per hoc verbum est, vel simpliciter vel secundum
quid: simpliciter quidem secundum praesens
tempus; secundum quid autem secundum alia tempora. Et ideo ex consequenti hoc verbum est
significat compositionem.” In
Perihermeneias 1.5, n.22
[12] “Sed duplex est esse: scilicet esse
essentiale rei, sive substantiale ut hominem esse, et hoc est esse simpliciter.
Est autem aliud esse accidentale, ut hominem esse album, et hoc est esse
aliquid.” De Principiis Naturae, c. 1. Cf. In Boethii De Hebdomadibus,
2, nn. 26-28.
[13] As St. Thomas wrote:
"...dicendum est quod illud a quo aliquid denominatur non oportet quod sit
semper forma secundum rei naturam, sed sufficit quod significetur per modum
formae, grammatice loquendo. Denominatur enim homo ab actione et ab indumento,
et ab aliis huiusmodi, quae realiter non sunt formae." De Potentia q. 7, a. 10, ad 8. Cf. also
e.g. Cajetan: "Verum ne fallaris cum audis denominativum a forma
denominante oriri, et credas propter formae vocabulum quod res denominans debet
esse forma eius quod denominatur, scito quod formae nomine in hac materia
intelligimus omne illud a quo aliquid dicitur tale, sive illud sit secundum rem
accidens, sive substantia, sive materia, sive forma." Cajetan (1939) p.
18.
[14] Cf. Quodlibeta
9.2.2.
[15] De Ente,
c. 4, cf. Cajetan (1590, 1964) q. 6.
[16]
Cf. the following passage from Aquinas’s commentary on Aristotle’s On
Interpretation: “Therefore 'passions of the soul' must be understood here
as conceptions of the intellect, and names, verbs, and
speech signify these conceptions of the intellect immediately according to the
teaching of Aristotle. They cannot immediately signify things, as is clear from
the mode of signifying, for the name 'man' signifies human nature in
abstraction from singulars; hence it is impossible that it immediately signify
a singular man. The Platonists for this reason held that it signified the
separated idea of man. But because in Aristotle's teaching man in the abstract
does not really subsist, but is only in the mind, it was necessary for Aristotle
to say that vocal sounds signify the conceptions of the intellect immediately
and things by means of them.” Aristotle, On Interpretation: Commentary by
[17] That is to say, using the notation of n. 10, SGT(1’’’)(P) = SGT(2’’’)(P) = SGT(2’’)(P) ¹ SGT(1’’)(P).
[18]
I would tentatively identify the significate of a proposition as the enuntiabile
expressed by the proposition, expressly called by St. Thomas an ens rationis in
1SN 41.1.5. I say “tentatively”, because of
[19] In Metaphysicam 6.4. For more on this interpretational issue see Klima (1993). Cf. also Nuchelmans, (1973) pp. 165-194; de Rijk (1967) pp. 357-359.
[20] For detailed discussion see Klima (1993).
[21] Cf. n. 12 above. For a detailed analysis of the idea that all predications can be regarded as predications of being with some qualification see Klima (1996). For discussions of the metaphysical implications of this idea see Velde (1995), Wippel (1987), and Klima (2000).
[22] Especially, In Metaphysicam 4.1, 5.9, 6.2.
[23] A description of the general technical apparatus used here can be found in Essay 5 of Klima (1988). The theory provided there, however, did not deal with details concerning the copula. A more specific system taking into account Aquinas’s theory of the copula can be found in Klima (1990); but the system presented there does not reconstruct the sense of the copula as obtained by means of the appropriate qualification of the primary sense of ‘is’.
[24] For more details on reconstructing supposition theory along these lines in relation to natural language semantics, generalized quantification theory, and free logic, see Klima-Sandu (1990), and Klima (2001).