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Whitehead and Aristotle On Propositions

by Peter J. Cataldo

Peter J. Cataldo is a graduate student and teaching fellow in the Department of Philosophy at Saint Louis University Saint Louis, Mo. The following article appeared in Process Studies, pp. 15, Vol. 12, Number 1, Spring, 1982. Process Studies is published quarterly by the Center for Process Studies, 1325 N. College Ave., Claremont, CA 91711. Used by permission. This material was prepared for Religion Online by Ted and Winnie Brock.


Although Whitehead’s theory of propositions has received treatment in many general studies of Whitehead’s philosophy, it has received little attention as a topic by itself. Our contribution is a general comparative study of the central differences among Whitehead’s and Aristotle’s theories about propositions. Specifically, we intend to show that the crucial point of difference, demanded by Whitehead’s metaphysics, is the fact that for Aristotle a proposition contains reference to what is believed to be an actual state of affairs -- either positive or negative -- as a predicable within the proposition, and that Whitehead’s theory does not have such an element. We will see that because of this built-in aspect of the Aristotelian proposition, its defining value is its truth value. The combination of these two elements in Aristotle’s theory generate the logical problem of "negative facts," i.e., affirming actuality of negations, e.g., affirming the fact denoted by the proposition, "The round square does not exist." We will proceed first with an examination of Aristotle’s position and its problems and then turn to Whitehead’s theory, contrasting it with Aristotle’s.1

A. Aristotle’s View of Propositions

In De Interpretatione chapters 4-6, Aristotle identifies propositions as such with (a) statements of affirmation or denial, and, therefore, with (b) the fact of existence or nonexistence of the corresponding content denoted by the proposition. The corollary of (b) is that truth value is inextricably bound up with the nature of propositions. Thus, in the case of true propositions a true affirmation corresponds to a positive state of affairs, e.g., "This thing is white," and a true denial corresponds to a negative state of affairs, e.g., "This thing is not white." In each case there is an actual fact -- positive or negative -- which must correspond to the assertion; this is significant since the correspondence is a constituent of the proposition qua proposition. If there is no state of affairs to which an affirmation or denial can correspond, the proposition is false and its opposite is true. The important point is that it is constitutive of the very nature of propositions that they either correspond or do not correspond to the asserted state of affairs. This aspect of propositions has the consequence of making truth value a conceptual constituent of any given proposition; put another way, propositional meaningfulness is dependent upon truth value. These aspects of Aristotle’s theory are illustrated in this passage: "We call those propositions single which indicate a single fact, or the conjunction of the parts of which results in unity: those propositions, on the other band, are separate and many in number, which indicate many facts, or whose parts have no conjunction" (17a 15-17). A look at some more passages from Aristotle will help exemplify these central points.

In Chapter 4 Aristotle explains that a word in insolation may have meaning but it is not a proposition. What is interesting about the passage is that in it he equates proposition with affirmation and denial: "The word ‘human’ has meaning, but does not constitute a proposition, either positive or negative. It is only when other words are added that the whole will form an affirmation or denial" (16b 28-30). Further on he equates propositions with their truth value:

Every sentence has meaning, not as being the natural means by which a physical faculty is realized, but, as we have said, by convention. Yet every sentence is not a proposition; only such are propositions as have in them either truth or falsity. Thus a prayer is a sentence, but is neither true or false. (17a 1-4)

. . .if all propositions whether positive or negative are either true or false, then any given predicate must either belong to the subject or not. (18a 34f)

To make an affirmation is to affirm the presence of an accident in a subject, and to make a denial is to deny this relation. The nature of a proposition is then to be the linguistic counterpart of the various ways in which predicates (accidents) can, or cannot be, found in subjects (substances). Conceiving of propositions in this manner necessarily entails that truth value be a conceptual constituent of propositions.

This theory of Aristotle’s puts him in the precarious position that Bertrand Russell found himself in centuries later, namely, being theoretically committed to the existence of "unreal objects" or "pseudo-objects." By identifying propositions with linguistic entities, and with their truth value, Aristotle must admit that a rightly denied proposition corresponds with an actual negative state of affairs. Such a proposition must assume the existence of a certain fact in order to deny its existence. Russell recognized that such was the case in propositions like "The round square does not exist."

One could show the same sort of logical inconsistency with Aristotle’s example of affirming or denying that son3ething will be white: " . . . if it is white, the proposition stating that it is white was true; if it is not white, the proposition to the opposite effect was true" (18b). Aristotle’s use of the future tense does not affect our point. For in any tense, if the latter assertion is true, then there still is the problem of having to assume that the privation of the property of whiteness is itself an existing fact which corresponds to a true denial. One is forced to assume such a fact while simultaneously denying that it has existential status.

B. Whitehead’s Theory of Propositions

The logical consequences of Aristotle’s metaphysics are that every proposition must be either true or false with respect to affirming or denying accidents of substances. His metaphysics demands this correspondence theory of truth which entails that the truth value of propositions be intrinsic to the nature of a proposition. Whitehead’s process metaphysics, however, entails a theory of propositions which distinguishes what Aristotle identifies in such a way as to make propositions a real factor in the "process" view of the world while avoiding the logical inconsistency of negative facts.

Whitehead rejects the notion that the Aristotelian subject-predicate form of propositions expresses an ultimate truth, namely, that Substance in the truest and primary and most definite sense of the word, is that which is neither predicable of a subject nor present in a subject" (2a 11; cf. PR 137/ 208). The Aristotelian subject-predicate form of statement in Whitehead’s opinion cannot properly allow for the creativity present in the self-realization of the subject, nor the transcendent creativity of the subject as superject.

Whitehead’s metaphysics of internal relations, embodied in the principle of relativity, needs a correspondingly appropriate theory of propositions.2 Whitehead provides such a theory which can account for the creative advance of the world, but which is naturally contrary to the sort of theory based on the subject-predicate form of statement.

In part II, chapter 9 of Process and Reality. Whitehead begins

A "singular" proposition is the potentiality of an actual world including a definite set of actual entities in a nexus of reactions involving the hypothetical ingression of a definite set of eternal objects. . . . The definite set of actual entities involved are called the "logical subjects of the proposition"; and the definite set of eternal objects involved are called the "predicates of the proposition." (PR 186/ 282f.)

Because of the fusion of eternal objects with actual entities within the potential setting of the proposition, certain qualifications are put on the meanings of "eternal object" and "actual entity." The predicate of a proposition loses much of its generality which it otherwise has in the strict sense of being an eternal object. Whitehead explains, "In the proposition, the eternal object, in respect to its possibilities as a determinant of nexus, is restricted to these logical subjects" (PR 257/ 393). Likewise, the actual entities involved in a proposition lose some of their characteristics qua actual entity.

. . . in a proposition the logical subjects are reduced to the status of food for a possibility. Their real role in actuality is abstracted from; they are no longer factors in fact, except for the purpose of their physical indication. Each logical subject becomes a bare "it" among actualities, with its assigned hypothetical relevance to the predicate. PR 258/ 394)

Thus from the synthesis in the proposition there results an elimination of the objective efficacy for that particular physical feeling from whence the actual entity is abstracted. Its objectification functions only insofar as it indicates the abstract definiteness that the logical subject has within the proposition. This qualified sense of objectification is necessary so that the logical subjects may correspond with the potential nature of the predicate.

One other important part of Whitehead’s theory is the "locus" of a proposition.

In a proposition the various logical subjects involved are impartially concerned. The proposition is no more about one logical subject than another logical subject. But according to the ontological principle, every proposition must be somewhere. The "locus" of a proposition consists of those actual occasions whose actual worlds include the logical subjects of the proposition. (PR 186/283)

This aspect of Whitehead’s theory, as we shall point out, is demanded by his metaphysics, and, more specifically, it is a consequence of the fact that for Whitehead truth value is not a part of a proposition as such.

One of the first steps to understanding the difference between Aristotle and Whitehead on the role of truth value, can be made with regard to Whitehead’s distinction between a judgment and a proposition. Contrary to the belief of the majority of logicians, a proposition is not identical with a judgment; moreover, a proposition, according to Whitehead, is not even a linguistic entity. Whitehead argues that the truth value of a proposition is not to be found in the judgment one makes about it; rather, a judgment is actually a subjective feeling of a proposition. Thus, truth and falsity are only ascribed to propositions, and correctness, incorrectness, or suspension are ascribed to judgments (PR 191/291). The correctness or incorrectness of a judgment is self-referential; there is a coherence within the judging subject if that subject correctly judges the truth or falsity of a proposition. A judgment is a feeling in the process of the judging subject, and it is correct or in correct respecting that subject. . . . This judgment [about a proposition] affirms, correctly or incorrectly, a real fact in the constitution of the judging subject" PR 191/ 291).

Whitehead summarizes the distinction between ajudgment and a proposition in the following:

A proposition emerges in the analysis of a judgment; it is the datum of the judgment in abstraction from the judging subject and from the subjective form. A judgment is a synthetic feeling, embracing two subordinate feelings in one unity of feeling. Of these subordinate feelings one is propositional, merely entertaining the proposition which is its datum. (PR 193/ 293)

Whitehead then shows the distinction even more strongly in the lines which follow this quotation, allowing, in effect, that the same proposition could possibly make up the content of contradictory judgments.

The same proposition can constitute the content of diverse judgments by diverse judging entities respectively. . . , this requires that the same complex of logical subjects objectified via the same eternal objects, can enter as a partial constituent into the "real" essences of diverse actual entities. The judgment is a decision of feeling, the proposition is what is felt; but it is only part of the datum felt. (PR 193/ 293)

Two conditions must be fulfilled in order for the situation described in the last quotation to take place. First, the judging subjects must have in their actual world the actual entities presupposed by the proposition. Secondly, the judging subjects must have the requisite knowledge of the world defined by the first condition (PR 193/294). If these conditions are not fulfilled, then the proposition is nonexistent for the first case, and the judgment is impossible for the second.

The truth or falsity of a proposition has importance in the determination of a correct or incorrect standpoint of the judging subject, but this importance is not relevant for the proposition qua proposition; as Whitehead explains: since each actual world is relative to standpoint, it is only some actual entities which will have the standpoints so as to include, in their actual world, the actual entities which constitute the logical subjects of the proposition" (PR 193/ 293f.). Since a proposition is not a verbal statement (nor some other linguistic entity), nor a judgment, propositional truth value is entertained in the feeling of propositions that may issue in linguistic entities or judgments, but as distinct from the proposition as such. Truth or falsity is established by means of the anchor that the logical subject has in given fact, but truth value is not intrinsic to the proposition in itself. Truth or falsity must be established somewhere along the line, but the primary reason for showing the distinction between judgments, linguistic entities, and propositions is that the truth value of what is being proposed (in the proposition) is not a part of that delimited content. The content’s truth value does not contribute to the intelligible aspect of that content. Whitehead states the following concerning the truth value which must eventually be established: "Truth and falsehood always require some element of sheer given-ness. Eternal objects cannot demonstrate what they are except in some given fact. The logical subjects of a proposition supply the element of givenness requisite for truth and falsehood" (PR 258f./ 395). Concerning truth or falsity of a proposition as such, Whitehead has this to say: "But its own truth, or its own falsity is no business of a proposition. That question concerns only a subject entertaining a propositional feeling with that proposition for its datum" (PR 258/ 394f.). For Whitehead, the critical problem with the Aristotelian propositional expression is that it identifies a proposition with its judgment, which, because of Aristotle’s substance/accident metaphysics, necessarily includes taking a stand on the proposition’s truth value. Another important way of understanding a proposition’s independence from truth value can be found in Whitehead’s description of a propositional feeling at the end of part III.

There is the arrest of the emotional pattern round this sheer fact as a possibility, with the corresponding gain in distinctness of its relevance for the transcendent creativity -- in the sense of its advance-from subject to subject -- this particular possibility has been picked out, held up, and clothed with emotion. (PR 280/ 428)

This synthesis of eternal object and actual entity can be "picked out," "held up" for valuation precisely because its truth value is not in the nature of the synthesis. For Whitehead it may be that the state of affairs picked out by a proposition is mistakenly accepted. Thus the state of affairs might not be true, but the propositions eventual truth value makes no difference to the state of affairs which is picked out. The existence or nonexistence of the state of affairs picked out by a proposition does, however, make a difference in terms of the proposition’s truth value. To say that a proposition is true or false does make a difference not to what is picked out, but to the proposition inasmuch as what was once a proposition is now something extrapropositional, i.e., insofar as it is no longer an entity between an eternal object and an actual occasion. Truth value pertains to a proposition not as such but qua extrapropositional.

C. The Significance of Propositions

Distinguishing a proposition from its judgment or its linguistic expressions enables Whitehead to show the real significance of a proposition. That significance is to be a lure for novelty. Propositions must be distinguished from these other related entities because propositions are metaphysically part of the creative advance of the world. The world’s creativity is fundamentally incompatible with a theory of propositions which reflects an Aristotelian metaphysics according to Whitehead. As a result of logicians identifying propositions with judgments, Whitehead tells us that "false propositions have fared badly, thrown into the dustheap, neglected. But in the real world it is more important that a proposition be interesting than that it be true. The importance of truth is, that it adds to interest" (PR 259/ 395f.).

Even propositions which are false can still be interesting, a lure for feeling.

If by the decision of the concrescence of an actual entity, the proposition has been admitted into feeling, then the proposition constitutes a lure of a member of its locus by reason of the germaneness of the complex predicate to the logical subjects, having regard to forms of definiteness in the actual world of that member, and to its antecedent phases of feeling. (PR 186/ 283)3

In the same vein, Whitehead states that a proposition "is a datum for feeling, awaiting a subject feeling it" (PR 259/ 395). Donald Sherburne gives an interesting example of Whitehead’s meaning in the following:

Many people in a given town may be aware of the existence of an empty lot in the center of town, but only one enterprising businessman may positively prehend the proposition indicated by the words restaurant on that corner. At the moment he first prehends the proposition, it is false. But this is not the important fact about the proposition. As a lure for feeling the proposition may lead the businessman to buy the lot and build the restaurant. (KPR 240)

Not only are propositions part of the concrescing process of the prehending subject, but they have what Martin Greenman calls an "eternally objective structure." The principle of relativity demands that all entities which are not contemporaneous be internally related; thus, propositions whose function it is to pick out the real possibility of novelty presuppose a metaphysical character of the universe which Whitehead describes as "a hierarchical patience involving systematic gradations of character" (PR 192/ 293). Greenman explains that a proposition is that proposition precisely because it takes its place in its eternally objective structure, or, what Whitehead would describe as its place in a hierarchy of wider and wider societies (FR 192/ 293).4

This metaphysical character of the universe is another way of justifying the claim that a verbal statement is never the full expression of a proposition. In any proposition it is always "a matter of convention as to which of the proximate societies are reckoned as logical subjects and which as background" (PR 192/293). Whitehead often refers to the proposition "Socrates is mortal" as an example of the shading off of logical subjects into the hierarchical patience of the universe. The proposition could be written as "It is Socratic and mortal," where each of the possible logical subjects would presuppose actual worlds which would exemplify certain systematic schemes in which the predicates would be realizable (PR 264f./ 403f.).5 This is another way of explaining the "locus" of a proposition mentioned in part B. If propositions were identical with judgments and their linguistic expressions and had truth value as a conceptual constituent, Whitehead’s notion of the "locus" of a proposition would not be possible.

Since Whitehead divorces the nature of a proposition from its corresponding judgment, he can avoid the problems that a theory like Aristotle’s encounters altogether;6 he need not posit negations as actual states of affairs in order to deny their existence. One does not actually discover or observe a rightly denied proposition, nor the falsity of a mistakenly held proposition; rather, one comes to know what one did or did not expect, and having this knowledge is different in positive ways from what one would know if the opposite were the case. This point would seem to be especially applicable to Whitehead’s theory of propositions since false propositions are not condemned to the dust-heap as logicians would have it. The judging subject in Sherburne’s example may be incorrect in affirming the proposition "There is a restaurant on that corner," but he would observe the proposition’s falsity in positive ways such as observing the boundaries of the empty lot, or an open area surrounded by other businesses on the block, etc. Ironically, for Whitehead, observing the falsity of the proposition in these positive ways would comprise the data for the propositional feeling itself. This would not seem to be a problem for Whitehead; quite to the contrary, it is a good illustration of how the data for the same proposition can on a logical level be the reason for the falsification of the proposition, yet on the level of prehensions be data in the proposition as a lure for the feelings of the judging subject.7

 

References:

BNT -- Grisez, Germain. Beyond the New Theism: A Philosophy of Religion. Notre Dame: University of Notre Dame Press, 1975.

KPR -- Sherburne, Donald W. A Key to Whitehead’s Process and Reality. Bloomington: Indiana University Press, 1966.

 

Notes

1 I found that the theory of propositions by Germain Grisez outlined in BNT 40-52 was similar in many respects to Whitehead’s. In his analysis Grisez shows the main points of difference between his theory and the sort of theory that Whitehead criticizes. For these reasons, I found Grisez’s treatment helpful in making the contrasts between Whitehead and Aristotle. Some citations to Grisez are made below in the notes.

2 The correspondence needed is not merely a paralleling, but rather one of reciprocity since propositions have primarily a metaphysical status in Whitehead s view.

3To describe a proposition as "interesting" or as a "lure" is not simply to give it methodological value as in the case of an hypothesis. A proposition is interesting according to Whitehead because it in some way influences the concrescence of an actual entity whether or not it is a true proposition. See Nathan Rotenstreich, On Whitehead’s Theory of Propositions," Review of Metaphysics,5 (1952), 389-404 for the criticism of Whitehead’s notion of "interesting."

4 See Martin Greenman, "A Whiteheadian Analysis of Propositions and Facts," Philosophy and Phenomenological Research 13 (1952.53), 477-86. at 484: ". . . any given fact, by virtue of its internal relations to all other facts, reflects in itself the eternally objective structure of the concrete world which includes it. It is that fact by virtue of its relation to all other facts within that concrete world. The real possibility of a novel fact is then defined by the relation of a given concrete world to the whole realm of possibility."

5 See BNT 48-50 for a similar recognition of the background of logical subjects and predicates.

6 There would not seem to be a problem for modal logic in Whitehead’s theory of propositions since a proposition as such is in principle exclusive of’ the question of existence, although the picked out content exists insofar as it is "picked out." Thus, for example, one could know what it would be like for a proposition to be necessarily true or false without actually knowing its truth value. See BNT 45f.

7 Cf. note 3.


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