20th WCP: Toward a Scotistic Modal Metaphysics

1. The Problem: Scotistic Modal Logic vs. Scotistic Counterpart Theory

Thanks to the resurgence of interest in modalities in the twentieth century, the history of modal logic has been studied more extensively than ever. One of the more important lessons is that Scotus rather than Leibniz is the father of the modern conception of logical possibility. (1) Insofar as it is not merely historical curiosity but a test of our intuition about modalities that we are interested in the predecessors of modern modal logic, we face the urgent task of reconstructing the Scotistic system of modalities. In fact,

Douglas C. Langston recently raised an interesting question as to which way of understanding possible worlds Scotus might endorse: the counterpart view or the canonical view? Based on Ordinatio, Book I, d. 44, q. 1, n. 11, he presents two alternative readings. Ultimately, however, he opts for the counterpart reading on the ground that it is more consistent with Scotus's remarks on how God knows contingents. An important consequence from the counterpart reading is that individuals are "world-bound" for Scotus. (2) Yet Langston's interpretation invites serious criticism. According to Simo Knuuttila, if the individuals in Scotus's model were world-bound, they would not have synchronic de re alternatives, which is not compatible with Scotus's reform in obligational principles. Knuuttila further points out that Scotus's well-known doctrine of human free will excludes the possibility of world-bound individuals. (3)

The problem we have to tackle in this article can be put succinctly: Do we have in Scotus a modal logic or a counterpart theory? We need to take a rather roundabout path to handle this problem. This is because, whether it be in Lewis's original formulation or in others' applications, the crucial concept of "counterpart" has never been clearly explicated. In section 2, I shall therefore examine the recent controversy concerning Leibniz's views on modalities, which centers around the counterpart relation. By fully exploiting the lessons learned from such an examination, then, I shall launch a trilemma against a Leibnizian in section 3. In section 4, I shall claim that, unlike Leibniz's case, Scotus's position is not endangered by the Leibnizian trilemma. One important premise will be adopted from my thesis presented elsewhere regarding the differences between Scotus's haecceitas and Leibnizian individual essence. Another will be secured from a brief report on Scotus's views on similarity, which might be utterly original to modern eyes jaundiced by contemporary set theories.

2. The Parallel Problem: Leibnizian Modal Logic vs. Leibnizian Counterpart Theory

In his influential article "Leibniz on Possible Worlds", Mates constructed a Leibnizian system of quantified modal logic. (4) Meanwhile, Lewis proposed his counterpart theory, which has served as a spur for sharpening our intuition about modalities. (5) Though Lewis declines to plunge into any controversy related to Leibniz scholarship, it is all too natural to apply the ideas of counterpart theory to Leibniz. Indeed, Mates objected to the use of counterparts for Leibniz. (6) On the other hand, G. Fitch claims that the notion of counterparts "does seem best to capture Leibniz's views on contingency and possible worlds". (7)

Among many interesting issues of both technical and non-technical character, we may highlight our varying intuitions regarding some of the most fundamental features of the counterpart relation. For example, Mates writes:

As presented by Lewis, the counterpart relation, though always reflexive, need not be symmetric or transitive. Further, it is possible for two or more different things in a given world to be counterparts of a single thing in another world, and it is possible for a single thing in a given world to be a common counterpart of two or more things in another world. These features block Leibniz from agreeing that 'your counterparts are men you would have been, had the world been otherwise.' (8)

Also, Mates claims that for Leibniz it must be symmetric and transitive, and "also that nothing is a counterpart of anything else in its own world". (9) Further, in what Fitch counts as the strongest argument against the use of counterparts for Leibniz, Mates derives an absurd consequence that "every concept in every world would be a counterpart of every other concept in any other world". He writes:

Actually, all that is needed for our purpose is the claim that any two concepts from different worlds can be joined by a discreet series of intermediate concepts (from different worlds) in which each concept is enough like its predecessor to qualify as a counterpart of it. Then, by the symmetry and transitivity of the counterpart relation, you would have the absurd consequence that every concept in every world would be a counterpart of every other concept in any other world. (10)

Now Fitch is willing to agree with Mates in that Leibniz would not allow one to have two counterparts in the same world, nor would he allow that one be the counterpart of two things in the same world. (11) But Fitch thinks that by restricting the counterpart relation slightly, it is possible to avoid the absurd consequence noted above without giving up Lewis's more fundamental intuitions about counterpart relation. (12) As a part of the semantics of the formal system of Leibnizian counterpart theory, Fitch characterizes the counterpart relation by the following conditions:

Here, "i" and "ii" amount to Lewis's postulate P6, and P4 cum P3, respectively. Also, C1 corresponds to Lewis's P5. (14) Further, Fitch claims that conditions C2 and C3 restrict the counterpart relation so as to avoid the alleged absurdity that Mates asserts. He claims that

Given restrictions C1, C2, and C3, all the troublesome cases are ruled out, yet the relation is neither symmetric nor transitive. (15)

It is interesting to note that , after presenting the eight postulates of his counterpart theory, Lewis enlisted some propositions that would not have been plausible to postulate: (P9) that the counterpart relation was transitive; (P10) that the counterpart relation was symmetric; (P11) that nothing in any world had more than one counterpart in any other world; (P12) that no two things in any world had a common counterpart in any other world; (P13) that, for any two worlds, anything in one was a counterpart of something in the other; (P14) that, for any two worlds, anything in one had some counterpart in the other. (16)

What Mates has done is none other than this. He first expanded Lewis's set of postulates of counterpart theory by adding (P9), (P10), (P11), and (P12) to fathom what it would be like to have a Leibnizian counterpart theory. Then, by using what he calls Leibniz's principle of continuity, he derived an absurd consequence from it. So, he concluded that the use of counterparts is not acceptable to Leibniz. On the other hand, what Fitch has done is this. He does not add (P9) and (P10) but only (P11) and (P12) to Lewis's counterpart theory, claiming that no troublesome case would arise in such a system. What is going on?

3. The Leibnizian Trilemma

I think the situation can be aptly summarized by the following trilemma:

If we have a Leibnizian counterpart theory, it is inconsistent.

If Leibniz's system is like canonical modal logic, there is the threat of the problem of transworld identity, which seems unavoidable due to his principle of the identity of indiscernibles.

If we fathom a Leibnizian modal logic in which individual concepts are world bound, we have to face some tough problems in trying to make sense of Leibniz's texts.

I do not have much to say about the second horn. For if we grasp this, we do not have the the least hope of solving the problem of transworld identity, and so we would be totally unmotivated to discuss the peculiarity of the Leibnizian system of modalities and thus be ignoring the whole point of considering the possibility of Leibnizian counterpart theory.

As far as the third horn is concerned, it is important to note that Mates also concedes that Leibnizian individual concepts are world bound. No doubt such a concession is necessary because he firmly believes that the identity of indiscernibles is an indispensible element in Leibniz's philosophy. In addition, Mates seems to think that because individual concepts are world bound, unlike contemporary modal logic, Leibnizian modal logic does not have to face the problem of trans-world identity. However, I concur with Fitch's incisive criticisms against Leibniz's talk about possible Adams. (17) For if individuals compared to Adam are world bound, and as a consequence in Mate's view qualitiatively different from him but not counterparts to him, in what sense could they be possible Adams?

Consequently, I would like to focus on the first horn, arguing that Fitch's move leads to an inconsistency. Suppose that P12 is true. Then, Lewis's proof that there might be a case of nonsymmetric counterpart relation fails. For, in order to show nonsymmetry, he used the following thought experiment:

Suppose x3 in world 3 is a sort of blend of you and your brother; x3 resembles both of you closely, far more closely than anything else in w3 resembles either of you. So x3 is your counterpart. But suppose also that the resemblance between x3 and your brother is far closer than that between x3 and you. If so, you are not a counterpart of x3. (18)

Clearly, any such common counterpart is not possible according to P12. This means that it is not implausible to postulate that the counterpart relation is symmetric. By adding P12 without also adding P10, Fitch seems to betray his own purpose. At least he has the burden of figuring out a new proof in order to show that the counterpart relation is not symmetric.

By combining Mates's criticism against Leibnizian counterpart theory under Lewis's axioms and my criticism against Leibnizian counterpart theory under Fitch's axioms, we may thus conclude that the first horn is not available for us to grasp. Hence, we have the trilemma in full force.

4. Scotistic Way Out

Now I claim that the situation is entirely different in Scotus's case, for he can grasp the second horn without tears. To sustain this claim, I invoke the following two premises:

(1) Haecceitas is not an individual essence.

(2) According to Scotus, similarity is not a reflexive relation.

Elsewhere I tried to show that haecceitas cannot be an individual essence, at least for Scotus. (19) Let me briefly indicate some of the major points. In his treatise on the problem of individuation, Scotus rejected a nominalistic theory according to which a material substance is of its nature singular and individual. (20) What is important to note is that Scotus's criticism of the nominalist view amounts to a major part of the first argument in his two arguments for postulating haecceitas. (21) In other words, if an individual essence were the principle of individuation, and as a consequence the material substance were of its nature this or that individual, then there would be no need to postulate haecceitas. Thus, haecceitas cannot be an individual essence for Scotus. In addition, for those who might think that Scotus's rejection of the nominalist theory does not entail the result that there is no individual essence in the modern sense, we may draw their attention to Scotus's triple analogy of an individual difference (that is, haecceitas ) and a specific difference. (22) If we consider the possible consequences of substituting "individual essence" for "individual difference" in the analogy, we get absurd results. For example, in the third way, we would have to say that any two individual essences are "primarily diverse differences" As long as they share at least one characteristic, however, individual essences cannot be ultimately different. Thus, Scotus's haecceitas (individual essence) cannot be an individual essence.

It is rather obvious why the distinction between an individual essence and haecceitas is relevant for our discussion. For, if one misunderstands Scotus's notion of haecceitas as an individual essence, he or she must thereby misunderstands Scotus's answer as to the question how the same individual could be identified in alternative states of affairs. For example, Knuuttila fell into the mistake of identifying an individual essence with haecceitas in his otherwise excellent discussion of Scotus's modal theory. (23)

I fail to find in Scotus's text any a priori reason why similarity cannot be a reflexive relation. What is needed for our purpose is merely to draw attention to an interesting text of Scotus's that witnesses that (2) above --similarity is not a reflexive relation -- is true. Scotus wrote:

In the chapter 'On Relation' in V Metaphysics [ch. 15] the Philosopher says that the relations based on 'oneness' are similarity, identity and equality. Now similarity is a real relationship, and as such it requires a real foundation, so there is something real at the basis of similarity -- something really one that serves as the proximate foundation for the relation. (For if the foundation were only conceptually one, there would be no foundation unless it were produced by an act of the mind and thus the relation of similarity would be only a mental or conceptual relation. Hence if the relation of similarity is real, its foundation must be real.) Now the oneness that serves as the foundation cannot be numerical unity, for nothing is similar to itself; therefore, the unity of this foundation must be both real and other than numerical unity. (24)

If these two premises are given, we may conclude that in Scotus we have a modal logic rather than a counterpart theory. For,

(3) Whether it be under Lewis's or Fitch's axioms, counterpart relations are a kind of similarity relation, which is reflexive.

(4) So, in Lewis and Fitch, an individual in a world is a counterpart to itself.

(5) According to Scotus, however, no individual in any world can be similar to itself.

(6) So, in Scotus, no individual in any world can be a counterpart to itself.

(7) So, there is no such thing as counterparts (in the sense of Lewis or Fitch) in Scotus.

(8) What makes an individual an individual (i.e., incommunicable and numerically different from other individuals) is its haecceitas by which it is contracted from the common nature.

(9) One and the same individual can be in different possible worlds, even if it shows qualitative differences in them.

(10) In Scotus, individuals are not world bound.

(11) Haecceitas is a principle of transworld identity as well as a principle of individuation in Scotus.

5. Conclusion

In this paper, I have shown that we have reasons to believe that in Scotus we have modal metaphysics with transworld individuals rather than counterpart theory with world bound individuals. I think that these reasons can further the controversy between Langston and Knuttilla in a constructive way. If so, we have taken one sure step toward a Scotistic modal metaphysics.

Notes

(1) Cf. S. Knuuttila, Modalities in Medieval Philsophy, (London: Routledge, 1993).

(2) D. C. Langston, "Scotus and Possible Worlds", S. Knuuttila, S. Ebbesen, and R. Tyoerinoja (eds.), Knowledge and the Sciences in Medieval Philosophy, Proceedings of the Eighth International Congress of Medieval Philosophy II (Helsinki: Luther-Agricola Society, 1990), 240-247.

(3) Knuuttila, Modalities in Medieval Philosophy, p. 144f; See also, Knuuttila, "Duns Scotus and the Foundations of Logical Modalities", L. Honnefelder et al. (eds.), John Duns Scotus: Metaphysics and Ethics, (Leiden: E. J. Brill, 1996), p. 131f.

(4) B. Mates, "Leibniz on Possible Worlds", in B. van Rootselaar and J. F. Staal (eds.), Logic, Methodology and Philosophy of Science, vol. 3, (Amsterdam: North-Holland Publishing Company, 1968), 507-29; Reprinted in Leibniz, (ed.) H. Frankfurt, (Notre Dame: University of Notre Dame Press, 1972), 335-364.

(5) D. Lewis, "Counterpart Theory and Quantified Modal Logic", Journal of Philosophy 65 (1968), 113-26; REprinted with Postscripts in his Philosophical Papers, Vol. 1, (Oxford: Oxford University Press, 1983), 26-46.

(6) B. Mates, "Individuals and Modality in the Philosophy of Leibniz", Studia Leibnitiana IV (1972), 110f.

(7) G. W. Fitch, "Analyticity and Necessity in Leibniz", Journal of the History of Philosophy 17 (1979), 29-42; Reprinted in Gottfried Wilhelm Leibniz: Critical Assessments, Vol. 1, (ed.) R. Woolhouse, (LOndon: Routledge, 1994), 290-307; Citation is from the latter, p. 306.

(8) Mates, "Individuals and Modality in the Philosophy of Leibniz", 111.

(9) Ibid., 112-3.

(10) Ibid.., 115.

(11) Fitch, op. cit.., 304.

(12) Ibid.., 301-6.

(13) Ibid.., 302.

(14) Lewis adopts the following eight postulates: (P1) Nothing is in anything except a world; (P2) Nothing is in two worlds; (P3) Whatever is a counterpart is in a world; (P4) Whatever has a counterpart is in a world; (P5) Nothing is a counterpart of anything else in its world; (P6) Anything in a world is a counterpart of itself; (P7) Some world contains all and only actual things; (P8) Something is actual. Lewis, op. cit., 27.

(15) Fitch, op. cit., 304.

(16) Lewis, op. cit., 28-9.

(17) Fitch, op. cit.., 297-301.

(18) Lewis, op. cit., 28-9.

(19) Woosuk Park, "Haecceitas and the Bare Particular", Review of Metaphysics, 44 (1990), 375-97.

(20) John Duns Scotus, Lectura II, dist. 3, q. 1 in Opera omnia, ed. Balic (Vativan: Typis Polyglottis Vaticanis, 1954-1982); Duns' Scotus' Early Oxford Lecture on Individuation, (ed.) A. B. Wolter (Santa Barbara: Old Mission, 1992).

(21) Scotus proposed two arguments that jointly demonstrate that there must be something positive in the category of substance that individuates the specific nature. His first argument aims to show that something positive is necessary for the individuation of the specific nature, thereby rejecting the nominalist position; dist. 3, q. 6, n. 166.

(22) Dist. 3, q. 6, nn. 170-2.

(23) He writes; "In Duns Scotus it is explained in terms of the Divine Omniscience and the individual essence(haecceitas)". Knuuttila, "Being Qua Being in Aquinas and Scotus", S. Knuuttila and J. Hintikka (eds.), The Logic of Being, (Dordrecht: D. Reidel, 1986), p. 212; It is also interesting to note that in young Leibniz's discussion of individuation in his Disputatio metaphysica de principio individui (1663) we find clear evidence that he distorted Scotus's notion of haecceitas. See W. Park, "Haecceitas and Individual Essence in Leibniz", Meeting Of the Minds: The Relations between Medieval and Classical Modern European Philosophy, (ed.) S. F. Brown, (Brespols, 1998), 359-375.

(24) John Duns Scotus, Lectura II, dist. 3, q. 1, n. 21; Duns Scotus' Early Oxford Lecture on Individuation, p. 13.