CRITICAL NOTICE OF ARMSTRONG’S AND LEWIS’
CONCEPTS OF SUPERVENIENCE

(Published in SATS – Nordic Journal of Philosophy vol. 3 (no. 1, 2002.), pp. 119-122.)

This notice has a simple message: Both David M. Armstrong and David Lewis are using concepts of supervenience that differ essentially from R.M. Hare’s corresponding concept. As far as I know, neither Armstrong nor Lewis, nor anybody else, has ever made this fact clear. Also, Armstrong’s and Lewis’ concepts differ from each other. All philosophers interested in problems of reduction have to keep Hare’s, Armstrong’s, and Lewis’ concepts of supervenience distinct.

The thought of writing a notice with this message came to my mind when I read Armstrong’s A World of States of Affairs.[i] It turned into actual writing when I read the new essays on Lewis’ philosophy that are collected in Reality and Humean Supervenience.[ii] As things turned out, I had just completed the notice when I heard about Lewis death (October 14, 2001). Perhaps there will now arise attempts to situate Lewis’ philosophy more definitely. If so, then this notice will be important.

In the last three decades, several Anglo-American philosophers have developed and defined concepts of supervenience like those of weak, strong, and global supervenience; and this discussion continues.[iii] However, since neither Armstrong’s nor Lewis’ definition has been an important part of this discussion, I will not relate to it either. That is, I will not discuss whether or not the concepts of weak, strong, and global supervenience can be subsumed under any of the three concepts that I will distinguish between: Hare-supervenience, Armstrong-supervenience, and Lewis-supervenience.

When Hare began to use the term supervenience in order to nail down a special feature that he found important for the analysis of prescriptive words (e.g. ‘morally good’),[iv] he very explicitly built two requirements into supervenience. Firstly and famously, he required that if two particulars are indiscernible with respect to base entities then necessarily they are indiscernible with respect to the supervenient entity, too. Let me call this ‘the indiscernibility requirement’. Secondly, he required that the supervenient entity should not be entailed by the base entities. I quote: ‘it is not the case that there is any conjunction C of descriptive characteristics such that to say that a man has C entails that he is morally good’.[v] Let me call this ‘the non-entailment requirement’.

When later on Hare gave some second thoughts on his own concept,[vi] he was equally definite that there are two requirements that a word that denotes a supervenient property has to meet. For instance, as Hare made clear, in spite of the fact that the property of being hexahedral meets the indiscernibility requirement, it does not meet the non-entailment requirement. Firstly, if two rooms are exactly similar with respect to their sides and the angles between them (i.e., with respect to some presumed base properties), then necessarily they are exactly similar with respect to their overall (hexahedral) shape, too. Secondly, a description of all the sides and the angles between them entails that the rooms are hexahedral. Therefore, being hexahedral is not a supervenient property.

According to Armstrong, ‘We shall say that entity Q supervenes upon entity P if and only if it is impossible that P should exist and Q not exist, where P is possible’, and ‘supervenience in my sense amounts to entity P entailing the existence of entity Q’.[vii] Two observations can easily be made. First, all entities that conform to Armstrong’s definition of supervenience conform to Hare’s indiscernibility criterion, too. If Q Armstrong-supervenes on P, then necessarily if two particulars have the same base entity P they have the same supervenient entity Q, too. Secondly, no entity that conforms to Armstrong’s definition can possibly conform to Hare’s non-entailment criterion. In order to apply the term ‘supervenient entity’, Armstrong requires entailment whereas Hare requires non-entailment.

Armstrong’s concept of supervenience is wholly distinct from Hare’s concept. Their extensions cannot have one single entity in common. That follows from the definitions, and both Armstrong and Hare stick to their definitions when they give examples. For instance, relations like ‘resemblance’ and ‘being longer than’ are Armstrong-supervenient on the joint existence of their relata. But they are not Hare-supervenient. Hare would, no doubt, reckon them as belonging to the same class as ‘being hexahedral’. Now to Lewis-supervenience.

In the introduction to volume II of his Philosophical Papers, Lewis says that many of the papers seem to him ‘in hindsight to fall into place within a prolonged campaign on behalf of the thesis I call “Humean supervenience”’.[viii] The same perspective is also stressed by G. Preyer and F. Siebelt, the editors of Reality and Humean Supervenience.[ix]

In a world or part of a world where there is Humean supervenience, there are by definition no necessities in and between the particulars as such. All the particulars of such an aggregate whole are in their spatiotemporal existence both logically and nomologically independent of each other. However, according to Lewis, even in such a contingent ‘spatiotemporal arrangement of local qualities’[x] other qualities can supervene. Both Lewis himself and Preyer and Siebelt give their readers the impression that Lewis is using a quite ordinary concept of a supervenience relation, but that he puts restrictions on what kind of base entities that are allowed to enter the relation. But this is a false impression. Lewis’ concept of supervenience differs from those of both Armstrong and Hare.

According to Lewis, ‘To say that so-and-so supervenes on such-and-such is to say that there can be no difference in respect of so-and-so without difference in respect of such-and-such’[xi], and ‘Supervenience means that there could be no difference of the one sort without difference of the other sort. Clearly, this “could” indicates modality’.[xii] Whereas most writers on supervenience are using formulations like ‘base entity indiscernibility entails supervenient entity indiscernibility’, Lewis is mostly using formulations like ‘supervenient entity difference entails base entity difference’. However, these two formulations are logically equivalent. Both of them forbid that there are two particulars that have the same supervenient entity but have different base entities.

Lewis does not take Hare’s non-entailment requirement into account when he defines supervenience. The indiscernibility requirement, which for Hare is merely one of two requirements on supervenience, becomes for Lewis the whole definition.

Some logical relationships that obtain between Lewis-supervenience, Hare-supervenience and Armstrong-supervenience are the following ones:

(a) every entity that is Hare-supervenient is Lewis-supervenient,

(b) every entity that is Armstrong-supervenient is Lewis-supervenient,

(d) every entity that is Lewis-supervenient is either Armstrong-supervenient or
Hare-supervenient.

Ad (a): Everything that conforms to Hare’s two requirements conforms to Lewis’ definition since this definition is identical with one of the requirements.

Ad (b): I have earlier pointed out that everything that is Armstrong-supervenient is Hare- supervenient, and since, as just remarked, Hare-supervenience entails Lewis-supervenience, Armstrong-supervenience entails Lewis-supervenience, too.

Ad (c): As I have remarked earlier, this follows from the definitions.

Ad (d): If an entity S is Lewis-supervenient on B (i.e., S meets the indiscernibility requirement), then either B entails S or B does not entail S; in the first case there is by definition Armstrong-supervenience, and in the second case there is Hare-supervenience since then both his requirements are met.

Next thing to be noted is that Hare-supervenience and Armstrong-supervenience are differently related to problems of reduction. Because of its non-entailment requirement, Hare-supervenience contains a kind of nonreduction. Armstrong-supervenience, on the other hand, means entailment and contains a kind of reduction. Consequently, if one only has proved that something (S) is Lewis-supervenient on something else (B), one has not thereby proved that S is reducible to B. However, that seems to be Lewis’ false opinion. According to him: ‘A supervenience thesis is, in a broad sense, reductionist’.[xiii]

Lewis’ grand philosophical project is to show that laws of nature, counterfactuals, causation, persistence in time, mind, language, and chance are all of them Lewis-supervenient properties on material particles and spatiotemporal relations, i.e., to show that they are Hume-supervenient.[xiv] As a ‘fairly uncontroversial’ example of what supervenience can be like, he offers his readers the following:

A dot-matrix picture has global properties – it is symmetrical, it is cluttered, and whatnot – and yet all there is to the pictures is dots and non-dots at each point of the matrix. The global properties are nothing but patterns in the dots. They supervene: no two pictures could differ in their global properties without differing, somewhere, in whether there is or isn’t a dot.[xv]

A dot-matrix pattern is of course Lewis-supervenient, but it is Armstrong-supervenient, too. The pattern is entailed by the simpler properties and relations in about the same way as being hexahedral is entailed by simpler properties and relations. If the dots are there, it is entailed that the pattern is there. That explains why, when one paints dots, a pattern comes into existence simultaneously. However, it seems as if Lewis mistakenly thinks that the same kind of entailment relation can be found in everything that he can show to be Lewis-supervenient. In other words, he gives the false impression that everything that is Lewis-supervenient is Armstrong-supervenient. Even if it would be true that laws of nature, counterfactuals, causation, persistence in time, mind, language, and chance are Lewis-supervenient on Humean base facts, this does not mean that they are nothing but patterns in Humean facts. They could just as well be Hare-supervenient nonreducible phenomena.

NOTES

[i] David Armstrong, A World of States of Affairs (Cambridge: Cambridge University Press, 1997).

[ii] G. Preyer and F. Siebelt (eds.), Reality and Humean Supervenience (Lanham: Rowman & Littlefield, 2001).

[iii] I am thinking of papers like those collected in the anthology edited by Savellos, E.E. and Ü.D. Yalçin, Supervenience. New Essays (Cambridge: Cambridge University Press, 1995). If one specific philosopher should be made the symbol of this kind of philosophy of supervenience, it ought to be Jaegwon Kim. His most important papers are reprinted in Kim, Supervenience and Mind (Cambridge: Cambridge University Press, 1993). A new anthology (edited by Kim) called Supervenience is announced to be forthcoming on Ashgate in 2002.

[iv] R.M. Hare, The Language of Morals (London: Oxford University Press, 1952).

[v] R.M. Hare, The Language of Morals, p. 145.

[vi] R.M. Hare, ’Supervenience’. Aristotelian Society Supp., vol. 58 (1984): 1‑16.

[vii] David Armstrong, A World of States of Affairs, p. 11.

[viii] David Lewis, Philosophical Papers vol. II (Oxford: Oxford University Press, 1986), p. ix.

[ix] See their preface and their own contribution (chapter 1) to Reality and Humean Supervenience.

[x] David Lewis, Papers in Metaphysics and Epistemology (Cambridge: Cambridge University Press, 1999), p. 226; see also Preyer and Siebelt, Reality and Humean Supervenience, pp. vii and 2.

[xi] David Lewis, Papers in Metaphysics and Epistemology, p. 29.

[xii] David Lewis, On the Plurality of Worlds (Oxford: Basil Blackwell, 1986), p. 15.

[xiii] David Lewis, Papers in Metaphysics and Epistemology, p. 29.

[xiv] David Lewis, Philosophical Papers vol. II, pp. xi‑xiv.

[xv] David Lewis, On the Plurality of Worlds, p. 14.