On natural properties in metaphysics

Barry Taylor

Michael Dummett has characterized the primary claim of realism as being that sentences are objectively true. But even if he is right, so that it is at the level of sentences that realism’s essence is revealed, realists have traditionally also had these to advance about the components out of which sentences are built. One of these, of course, is the claim that at least some singular terms stand for entities which exist objectively and independently of mind. Another, the topic of this paper, is that at least some predicates stand for natural properties; that is, that they record objective cleavages in nature, schisms in things independent of human psychology or convention, marking entirely mind-independent similarities between things.

Historically, the importance in realist metaphysics of doctrines of natural properties will be obvious: in Plato’s distinction between predicates like “just” and “pious” which mark the Forms, and those like “dirt” and “hair” which do not; in Aristotle’s contrast between predicates like “man” which stand for substantial forms, and those like “musician” or “statue” which correspond to mere accidental unities or to artifacts; and in the consequent doctrines of species, genera, and real essence which run through the scholastics to the moderns. But with Kant and the passing of traditional realism, and more so with the linguistic turn and the passing of traditional metaphysics in its entirety, doctrines of natural properties went rather out of fashion, and in the analytic tradition of this century they find few defenders. True, Quinton (1957) and Quine (1969) dabble with the natural, but both end up with an account too tainted with psychology to count as a true doctrine of natural properties in the present sense. Which leaves just a few isolated figures, such as the trope theorist Donald C. Williams (1953), as the last friends natural properties have.

Or did, until quite recently. For as the linguistic turn loses impetus, metaphysics has been reborn within the analytic tradition and realists have re-embraced doctrines of natural properties. Keith Campbell (1990) and David Armstrong (1978) are prime exemplars of the trend. But nowhere are natural properties put to more sophisticated use than in the metaphysical system of David Lewis. This paper examines the reasons Lewis gives for believing in natural properties, and charts and evaluates the way he deploys them. In so doing, my discussion per-force engages with the detail of Lewis’s system, but I trust the morals drawn are more general; that clarifying the standing of natural properties within the most comprehensive contemporary system of realist metaphysics sheds light on their significance for any system with reasonable claims to be an alternative.


What then are the ways Lewis appeals to the notion of a natural property in elaborating his metaphysics?

(a) There is the use of the notion to found the concepts of the theory of duplicates. Two things are defined as duplicates iff they have the same perfectly natural properties (Lewis 1983,p. 356 and 1986a,p. 61, treating the second clause as redundant; all subsequent references are also to the works of Lewis, unless otherwise specified). Then intrinsic properties emerge as properties which can never differ between duplicates (1983, p. 62; 1986a, p. 355). Generalizing this definition beyond the monadic case gives the category of internal relations (1983, p. 356 fn. 16; 1986a, p. 62). And events are properties of regions which are predominantly intrinsic (1983, p. 369; 1986c, p. 7). Thus these categories, arising through duplicate theory out of the perfectly natural properties, become available for use in familiar dilemmas and theses of Lewisian metaphysics. So for example the problems of accidental and temporary intrinsics (1986a, pp. 201-2), central to his doctrines in the metaphysics of identity, make essential use of duplication-theoretic terminology. So too does the dilemma posed for the “magical ersatzist” (1986a, pp. 179 ff.), who is embrassed by a demand to classify his relation of “selection” as internal or external. Duplicate theory is used to frame the ban on “backtracking counterfactuals” critical in the celebrated analysis of causation (1983, p. 361; and see the references there cited). And it figures in the formulations of some of the central supervenience claims which shape debate in the Lewisian system, such as materialism–the doctrine that “among worlds where no natural properties alien to our world are instantiated,… any two…that are exactly alike physically are duplicates” (1983, p. 364); or the even more fundamental thesis of “Humean supervenience” (1986b, pp. ix ff.).

(b) Natural properties also play a role in the analysis of legality. It won’t quite do, according to Lewis, just to say Ramsey-style that laws are those regularities which are entailed by a systematization of the truths which combines maximal breadth of coverage with maximal simplicity. For the simplicity of the systematizsation will depend in part on the vocabulary in which it is stated, and without some prior constraint on permissible vocabulary the simplicity requirement is too easily satisfied to have any real bite. The solution is to constrain the vocabulary by requiring that its primitive predicates must stand for perfectly natural properties (1983, pp. 366-8; 1986b, pp. 123-4). It follows that perfectly natural properties are implicated not only in the analysis of laws themselves, but also in other concepts into whose analysis laws enter–most notably, causation, since laws are involved in spelling out its counterfactual analysis (1983, p. 368). There is, however, some overkill here, since duplicate-theory has already entangled causation firmly in the web of natural properties, through the formulation of the ban on backtracking and the analysis of the events which cause connects (1983, p. 369).)

(c) Finally, there is the use of natural properties to formulate a constraint on the assignment of content, primarily of content to propositional attitudes. It is a commonplace in the theory of interpretation that the assignment of content to propositional attitudes should obey principles of fit, so that content is assigned in such a way that an agent is attributed a system of beliefs and desires which so far as possible “rationalize” their behaviour; where a belief/desire system rationalizes behaviour if that behaviour, given the attributed beliefs, can be seen as directed towards fulfilment of the attributed desires. Lewis’s complaint is that such principles of fit do not go far enough in restricting assignments of content, leaving too many bizarre assignments still legitimate. So be proposes the imposition of a further constraint (the “principle of humanity”, as he sometimes calls it), dictating that amongst content-assignments which satisfy the principles of fit we should prefer those in which the assigned content deals with more natural properties (1983, p. 1986a, pp. 38-9 and 107).

Two puzzles get solved by wielding this principle. One is the Wittgensteinian rule-following conundrum (in Kripke’s formulation), of whether an agent is to be interpreted as adding or quadding (where to quadd is just like to add, until the sum reaches some limit which our agent’s additions have in fact never yet reached; after which limit quadding diverges from adding, and always yields 5 as the result of the quaddition). For though attributing to the agent either the desire to add or the desire to quadd is equally consistent with the principles of fit, because adding is a more natural property than quadding the principle of humanity forces interpretation to regard the agent as an adder rather than a quadder (1983, p. 376). A second application uses the principle of humanity to turn a nasty cardinality objection to modal realism coming from Kaplan/Peacocke. This objection rests on the assumption that any proposition can be the object of a legitimate belief; but Lewis feels safe in rejecting the assumption, on the ground that propositions involving grotesquely unnatural properties could never figure in belief-attributions legitimized by the principle of humanity (1986a, pp. 104-8).

There is a further, derivative deployment of the same principle. For, fully spelt out, the principles of fit entail that there should be a harmony between the meanings assigned to an agent’s words, and the contents assigned to their attitudes. It follows that the principle of humanity, as an additional constraint on the assignable contents to attitudes, must involve a further constraint on the legitimate assignment of meanings. Roughly, this constraint requires that no legtimate assignment of meanings can construe predicates as standing for properties which are too unnatural. Putnam’s celebrated model-theoretic argument against metaphysical realism, however, depends on counting as legitimate a meaning-assignment which cannot be shown to pass this test. Which gives Lewis his best and most serious argument against Putnam (1984, pp. 226-9).

Thus the familiar theses of modal realism, and the arguments Lewis deploys in its defence, depend not only on the obvious modal paraphernalia–the plurality of worlds and their inhabitants, the relations of counterparthood and closeness–but also on the natural properties, and the apparatus which they underpin. The point will be a familiar one to anyone who has read Lewis’s systematic statements of his overall position, but may come as news to any who, concentrating on detailed work on specific topics, may be tempted to take the odd mention of natural properties as an eliminable obiter dictum.


What is the logical status of the notion of the natural in Lewisian metaphysics? Lewis vacillates between two alternatives (1986a, pp. 63-9): whether it is best treated as primitive, or as defined within a deeper underlying metaphysic.

Suppose first it is a primitive; precisely what is the primitive required? In framing duplicate theory and analysing legality, we made use of an absolute concept (“perfectly natural properties”), whereas in writing the constraint on content the notion needed is relative (“more natural properties”). The obvious approach is to treat the relative notion as the more basic. Then we may take as our primitive the two-place predicate “[P.sub.1] is at least as natural as [P.sub.2]” (where P.sub.1] and [P.sub.2] are properties–i.e., in Lewis’s terms, classes of this- and other- worldly individuals), and define a perfectly natural property P as one which is at least as natural as any property [P.sub.1]. Alternatively, we can treat the absolute notion as the more basic, taking as our primitive the one-place predicate “P is perfectly natural”. Then we can introduce a measure of the complexity whereby other properties are definable out of the perfectly natural ones, and explain the relative concept “[P.sub.1] is more natural than [P.sub.2]” as meaning that [P.sub.1] is definable out of perfectly natural properties in a less complex way than is [P.sub.2]. This second alternative seems messier than the first, but seems to be the one Lewis himself has in mind (1983, p. 376; 1987a, p. 61).

One complication. Properties, it was just said, are classes for Lewis; but in fact in his most recent work(1) he advocates reducing use of specifically class-theoretic apparatus to an absolute minimum, and mereology and plural quantification are made to do much class-theoretic work. This means that in the most up-to-date presentation of his theory, the primitives would not be predicates of properties/classes as here, but would rather be “multigrade” predicates of individuals with no fixed adicity. So the primitives would be “[x.sub.1], [x.sub.2], [x.sub.3] … are jointly at at least as natural as are [y.sub.1], [y.sub.2], [y.sub.3] …” if the relational notion is taken as basic; or “[x.sub.1], [x.sub.2], [x.sub.3] … are jointly perfectly natural” if the absolute notion is favoured. We shall, hovever, continue to talk class-theoretically for the sake of perspicuity; if Lewis’s strategy works, applying his techniques will eliminate such talk here as in other contexts.

What of the alternative approach to taking natural properties as somehow primitive, namely somehow founding them upon an underlying metaphysics? Specifically, what Lewis has in mind is that the underlying metaphysics should take the shape of an ontology either of universals or of tropes (1986a, pp. 64-9). The version of the theory of universals he considers is one which posits universals corresponding precisely to the perfectly natural properties, so that to each perfectly natural property there corresponds a universal and vice versa. Then a perfectly natural property can be defined as a maximal class of individuals all of which instantiate some one universal. Similarly, his preferred theory of tropesis one which posits, for each perfectly natural property, a class of duplicate tropes, precisely one of which is present in any individual displaying the property in question. Then call a class trope-unified if in each member of the class there inheres a trope which is a duplicate of some trope inhering in any other member of the class, and we can define a perfectly natural property as a maximal tropeunified class. (Notice how, in both cases, it is the absolute, nonrelative notion of natural property which emerges with most ease from the underlying metaphysic. This perhaps is why Lewis seems to favour this as the more basic notion, even though, as we noted two paragraphs back, it would otherwise seem more attractive to take the relative concept as the more fundamental.)

Though Lewis is officially undecided as to which of three ways of treating natural properties–assumption as primitive, or metaphysical foundation in either the universal or the trope version–is the best (“I think the honours are roughly even, and remain undecided” (1986a, p. 64)), there is also evidence that his preferences lie on the side of ontological underpinning if that can in any way be made to work, with his reluctance to come out on that side outright being due to misgivings about the solidity of the underpinnings–about the possibility of fully articulating and defending a theory of tropes or universals in detail irrelevantfor present purposes but crucial for its metaphysical credentials. Thus he writes “I would willingly accept the distinction as primitive, if that were the only way to gain the use of it elsewhere in our analyses” (1986a, p. 63; my italics), and the structure of his sentence betrays his preference for a version which avoids primitive predicates in favour of defined ones. But the grounds for this preference are unclear. For the ontological underpinned versions of the theory merely replace a primitive predicate with equally primitive ontological assumptions of the existence of appropriate metaphysical entities. The definitions canvassed of the primitive predicate involve no dismantling of murky conceptual components, offer no insight into the metaphysically obsure.

A speculative explanation for Lewis’s preferences here may be that the ontologically-based verions have in his eyes the ment of emphasizing the objective character of facts about natural properties; that they are, as he puts it, “carved at the joints, so that their boundaries are established by objective sameness and difference in nature” (1986a,p. 227), so that the distinction between natural properties and the rest is written into the world and independent of us and our interests –“it’s not that we’re built to take a special interest in natural properties, or that we confer naturalness on properties when we happen to take an interest in them” (1983,p. 377). Now there is in Lewis a tendency to locate the springs of all realism in the existence of some kind of objects: “For me, the question is of the existence of objects–not the objectivity of a subject-matter” (1986a, p. viii). (True, the primary reference of “the question” in this quote is to modal realism, but the context links the passage to more general “present day discussions of what ‘realism’is”.) Perhaps, then, Lewis’s predilection for ontologically-based versions of natural properties arises from this tendency to connect all objective distinctions with the existence of appropriate objects. Be this as it may, there is no evident need for anyone else to follow Lewis in this idiosyncrasy: the points he wants to make about natural properties can be just as well made within a framework of primitive naturalness by stressing that it is an objective and mind-independent matter whether or not a propery falls into the extension of the perfectly natural. That is, prima facie the point can be entirely accommodated by talking of the objectivity of facts (about the extensions of predicates), and failing further argument to the contrary there seems no point in following Lewis’s tendency to seek to explicate this in terms of the existence of objects.

Mention just made of the connexion between perfectly natural properties and “objective sameness and difference in nature” might suggest that exploiting this connexion could lead to the sort of insightful conceptual analysis of natural properties which, it seems, the metaphysics of universals or tropes are impotent to provide. Lewis toys with this idea in a footnote.(2) It turns out that to make it work even at a formal level we need to help ourselves to a complex relation of property contrast to record the facts of objective sameness and difference, viz. the relation

the elements of [P.sub.1] resemble one another and do not likewise resemble

any of the elements of [P.sub.2] or R([P.sub.1], [P.sub.2]) for short. Then we can define “P is a perfectly natural property” as

(Mathematical Expression Omitted). But Lewis is surely right in judging that we have too little independent grasp of this outre relation R of property contrast to regard this definition as marking any real progress in conceptual elucidation.

In sum, it seems that a version of Lewis’s theory which takes natural properties somehow as primitive suffers not at all by comparison with any alternative. For no viable analysis of natural properties is yielded by alternative primitives, or by metaphysical reduction; nor does anchoring natural properties in ontology genuinely secure the objectivity of the natural in a way that taking it as primitive does not. For concreteness, we shall accordingly regard the primitive treatment as canonical; more specifically, the treatment which takes as primitive the non-relational predicate of properties “P is perfectly natural”, that evidently being the version of the primitiveness option favoured by Lewis himself, the merits of a relational alternative notwithstanding.


Why believe in this division of properties into the perfectly natural and the rest? Lewis gives us two distinguishable but related reasons: the division is needed to accommodate Moorean facts of commonsense (1983, pp. 351-5); and it is indispensably presupposed by systematic philosophy (1986a, p. 63).

What are the Moorean facts which can be accommodated only by appeal to the division? Lewis’s discussion of the point is complicated by the fact that it is intertwined with his assessment of Armstrong’s views on universals. So he takes over Armstrong’s examples and terminology, and accepts part of the Armstrongian mix whilst rejecting other elements; and a little care is needed to keep track of just which elements are being endorsed. Certainly, Lewis thinks, and convincingly argues, that Armstrong’s beloved One over Many Problem is a pseudo-issue. Accordingly, he rejects Armstrong’s attempts to connect accommodation of Moorean facts with solving the Problem. Still, that there are Moorean facts to be accommodated is common ground, and Lewis evidently also goes along with Armstrong’s identification of what these facts are: they are facts of “apparent sameness of type” (1983, pp. 351 ff.; cf. Armstrong 1978, pp. 12 and 16). Here “apparent” does not mark any connexion with the phenomenal, nor is it meant to imply that the Moorean “facts” might only seem to obtain; rather, it signifies that the “sameness” in question is less than absolute or complete, being a sameness holding between particulars which are uncontroversially distinct. So the Moorean facts in question are of the form “a and b are of the same type”, or “have some common property” (1983, p. 355). Giving an account of these Moorean facts is, in words Armstrong uses (1978 p. 17) and Lewis endorses, “a compulsory question in the examination paper”. And we can give such an account only by helping ourselves either to a primitive notion of naturalness (so that we can explain that “a and b are of the same type” means “there is some natural property which is instantiated by both a and b”), or else to other apparatus which can be used, by the techniques of the last section, to underpin the natural.

Or so Lewis puts it, at any rate (1983, p. 352). Evidently there is some simplification going on. For the canonical version of Lewis’s theory, as we saw, takes as its primitive not the simple predicate “is a natural property”, but the more sophisticated “is a perfectly natural property”. Now in Lewis’s view, the perfectly natural properties are few in number, and, in paradigmatic cases at least, they apply not to the medium-sized objects of commonsense but to the point-particles of science; typical examples he gives are properties of mass, of charge, and of quark flavour and colour (1986a, pp. 66-7; 1986b, pp. ix-x). Hence we can directly explain what it is for a and b to be of the same type using the canonical primitive of perfect naturalness (“a and b are of the same type iff there is some perfectly natural property which is instantiated by both a and b”) only in the special cases where a and b are point-particles, or similar arcane items. Explananda like these are, however, odd examples of Moorean facts, if these are to bear any resemblance at all to the sort of facts which interested the Moore who once professed in Cambridge. For the resemblance to hold, we should rather expect Moorean facts to be statable in the everyday language of ordinary folk and to relate more directly to their interests–to be such facts as that a (Pharlap) and b (Tulloch) are of the same type (horses). Explaining facts like these in terms of the perfectly natural properties (or of apparatus apt to underpin them) will be a messy indirect business–“Pharlap and Tulloch instantiate some property definable in some not-too-complicated fashion out of perfectly natural properties.” Lewis’s point remains intact; these Moorean facts, he will maintain, can be accommodated only by invoking perfectly natural properties or apparatus apt to underpin them. Still, the genuinely Moorean facts are accommodated less directly and more messily than are pseudo-Moorean ones concerning point-particles.

To Lewis’s own Moorean facts of apparent sameness of type, borrowed from Armstrong, we may suggest adding some more, viz. those of “comparative communality”. I mean such facts as that horses have more in common than can-openers, green things than blue-or-green ones, and so on. For these evidently fit the bill for Moorean status, as commonsense truisms or ordinary folk; and the claim that they can be accommodated only by appeal to perfectly natural properties or apparatus apt to underpin them seems every bit as strong as in the case of facts of apparent sameness of type. They would, of course, be most neatly and directly accommodated within that version of Lewis’s theory which we have deemed non-canonical, and which takes the relation “is more natural than” as its primitive. But other versions of the theory will also serve to accommodate them, each in their own clumsier and less direct fashion.

If accommodating these Moorean facts is a compulsory question on the philosophical examination-paper, then Lewis’s first ground for insisting on the division of properties into the perfectly natural and the rest–that the division must be invoked for the facts to be accommodated–is just a special case of the second ground, that there can in general be no good answer-paper to the philosophical examination which does not invoke the division. Although the first argument from Moorean facts is thus in a sense subsumed under the second argument from the general demands of philosophy, it is helpful to have it separated out as of special importance. For as we shall see, its specificity enables a sharper debate than is easily conducted over the sweeping general claims of the second argument.


None of the above withstanding, I come to bury natural properties rather than to praise them. In describing the natural properties as those which carve nature at the joints, I have faithfully reproduced the doctrine of their proponents; but I confess to finding these joints utterly mysterious, the manner of the carving entirely arcane. Systematic theorists do better, I suggest, to eschew such esoterica. In their place, I offer a vegetarian substitute: the cosy properties, or more precisely, the T-cosy ones–those properties which are cosy relative to a theory T. These I envisage as defined in terms of a more primitive notion, that of the T-cosy predicates. The basic idea is that these are the predicates playing the more central and fundamental classificatory roles within T.

One method, and my preferred one, for trying to make this idea more precise is to attempt to explicate it in terms of the deductive connexions between predicates revealed in an axiomatic formulation of T. This method in turn could be implemented in a number of ways. The one I shall try depends on the idea that a primitive predicate F of T is to be deemed more central to T (or T-cosier than) another primitive predicate G if, by T’s lights, G can be instantiated only if F is; whilst nonprimitive predicates will derive their cosiness from the primitives out of which they are constructed.

Descending to details: let the atom of an n-place predicate F of T be the formula [[unkeyable]x.sub.1]…[[unkeyable]x.sub.n][Fx.sub.1]…[Fx.sub.n]. Say that atom a T-implies atom b iff a [[unkeyable].sub.T]b, and that a and b are T-equivalent iff a T-implies b and b T-implies a. Form equivalence classes of atoms under the relation of T-equivalence, and call these the atom-classes. Then the atom-classes are partially ordered by the relation [is less than or equal to], where x [is less than or equal to]y iff every atom in x T-implies every atom in y. Now take a primitive predicate F as T-cosier than a primitive predicate G iff F’s atom belongs to an atom class higher in this partial ordering than the atom class to which G’s atom belongs; and take a primitive predicate F as perfectly T-cosy iff its atom belongs to an atom class which is a maximal element in the partial ordering. (There will be some of these, of course, assuming there are only finitely many primitive predicates in T.) Notice that it follows from these definitions that primitive F is T-cosier than primitive G iff the atom of F T-implies the atom of G; and that primitive F is perfectly T-cosy iff it T-implies only atoms by which it is itself also T-implied.

Two wrinkles on this. The idea is that a predicate earns its cosiness rating by being treated in the proof theory of T as comparatively more fundamental than other predicates. But it will be too easy for any predicate to become perfectly cosy simply by T deeming its atom an axiom. Therefore the relation [[unkeyable].sub.T] appealed to in the above definition of T-implication should more accurately be taken as [[unkeyable].sub.T*], where T* is T minus any existential axioms. For similar reasons, the logical predicate = had better be excluded from any place in the ranking, else it will count trivially as the only perfectly T-cosy predicate, no matter what T should happen to be.

Now we can extend the notion of cosiness to predicates beyond the primitive using a move similar to one we have seen Lewis employ. Begin by defining a metric of T-cosiness over the primitive predicates, based upon the partial ordering just established. (I suggest as a starter that we might take a predicate’s degree of T-cosiness as the number of atom-classes which, in the partial ordering, intervene between its own atom-class and a maximal element. This will give the perfectly T-cosy predicates a degree of T-cosiness of 0, and higher ratings as T-cosiness decreases.) Then take the degree of T-cosiness of a nonprimitive predicate as a function of the complexity of its definion in terms of primitive predicates and of the degree of T-cosiness of those primitives. For present purposes, nothing will depend on the details of the way this is done, though we will assume that a complex predicate always has a lower degree of T-cosiness than does any primitive predicate involved in its definition. It will follow that only a primitive predicate can be perfectly T-cosy. But notice that nothing prevents a complex predicate from being merely T-cosy–all that is needed is that the extended metric rates it as having a degree of T-cosiness at least as high as that awarded to some primitive predicate already counted as T-cosy.

And now by semantic descent we can reflect this terminology onto the ontological level. Thus, a T-cosy property is the class of all this and other-worldly things of which is true some T-cosy predicate; and so on.

The theories to which cosiness is thus relativized are intended, of course, to be formalized ones; otherwise it is unclear what are to count as the “primitive predicates” of my definitions, nor will the proof-theoretic relations on which those definitions depend be properly defined. This means it is difficult to illustrate the notions just introduced in detail, failing detailed elaboration of proposed sample formalizations. Still, relative to any reasonable formalization of the theory of commonsense, we may confidently predict that “horse” will be less cosy than “animal”, and “coloured” than “extended”, since in each case the atom of the former will imply within regimented commonsense the atom of the latter. And within regimented physics, and unified science if that elusive theory ever gets regimented, “quark” and the properties and relations of point-particles will rate as very cosy indeed, plausibly as perfectly cosy.

There are, I claimed earlier, other ways in which one might try to explicate the intuitive idea of the cosy predicates as the central and fundamental predicates of a theory, besides this attempt to do so in terms of the deductive relations holding within the theory. One such alternative would be to appeal to the way in which predicates are used by the adherents of the theory. And one way of implementing this strategy would be to emphasize the importance of the uses of predicates in acts of inductive projection, and to identify the degree of cosiness of a predicate of T with its degree of entrenchment in the sense of Goodman (1983). I prefer not to take this as my first explicatory option, since it introduces temporal complications and needs development if relational predicates are to be properly incorporated. But it will do as a strong fallback position.(3)

Like Lewis’s division of properties into the natural and the rest, the cosy/non-cosy divide, however explicated, separates properties in a way roughly coinciding with their felt importance. There the resemblance ends. My division is relative; his is absolute. More importantly, mine is grounded in human classificatory practices, being nothing more in fact than a systematic enshrinement of the familiar; his is grounded in the nature of things, the purported joints of reality. I have confessed already to finding these joints entirely mysterious, and submit that an unmysterious dichotomy like mine must be preferable, if only on the ground that it can, one way or another, be analyzed and explained rather than taken as primitive. Provided, of course, that with its aid Lewis’s arguments in favour of his own division can be countered.


First: can I, armed with my own paltry distinction, meet Lewis’s challenge and answer Armstrong’s compulsory question on the philosphical examination paper, the one about the Moorean facts concerning apparent sameness of type?

Good examinees always read the question carefully before attempting an answer. In this case, however, neither Armstrong nor his co-examiner Lewis has bothered to spell the question out. Setting the question seems to be part of the exercise.

Looking at the works of the historical Moore for clues, what we primarily find is a claim rather than an interrogation; the claim, namely, that certain basic precepts of commonsense are true, and are known with certainty by ordinary people to be so. Perhaps, then, the question our examiners have in mind demands that we provide a defense of Moore’s claim, taking the relevant precepts as everyday judgements about apparent sameness of type. If so, it is doubtful that they have been entirely fair in making the question compulsory–venerable though Moore’s views might be, it remains philosphically entirely respectable to maintain that his heroic attempt at the refutation of global scepticism does not in the end come off. A fairer question, accordingly, is one which demands not that we actually defend Moore’s claim, but only that we explain its attractiveness, by so explicating the precepts in question as to make it at least highly plausible that they should be true, and should be confidently believed to be true by ordinary folk.

Cosy properties are all I need to answer the question as thus phrased. A commonsense judgement of the apparent sameness of type of objects a and b I construe as meaning that a and b share a property which is cosy relative to commonsense. (So Pharlap and Tulloch are of the same type because they share the property of being a horse, a property which is cosy relative to any reasonable regimentation of commonsense.) The theory of commonsense has stood us in good stead for many a long century, enabling us efficiently to hew wood and draw water. So there is every reason to believe that judgements made by experts in its use are true, especially when the judgements concerned are simple ones involving the more familiar of the categories commonsense employs. But ordinary folk are experts in the use of commonsense, judgements of apparent sameness of type are simple ones, and the cosy predicates are those which mark the more used and familiar categories. So there is every reason to think that the commonsense judgements of apparent sameness of type made by ordinary people are true. And since all of this is itself just commonsense, not only do we have reason to believe these judgements true; so too do the ordinary folk themselves. Similar points can be made about about judgements of comparative communality, suggested above as worthy of setting in the same Moorean class as those of apparent sameness of type. Treating “Fs have more in common than Gs” as meaning that, according to commonsense, being F is cosier than being G, considerations parallel to those just adduced will again yield the result that commonsense judgements of this form are almost certainly true, and can be known to be so by ordinary people.

Indeed, now that the examination question has been explicitly set, it is not entirely clear how Lewis himself has provided an answer to it. Suppose, with Lewis, that “Pharlap and Tulloch are of the same type” is to be explicated as “Pharlap and Tulloch instantiate some property definable in a not-too-complicated way out of the perfectly natural properties”; how does that help us to explain why the original judgement is likely to be true, or that ordinary folk have good reason to think that it is? Of course, Lewis is as free as anyone else to advert to the nature of commonsense and our everyday expertise in order to account for these facts; the point is however that his explication, unlike mine, will be idle in such an account, because his natural properties are in no direct way connected with commonsense expertise.

Indeed his explication may even seem to be directly at odds with the possibility of folk expertise on facts of apparent sameness of type. For if perfectly natural properties are the arcane properties of point-particles which Lewis evidently thinks they are, they are beyond the ken of ordinary folk; so too, a fortiori, are the details of any definitions which link the perfectly natural properties to the classifications of commonsense; hence if Lewis is right about what it takes for Pharlap and Tulloch to be of the same type, knowledge of this simple fact would appear to involve considerations well beyond the comprehension of us ordinary types.

This last point is, however, unfair. Moore (1959, pp. 37, 53 ff.) was at great pains to distinguish between the (ordinary) meaning of the critical propositions of commonsense, and their analysis. The former is transparent, known to all competent in the language, and gives the content of the certainly-known judgements of ordinary people; the latter is highly controversial, often difficult to discover, the subject of the legitimate doubts of philosphical theorisers. There are, of course, well-known difficulties with the distinction, centring largely on the question of how meaning and analysis should relate. But difficulties notwithstanding, some such distinction seems to be constantly presupposed by analytical philosophy. All Lewis need do is insist that his explication is along the lines of a Moorean analysis to free himself from any objection based upon an attempt to mix the content ordinary users judge to be true with that imputed to their judgements by philosophical theory.

But this defensive sword cuts two ways. I suspect that Lewis and Armstrong see one of the great virtues of their explication of judgements of apparent sameness of type as being that it emphasizes the totally objective nature of the facts such judgements concern; indeed, that they regard it as part of the core Moorean meaning of such judgements that they are in this way totally objective and independent of human minds and classifications, so that accounts such as mine, which ground these facts rather in the classifications imposed by human theory and habit, can be rejected out of hand as incompatible with core meaning. I reply that this depends on misplacing the alleged commitment to the objective; that the question of whether there is any such commitment properly belongs to problematic analysis rather than uncontroversial core meaning, and so is up for legitimate debate. In this, incidentally, I seem to have Moore (1959, pp. 57 ff.) as an ally: amongst his live candidates for the analysis of “This is a human hand” is a Millian account in terms of possibilities of sensation, finding at the level of analysis a hidden subjective component in a judgement which is prima facie as objective as any.


I think I have turned Lewis’s first argument in favour of his property dichotomy, the argument from Moorean facts. What of his second argument, that from the alleged indispensability of the dichotomy to systematic philosophy in general?

The claim involved in the argument is sweeping; it is also vague, in the absence of any ageed criteria as to what should count as adequacy in a proposed alternative philosophy. These factors combined mean that stubborn obstinacy will always ensure at least the formal show of defence for Lewis’s position against any counterargument, at any rate against any counterargument which tries to meet his claims head-on and rebut them by developing an adequate philosophy which eschews his dichotomy. For it can always be maintained that the proposed alternative is less than adequate in its treatment of at least some topics, by some austere unstated standard of adequacy; or that, though it may fare more or less well over the topics it discusses, further unspecified topics lurking over the philosophical horizon will necessitate the invocation of natural properties. For the purposes of discussion, however, I shall assume that the burden of proof will be cast back on Lewis if it can be shown that the uses he himself makes of natural properties can be bypassed, where the adequacy of an alternative is to be assessed by doctrinally neutral criteria, which do not presuppose that adequate philosophy must take some predetermined stance on subjects of philosophical controversy. And here “bypassing Lewis’s uses of natural properties” does not mean reaching a similar conclusion to Lewis himself on all issues, though without benefit of natural properties. Sometimes, indeed, this may be the way to go; on other occasions, and particularly when Lewis’s application of the notion is to address questions highly internal to his own metaphysic, the foe of natural properties may just dismiss Lewis’s position as irredeemably tainted by false ideology. The question is whether the sum of the positions thus adopted on specific issues constitutes (or can be embedded in) a coherent, prima facie adequate, alternative to Lewis’s philosophy.


Consider first Lewis’s use of natural properties to found the concepts of duplicate theory–of duplicates themselves, of intrinsic and extrinsic properties, of internal and external relations. I know of no other way of respectably systematizing these notions. True, we apparently could adopt them as primitive, consistent with still denying natural properties; for there is no apparent way of reversing Lewis’s analyses and defining natural properties in terms of these other concepts (1983, p. 357). But that hardly fits the spirit of present approach. For example, to accept a primitive, objective extrinsic/intrinsic distinction is to allow the world directly to determine which properties are relational and which are not, a line which sits ill with an approach whose emphasis has been to derive the characteristics of properties rather from the theoretical formulation and use of corresponding predicates. I do best accordingly to take a more heroic line, to deny outright the existence of true duplicates, and to accept that with them we lose the legitimacy of the distinctions between intrinsic and extrinsic properties and between external and internal relations. True, this means bidding farewell to old friends from traditional metaphysics, but that in itself hardly establishes that no systematic philosophy can make the break and survive. We have after all got on fairly well for a long time without the real darling of traditional metaphysics, the apparatus of ideas; and the notions currently under scrutiny have in any case been used only with sparing suspicion by most philosophers in the analytic tradition, with renegades like Lewis who want to resuscitate them the exception rather than the rule.

Though the suspect notions themselves must go, we can of course find vegetarian substitutes for them, by parodying Lewis’s definitions but this time using cosy predicates as our base. Thus, objects are T-duplicates iff they share all properties which are T-cosy; a property is T-intrinsic iff any two objects which are T-duplicates must agree in either both possessing or both lacking the property; and so on. Then these vegetarian substitutes become available for use in framing analyses which parallel those of Lewis, and sometimes at least analyses so framed can apparently be defended as embodiments of Lewisian insights purged of his overweening adherence to the objective standpoint.

A simple example is the use of duplicate theory in framing the ban on back-tracking counterfactuals in the analysis of causation. Lewis’s requirement is, in a nutshell, that actuality and relevant counterfactual alternatives should be duplicates up to (very near) the time of the causing event (1983, p. 361; and see the references there cited). A formally analogous constraint is obtained by replacing this by the requirement that they be T-duplicates merely–though of course this will serve only in the analysis of a weaker notion of causation, similarly relativized to a theory T.

Again, Lewis analyzes an event as a (predominantly(4)) intrinsic property of regions, the point of the restriction to intrinsic properties being to rule out as events such properties as Xanthippe’s being widowed (= being a region at which Xanthippe is located when someone married to her dies), whose instantiation at a region is entirely independent of that region’s qualitative character (1986c, p. 262). We may parody this analysis, and define an event relative to T as a property of regions which is (predominantly) T-intrinsic; and–assuming T is anything like a straightforward regimentation of commonsense or some more embracing physical theory–the restriction will serve a parallel purpose of preventing the same renegade property from counting as a parameter-relative event. Now choose a sufficiently salient T–say, contemporary physics, or some idealized unified science. Then events relative to T can be proffered as hygienic analogues of Lewis’s own red-blooded metaphysical excesses.

But other applications Lewis makes of the notions of duplicate theory depend essentially on the more carnivorous features of his metaphysical underpinning or of the context in which the notions are deployed, so that there is no analogous move for us vegetarians to make. Recall, for example, his explication of materialism as the doctrine that “amomg worlds where no natural properties alien to our world are instantiated, …any two …that are exactly alike physically are duplicates” (1986b, pp. ix ff.). Were there no alien natural properties–natural properties neither instantiated in our world, nor analysable in terms of instantiated natural properties–the restriction of the quantifier over worlds in this explication would be idle, and the whole equivalent to a version Lewis has already seen reason to reject (see M1, 1983 p. 362; Lewis rejects it because it renders materialism a contingent thesis). But, relative to many a reasonable T, there are no alien cosy properties, since the only primitive predicates in T are instantiated in this world and hence not alien. So this time we cannot reduplicate Lewis’s manoeuvre within the vegetarian framework. Again, Lewis’s argument from dilemma against magical erstazism (see above, under (a) in section I) depends for one horn on the thought that any relation holding necessarily between two things must hold in virtue of the intrinsic natures of those things. That thought may be reasonable if the intrinsic natures are, as Lewis conceives them to be, rich repositories of the intrinsic properties handed out by a bountiful nature. But it is not reasonable if the natures are at best thin creatures, perforce limited to containing only properties specifiable in some theory, as we niggardly vegetarians must think of them. Further (to take an application not reviewed in my opening catalogue of Lewis’s uses of natural properties), we must do without Lewis’s definition of the analogically spatiotemporal relations, which unite the members of a single world (1986a, pp. 75-6).(5) These are defined as relations which are, inter alia, external and natural; the role of the latter condition is indispensable, but it can only work if natural relations can be singled out even in worlds so bizarre as to differ from ours even in spatio-temporal framework. There is accordingly no chance that merely cosy relations could fill any analogous role, since no matter what the theory to which they are relativized it will perforce be too entangled with the details of this world to be able to supply the relations required.

It may be argued that these consequences follow only from an unwarranted restriction of theories to those which are either already at hand, or which we can at any rate envisage as extrapolations from such theories; and that we could at least go further towards reconstruction of Lewis’s positions if we allowed ourselves to consider also alien theories, constructed to describe other worlds entirely from an other-worldly perspective. Then alien natural properties and relations could be reconstructed as those generated by the predicates which are cosy relative to some such alien theory. But this is not a path I am keen to tread. These alien theories are shrouded in too much mystery, and invoking them means surrendering the bluff robustness which I find one of the more endearing features of my view. Nor is there any real need to take this track. For even if I admitI have no way of echoing these moves of Lewis’s, there is still a long way to go establish that my position does not constitute a basis for a sound and systematic alternative philosophy. If materialism can only be sharply formulated with the aid of suspect apparatus, perhaps that just goes to show what many have suspected all along–that there is here no single and coherent doctrine at all. And Lewis’s disputes with magical ersatzists and his problems defining the boundaries of his worlds are very much his own business, into which an alternative systematic philosophy may well be thankful not to enter.

Likewise, we will also do best not to follow Lewis in a final deployment of duplicate-theory, perhaps that dearest to his heart–its use to set up and solvethe problems of temporary and accidental intrinsics (see above, again under part (a) of section I). In the temporal case, which for present puposes entirely parallels the modal, one solution to this problem is to deny that purportedly intrinsic properties like shape are genuinely so, and to take the lesson the problem teaches as being that these are properly speaking relations to times. Lewis rejects this solution out of hand: “This is simply incredible…If we know what shape is, we know that it is a property, not a relation” (1986a, p. 204). From any perspective, this response seems rather thin. But it is peculiarly unattractive from my standpoint, which emphasizes that on a proper construal the whole apparatus of duplicate-theory is entirely relative to the syntactic forms which theory finds convenient.


As noted in my preliminary survey (section I), another use Lewis finds for natural properties is to solve a problem in the analysis of lawhood. Lewis favours a “best-system” theory, according to which–roughly–laws are those regularities which are entailed by an axiomatic systematization of truths which simultaneously maximizes both simplicity of axiomatization and breadth of coverage; the idea being that a true regularity will be dismissed as merely accidental when the added breadth achieved by adding it (or the resources to derive it) as an axiom is out-weighed by the loss of simplicity the addition entails. The caveat “roughly” is eliminated, and natural properties come into their own, when it further required that the best system be so formulated as to take only predicates referring to perfectly natural properties as primitive. Without that restriction on the form of the best system, Lewis holds, the identification of laws will vary overmuch with the way we choose to systematize “the same content”.

Here much depends on the strength of “overmuch”. Certainly, it would spell diaster for the whole best-system approach if it could be shown, as Lewis claims (1983, p. 367), that without the restriction any bunch of truths is guaranteed asystematization of utter simplicity, so that the critical tradeoff between simplicity and coverage becomes nugatory. But Lewis himself indicates how this result is avoided if we insist that the axioms of a best system should “entail” the laws via deducibility in a specific respectable system of proof theory, not just by strictly implying them (1983, p. 368). And if total global disaster can be averted, I see no reason why one should not just bite the bullet and accept that laws are relativeto a suggested formulation of best system, even if differing formulations do in some intuitive sense seek to capture the “same content”. The resulting relative notion of law may not be Lewis’s, but it needs to be demonstrated that it cannot do the respectable philosophical work to which the concept of a law is usually put. (Further, it may be added that it is unclear that Lewis himself really avoids the need to thus relativize the notion of a law. For even with his restriction in place,the vocabulary of a best system is not entirely fixed. Moreover, different axiomatizations will play off breadth against simplicity in different ways. So even for Lewis, different regularities may emerge as laws relative to different but equally respectable best systems (1986b, p. 124). His preferred solution is to reserve the title “law” just for those regularities which are laws relative to all such systems. But there is no watertight guarantee even that there are any laws, thus defined; and certainly not that there will not be an uncomfortably large number of regularities left in limbo because of the varying judgements of different best system.)

Actually, a sympathsizer of the position being developed here will probably prefer to eschew the best system approach to laws altogether. For the best system approach presupposes a fixed body of predetermined truths which the best system systematizes; and this doctrine of a presystematic body of truths sits ill with the emerging tendency of my position to relativize all concepts to the perspective of a theory. Perhaps, then, we do better to attempt to disentangle the accidental generalizations of a theory from its lawful ones in some quite different way–say, by using Goodman’s notion of entrenched predicates, a notion clearly close to the spirit of my cosy predicates even if not my first choice for actually explicating them. We need not decide here between these and other alternatives to conclude at least that there are a number of plausible avenues for attacking the analysisof legality outside a framework of natural properties.


What, finally, of Lewis’s use of natural properties in the theory of interpretation, where they are invoked to frame the “principle of humanity” with which the interpretative “principles of fit” need to be supplemented?

It is apparent from the start that the title “principle of humanity”, borrowed by Lewis from Grandy (1983, p. 375; 1986a, p. 39 fn.), is an odd one for a principle which urges favouring interpretations of others which bring their classificatory patterns into line with the joints of nature. For where does mere humanity come in? Presumably, we come in because it is presupposed that our classifications too are constrained by nature’s joints. (Where would the alleged universality of the proposed principle be otherwise?) But then it would seem that by triangulation it should be possible to state the principle without reference to natural properties, that it will become the demand that amongst interpretations satisfying the principles of fit we should favour those that attribute familiar beliefs and desires using familiar concepts–the old “principle of charity”, in other words, roughly stated. And indeed, Lewis accepts this as an alternative title for his principle (1983, p. 375). So the new principle, it seems, is a familiar one, now seen as entangled in the metaphysical net of the natural properties. If we disentangle it again, will it still do the work Lewis asks it to do?

It seems that it can still be called upon to refute the Kaplan/Peacocke objection to modal realism. For amongst the indenumerably many propositions (classes of worlds) there will be a vast subclass with content so bizarre that the principleof charity will rule them unfit to figure in any interpretative scheme (because, whenever there is a pattern of behaviour these contents can be made to fit, some more familiar contents can be made to fit the pattern too).

On the other hand, it will not work to solve the Wittgensteinian problem about adding and quadding. For the whole point of this puzzle is that it can be applied self-reflexively to raise questions about the identity of our familiar concepts–are we ourselves adders, or do we quadd?–thus rendering any application of charity here entirely question-begging. Nor, I think, can the principle of charity, purged of its associations with natural properties, be wielded to knock out Putnam’s argument against metaphysical realism. Here we are dealing with a hypothesized ideal theory T, and the interpretation of its sentences by a model M which Putnam constructs. To use the principle of charity to rule out the intrepretation as inappropriate, we need to show that the interpretation M proposes utilizes arbitrary and gerrymandered concepts rather than familiar ones; and here the standard of familiarity should be not ours, but that set by the hypothesized ideal theory itself. If, then, Putnam’s model corresponds to a “homophonic” assignment of meanings to the sentences of T–an assignment of meanings under which each sentence receives a truth-condition which can be stated using that sentence itself–there will be no showing, by the principle of charity, that it constitutes an inadequate interpretation. But I have argued elsewhere (Taylor, 1990) that there is no nonquestion-begging argument against the claim that Putnam’s model is homophonic in this sense. Therefore there is no good case from the principle of charity against Putnam’s argument.

What does it matter that, having eschewed natural properties, I cannot echo these two deployments of Lewis’s interpretative principle? Not at all, I think,that I cannot rebut Putnam’s argument; the cards on this one should fall where the dialectic decides, and I am inclined on balance to think this argument is sound. On the other hand, somehow coming to grips with Wittgenstein’s problem becomes an urgent item on my philosophical agenda–as indeed on many others. At the same time, I feel little temptation to return to natural properties on this account, since of all Lewis’s appeals to the notion this strikes me as the most implausible. Even granted that the physical world might come jointed, the notion that what makes adding more natural than quadding is the prior jointedness of mathematical reality, rather than the way we think about it, is peculiarly unappealing.


What becomes of Lewis’s metaphysical system if the natural properties are removed? And what are the morals of our examination for the realist enterprise in general?

Without natural properties, as we have seen, some of the usefulness of the apparatus of possible worlds evaporates, as witness some of the uses of duplicate theory. There remain, however, a vast and impressive array of applications catalogued by Lewis and unimpaired by any eschewal of natural properties. It is still true, the, that he has provided us with a very strong case for invoking the machinery of possible worlds. But the overall effect of the elimination of natural properties is to strengthen the case for an ersatzist construal of that machinery, rather than a realist one. For not only is ersatzism more in line with the general tendency of philosophy without natural properties to emphasize the human perspective on things, but the scope for ersatzism has been increased with the removal of the main specific objection to the doctrine in its “magical” form; and the attraction of the realist perspective has been decreased by the demolition of the analysis of worldmates through analogically spatio-temporal relations.

More generally, as we have seen, the price metaphysics pays in foregoing natural properties is to relativize key concepts–laws, causation, events–to human perspectives on things (theories). By thus importing the human standpoint into metaphysics, philosophy without natural properties shows itself no friend to realism in the full-blooded form espoused by Lewis and celebrated in Sydney; and this enmity is further displayed by the support we have seen it lend to Putnam’s attack on realism at its most full-blown. At the same time, we are still well short of the denial of bivalence and Dummettian antirealism. Rather, we have an intermediate position, which asserts with Dummett’s realist the objectivity of sentential truth whilst denying the full-blooded realist’s claim of an objective connexion between the world and subsential predicates; the position, perhaps, which some have tried to characterize in different terms as “internal realism”.

(1) See Lewis 1991; and see also footnote 9 of Lewis 1983, which inter alia anticipates this complication.

(2) Footnote 9 of Lewis 1983. I have recast the definitions into class-theory out of multigrade originals.

(3) Mention of Goodman prompts the query of the rating of the cosiness spectrum of “grue”, one of Lewis’s main examples of the highly unnatural. Obviously, iwth cosiness explicated as cosiness, it will for Goodman’s reasons rate lowly too on the score of entrenchment. My preferred explication will on the other hand allow it to count as quite cosy relative to a T which treats is as primitive and adopts appropriate axioms; but here the point is that no such T can fairly claim to be proper representation of any theory we take seriously.

(4) The proviso amounts to a slight weakening of the universal quantification (“any two duplicates”) in the definition of intrinsic property: see 1986a, p. 264.

(5) I owe this point to John Waugh.


Armstrong, David 1978: Universals and Scientific Realism. Volume One. Cambridge: Cambridge University Press.

Campbell, Keith 1990: Abstract Particulars. Oxford: Basil Blackwell.

Goodman, Nelson 1983: Fact, Fiction, and Forecast. Fourth Edition. Cambridge, Mass. and London: Harvard University Press.

Lewis, David 1983: “New Work for a Theory of Universals”. Australasian Journal of Philosophy, 61, 4, pp. 343-77.

–1984: “Putnam’s Paradox”. Australasian Journal of Philosophy, 62,3, pp. 221-36. –1986a: On the Plurality of Worlds. Oxford: Basil Blackwell. –1986b: Philosophical Papers. Volume Two. Oxford: Oxford University Press. –1986c: “Events”, in his 1986b, pp. 241-69. –1991: Parts of Classes. Oxford: Basil Blackwell.

Moore, G. E. 1959: “A Defence of Common Sense”, in his Philosophical Papers. London: Allen and Unwin, pp. 32-59.

Quine, W. V. 1969: “Natural Kinds”, in his Ontological Relativity and Other Essays. New York and London: Columbia University Press, pp. 114-38.

Quinton, Anthony 1957: “Properties and Classes”. Proceedings of the Arisotelian Society, 48, 3, pp. 33-58.

Taylor, Barry 1991: “Just More Theory’: A Manoeuvre in Putnam’s Model-Theoretic Argument against Metaphysical Realism”. Australasian Journal of Philosophy, 69, 2, pp. 152-66.

Williams, Donald C. 1953: “On the Elements of Being”. Review of Metaphysics, 7,1, pp. 3-18 and 2, pp. 171-92.

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