CHAPTER II

The Ground of Necessity

§1. The Identity of Physical with Logical Necessity. Ultimately, I shall show that the practice of action based on prior experience is incompatible with the view that there are no physical necessities, that is, no physical necessities whose necessity is objectively based. That proof will be postponed until it is made reasonably clear what physical necessity is. In making this clarification, I shall be led to introduce natures as the objective basis for physical necessity. And so the kind of necessity called for by practice is a “natural” necessity, that is, a necessity grounded by natures. In view of its etymology, ‘physical’ should mean what ‘natural’ means. However, let us agree to mean by a “physical” feature one that any entity has only if it is a spatio-temporal entity. Correspondingly, a necessity will be physical if it is a necessity of an entity having certain physical, and not merely logical or other non-physical, features. It is no mere tautology, then, that the necessity of a physical necessity is based on natures.

It is crucial here that a distinction be made between a necessity and necessity itself. A necessity is some condition of entities; if the condition of this gas to expand when heated under constant pressure is a condition that obtains with necessity, then this condition is a necessity. Sometimes, though, it is more convenient to call propositions necessities. This is the procedure I shall follow in the present chapter. Propositional necessities are necessities only if the conditions making them true are necessities. Action based on prior experience does not require propositions, and so requires only necessities as conditions. Further, the necessity of a necessity, in either sense, is a modality of a condition’s obtaining or of a proposition, but is neither a condition nor a proposition.

There is surely a need to clarify the modality of physical necessity. For it is often wrongly believed that the necessity called in by an appeal to physical necessities is something totally unexplained and unfamiliar. Behind this belief is the following train of thought.

The appeal to physical necessities is not reducible to an appeal to mere regularities. So the necessity involved is not to be explicated in terms of regularities. Further, the appeal to physical necessities is not an appeal to logical necessities. So the necessity involved is not to be identified with that of logical truths. There is nothing else with which it could plausibly be identified. Hence the modality of physical necessity is totally unexplained and unfamiliar. In Hume’s terms, there is no idea of physical necessity, and thus an appeal to it is meaningless.

The flaw here is not hard to find. For the distinction between a necessity and necessity itself has been overlooked. Physical necessities are not the same propositions as logical necessities. The proposition that this gas expands when heated under constant pressure is not a logical necessity, though the proposition that this gas expands when it expands is a logical necessity. All that follows, however, is that there are two sets of necessities. It in no way follows that the necessity itself–the modality–of a physical necessity differs from that of a logical truth.

To make it follow, two additional premisses might be added. The first premiss is that logical truths unlike physical truths have contradictory denials; the second is that having a contradictory denial is their necessity. Thus not only are logical and physical necessities different propositions but their very necessity is different. Caution should be exercised here lest one confuse a characteristic of logical truths with an analysis of their necessity. Granting that logical truths have contradictory denials, can we safely assert that saying that they are necessary amounts to no more than saying that they have contradictory denials? If so, then saying that a contradiction cannot be true is merely saying that a contradiction is a contradiction. But this is manifestly not the case. A contradiction affirms and denies the same thing, and it is an important, even if familiar, fact that such a claim cannot be true. So its impossibility does not consist in its being contradictory.

Physical and logical necessity are distinguished not by distinguishing two species of necessity but by distinguishing the physical from the logical truths to which the necessity applies. Thus, to say A is “physically” necessary is to make the conjunctive claim (i) that A is a physical truth and (ii) that necessarily A. Even when (ii) here is a so-called de re modal proposition, the claim that A is physically necessary will not be a purely de re modal proposition, since (i) has a de die to character (cf. §5, following). Similarly, to say A is “logically” necessary is to say (i) that A is a logical truth and (ii) that necessarily A.

By a physical (logical) truth I mean a truth whose truth conditions require that appropriate entities have certain physical (logical) features. Having the property of igniting if struck would be to have a physical feature; whereas, having the property of lacking and possessing a certain property would be to have a logical feature. There will doubtless be difficulties in delimiting the classes of physical and logical features, but my task here is merely to indicate that this is where the difficulties lie, rather than with distinguishing two species of necessity.

Since the necessity is identical in both cases, physical and logical necessities may well be alike in being natural necessities. That Jones does not both have and lack a nose may be necessary for the reason that it is Jones’s nature not to have and lack the same part. A logical truth would not then be necessary because its denial is contradictory or because its truth is invariant under changes in non-logical content. Rather, the logical truth would be necessary because it is the nature of the entities covered by the truth to support truths of that sort. This is not to rest the thesis of the univocity of necessity on the view that both physical and logical necessities are natural necessities. The present discussion merely illustrates the point that the univocity thesis allows both necessities to be viewed as natural. Moreover, forms of the univocity thesis that try to avoid natures are, as I shall show in §2 and §3, less than satisfying.

The univocity thesis is not a new one. Kneale said that “since men undoubtedly speak of necessity in nature, we find ourselves driven to say that the word ‘necessity’ must have a special meaning in this context and cudgel our brains to give an analysis. In fact, the word ‘necessity’ is the least troublesome of those with which we have to deal in this part of philosophy. For it has the same sense here as elsewhere.”¹ Kneale’s view did not go unchallenged. Popper said in reply that, “Compared with logical tautologies, laws of nature have a contingent, an accidental character. . . . For there may be structurally different worlds–worlds with different natural laws.”²

The intuitive substance of Kneale’s view, as of my own, is that necessities restrict alternatives and that one should not confuse the restriction of alternatives with the different sources of restriction. A restriction is a restriction whether it comes from the logic or the physics of the world. It is misleading to speak of one source as giving rise to a weaker or looser restricton than another. For a restriction on alternatives either closes down alternatives or it does not. If being weaker means leaving an alternative partly open, then a weaker restriction is just not a restriction on alternatives. If it means that a restriction genuinely eliminates an alternative, then it is just misleading to call the restriction weak.

Popper’s argument patently begs the question. Grant that among the logically possible worlds there are worlds in which different physical laws hold. Popper first identifies the logically possible worlds with the possible worlds. He then validly concludes that physical laws are contingent since they do not hold in all possible worlds. But the identification is precisely what is in question. For consider what it is based on. A logically possible world is one in which logical necessities hold. We can identify a logically possible world with a possible world only if we assume that the logical necessities are the only necessities, or at least the only necessities in the sense in which Popper here speaks of necessity. Thus the identification rests either on denying that there are physical necessities in any sense or on affirming that physical necessities are necessities in a different sense. Popper is not willing to deny that there are physical necessities in any sense, so his argument assumes its conclusion that a physical necessity is a necessity in a different sense, and is hence contingent in the sense of the word as he originally used it.

In sum, there is nothing for the equivocity thesis to stand on. In the remainder of this chapter, I shall provide a foundation for the univocity thesis. Once univocity is accepted, the appeal to physical necessities can be rejected as meaningless only if one is prepared to call the notion of logical necessity meaningless. Moreover, it will be seen in Chapter VI that the identity of necessity in the two cases is compatible with the allegation that logical necessities are analytic and a priori, whereas physical necessities are neither. For even if logical necessities were analytic and a priori, their being so would not follow from their necessity.

§2 . Laws in Ontological Perspective. Even while holding that the necessity of physical and logical necessities is identical, there is no obstacle to thinking of necessity simply as lawfulness. For, there are both physical and logical laws, and what holds under each is said to hold necessarily. But what makes something a law? The answer to this question requires us to take a route that is no shorter than the one that we would have had to take in answering a similar question about necessity, and the two routes end at the same place. So, switching to lawfulness gets us no closer to the goal of finding an objective basis for necessity. Moreover, there are necessities which turn out to be crucial, that cannot be treated as laws or derivatives from laws. For example, the necessity that an individual has of belonging to a certain natural kind is not a matter of laws. No law is the basis for its membership in that kind. Rather, a law always tells us what is characteristic of individuals of a given natural kind.

Nonetheless, there is a reason for talking about laws. The route commonly followed in saying what makes something a law leads to the intentional rather than to the real. Taking this “flight to intentions” for the lawfulness of laws will, accordingly, lead to an intentional basis for the necessity of corresponding necessities. Something is to be gained by pointing out that this intentional account will not do for necessity and hence not for lawfulness.

The kind of necessity needed if experience is to support propositions about the as-yet unexperienced has an objective basis and is thus real rather than intentional. The necessity of A would be “intentional” if all it implied, beyond the truth of A, were that the proposition A had a certain place in a system of thought, that the mind was conditioned to believe it, that it was promulgated by a high authority as true, or that linguistic propriety would not admit an expression of its negation. In broadest terms, the necessity of A would be intentional if its being necessary meant, beyond the truth of A, a certification of A indicating A stands in a certain relation to consciousness. The necessity of A would be “real” not just if A were true but only if there were in the entities that A is about a basis that were sufficient for their having the features that makes A true of them. Such a basis might be a material stuff, microparticles, capacities, or natures. Why it cannot be some of these will become clear only gradually. Of course, a real necessity about consciousness itself would be such that this necessity is true on the basis of some feature of consciousness; it will not be an intentional necessity since it does not as a necessity have this relation to consciousness, but only as something about consciousness.

The contrast between the real and the intentional does not require that there be entities that are not real. For to say that a modal proposition has an intentional basis is not to say that there is an entity other than a real one that is involved in the conditions that make this proposition true. Rather, it is to say, first, that the truth conditions for the modal proposition-necessarily A-involve not just the entities A is about but also the non-modal proposition A. Second, it is to say that the non-modal proposition-A□is by its role in human thought or expression (which makes it about other entities) involved in the truth conditions for the modal proposition-–necessarily A. This conception of an intentional basis does not require us to say that either propositions, human thoughts, or expressions, are not real. (If, independently, propositions are shown to be unreal, a parallel characterization of an intentional basis might be given using, instead, the notion of a sentence.) In so far as propositions, sentences, concepts, and words are about entities, they are themselves intentional entities. But it cannot be inferred from their intentionality that they are not real.

It is important to see why the necessity of the physical necessities called for by the fact that experiences support or confirm propositions has to be a real necessity. When the necessity is real, certain physical features belong to entities on the basis of factors in these entities. The argument–point (I) of which is worked out in Chapter IV-is as follows.

(I)One cannot contend that past experience is the guide to the future and at the same time hold that there are no necessities. Ultimately, such guidance goes back to the simple inductive projection of features of observed individuals onto unobserved individuals. Such a projection-of, for example, the conditional feature of being G if F– is warranted only if there is a chance that, if observed individuals have the feature of being G if they are F, then any arbitrary unobserved individual is G if it is F. There would be no chance of this connection between the observed and the unobserved individuals if all the features of the former were contingent. It would then be only owing to the peculiarities of the circumstances that the observed individuals had the features they did. There would be no basis for claiming that an arbitrary unobserved individual would have any of those features.

(II) But is the necessity required real or intentional? Suppose it is intentional. Thus, if an observed individual were of necessity to have the feature of being G if it is F, the proposition that it has this feature belongs to a coherent deductive system, or it is propounded by an authority, or it cannot be denied without violation of certain linguistic conventions. Now the point of introducing necessities would be defeated if it were highly improbable that if one individual had a projectible feature of necessity, then any other individual, whatever its circumstances, would also have it. If it were highly improbable, then the necessity of the projectible feature would provide no basis for attributing that feature to other individuals. Yet it would be highly improbable if the necessity were merely intentional. No restriction put on the proposition that an individual is G if it is F in order to make this proposition intentionally necessary would tend to influence physical reality in such a way that we could expect another individual to be G if it is F. The feature of being G if F is a genuine part of reality, and how we happen to conceive of it will not, by itself, influence its distribution among individuals. Thus intentional necessity fails to satisfy the requirement that, for properties that we project by induction, the necessity of any such property in one individual provides a chance, however small, that it is realized in any other individual.

(III) One must conclude that only the real necessity of a feature’s belonging to an observed individual can make it at all likely that an unobserved individual will have a similar feature. Observe that the projected features are those that individuals could have by law. Hence we could have said in (I) that some features of individuals must be had by law. The argument of (II) would then have reached the conclusion that lawfulness, like necessity, cannot be merely an intentional characterization of a truth. Necessity, and hence lawfulness, of the sort needed for induction, are real rather than intentional.

Yet it has become a dogma that the basis for lawfulness is intentional. It is thought, for example, that A’s holding by law is to be analyzed exhaustively in term.of A’s truth and with reference either to A’s place among other propositions of a deductive system³ or to the place of expressions for A in the hierarchy of linguistic expressions arranged by familiarity.⁴ Efforts based on this dogma may well prove fruitful as a means of identifying laws, but the dogma acts as a blinker that cuts off from view the ontological base of lawfulness. Since a’s being F by law implies a’s being F by necessity, when a is F by law, a has the property F on the basis of some factor about a other than F Lawfulness is, then, real rather than intentional.

If the belief that lawfulness is intentional persists as a dogma, then there must be some reason favoring the intentional view of lawfulness. The remarkable thing is that a variation on Hume’s argument against necessary connections is still used in this regard, with no effort to firm up its ontological foundation. If there were real lawfulness, then there would be real necessity. But, it is asked, do we ever encounter the necessity of a real necessity? We encounter temporal conjunctions, but nothing like the necessity of a necessary connection. Perhaps we have not looked hard enough. No; the necessity of a necessary connection simply cannot be found. But do I not observe that the door must shut when I push it or that the paper must flame up when I hold a lighted match to it? Against this appeal to perception, the Humean is forced to bolster his epistemological argument with an ontological one. We are to believe that there are no observations of necessity since things in the knowable world are merely collections of their conditions, and as to conditions it is obvious that what is distinct is separable. Accordingly, if there are no entities in the knowable world that can be necessarily connected, there is no necessity to be detected. But the only reason suggested for believing that things are reducible to conditions is that if they were not, necessary connections and hence real necessity would return to plague us. These are hardly impressive credentials for treating necessity and hence lawfulness as intentional.

Granting that lawfulness is real rather than intentional, what precisely is its real base? In answering this question, we also answer the same question for necessity. Let us consider several possibilities.

(A) Suppose F’s are G by law. Could the real basis for its being a law be an entity called a “necessary connection” that stands, somehow, between anything’s condition of being F and its condition of being G? But then lawfulness, and hence necessity, would be based on the merely contingent presence of a special entity. This is absurd, however, for, if the special entity–the necessary connection–could be absent, then it is not a law or a necessity that F’s are G. So this entity must be present between anything’s being F and its being G. Yet why should it be present between being F and being G rather than between being F and, say, being Hwhere, we suppose, being H does not always accompany being F. Our search in this direction for a real basis has come to a dead end.

To avoid confusion, it is well to digress now to note that even though it may be a law that if anything is an F it is G, the proposition that if anything is an F it is G is not, in general, a modal conditional. For, if it were, then the proposition that it is necessary that if anything is an F it is a G would be doubly modal. Thus in looking for a model best suited to conditionals that are laws, we must try to find a non-modal conditional. This requirement is satisfied by Anderson and Belnap’s “relevant” implication⁵ rather than by Lewis’ “strict” implication,⁶ which is modal.

Throughout this book I shall make frequent use of the concept of relevant implication, symbolizing it by the→ . It will be especially important in showing how necessities are based on natures, how relational properties are based on their foundations, and how capacities are reduced to actualities. Lewis’ strict implication, symbolized by the –₃ , is such that for any propositions A and B, (A –₃ B) implies □   ~ (A • ~ B ), that is, that it is necessarily not the case that both A and not֊B. But, since a relevant conditional is non-modal, (A → B) does not imply □ ~ (A • ~B). Moreover, the paradox-free character of relevant implication makes it more desirable than “material” implication–to be symbolized by the כ for the discussion of all the matters mentioned. That is, though (A כ (B כ A)) is valid, as is ((□ A) –₃ (B –₃ A)), neither (A (B → A)) nor (□ A) → (B → A)) can be a theorem of relevance logic. This agrees with the common-sense observation that, since A may be totally irrelevant to B, A will not in general imply that B implies A.

(B) Perhaps the real basis of lawfulness is to be found in a “middle term.” If F’s are H by law and H’s are G by law, then H is the real basis for F’s being G by law. H might be a feature of the microstructure of entities that are F. Whatever the supposed middle term may be, however, this procedure leads to a regress. We now have two additional laws, those relating the middle term to the extremes. On the one hand, there is nothing to justify the assumption that however far the regress takes us, there will still be a middle term. On the other hand, even if the regress is infinite, lawfulness remains ungrounded, since each middle term appealed to at each stage must be appealed to as one that is related by law to the extremes. The regress is then vicious, as I shall establish in more detail in Chapter X, §5.

(C) What is needed, in view of (B), is not a third term that itself stands in connections that are lawful, but rather a third term whose role is merely to back up laws. This will have to be a very special entity indeed. For if we think of properties, dispositions, stuffs, and particles as the normal sorts of components, then components seem always able to enter into lawful connections with one another. But a nature is exactly the kind of component of an entity that is limited to the role of backing up laws without entering into them.

It is important to distinguish between a nature itself and what takes place by virtue of that nature. Even if it is the nature of salt to dissolve, the dissolving itself is not the component of the salt that is its nature. Rather this process takes place by the nature of salt. Digging behind appearances to the ionic structure of the salt crystal, we do not find the nature itself of the salt, but at best something it has by nature.

In view of (A), it is not enough to say that natures do not have lawful connections, but merely stand behind such connections. They must also inhere in individuals or things* as their “being” or “substance.” For the being of or the substance of an individual will be selective in its support of connections between that individual’s conditions. By contrast, the entity introduced in (A) was merely a relation between conditions. There was no basis for saying that it had to be a connection between certain conditions, but not others. It was external to individuals since it stood only between their conditions. Natures must, however, be internal to individuals in such a way that we can say that they are their being or substance.

When Aristotle asked what the being (ousia) of an individual is, he was aware that he was asking a question about a principle at the root of what the individual is, that is, about its nature. So he says “the nature of a thing is clearly its primary being (ousia)"⁷ But his answer to this question involved a fatal compromise with epistemology. According to him, the being, substance, or nature of an individual is expressible by a definition of it.⁸ Thus the properties or parts an individual has by its very being or nature become its very being or nature. Otherwise, he thought, the being or nature of an individual would not be “intelligible.”⁹ So the being or nature of an individual is identified with what properties or parts it has of itself.

Now, on the one hand, it does not appear to me necessary to turn the nature of an individual into what the individual is by its nature in order to make natures intelligible. Natures are intelligible in terms of the role that they play as the basis for certain properties and parts. On the other hand, making natures into properties and parts leaves no basis for the necessity of these properties and parts to the individuals having them.

It is difficult to hold the idea of a nature as something behind essential properties and parts alike in face of the universal acceptance of Locke’s belief that “If anyone will say that the real essence and internal constitution on which these properties depend, is not the figure, size, and arrangement or connexion of its solid parts, but something else, called its particular form, I am further from having any idea of its real essence than I was before.”¹⁰ Locke’s idea of a nature as a constitution of parts is more restrictive than the Aristotelian idea that allowed for natures composed of properties. But both are united in denying the intelligibility of the idea of a nature as something behind essential properties and parts alike.

If the only components one can have ideas of are properties, particles, stuffs, and dispositions, then Locke is right that one cannot have an idea of what I have called a nature of an individual. But even an empiricist theory of ideas might allow that there can be an idea of a nature as a component distinct from all of these. Of course, one might have the idea of a nature merely by knowing that it played the role of a ground of necessity. But such an idea would lack solid empiricist credentials. There is, however, no need to settle for less than an idea of a nature that is tied to the experience of individuals’ having natures. When I experience an individual’s having a property that I am right in judging essential to it, it is entirely plausible to suggest that I then experience that individual’s condition of having the nature that gives rise to this property. I then experience the individual as having its being or substance, thereby settling negatively the question of whether I am encountering a collection of distinct entities rather than a unitary individual. According to the view of Chapter VI, if natures, microparticles, and other components could not be experienced as had by individuals, then expressions for them would lack significance.

§3. Possible Worlds Controlled by Population. Can one get at the roots of necessity through the idea that necessity is truth in all possible worlds? One can say at least that if a possible world is simply a world in which laws hold or a world in which entities behave in accord with their natures, then the notion of a possible world is derivative from the notions we have already explored. Is there, perhaps, some conception of a possible world that gets behind the notions of law and nature and still reaches the roots of necessity? My conviction is that there is not and hence that the use of the notion of a possible world as a quasi-explanatory category in physical ontology leads away from rather than to the roots of necessity.

Once the restrictions imposed by laws and natures are passed by, there appears to be a great deal of arbitrariness in settling on any other single standard for possible worlds. So one is very understandably led to the point where any set of entities together with a distribution of properties over them can, if one chooses, be considered a possible world. The set of possible worlds is simply a set of sets of entities with specified properties.

This leads to the result that necessity is not univocal, for it changes its meaning each time the set of possible worlds is changed to a different set of sets of entities with specified properties. But to bring this view of necessity into line with our univocalist conception, it suffices merely to relativize the notion of necessity. Let ‘L’ and ‘P’ be constants designating different sets of sets of entities with specified properties. These designations are to be defined without reliance on laws and natures. They are defined by stating which entities with what properties are in the worlds included in the sets. Thus I shall say that they are designations for sets of possible worlds “specified by population.”

An L-necessity will hold in all of the worlds designated by ‘L’. One can think of L-necessity and of Popunecessity as being relative necessities. Both are then instances of the univocal concept of necessity relative to some set of possible worlds specified by population. The expression ‘X-necessity’ will signify this univocal concept. Roughly, the relativizing of necessity to various sets of sets corresponds, in the semantics of modal logic, to interpreting formal modal languages containing non-relativized modal operators by means of models on various “model structures.”¹¹

Let us then grant that there is such a univocal concept of relative necessity, that is, the concept of X-necessity. However, it is so constructed as to be unilluminating about the basis of the necessity of whatever kind of necessary truth one considers. This can be seen in two ways.

First, suppose that the set L is in fact the set of logically possible worlds and that the set P is in fact the set of physically possible worlds. But qua L-possible and P-possible sets, they have not been specified, respectively, as sets of worlds in which logical and physical laws hold. L and P are, rather, sets whose worlds are specified by population. It will not then follow from the fact that a certain proposition is Lor P-necessary that the proposition is logically or physically necessary. In each case we get only an extensional equivalence. It would thus be absurd to claim that we are getting at the roots of logical and physical necessity through instances of the notion of X-necessity.

Now in applying the concept of X-necessity it will have been, in general, already assumed that the specific set of sets chosen conforms to logical laws. So any X-possible world is logically possible in a sense that relies on an appeal to logical laws. The different species of X-necessity are, then, determined by various “cut-downs” on the set of logically possible worlds. If, on the one hand, the cutdown to physically possible worlds is also made by an appeal to laws and hence to natures, then the whole project of getting at the roots of necessity through possible worlds in a way that by-passes laws and natures is abandoned. If, on the other hand, the cut-down to physically possible worlds is made by means of a specification by population, then not only is the treatment of physical necessity incoherent with that of logical necessity but also the specification by population can at most generate an extensional equivalent for the notion of physical necessity.

Second, letQ be the set of two worlds such that a single piece of paper is contained by both worlds and that neither contains anything else. In one of the worlds it is red, and in the other it is green. But in each world it is circular. It is then Q-necessary that the paper is circular. Yet if R is the set containing only the single world in which the same paper is red, then it is i?-necessary that the paper is red. All that can be claimed for Q- and R-necessity is that they are only certain similarities between sets.¹² The sets of Q are similar in that they have the same piece of circular paper. This is what it means to say it is Q-necessary that the paper is circular. When it is driven home by considering these simple examples that this is what any instance of X-necessity amounts to, one recognizes the vast conceptual chasm between X-necessity and the necessity involved in physics and logic. The former is related to the latter in name only.

The source of the trouble is the attempt to make philosophical use of the metalogically useful notion of a cut-down on logically possible worlds. The motivation for interpreting modal languages in a way that gives importance to the notion of a sub-set of the set of logically possible worlds was the desire to show the completeness of certain formal modal languages. To get completeness in these cases it will not do to define validity as truth in all logically possible worlds. It must be defined more demandingly as truth in all worlds in any sub-set of the set of logically possible worlds.¹³ The idea is that, for any atomic proposition A, the proposition possiblynot-A is not a theorem in Lewis’ system S5, but this proposition holds in every logically possible world. For, any atomic proposition fails in some logically possible world. A way of defining validity is then devised so that S5’s failure to contain this logical truth is not a mark against this system. For A, take the proposition that this is red, where this is the piece of red paper in the sole world of R. With R as the reference set for deciding modal truths, possibly-not-A is false in the sole world of R since there is no other world in R and a fortiori no other world in R in which A is false. Hence, possibly-not-A is not valid in the demanding sense of being true in all worlds in any sub-set of logically possible worlds. The brilliance of this device for achieving completeness for S5 is not in question. But one should not be so dazzled by it that one confuses the heuristic value of deciding modal truths by reference to different sub-sets of logically possible worlds with a sign of philosophical fruitfulness.

Even if the above difficulties of getting at the roots of necessity via possible worlds are overlooked, the limited usefulness of the notion of possible world turns up in another way. On the assumption that natures are the real basis called for by necessity, one cannot ask what natures are possible. It may be impossible for an entity to behave in a certain way in view of its nature. But how could it be impossible for an entity to have a certain nature, say a nature to be contradictory? Perhaps there would be a conflict with a more basic aspect of the natures of entities; thus it would be the nature of any entity to be non-contradictory. But this can indicate only that ‘entity’ is not yet the broadest designation, as we intend it to be. In the intended broad sense, it is possible for an entity to have any nature. Thus the idea of all possible worlds is too broad to make any useful discriminations. Only after we have limited the worlds to those containing entities on the natures of which logical necessities or logical and physical necessities are grounded do we have a useful set of possible worlds.

§4. Natural Necessity. The kind of necessity required by the fact that at least some propositions are supported by prior experience is a real rather than an intentional necessity. Moreover, since natures are the real factors at the base of this necessity, it is appropriately called a natural necessity. In view of the identity between the necessity of physical and logical necessities, it must be recognized that logical necessity is a real necessity of the natural sort. The equivalence:

(1) Necessarily A if and only if A by nature

holds for both physical and logical necessity. (It is intended to hold only for so-called de re necessity, but it will soon be shown that natures also play an important role in regard to so-called de dicto necessity.)

There are several ways one might interpret ‘by nature’ in (1). It might be interpreted as an entity’s manner of being something, where its manner is taken to be based on nothing else. Then the manner of Jones’s being humanhis being human naturally would not point back to a further entity, a nature. The manner of being would itself be ontologically ultimate. This has two drawbacks. In the first place, ‘necessarily’ is already an expression of manner, and the search for a basis for necessity was a search for a basis for a manner of being. Simply saying that this manner of being can be equally well expressed by the phrase ‘by nature’ is to abandon the search for the basis of the manner of being. In the second place, unless a manner is based on objective factors, there seems no alternative but to treat the manner as having an intentional basis. That is, the notion of a manner of being that is ontologically ultimate is just not acceptable (cf. Chapter VIII, §4). Going in one direction–that which one takes with ‘obviously’, which is applicable on the basis of some relation between given data and the proposition in question-–leads to an intentional interpretation of modality, which has already been rejected. Going in the other direction–that which one takes with ‘swiftly’, which is applicable on the basis of the kind of action performed and the rate of its being done–takes us beyond mere manners of being to the natures that are the real factors at the basis of necessity.

How then are we to express an interpretation of ‘by nature’ in terms of entities rather than of manners of being? As a first step, consider an interpretation of ‘a is ø by nature’ as ‘The nature of a is such that a is ø’. But this does not unequivocally commit us to natures as entities. For, if we treat ‘the nature of a is such that’ as an operator on a par with ‘some x is such that’, then everything but ‘a’ in the operator might be relegated to the syncategorematic. I am then led to propose that ‘a is ø by nature’ be interpreted as ‘There is a nature such that a has it and if a has it then a is ø’. Thus where ‘n’ is a variable for natures:

(2) øa by nature if and only if (Ǝ n)(a has the nature n • (aa has the nature n → øa))

Or in general:

(3) A by the nature of certain entities if and only if there are natures that those entities have and A is implied by the fact that they have those natures.

The use of ‘by the nature of certain entities’ in (3) in place of ‘by nature’ in (1) gives recognition to the fact that (1) has been simplified on both the left and the right hand sides. In asserting a necessity, one must be clear as to which entities the necessity is of. Correspondingly, when something is asserted to hold by nature, it should be clear of which entities it is by nature. It will be taken for granted here that the certain entities whose natures support A are entities that A is about.

How does this treatment of necessity avoid an infinite regress? Suppose øa is indeed necessary. If in addition (2) is true, then one must be prepared to admit still further necessities. For, first, a must have some nature, and it turns out that whatever nature it has it has necessarily. Otherwise, (2) would conflict with the modal laws of Lewis’ S5. This can be seen as follows.

What would happen if a could have the nature M that is different from its actual nature N? Because of their difference, these natures will “support” different properties. That is, either (i) having M implies having some property ψ though having N does not imply having ψ or (ii) having N implies having some property 6 though having M does not imply having 0, or both. If (i) were the case, then by (2) a could have ψ by nature, and hence necessarily, even though by (2) a actually does not have ψ by nature, and hence has it only contingently. But this conflicts with the modal law of Lewis’ S5 that the possibly necessary is actually necessary. If (ii) were the case, then by (2) a might have 6 only contingently, even though by (2) a actually has ø necessarily. But this conflicts with the modal law of Lewis’ S4, which system is contained in S5, that the actually necessary is not possibly not necessary. So if (2) and S5 are accepted, true instances of the formula that (a has the nature n) are necessary.

Faced with the additional modal claim that a has the nature N necessarily, one must ask how a regress is to be avoided. If this necessity required still a further nature, then a regress would be unavoidable. But our position does not require appeal to a further nature. Our position is that whatever a has necessarily it has because of its nature. So if a has N necessarily, this is simply because of N itself, and the regress to other entities is stopped.

Second, true instances of the conditional formula that (a has the nature n →øa) will have to be necessary if (2) is to be satisfactory. Otherwise, even though the antecedent is necessary, the consequent might be false. But if øamight be false, the left side of (2) would be false. To accommodate this need for a necessary conditional, there is no need to retreat to a further nature. The nature, N, of a makes it true of a that it have the relevant conditional property. It supports the conditional property that any entity x has when it is true that (x has the nature N → øx).

But are all the modal laws of S₅ with relevant implication, and hence of the weaker systems S1-S4 with relevant implication, true here? That is, once (1) and (2) are used to interpret the modalities in these laws, are the modal laws of S₅ and hence of S₁-S₄ demonstrable? The answer is that they are. The demonstrations are straightforward enough to need no presentation here. For example, in the case of the law of S₄ used above, that the necessary is necessarily necessary, it is to be shown that, where ‘P’ is ’is the nature of, from (ŽŽƎn) (nPx • (nPx → Fx)), it follows by simple logical steps that (Ǝ n) (nPx • (nPx→ Ǝ m) (mPx • (mPx → Fx)))). For the law of S₅, that the possibly necessary is actually necessary, one needs to add the assumption that any individual has a nature. These and the other laws of Lewis’ modal systems are then seen to express truths about natures.

To apply the general idea expressed in (3) to cases beyond the atomic one that is considered in (2), a recursive schema would be desirable. In lieu of developing such a schema, I note only that (3) is intended to have these applications:

(4) (x)øx by the nature of x if and only if (x) (ŽŽƎ n) (x has the nature n• (x has the nature n→øx)),

(5) øa→ ψb by the natures of a and b if and only if (Ǝ n,m) (a has the nature n • b has the nature m • ((a has the nature n • b has the nature m) → øa→ ψb))).

The right-hand sides of (2), (4), and (5) indicate in exactly what sense natures are real bases, grounds, or foundations of necessity. Necessity and lawfulness are not themselves entities. But if there is a true proposition asserting the necessity or lawfulness, for certain entities, of a certain fact, then the condition for its truth is that there be natures that those entities have and that their having them implies that fact. So natures ground necessity and lawfulness in that the existence of natures and of their implications are conditions for the truth of claims of necessity and lawfulness.

§5. Natures and de Dicto Necessity. The necessity claims thus far considered were called de re necessity claims. In making such claims, certain entities are said to be certain ways necessarily. Now these are the entities that the corresponding non-modal claims are about. Since the proposition that Jones is two-footed is about Jones and no one else, the corresponding de re necessity claim asserts of Jones and of no one else a necessity to be two-footed. But what I termed a de dicto necessity claim is not limited in this way. The entities whose natures are relevant to the truth of this claim need not be entities limited to the ones that the corresponding nonmodal claim is about. This does not mean that intentional entities enter the truth conditions of de dicto claims. It means only that the natures of entities beyond those referred to are often involved. Suppose there is a cage that contains only cats. Cats, we assume, purr by nature. But the nature of the cage is not such as to make animals in it purr. Now interpret the proposition that all animals in the cage purr as being about any animal in the cage, rather than about any entity whatsoever. It might then be expressed as ‘(x є {C})Px\’. Here xє {C}’ is a restricted variable of quantification. And so the sentence reads ’Any animal-in-the-cage, x, is such that x purrs’. Under the suggested interpretation, the proposition would not be expressed with the unrestricted variable as ’(x)(Cx→Px)\’. For this is about any entity whatsoever, and not just about animals in the cage. When the cage is empty, ’(x)(Cx→ Px)‘ but not ’(xε{C})Px’ would still be about entities. Now the modal claim that all animals in the cage necessarily purr –that is, that any animal-in-the-cage, x, is such that x necessarily purrs–is a true, de re claim. For the natures of the entities that the corresponding non-modal claim is about suffice for the truth of the modal claim. (Where it is feasible, a de re claim will be distinguished from a de dicto claim by the convention of placing the modal adverb adjacent to the main verb.)

Universal modal propositions such as:

(1) All animals in the cage necessarily purr

that depend for their truth on the natures of just the entities of a restricted class are familiar enough. It is clearly a mistake to try to analyze them by using the universal conditional with an unrestricted variable. For (1) says what the entities in the cage necessarily do. It does not say that any entity is necessarily such that, if it were an animal in the cage, it would purr. This would make the truth of (1) depend on the natures of all entities, whereas it depends only on the natures of those in the cage. Moreover, it does not say that any entity is such that, if it were in the cage, it would necessarily purr, thereby limiting the modality to the consequent. The proposition (1) does not say this since it speaks categorically, not hypothetically, about the animals in the cage.

On the other hand, suppose one wants to say not just that all the animals that happen to be in the cage have a nature to purr but also that any entity is by nature such that if it is an animal in the cage it purrs. Here one considers not just the entities in the cage but all others as well. Thus, not only must it be true that (x ε {C})Px by the nature of x ε{C}, but it must also be true that (x)(Cx → Px) by the nature of x. The proposition that is true under these stronger conditions will be the de dicto counterpart of the de re proposition (1). (The de dicto claim will be expressed with the modal adverb as prefix, rather than as adjacent to the verb.) So the de dicto proposition:

(2) Necessarily all animals in the cage purr

is true precisely when the animals in the cage purr by nature and it is by the nature of any entity to purr if it is an animal in the cage. Since one could put a dog in the cage, (2) is false even though (1) is true on the supposition that only cats happen to be in the cage.

Though it goes beyond the corresponding de re claim, a universal de dicto claim in no wise introduces a necessity based on intentions. The dictum is the scope of the necessity operator and not the basis of the necessity. In fact, the de dicto necessity is grounded in natures and is thus a real necessity. The reason it is not de re is that it goes beyond the res of the corresponding non-modal claim. In going beyond what the corresponding non-modal claim is about, it still has its ground in the real rather than the intentional.

This view of universal de dicto claims is summed up by the following schema, where ‘(x ε {F})Gx’ means ‘Any F, say x, is such that Gx’ which means ‘All F are G’:

(3) Necessarily (x ε {F})Gx if and only if (i) (x ε {F}) Gx by the nature of x ε {F}, and (ii) (x)(Fx→ Gx) by the nature of x.

It follows from (3) that when {F} is the class of all entities–when the variable of quantification in ’x ε {F})Gxי is unrestricted –the universal de re and de dicto claims are equivalent. So it follows from (3) that the two Barcan laws hold–that all entities are necessarily G implies that necessarily all entities are G, and conversely that necessarily all entities are G implies that all entities are necessarily G. The reason for this result is that ’x’ has been assumed to range only over actual entities. Had this not been assumed, had non-actual entities been introduced into the range of ’x’, then even when {F} is the class of actual entities, it would impose a significant restriction on the range of ’x’, and the equivalence would fail. The reason for this assumption is that non-actual entities are no part of the ontology required by the practice of action based on prior experience. The required ontology is then uncompromisingly actualist. “No new entity is spawned in a possible world.”¹⁴ Apparent non-actual entities admit of reduction via an analysis of the acts of which they are the intentional contents.

So far there is no reason to regard Quine’s claim that necessity “resides in the way in which we say things, and not in the things we talk about"¹⁵ as even partially true. But we have yet to consider the most troublesome case, that of singular de dicto claims. The invalidity of existentially quantifying into such claims seems to warn us that here we are dealing with how things are conceived rather than with the natures of things. I contend, however, that the necessity of a singular de dicto claim need not be an intentional necessity.

Assume that the first human born at sea was the first animal born at sea. Now the singular de dicto claim that necessarily the first human born at sea was risible is true since two important conditions are satisfied. First, the corresponding de re claim is true. That is, the first human born at sea was necessarily risible just because it was an individual whose nature was to be risible. Second, anything is necessarily such that if it is the first human born at sea then it has the property humanness; and, if it is human, then necessarily it is risible. So the conditions involve both a singular and a general de re claim. By contrast, the singular de dicto claim that necessarily the first animal born at sea was risible is false. For, the second condition fails. There is no property necessarily implied by being identical with the first animal born at sea that in turn implies being risible.

The schema for singular de dicto claims is then:

(4)   Necessarily Fa if and only if (i) Fa by the nature of a, and (ii) (x)(ŽŽƎ ø)((x = a → øx) • (øx → Fx)) by the nature of x.

It is clear from this why there is a difficulty about quantifying-in. If (ŽŽƎ y) (necessarily Fy) is true, then it will be true that (ŽŽƎy)(x) (ŽŽƎ ø ((x = y → øx) • (øx → Fx)) by the nature of x. But plainly the latter is not true, except where F is merely a property implied by the properties of identity. For there is no individual mere identity with which as an individual will imply having a property such as humanness. The device of quantification abstracts from any content that supports such an implication. Though, for any x, it is true that (x = the first human born at sea → x is human), it is not true that (ŽŽƎy)(x = y → x is human).

If this is why existential quantification is not valid, the nonintentional character of the necessity is left intact. One cannot quantify-in because the mechanism of denoting individuals has been made crucial use of also to signify properties of those individuals. Quantifying wipes out the signifying role of the mechanism of denotation. But even though that role has been relied on, it is decidedly not the case that the truth of the proposition expressed by mobilizing that role depends on anything other than nonintentional factors. Thus its being true that anything identical with the first human born at sea is a human is based simply on the nature of any entity that one may care to consider. Still one cannot quantify into this proposition since the denotational expression ‘the first human born at sea’ is also relied on to signify the humanity of the denoted individual.

A case has already been considered in which clause (ii) of (4) failed. Failures of clause (i) present an interesting variety. It is not true that necessarily the first human born at sea was born at sea. For though the nature of the first human born at sea is to be human, it is not of the nature of this individual to be born at sea. To accommodate this and like cases, one can define a special sense of de dicto necessity by clause (ii) alone. This kind of necessity could be called “incidental.” For it is grounded not on the nature of the individual but on some feature incidental to it. It is incidentally necessary that this human, who is a ø is ψ where a human is not by nature a ø but where a ø is necessarily a ψ (For Aristotle, a man born at sea is an “incidental being” since he is not of himself born at sea, but any man is a “per se being” since he is of himself a man.¹⁶)

Moreover, it is also false, in view of (i) of (4), that necessarily the president is a citizen, assuming no one is a citizen by nature. But here even (ii) fails, since being president implies being a citizen not by nature but by the Constitution. This can then be defined as an intentional necessity. It will be intentional not because of failure of quantifying־in, but because the necessity is based on an intentional entity, the Constitution.

Having reduced real de dicto necessity to real de re necessity, it is well to consider the alternative of making the reduction go the other way. The motivation for this converse reduction might well be a prejudice against natures. But since the de re necessities I am concerned with must be real, this reduction cannot lead to de dicto necessities based on intentions. Suppose somehow the reduction to de dicto necessity could be effected, what account could then be given of de dicto necessity itself? Aristotle’s concept of nature seems suited to the job in view of the peculiarity that his is a kindrelative concept of nature. It differs in this respect from the concept of nature I am using. For him, a given entity has a nature as, say, a yew, but not as a topiary, even though the given entity is a topiary and this topiary is just a yew fashioned by the gardener’s art as a bird. On the other hand, the view taken here is that an entity has a nature by itself, irrespective of kind. Yet Aristotle’s concept gives a direct basis for de dicto necessity, without detour through de re necessity. The de dicto claim that necessarily every cat, or even this cat, purrs amounts to the claim that, in view of its kindrelative nature, a cat, or this cat, purrs. The non-relative natures of the cats would, as we have seen, be powerless to support these de dicto claims. What then are the kind-relative natures? The nature of an F, or of this F, is an explanatory principle of change in an F, or in this F, qua F.¹⁷ In other words, a topiary, being a product of art, has no nature as topiary since any principle of its growth is in it not qua topiary but qua yew. Either the reduction of the de re to the de dicto is bought at the expense of adding the primitive concept of gimness, or this concept is itself reducible. But when we go to reduce it, we are led straight back to de dicto necessity, for which we were presumably getting a real basis. An F, or this F, qua F is G if and only if necessarily an F, or this F, is G. On the Aristotelian kind-relative view of natures there is either no grounding of de dicto necessity or there is the addition of quaness.

* Things and individuals are to be distinguished from properties and conditions, but things are distinguished from other individuals as ones with capacities to act (Chapter XI, §1). Nothing here rests on the latter distinction.