1 A modal paradox

I shall say that an object x has a property P modally essentially (and that P is a modally essential property of x, and is modally essential to x) iff it is metaphysically necessary that x has P. An object x is said to have a property P modally accidentally (and P is said to be a modally accidental property of x, and modally accidental to x) iff both x has P and x does not have P modally essentially (i.e., x has P and it is metaphysically possible that x lacks P).Footnote 1

There is a class of paradoxes (antinomies) that invoke nested metaphysical modality and are modal variations on the ship of Theseus.Footnote 2 An oversimplified version of one such paradox, often called ‘Chisholm’s paradox’, may be set out as follows. We consider a tripod, which we name ‘Troy’, and which is the only tripod originally made in the actual world w1 of three intrinsically purely qualitatively identical interlocking legs L1, L2, and L3. Let L4 and L5 be intrinsically similar legs that are distinct from each other and from each of L1, L2, and L3.Footnote 3 We assume a principle of origin-tolerance or flexibility, Tol, that any tripod with Troy’s plan could have been the only tripod made originally from two of the same original legs with a different qualitatively similar third leg. Let ‘h’ and ‘h′’ be variables that range over kits consisting of three legs intrinsically similar to L1; let ‘M’ be a dyadic predicate for the relation of x being the tripod made originally from a tripod kit h; and let ‘O’ be a dyadic predicate for tripod kits that have at least two legs in common. We assume also that the relationship of overlap between tripod kits is modally essential to those kits. Then we have:

$$Tol:\quad \forall x\forall h\forall h\prime [{\text{M}}\left( {x,h} \right)\& {\text{O}}(h,h\prime ) \to \diamondsuit {\text{M}}(x,h\prime )].$$

Tol is not the sort of principle that can be true only contingently. If true, it is necessary, necessarily necessary, and so on. Indeed, according to the conventionally accepted system S5 of propositional logic of metaphysical modality (and according also to the weaker S4), any proposition that is necessary is necessarily necessary—hence necessarily necessarily … necessarily necessary, for every number of iterations.

We also assume a principle of modal essentialism, Ess, that no tripod of Troy’s plan could have been the tripod originally made from only one of the original legs and with two different legs in place of both of the other original legs, let alone from three different legs entirely. Any such tripod in another possible world is not Troy:

$$Ess:\quad \forall x\forall h\forall h\prime [{\text{M}}\left( {x,h} \right)\& \sim{\text{O}}(h,h\prime ) \to \square \sim{\text{M}}(x,h\prime )].$$

Let ‘t’ be an individual constant for Troy. Let ‘h1’ be an individual constant for the tripod kit consisting of L1, L2, and L3; let ‘h2’ be an individual constant for the tripod kit consisting of L2, L3, and L4; let ‘h3’ be an individual constant for the tripod kit consisting of L3, L4, and L5. The simplified version of Chisholm’s paradox is the following derivation:Footnote 4

1.

M(t, h1)

Initial condition

2.

O(h1, h2)

Initial condition

3.

□[h2 exists & h3 exists → O(h2, h3)]

Initial condition

4.

~O(h1, h3)

Initial condition

5.

◇M(t, h2)

1, 2, Tol, logic

6.

◇◇M(t, h3)

3, 5, □Tol, T modal logic

7.

~◇M(t, h3)

1, 4, Ess, T modal logic

8.

◇M(t, h3)

6, S4 modal logic

2 Resolution

Chisholm’s paradox is straightforwardly resolved, following Chandler 1976, by rejecting S4 as the logic of metaphysical modality. Although the prospect of Troy being made originally from h3 is metaphysically impossible, had Troy been made originally from h2 instead of h1, as it might have been, it would have been possible for Troy to have been made originally instead from h3. Some impossible prospects are such that they might have been possible. The paradox may be seen as a proof that the logic of metaphysical modality is not S4, which declares lines 6 and 7 inconsistent. This verdict of inconsistency is intuitively incorrect.

Given Ess and □Tol, Troy’s modally essential properties are not preserved between possible worlds. In (i.e., according to) the actual world w1, Troy’s property of not being made originally from h3 is modally essential to it. There is a possible world w2 (a world accessible to, i.e., possible according to, the actual world w1) in which Troy is originally made from h2. In w2, the property of not being made originally from h3 is merely modally accidental to Troy. There is a third world, w3, which is accessible to w2 and in which Troy is the tripod originally made from h3. But in the actual world w1, w3 is an impossible world.

I shall call this response to Chisholm’s paradox ‘AR’, an abbreviation for ‘the accessibility resolution’. AR accepts Tol, ⌜Tol → □Tol⌝, Ess, and lines 1–7 of the paradoxical derivation, while rejecting the S4 inference at line 8 as an instance of the modal fallacy of possibility deletion.

3 Leslie’s objection to the foregoing resolution

Sarah-Jane Leslie (2011) objects that AR itself is inconsistent, and that the paradoxes of nested modality are not genuine and therefore not to be taken seriously. Leslie’s remarks are quoted here at length with alterations to adapt the remarks to the present example:

I do not think that it is ultimately satisfactory, for a reason that has not been noted. Salmon’s treatment of the paradox faces a destructive dilemma: either the ‘paradoxical’ argument stops at the second world, in which case there is no paradox to be explained away by Salmon’s appeal to the ‘deletion fallacy’ or he is committed to the view that an item’s essence could have been different than it is, even if we restrict our interpretation of the relevant ‘could’ to the accessible worlds — i.e. the worlds that are possible simpliciter. The world w2 is accessible from w1 and vice versa; each represents straightforward possibilities for the items that exist in the other. But on Salmon’s description of the case Troy in w1 has a different essence from Troy in w2. …

What is not possible — not possible simpliciter, since it conflicts with the very notion of essence — is an object having … an essence that varies from possible world to possible world …. An object’s essence is its essence in every possible world; any item with a different essence simply cannot be identical to the original object. …

… Salmon’s treatment of the paradoxes implies that Troy’s essence could have been different than it is. We in w1 build Troy with L1, L2, and L3, and agree that Troy’s essence is tolerant in that it could have been made with one part different. What this means [sic] is that Troy could [only] have been made with two out of those three parts, plus a new [sic] part of the relevant sort as needed …. If we accept Salmon’s description of the case, then at w2 — where Troy is made from L2, L3, and L4 — Troy’s essence is there such that it could [only] have been made from two out of those three parts (plus a new [sic] part of the relevant sort as needed). But then Troy has an essence at w2 which is different from its essence at w1. Since w2 is accessible from w1, we have it that Troy’s essence could have been different than it is.

This is just not consistent with the notion of essence. A thing’s essence could not have been different than it is. (pp. 284–285)Footnote 5

The word ‘essence’ is susceptible to a multitude of interpretations in the current philosophical literature. Leslie uses the word for a “combination of essential properties,” adding “for the essentialist, an item’s essence determines its conditions for existence” (pp. 279–280; see note 1 above). For present purposes, we adopt the following definitions congenial to Leslie’s remarks. Where K is any class of properties, we shall say that an object x has K iff x has every element of K. We say that x has K modally essentially iff x has every element of K modally essentially, and that x has K modally accidentally iff x has K but not modally essentially (x has at least one element of K only modally accidentally). We call the class of x’s modally essential properties the modal essence of x. Finally, we say that K is a modal essence iff K is the modal essence of something or other. On this usage, every object x has exactly one modal essence, and x has its modal essence modally essentially.

One reason for adopting this nomenclature is that it accords with Leslie’s claim that in accepting w3 as a world accessible to w2 but inaccessible to w1, AR logically entails that Troy’s “essence” varies between w1 and w2. The nomenclature is strictly a matter of terminology, not of substance. The present terminology, which appears to coincide nearly enough with Leslie’s, facilitates the presentation below, but nothing in the analysis depends crucially on the terminology itself. Indeed, each definiendum may be replaced everywhere it occurs by its definiens with no effect on the content of the analysis.

Leslie makes, or appears to make, a couple of puzzling claims. One is that AR’s entailing that Troy has varying essences among possible worlds (i.e., among worlds accessible to w1) had escaped the notice of previous philosophers (op. cit., p. 284). She also claims that previous philosophers—including Hugh Chandler, Roderick Chisholm, Graeme Forbes, Saul Kripke, David Lewis, Penelope Mackie, and yours truly—have uncritically accepted a purportedly inconsistent hypothesis, to wit, that Tol is true with respect to both w1 and w2 (pp. 286–287). To understand why she makes these claims, one must look more closely at Leslie’s conclusions. In the quoted passage she states a disjunctive conclusion (mislabeled ‘a destructive dilemma’): Either (1) Tol is not true with respect to the possible world w2, so that there is no paradox for AR to resolve; or else (2) in advocating AR, I am committed to Troy having differing essences among possible worlds. This misstates Leslie’s actual conclusion, which is significantly stronger. She in fact argues for the conjunction: (1); furthermore (2).

Leslie bases her alternative resolution of Chisholm’s paradox on a contentious postulation of a plenitude of objects made from exactly the same matter as Troy.Footnote 6 Leslie’s preferred account has it that in any possible world in which Troy is originally made from h2 instead of h1, there is a physical replica of Troy also made from h2, hence exactly coincident with Troy, such that the replica, but not Troy itself, could have been originally made from h3. It was stipulated, however, that in w2, (whatever else there might be) Troy is the only tripod originally made from h2. Any replicas in w2 made from the same matter as Troy are not tripods, and hence all but completely irrelevant to the paradox. An inconsistent set of premises cannot be rendered consistent by supplementing the premises with additional theory. A full resolution ultimately must jettison one (or more) of Ess, Tol, ⌜Tol → □Tol⌝, and the S4 principle that whatever is (metaphysically) necessary is necessarily so. Preferably a plausible explanation for the rejected principle’s appeal should also be provided. Importantly, it is not sufficient merely to reject Ess, for example, or Tol, and to provide a weakened substitute. In contrast to the S4 principle, each of Ess, Tol, and ⌜Tol → □Tol⌝ enjoys prima facie, pre-theoretic appeal. Those theses, and their consequences, command default assent in the absence of countervailing considerations. A plausible rationale would need to be provided for rejection of any one of them.

Leslie rejects □Tol. (It is unclear whether she also rejects Tol itself.) Her rationale is a bold charge: □Tol by itself is inconsistent. (See note 5.) Leslie calls the property of having varying essences among possible worlds ‘a variable essence’.Footnote 7 She writes:

Clearly Tol cannot be necessary and true, for consider a pair of mutually accessible worlds in each of which x exists, but which are such that the difference between x’s constitution in the two worlds approaches but does not quite meet the allowable limits [sic-—Leslie means ‘does not exceed the allowable limit’] imposed by the requirement of “sufficient substantial overlap”. If Tol is necessary it follows that x’s essential origins are tolerant in the second world in a way that they are not in the first world. That is, it follows that there are possibilities of variable realization of x’s essence in the second world that are not found in the first world. This is just what cannot happen, for this implies that x has a variable essence — an essence that changes from world to world — not just a variably realizable essence. (p. 286)

Accordingly, Leslie criticizes previous philosophers’ uncritical acceptance that if Tol is true with respect to w1 then it is equally true with respect to w2: “True, once we indulge in this kind of thinking the familiar paradoxes get underway. But the thinking is itself already paradoxical, indeed it is genuinely inconsistent, for it entails that Troy has a different variably realizable essence depending on whether we start with w1 or w2. This, once again, is the incoherent idea of a variable essence” (pp. 286–287). What Leslie thinks her predecessors failed to recognize is not merely that AR countenances variable essences, but that □Tol alone already attributes variable essences, and that therefore □Tol itself is inconsistent (or inconsistent with Ess—see again note 5) and the alleged paradoxes of nested modality are not genuine.

Leslie’s objection to AR can be encapsulated by the following valid argument:

  • P1: According to AR, Troy has a variable essence.

  • P2: The prospect of an object having a variable essence is inconsistent with the very notion of essence.

Therefore, AR is inconsistent.

4 The crux of Leslie’s objection

Leslie supports her premise P1 by observing that according to AR, Troy’s essence in w1 includes not being made originally from h3 whereas Troy’s essence in w2 excludes this same property. The prospect of a variable modal essence is indeed integral to AR. No less crucial to Leslie’s objection is her premise P2. Yet she provides no rationale for P2, and it is far from obvious why she believes it.

It is trivial that AR depicts Troy as having a variable modal essence; that is indeed the very point of AR. It is also trivial that AR is consistent. The combination of Ess, □Tol, and lines 1–4 of the paradoxical derivation, together with their consequence that Troy has a variable modal essence, has a Kripke B model—a reflexive, symmetric, non-transitive accessibility model—that interprets all the non-logical constants as intended (‘M’, ‘O’, ‘t’, etc.). The metaphysical picture painted by this combination of propositions is not merely coherent. It represents a very plausible theory, which many endorse, of the metaphysical facts about material artifacts. Metaphysical necessity is a special way of being true. The characteristic T axiom ‘□p → p’ is straightforwardly analytic if ‘□’ means metaphysical necessity. The characteristic S4 axiom ‘□p → □□p’ does not enjoy this same status. The mere coherence of AR places the burden of proof squarely on supporters of S4 (or something stronger) as the logic of metaphysical modality. Unreserved assertion of P2 is no substitute for an argument.Footnote 8

I submit that Leslie’s tacit rationale for P2 commits the informal fallacy of equivocation, perhaps several times over. If her phrase ‘a variable essence’ is used in a sense on which P1 is true, P1 is then quite obvious; and on that sense P2 is straightforwardly false, as Kripke B and T models attest. Contrariwise, if the phrase ‘a variable essence’ is used in a sense on which P2 is true, on that sense P1 is simply false and altogether lacking in intuitive support.

A compelling interpretation of Leslie on P2 arises out of an observation of Teresa Robertson Ishii’s: that Leslie appears to slide between the nested modal notion of x modally accidentally modally essentially having a property P and the incoherent notion of x having P both modally accidentally and modally essentially. More generally, Leslie appears to slide between a proposition p being contingently necessary and p being both contingent and necessary. One argument in support of P2 that is strongly suggested by the passage quoted above is the following purportedly logical deduction:

By the definition of ‘modal essence’ (by “the very notion of essence”):

  1. (1)

    For every object x, x’s modal essence is such that x has it in every possible world (in which x exists—see footnote 1).

Therefore,

  1. (2)

    For every object x, x has the same modal essence in every possible world (in which x exists).

Therefore,

  1. (3)

    For every object x, x’s modal essence is the same in every possible world (in which x exists).

The initial observation (1) is correct. However, there is equivocation at (2), which is both ambiguous and slippery. The two relevant readings are given by the following:

  1. (2′)

    For every object x, there is a modal essence E such that x has E in every possible world (in which x exists).

  2. (2″)

    For every object x, there is a modal essence E such that E is x’s modal essence in every possible world (in which x exists).

Unlike (2′), (2″) entails that for every pair of possible worlds w and w′ (in which x exists), x’s modal essence in w is the same as x’s modal essence in w′. Whereas (2′) is a consequence of (1), it does not yield (3). Alternatively, (2″) delivers (3), but it is not a consequence of (1). To interpret (2) as (2″) is in effect to treat the phrase ‘x’s modal essence’ in (1) without justification as a rigid designator. It is analytic that every object has its modal essence modally essentially, but there is no inconsistency in the idea that an object might have had what is actually its modal essence without that being its modal essence. Thus (2″) is no mere analytic consequence of (2′)—unless S4 (or something stronger) is illicitly assumed as the background modal logic.

The ambiguity of (2) is one of scope, not lexical. There is an alternative potential basis for Leslie’s premise P2. On the most straightforward interpretation, Leslie does not use ‘essence’ univocally to mean modal essence. (See note 1.) Let us say that x has a property P logically essentially iff x has P in every logically possible (i.e., in every consistent) world, whether metaphysically possible or metaphysically impossible; and let the logical essence of x be the class of properties that x has logically essentially. (See Salmón 1989.) The hypothesis that by ‘essence’ Leslie means logical essence rather than modal essence would explain her repeated assertion without support, as if none is needed, that the prospect of an object having “a variable essence” is incoherent and “conflicts with the very notion of essence.” The idea that an object’s logical essence somehow varies among possible worlds is indeed extremely dubious.

If one uses the word ‘essence’ to mean logical essence, then it may be correct to say that the notion of “a variable essence” is inconsistent, meaning thereby that the notion of a variable logical essence is inconsistent. But it is then incorrect to say that AR has the consequence that an artifact has “a variable essence.” An object’s logical essence is an extremely meager lot compared to the object’s modal essence. Troy’s logical essence, which includes properties like being either round or not, also includes Troy’s haecceity—its thisness, the property of being Troy—and any properties logically entailed by it (e.g., the property shared by Troy and Woody Allen of being either Troy or Woody Allen, and even the property of being either Troy or made originally from h3). It does not include Troy’s more lionized modally essential properties. According to AR, Troy has the property of not being made originally from h3 in every world that is accessible to w1. AR does not cast this property as one that Troy has in every logically possible world. On the contrary, AR explicitly depicts Troy as lacking this property in w3. Leslie sees AR as depicting Troy as having “a variable essence,” merely on the ground that it denies that the properties that Troy has in every (Troy-inclusive) world accessible to w1 are the same as those that Troy has in every (Troy-inclusive) world accessible to w2. It does not follow from this depiction of Troy that the issue of which properties it has in every (Troy-inclusive) logically possible world is somehow relative to w1 or w2. The properties that Troy has in every (Troy-inclusive) logically possible world are the very same according to w1, w2, and w3.

Leslie appears to confuse modal essence with logical essence, with resulting equivocation in her use of the word ‘essence’. She argues for her premise P1 by observing that according to AR, not being made originally from h3 is modally essential to Troy in w1 but is modally accidental to Troy in w2. If by ‘essence’ she means modal essence, then her argument for P1 is correct but her assertion of P2 is incorrect. If instead by ‘essence’ she means logical essence, then P2 is justified but her argument for P1 is then fallacious. AR does not have the consequence, which is of dubious coherence, that Troy has a variable logical essence. If by ‘x’s essence’ Leslie means that which is both x’s modal essence and x’s logical essence, then there is a more radical failure. AR entails that Troy does not have a modal-cum-logical essence.

The very same issues arise in connection with an alternative interpretation of the word ‘essence’. As Teresa Robertson Ishii (2013) points out, although Leslie is objecting to AR, which employs the notion of an object x’s modally essential properties, she sometimes appears to employ instead, or in addition, an Aristotelian notion of “essence” urged by Joseph Almog, Kit Fine, and Stephen Yablo: what x is, or what it is to be x (pretending these are the same thing). An object’s quiddity essence—its whatness—is supposed to be a very select, privileged segment of the object’s modally essential properties (but presumably not merely the object’s haecceity).Footnote 9 If there is such a thing as Troy’s quiddity essence—if Troy has a whatness (and only one)—it is a severely restricted subclass of Troy’s modal essence. As Robertson Ishii notes, Leslie’s terminology blurs together modal essence and quiddity essence. Contrary to some grandiose claims the alternative uses of ‘essence’ are not competing, but they are different. The modal concept is clear; the quiddity notion is unclear. But it is clear that what has just been said concerning an object’s logical essence is equally true of its alleged quiddity essence. The idea that Troy’s quiddity essence varies among metaphysically possible worlds is indeed of dubious coherence. Fine (2005), pp. 348–349 writes that

the identity of an object is independent of how things turn out, … not just in the relatively trivial sense that the identity of an object is something that will hold of necessity. Rather it is the core essential features of the object that will be independent of how things turn out and they will be independent in the sense of holding regardless of the circumstances, not whatever the circumstances. The objects enter the world with their identity predetermined, as it were; and there is nothing in how things are that can have any bearing on what they are.

I take it that Fine means to say this: The quiddity essence of a possible object is independent of the circumstances of a world, not only in the trivial sense of ‘holds in every possible world whatever its circumstances’, but furthermore in the stronger sense of ‘holds in a possible world quite independently of its circumstances’. A possible object supposedly has its quiddity essence in every possible world precisely because quiddity essence is world-independent. The world-invariance is a consequence of the world-independence.Footnote 10

If by ‘essence’ Leslie means quiddity essence, then again, even if P2 is justifiable her argument for P1 is fallacious. Kripke models demonstrate that varying modal essences are consistent with fixed quiddity essences. It is perfectly compatible with AR that although Troy’s modal essence varies among w1, w2, and w3, Troy’s quiddity essence—what it is to be Troy—supposing Troy has such a thing, is the very same in all three worlds.Footnote 11

In fact, it would seem that Troy’s quiddity essence (assuming it has one) must be the same in all transitively metaphysically possible worlds (where a transitively metaphysically possible world is one that is metaphysically possible, metaphysically possibly metaphysically possible, or so on). For if Troy’s quiddity—if what it is to be Troy—were different in any pair of worlds w and w′, Troy would not be in w′ exactly what it is in w, to wit, that very tripod. In both worlds, Troy has the property of being a tripod, for example, and in both worlds Troy has the very same haecceity, the property of being this very thing.

It should be noted that contrary to Fine, objects can nevertheless lose even their quiddity essences in some far away worlds. In a logically possible world in which Troy is a credit-card account or a poem instead of a tripod—a metaphysically impossible way for things to be that is not even transitively possible—Troy presumably lacks the quiddity essence that it has (assuming it has one) in w1, w2, and w3. (Troy retains its haecceity even in such far away worlds.)

5 A final interpretation

It is possible that Leslie uses the phrase ‘a variable essence’ altogether differently. In an alternative nomenclature one might define ‘the essence of’ an object x in a world w to be the class of properties that x actually has modally essentially, i.e., the class of properties P such that x has P in every world w′ that is accessible to the actual world w1 (rather than to w). In the terminology of the present essay this is x’s actual modal essence, i.e., the modal essence of x in the specific world w1. Of course, the actual modal essence of an object x is just x’s modal essence, nothing more and nothing less. For this reason, it is easy to confuse the notion of an object’s modal essence with that of an object’s actual modal essence. There is a very important difference between the two notions. The difference shows itself in non-actual worlds, e.g., in merely possible worlds like w2. It is an element of Troy’s actual modal essence that Troy not be made originally from h3. This same property—not being made originally from h3—is not an element of Troy’s modal essence in w2, but it remains an element of Troy’s actual modal essence in every world, including w2.

What is actual (in the indexical sense) is actual in every world; the idea that an object’s actual modal essence varies among different worlds is incoherent. That Troy’s actual modal essence is invariant among (Troy-inclusive) possible worlds is a potential basis for Leslie’s assertion of P2. The prospect of an object having a variable actual modal essence is indeed inconsistent with the very notion of an actual modal essence.

This is not to say that Leslie and I mean different things by ‘essence’ so that the differences between us are merely verbal. Leslie and I sharply disagree on matters of both metaphysical and modal-logical substance. All parties should agree that Troy’s entire actual modal essence is the same in w2 as it is in w1. In particular, the property of not being made originally from h3 is as much an element of Troy’s actual modal essence in w2 as in w1. AR also has it that in w2, Troy could have been made originally from h3, i.e., if w2 had been realized—as it might have been—then it would have been possible for Troy to have been made originally from h3. That Troy’s actual modal essence precludes the prospect that Troy is made originally from h3 merely confirms that Troy’s modal essence in w2 is different from Troy’s actual modal essence (i.e., from Troy’s modal essence in w1). By contrast, Leslie contends that insofar as Troy could not have been made originally from h3, even if Troy had been made originally from h2, it would still have been metaphysically impossible (by the very notion of “essence”) for Troy to be made originally from h3.

It is a consequence of Leslie’s view of the matter that given Ess, the putatively metaphysically impossible world w3—which she stipulated to be a world (assuming there is one) in which Troy is made originally from h3 (p. 283)—is impossible even according to w2. Yet Leslie asserts that Troy does not exist in w3 (pp. 288–289), directly contrary to her stipulation. This provides indirect evidence that by ‘essence’ she means actual modal essence. Leslie mistakes the stipulated impossible world w3, which includes Troy, for a possible world w1′ in which Troy is absent and a different tripod, Trevor, is made from h3. In effect, Leslie misidentifies w3 with its metaphysically possible twin. (On Leslie’s view, w1′ is also possible according to w2. On my view, it is not.) The likely explanation for her confusion of w3 with w1′ is that Leslie does not recognize actually impossible worlds and sees only actually possible worlds.Footnote 12 Whereas w3 is not among the possible worlds, w1′ is. When her attention is directed toward the impossible world w3, Leslie attends instead to its possible counterpart.

In (1989) I referred to the general confusion of the notion of necessity with that of actual necessity, as ‘the ostrich approach to metaphysical modality’, because it fails to acknowledge worlds like w3 that are possibly possible but not possible simpliciter. The ostrich approach maintains the discredited S5 as its modal propositional logic by ignoring worlds inaccessible to the actual world. The “logical space” of the ostrich approach is metaphysically impoverished. It is missing a plenitude of impossible worlds.

If by ‘essence’ Leslie means actual modal essence (or modal-essence-cum-actual-modal-essence), then her assertion of P2 is justified but her argument for P1 is fallacious. AR does not have the incoherent consequence that Troy has a variable actual modal essence.

It is possible that Leslie does not equivocate with (2) (or anything similar) in support of her crucial premise P2. It is possible that she does not confuse modal essence with logical essence or with quiddity essence or with actual modal essence. It is equally possible that she equivocates in all these ways. If her tacit rationale for P2 is not mistaken in any of these ways (nor in the way criticized in note 8), then I am unable to guess what that rationale is.

It is inconceivable that Kripke, Lewis, and others who have addressed AR were all unaware that it has the consequence that an artifact might have had some of its actually modally essential properties merely modally accidentally. The reason they had not noticed that AR is inconsistent is that it is consistent. The intended Kripke model establishes consistency. (See notes 7 and 8.) Leslie’s rationale for rejecting □Tol thus collapses. AR is not merely consistent in T and B modal logics. Its core theses—Tol, ⌜Tol → □Tol⌝, and Ess—reflect metaphysical common sense. Artifacts, and presumably also material objects of some natural kinds, genuinely have different properties modally essentially in different possible worlds. The modal essence of any material artifact genuinely could have been different than it is.

Leslie says that AR runs a gamut, being at once ingenious, influential, based on confusion, incoherent, and inconsistent (pp. 283–287). As far as I am able to determine, AR is in fact none of the above. Numerous philosophers who reason with modality persist in embracing S5 as the presumed propositional logic of metaphysical modality. Allegiance to S5 modal logic notwithstanding, the axioms and rules of S5 were not handed down unto us engraved on sacred tablets. That it is at least logically possible that some de re metaphysical necessities are only contingently necessary—so that the logic of what might have been is not even as strong as S4—is little more, but nothing less, than good philosophical sense.