In Defense of the Possibilism-Actualism Distinction Christopher Menzel* Texas A&M University In his important 2013 book Modal Logic as Metaphysics, Timothy Williamson claims that "there is a widespread feeling of dissatisfaction with the possibilism-actualism [P-A] distinction" and, indeed, that usage of the terms 'possibilism' and 'actualism' "has become badly confused". The claim is surprising, as the P-A distinction is widely discussed in the philosophical literature and, while there is substantial metaphysical disagreement to be found, there is in fact very little evidence of any deep confusions over exactly what the disagreement concerns. The reason for that, I will argue, is that the distinction is entirely coherent and that Williamson's charges are mostly unwarranted. Specifically, in §1 of this paper I discuss some of the historical antecedents of what I call the modern subsistence conception of the P-A distinction, which I refine in §2. I then turn to Williamson's attack on the P-A distinction in §3 and examine in particular two arguments that he sketches that purport to show that problems will arise for any proposed definition of the distinction; I find both arguments wanting. In §4 I discuss Williamson's preferred distinction between necessitism and contingentism and argue that, broadened so as to enable necessitists to fend *My thanks to Ross Cameron, Matt Davidson, Kris McDaniel, and Ed Zalta for helpful comments on earlier versions of this paper, and to audiences at the Munich Center for Mathematical Philosophy, the University of Utah, the Society for Exact Philosophy (2016 meetings), the University of Notre Dame, Georgetown University, the University of Vienna, the Kurt Gödel Research Center for Mathematical Logic, and the universities of Oslo and Bergen for fruitful, challenging, and stimulating discussions in response to talks I gave based on the issues discussed herein. I am particularly grateful to Benjamin Schnieder for his detailed answers to several questions I had concerning his important and informative paper on Bolzano's modal metaphysics. Finally, special thanks to the Notre Dame Center for Philosophy of Religion, where I completed a significant draft of this paper during my tenure as the 2016-17 Alvin Plantinga fellow. off contingentist objections, the subsistence conception of the P-A distinction can be faithfully reconstructed within Williamson's own framework and, hence, that it is, at least, no more confused or unsatisfying than the necessitism-contingentism distinction. However, Williamson's critique does point to a genuine shortcoming in the subsistence conception as commonly formulated. In §5 I propose an alternative definition of the P-A distinction in terms of essential properties that I believe avoids this shortcoming. 1 Historical Underpinnings of the Subsistence Conception The heart of the P-A distinction that, I claim, is at stake in Williamson's attack turns in the first instance on the question of whether or not being is bifurcated, that is, whether or not what there is, in the broadest sense, divides non-trivially into two jointly exhaustive, mutually disjoint ontological categories: things that exist, or are actual, and things that merely subsist. Roughly and incompletely put for now, existence includes at least everything that is within the causal order, and subsistence includes, if not all, at least only things that are not within the causal order. A merely possible object - possibile, for short - is thus a subsistent object that could have existed and possibilism the view that there at least could be possibilia. I will call this the subsistence conception of possibilia/possibilism and I will argue that it is the basis of the P-A distinction.1 Part of my defense of the P-A distinction is that the subsistence conception of possibilia has a lengthy historical pedigree. The bifurcation of being, in particular, can be traced back at least to the Stoics, who introduced a highest genus above existence encompassing both concrete existents as well as "incorporeals" that fail to exist but, rather, "have a derivative kind of reality the Stoics term subsistence (ὑπόσvτασvις)" (de Harven 2015, p. 406)2: The Stoics want to place above this [the existent] yet another, more primary genus. ... Some Stoics consider 'something' the first genus, and I 1There is, of course, a well-known alternative to this conception of possibilia, viz., David Lewis's (1986). Following Williamson (ibid., p. 22), I do not consider Lewis's reductionist account to be relevant to the modalist version of the debate under discussion here. 2See also Caston 1999. My thanks to Professor Caston for pointing me to the Seneca quote here. 2 shall add the reason why they do. In nature, they say, some things exist, some do not exist. But nature includes even those which do not exist - things which enter the mind, such as Centaurs, giants, and whatever else falsely formed by thought takes on some image despite lacking substance. (Seneca, Letters 58:13-15, quoted in Long and Sedley 1987, p. 162.) Here, and in many subsequent discussions, bifurcation is motivated not by explicitly modal considerations but by intentional considerations, our ability to conceive of things that fail to exist, an ability that seems to require that there be something to serve as the "proper subject of thought and discourse" (Long and Sedley 1987, p. 164). A notable adumbration of the P-A distinction proper motivated not by intentionality but by theological considerations is seen in the distinction between thing (shay′) and existent (mawjūd) in early Islamic philosophy. The distinction arose out of exegetical struggles with two passages of the Qur'an (16:40, 36:82) suggesting that creation consists in God saying "Be!" to a thing, causing it thereby to exist, to become an existent (Wisnovski 2003, p. 147). The apparent implication here - embraced explicitly by the Mutazilite theologians in the 9th and 10th Centuries - was that, because things are commanded to exist, they must in some sense have been prior to God's creative commands and, hence, that shay′ encompassed not only existents but non-existents as well - specifically, those that have ceased to exist but were called into existence, those that will be called into existence, and those that only could be, but never in fact are, called into existence (op. cit., pp. 1458). Non-existents of this third sort, of course, clearly foreshadow possibilia in our sense. In much subsequent discussion in the late medieval period, the question of possibilia was framed in terms of a Euthyphro-style grounding dilemma, i.e., whether (a) things are possible because God has the power to make them or (b) whether God has the power to make them because they are possible (see M. Adams 1987, p. 1065). The influential Islamic philosopher Avicenna, who was strongly influenced by the antecedent theological debates over shay' and mawjūd, appeared to grasp horn (b) of the dilemma, arguing explicitly for something very much like the subsistence conception of possibilia: It is necessary with respect to everything that came into existence that before it came into existence, it was in itself possibly existent. For if 3 it had not been possibly existent in itself, it never would exist at all. Moreover, the possibility of its existence does not consist in the fact that an agent could produce it or that an agent has power over it. Indeed, an agent would scarcely have power over it, if the thing itself were not possible in itself.3 Subsequent Catholic philosophers, following Augustine (1982, pp. 79-81), opted to ground possibilia and other non-concrete entities ontologically in the divine mind, by either identifying them with divine intellective acts or with the "objective contents", or products, of such acts.4 Most medieval thinkers, in turn, grounded their possibility - that is, the possibility of their exemplification - in God's power to actualize them5, thereby grasping the other horn of the grounding dilemma. Particularly important for our purposes, however, is that the idea of bifurcation is still prominent: mere presence in the divine intellect confers on possibilia (so understood) a sort of lesser or "diminished" being (esse diminuta). Thus Peter Auriol, as quoted by Ockham (M. Adams op. cit., p. 79): An act of intellect is very similar to the thing it is about. Therefore, through this likeness ... the thing seizes a certain existence through the act of understanding insofar as [that act] is very similar to the thing, so that understood existence is not a mere denomination, but a certain diminished intentional or apparent existence ... . And although Auriol here speaks of objects of thought generally, Henry of Ghent, Duns Scotus, and William Ockham (in his earlier writings, at least) all emphasized that this less robust mode of being includes possibilia alongside fictional objects, impossible objects, and logical objects.6 In more recent times, Meinong is well-known for postulating an ontology of nonexistent objects (Gegenstände) to ground his general theory of meaning, cognition, and intentionality.7 In his work, however, we find both more, and more 3Quoted in M. Adams 1987, p. 1068. See also McGinnis 2010, pp. 162-3 and See also Wolter 2003b. 4Cf. De Rijk 2005, pp. 33-37, 77-78, and M. Adams 1987, pp. 79-83. 5See M. Adams, op. cit., chs. 24 and 25, Wolter 2003a, and De Rijk 2005, pp. 79-95. 6Cf., respectively, De Rijk, op. cit., p. 81, Wolter 2003b, pp. 137-8, and M. Adams 1977, p. 147. 7Meinong 1960 is the locus classicus of his account. See Marek 2013 for an illuminating and accessible exposition. 4 fine-grained, metaphysical divisions than existence and subsistence and, moreover, a rather startlingly different understanding of what sorts of objects belong where among these divisions. In order to explain our ability to speak and think meaningfully about the likes of Homeric gods, golden mountains, and the round square - if only to deny their existence - Meinong famously adopted, or at least presupposed, a semantic principle to the effect that every definite or (in intentional contexts, at least) indefinite description denotes an object that exemplifies the properties expressed in the description, that is (perhaps a bit anachronistically put), the principle: MSP For (perhaps quite complex) adjectives α and common noun phrases N , pthe/a(n) αNq denotes an object that is both α and an N.8 Thus, "the golden mountain" denotes an object that is both golden and a mountain; likewise, "the round square" denotes an object that is both round and a square. However, notwithstanding this semantic principle, according to Meinong there are not, in any sense, any Homeric gods or round squares. Hence, he divided the class of objects into two subclasses: those that have being, {x : B!x}, and those that lack it, {x : ¬B!x}. The former included both existing (existierende, reale, or wirkliche) objects - concrete objects that are part of the causal order and hence in space and time - and "ideal" (ideale) objects like numbers, properties, and propositions (Objektive) that "do intdeed subsist (bestehen), but which do not by any means exist (existieren)" (op. cit., p. 79), as they are by nature outside of the causal order and, hence, outside of space and time. The latter - those objects lacking being altogether - include in particular the class of "incomplete" objects {x : ∃F(¬Fx∧ ¬Fx)}, i.e., those objects that, for at least one property F, have neither F nor its complement F. This class includes fictional objects like the Homeric gods but also, notably, objects like the golden mountain and the round square that are denoted by simple definite descriptions.9 8Meinong's actual account is rather more subtle than this, although I think MSP is faithful enough for purposes here. See Parsons (1974) (pp. 573ff) formal reconstruction of Meinong's semantics and Simons 1992 ch. 7 (esp. §2.1 and §3) more detailed philosophical account. 9Obviously, lest such objects lead directly to contradiction, in a Meinongian object theory (expressed in classical logic), Fx will not follow from ¬Fx; equivalently, Fx will not follow from ¬Fx, i.e., failing to have F will not entail having its complement F. This is a familiar sort of restriction for avoiding Russell-style paradoxes in logics with property-denoting expressions. See, e.g., Turner 1987 and Menzel 1993. 5 Now, possibilia in any sense resembling the subsistence conception do not appear to be among any of Meinong's objects.10 Thus, Meinong's division of being into existing and subsisting objects - objects within and without space and time, respectively - seems to be little more than the traditional distinction between material, concrete objects and abstract, platonic objects. It was Russell, in his early career, who broadened the subsistent realm beyond the abstract to include some of Meinong's Nichtseiende and who, thereby, at least made room for possibilia. Meinong's influence on Russell was profound but, even in his most ontologically profligate years shortly after the turn of the century, Russell was repelled by the idea of objects that do not so much as subsist, let alone those like the round square whose nature is logically contradictory.11 He did, however, still find Meinong's semantic/cognitive arguments in the main convincing and, hence, continued (until around 1905, at least12) to embrace a restricted version of MSP and, as a consequence, at least some of the objects found among Meinong's Nichtseiende, fictional objects in particular. In order to embrace such objects without committing to Nichtseiende as such, Russell simply retained Meinong's bifurcation of being and squeezed fictional objects and their ilk into the realm of subsistent objects - objects that have being but do not exist within the causal order (Russell 1903, p. 449): Numbers, the Homeric gods, relations, chimeras and four-dimensional spaces all have being, for if they were not entities of a kind, we could make no propositions about them. Thus being is a general attribute of everything, and to mention anything is to show that it is. ... Existence, on the contrary, is the prerogative of some only amongst beings. ... 10This isn't to say Meinong was skeptical of modality. But he never really appeals to his ontology to ground, or explain, such modal facts as our possible nonexistence or the possibility that there could have been more, or other, things. See Peter Simons' (2013) detailed account of the elaborate theory of modality in Meinong's huge 1915 treatise. Meinong also seems to suggest at one point that objects that are not in fact part of the causal order but could be are also real (Meinong 1899, p. 198). Unfortunately, he does not seem to have elaborated on this suggestion. 11See Chisholm 1973 for an attempt to render Meinong's Nichtseiende coherent. In fact, though, according to Meinong, all objects as such - even existing objects (hence more generally those that have being B!) - qua pure objects, are ausserseiend, or "beyond being and non-being". See Meinong 1960, §4, esp. p. 86, and Marek op. cit., §4. This is Meinong's "principle of the indifference of pure objects to being" (ibid.). 12Once he had formulated his theory of descriptions, of course, Russell (1905) denied that definite and indefinite descriptions, as well as ordinary proper names like 'Pegasus', were genuine denoting expressions. 6 [T]his distinction is essential, if we are ever to deny the existence of anything. For what does not exist must be something, or it would be meaningless to deny its existence; and hence we need the concept of being, as that which belongs even to the non-existent. Now, similar to Meinong, Russell also did not explicitly make a place for possibilia in our sense in his ontology, although in his case this had less to do with the finer theoretical details of an elaborate ontology than with his skepticism about modality generally.13 Accordingly, he did not ever provide any examples of subsistent entities whose descriptions were explicitly modal. Importantly, though, his arguments above apply just as well when, say, we deny the existence of the possible person who would have developed from the union of this sperm and that egg or the possible knife consisting of this blade and that handle. Thus, his skepticism of modality notwithstanding, there seems little doubt that the subsistent - understood generally to comprise things outside of space and time - is the natural home of possibilia in the early Russell's bifurcated ontology. In his famous 1948 essay "On What There Is", Quine makes the inclusion of possibilia among the subsistent explicit via the voice of his ontologically promiscuous fictional philosopher Wyman (p. 22): Pegasus, Wyman maintains, has his being as an unactualized possible. When we say of Pegasus that there is no such thing, we are saying, more precisely, that Pegasus does not have the special attribute of actuality. Saying that Pegasus is not actual is on a par, logically, with saying that the Parthenon is not red; in either case we are saying something about an entity whose being is unquestioned. ... Existence is one thing, he says, and subsistence is another. Unfortunately, although he gets this critical element of the modern conception right, Quine's account still suffers from a fundamental confusion lurking in the Meinongian semantic principle MSP. The confusion in question is revealed in the well-known rhetorical questions Quine raised concerning identity conditions for possibilia (pp. 23-4): 13See Meinong 1965, p. 152 for a particularly striking example. 7 Take, for instance, the [merely] possible fat man in that doorway; and, again, the [merely] possible bald man in that doorway.14 Are they the same possible man, or two possible men? How do we decide? How many possible men are there in that doorway? Are there more possible thin ones than fat ones? How many of them are alike? Or would their being alike make them one? Are no two possible things alike? Is this the same as saying that it is impossible for two things to be alike? Or, finally, is the concept of identity simply inapplicable to unactualized possibles? But what sense can be found in talking of entities which cannot meaningfully be said to be identical with themselves and distinct from one another? Quine's questions were clearly intended to serve as a reductio of possibilism. Whether they do is much less clear. The questions obviously assume at least some variant of MSP from which it follows in particular that the merely possible fat man in the doorway is possible (i.e., a possibile), a man, and in the doorway; likewise, the possible bald man in the doorway. Hence, both of the possible men in question are in the doorway. Quine's subsequent questions - whether we have one or two of them and, in either case, in virtue of what is it the case, and so on - are thus entirely natural ones. Far from yielding the desired reductio, however, Quine's questions can, at the least, equally be taken to reflect shortcomings in MSP and in Quine's resulting conception of possibilia - shortcomings that he likely would have avoided if only had he been aware of Bolzano's trenchant (and, at the time, over a century-old) analysis of modal descriptions and his sophisticated modal metaphysics. Bolzano appears (again, somewhat anachronistically put) to have accepted a qualified form of MSP insofar as he thought that a noun phrase of (in particular) the form "merely possible F" expresses an idea (Vorstellung) that is "objectual" (gegenständlich), i.e., that has something falling under it, and hence that "a/the merely possible F" denotes, so long as it is not logically or metaphysically incoherent.15 Bolzano is clear, however, that the objects of such ideas are not the incom14I add the qualification "merely" here simply because Quine clearly intended to be discussing possibilia whereas, since actual individuals are possible, if by chance there happened to be an actual bald or portly man in the doorway, the expressions in question would (contrary to Quine's intentions) pick him out rather than any (alleged) possibilia. 15See Bolzano 1837a, §352, p. 406 and its translation in Schnieder 2007, p. 541. 8 plete objects of Meinong's realm of non-being but, rather, are fully determinate objects in a fully-fledged realm of being that includes both traditional abstract objects and possibilia: [A]part from those things which have actuality (Wirchlichkeit) ..., there are also others which have mere possibility (blosse Möglichkeit), as well as those which can never make the transition to actuality, e.g., propositions and truths as such (Bolzano 1837b, §483, pp. 184–85; trans. in Schnieder 2007, p. 529). Not only actual objects ... but even merely possible objects as well as objects that can never become actual - in brief, all objects without exception are completely determinate (Bolzano 2014, §45, p. 209). Bolzano thus firmly embraced a bifurcated conception of being comprising both objects within the causal order - those with actuality - and objects outside of it, where the latter comprise both traditional abstracta and fully determinate possibilia, objects that only contingently fail to be actual. Although Bolzano's conception of possibilia is much clearer and more explicit on the matters of determinacy and ontological status, thus far it does not differ appreciably from that of Quine's Wyman. Critically, though, as Schnieder (2007) convincingly shows, Bolzano argued that, contrary to Quine's understanding of MSP, the usual function of "possible" in a common noun phrase of the form ppossible αNq is not to add a further property - possibility - to the properties that α predicates of an N . Indeed, while pthe/a possible αNq certainly picks out an object o for Bolzano (so long as pαNq is logically coherent), the qualification 'possible' cancels the implication that o is either α or an N . Hence, in particular, even if we agree that "the possible fat man in the doorway" and "the possible bald man in the doorway" denote objects, it follows only that those objects could be portly/bald men in the given doorway; nothing follows about what or where they in fact are - indeed, if they denote genuine possibilia and hence have no spatio-temporal location, they are most certainly not men and not in the doorway. On this understanding of modal descriptions, then, Quine's questions all either have straightforward answers - e.g., there are no possible portly/bald men in that empty doorway - or are no harder to answer than parallel questions that might arise in any other case where we are unacquainted with the referents of two descriptions. 9 It is unfortunate that Bolzano's robust conception of fully determinate, subsistent possibilia went largely unnoticed - had it not, it seems likely that the subsequent history would have involved far less confusion over the nature of the possible and considerably less skepticism about de re modality in general. Fortunately, underwritten by modern possible world semantics, what is essentially Bolzano's conception sprang out of the ashes of Quine's skepticism and is found (though not necessarily endorsed) in a wide swath of the modern literature on modal metaphysics - see, e.g., Plantinga 1976, Kaplan 1975, R. Adams 1981, Zalta 1983, Fitch 1996, Fine 2005, and Parfit 2011 (notably, Appendix J). 2 The Modern P-A Distinction The subsistence conception of possibilia, then - basically as found in Bolzano's largely neglected account - serves as the basis for the subsistence conception of the P-A distinction itself. To reiterate: possibilism on this conception is the view that being - everything there is in the broadest, most unrestricted sense - is bifurcated into two categories: subsistence and existence, a.k.a. actuality. Subsistence includes (at least) the possibilia - fully determinate (albeit non-spatiotemporal) objects that contingently fail to exist, objects that could have existed but do not, in fact, exist. Formally, then, and a bit more generally, using the predicate E! for existence/ actuality, possibilism on the subsistence conception is simply the view that there at least could be possibilia: Poss ^∃x(¬E!x∧^E!x) Actualism, then, on the subsistence conception, is simply possibilism's denial: there are no possibilia, nor could there have been; necessarily, everything (in the broadest sense) that could exist, already does. Act ∀x(^E!x→ E!x) Call this the basic subsistence conception of the P-A distinction (the basic P-A distinction, for short) and Poss and Act basic possibilism and basic actualism, respectively. 10 Necessarily Actual Contingently Actual Contingently Non-actual (i.e.,"merely possible") Bolzanian Possibilism Bolzanian Actualism Being Necessarily Non-actual (i.e., "abstract") Necessarily Actual Contingently Actual Contingently Non-actual (i.e.,"merely possible") Being Necessarily Non-actual (i.e., "abstract") Figure 1: The "Bolzanian" P-A Distinction Abstracta and Actuality. The basic P-A distinction is so-called because it divides the world into two broad categories but it is silent on finer ontological subdivisions that might be required by such things as God and abstracta. As seen above, Bolzano categorized abstracta alongside possibilia as subsistent things outside the causal order, the difference being that, unlike possibilia, they subsist necessarily; they "can never make the transition to actuality". And while Bolzano (1837 §79, p. 364) apparently did not consider God to occupy space and time, he nonetheless considered God, as creator, to be part of the causal order (Bolzano 1973 §175, p. 259) and hence to be actual, albeit, again, necessarily so. Making these aspects of Bolzano's modal ontology explicit yields what we can call the "Bolzanian" P-A distinction, depicted in Figure 1. However, there are good reasons to depart from Bolzano and follow Quine in the classification of abstracta. Specifically, Quine (speaking in his own voice contra Wyman) breaks the connection between subsistence and causal inertness/nonspatio-temporality and grants existence proper to mathematical objects (1948, p. 23): If Pegasus existed, he would indeed be in space and time, but only because the word 'Pegasus' has spatio-temporal connotations, and not because 'exists' has spatio-temporal connotations. If spatio-temporal reference is lacking when we affirm the existence of the cube root of 27, 11 this is simply because a cube root is not a spatio-temporal kind of thing, and not because we are being ambiguous in our use of 'exist'. Generalizing Quine's conception to all abstracta, then, subsistence is exactly the domain of the merely possible. And note this classification arguably comports better with the idea first hinted at by the Mutazilites that existence is a more robust way of being. There is perhaps a temptation to identify robustness with spatiotemporality but, as Bolzano already noted, that would classify God as merely subsistent. A more plausible basis for the distinction that would keep God among the actual but abstracta among the subsistent is participation in the causal order, but that raises fraught questions concerning, notably, the nature of causation and the status of some mental entities. Better, I think, to take the robustness in question to be a feature of things that are "fully realized" - consider in particular the difference between a purported merely possible person x subsisting as a mere possibile, dwelling with no (non-modal) distinguishing characteristics in logical space, and that same object x after coming to exist as a fully realized human being. By contrast, abstracta are already, so to say, all they can be; unlike possibilia, their "potential" is fully realized, their non-spatio-temporality notwithstanding. Classifying abstracta as actual also accords far better with the intuitive understanding of actualism. For, if abstracta only subsist, as on the Bolzanian conception, then it remains the case under actualism that there are still things that do not exist. But actualism's guiding intuition is that there is no bifurcation in being - to be is to exist is to be actual. Classifying abstracta among existing things enables the actualist to preserve this unified picture. We can force this classification explicitly by means of a principle that rules out the possibility of necessarily subsistent things altogether, viz., ^E! ∀x^E!x. In addition to classifying abstracta as existent, the principle also has the salutary effect (for the actualist, anyway) of ruling out impossibilia - round squares and the like that can't possibly exist due to some sort of internal logical inconsistency. Given ^E!, Act is rendered equivalent to what is arguably the most familiar formulation of actualism, viz., that, necessarily, everything is actual,16 16See R. Adams 1981 (p. 7), Menzel 2014 (Introduction), Parfit 2011 (p. 719), and Plantinga 1976 (p. 143), among others. 12 Act∗ ∀xE!x; likewise its possibilist correlate Poss∗ ^∃x¬E!x. This historically grounded conception of the P-A distinction is depicted in Figure 2. Call it the modern (subsistence conception of the) P-A distinction and, accordingly, call its component theses modern possibilism and modern actualism.17 The modern P-A distinction, I believe, is the focus of Williamson's arguments. (Henceforth I will typically drop the adjective "modern".) Contingently Non-actual (a.k.a. "merely possible") Necessarily Actual Contingently Actual Contingently Non-actual (a.k.a. "merely possible") Contingently Actual Modern Possibilism Modern Actualism Non-abstract Abstract Being Being Necessarily Actual Non-abstract Abstract Figure 2: The Modern P-A Distinction 3 Williamson's Attack on the P-A Distinction As noted, Williamson claims that "[t]here is a widespread feeling of dissatisfaction with the possibilism-actualism distinction." As far as I can see, however, Williamson evinces precious little support from the relevant literature for this 17The picture might be somewhat more complicated for modern actualists and modern possibilists alike whose ontology includes "impure" abstracta like the set {∅,Obama} and so-called "singular" propositions like Obama was born in Hawaii that contain, or "involve", contingent individuals. Though fascinating, the issues are largely orthogonal to those under discussion here. 13 claim.18 Be that as it may, he does provide some arguments that purport to provide reasons for the alleged dissatisfaction. On Williamson's telling, "[t]he actualist holds that everything is actual, while the possibilist holds that not everything is actual, although everything is possible" (2013, p. 22). So, formally, we have PossW ∃x¬E!x∧∀x^E!x, and actualism is simply the denial of the first conjunct: there are no possibilia; everything (in the broadest sense) exists: ActW ∀xE!x. Williamson's portrayal misses some of the modal character of Poss and Act, but PossW entails Poss (and an unnecessitated version of ^E!) and, presumably, he would allow that ActW is a necessary truth. So Williamson's portrayal is largely in agreement with the modern subsistence conception. Williamson's first attack on the P-A distinction proceeds by way of the question (p. 22), "what is it for something to be actual, or to be possible?" After (rightly, in my view) rejecting Lewis's (1986) answer,19 Williamson tries again: "On a less loaded account [than Lewis's], what is actual is simply what there actually (unrestrictedly) is. . . . Analogously, what is possible is what there could be (unrestrictedly)" and so, presumably, what is merely possible is what there could be but actually is not. That is, Williamson is suggesting that uses of the verb phrase "is actual" be spelled out in terms of quantification, identity, and the adverb "actually", expressed formally by the semantically well-understood modal operator "@" (see, e.g., Hazen 1976; H. Hodes 1984, 1984; Stephanou 2005). On this account, then, actualism is the thesis that everything is actually identical to something, i.e., 18See note 22. 19In a nutshell, Williamson rejects Lewis's modal reductionism that interprets the modal operators as quantifiers over Lewisian worlds, i.e., maximally inclusive, mutually non-overlapping spatio-temporal regions (Lewis 1986, p. 2; Menzel 2016, §2.1.1). On such a conception, Williamson writes (ibid.), "we cannot explain what is at stake in the actualism–possibilism debate". This can be spelled out in terms of the subsistence conception. For Lewis, there is no bifurcation of being: the denizens of other worlds exist in a manner no different from those in our world (cf. ibid., pp. 2-3); they are simply not here, in the broadest possible sense of 'here'. Hence, the existence predicate E! - under its intended meaning on the subsistence conception, i.e., the more robust of two modes of being - in Lewis's framework is simply true of everything in every world, i.e., we have ∀x(E!x ↔ ∃y y = x). Lewis's modal reductionism thus renders Poss trivially false and Act trivially true. Hence, Lewis's reductionist framework begs the question in favor of actualism and so "we cannot explain what is at stake" in the P-A debate. 14 Act@ ∀x@∃y y = x, and possibilism is the thesis that there are things such that while, actually, or in fact, there is nothing identical to them, there nonetheless could be, i.e., Poss@ ∃x(¬@∃y y = x∧^∃y y = x). However, as Williamson (p. 23) notes, "on standard accounts of the logic of 'actually', it is a modal operator whose insertion makes a difference to truth value only when in the scope of another modal operator such as 'possibly' or 'necessarily'," a consequence of which is that Act@ is equivalent to the logical truth ∀x∃y y = x and Poss@ entails its negation. Hence, on the suggested analysis, Act@ is logically trivial and Poss@ logically false. Clearly, then, the "is actual" predicate cannot be analyzed in terms of the "actually" operator. But it is equally clear why this exercise goes wrong: the two have entirely different logical functions. In the context of the P-A debate, the function of the predicate is to express a purported property that, according to the possibilist, necessarily, only some things have.20 By contrast, the function of the operator is to force the sentence it qualifies to be evaluated with respect to the world that happens to be actual - a contingent fact utterly irrelevant to the function of the "is actual" predicate. It is therefore no surprise that neither is analyzable in terms of the other. For Williamson, the failure of the analysis of the P-A distinction in terms of the 'actually' operator simply points to the fact that the distinction is fundamentally wrong-headed, indeed "hopelessly muddled" (pp 23-4). His grounds for this assertion, beyond the analytic failure just noted, appear to rest on two arguments. The first (p. 23): On the supposed alternative [to the operator account] ..., being actual had better be actually doing something harder than just being, otherwise the supposed dispute is silly. But what is that harder thing, if a dispute about whether everything does it is as fundamental to modal metaphysics as the dispute between actualism and possibilism is supposed to be? 20Under reasonable assumptions there are (in a possibilist ontology) incompossibles - pairs of objects that can't be jointly actual. Hence, necessarily, not all possible objects are actual. 15 It's not entirely clear how the argument goes here. Obviously, the actualist cannot sensibly claim that, necessarily, everything does some harder thing - being actual, presumably - when, according to modern actualism Act∗, necessarily, nothing fails to do it. But that very fact seems to be the purported worry here. So understood, the argument seems to be, the existence/actuality predicate is otiose; the actualist could just as well define the predicate in terms of the existential quantifier thus: ∃E! E!x =df ∃y y = x, thereby rendering actualism logically trivial, as Act∗+∃E! yields the simple logical truth Act∗∃E! ∀x∃y y = x. How then can actualism possibly be considered a substantive philosophical claim? However, this characterization of things is misleading. For actualism is not put forward in a philosophical vacuum as an independent thesis; it is defined solely in contrast to possibilism. Actualism's bite lies in what it denies, not in what it asserts. Actualism is the denial of possibilism's purported ontological bifurcation; it is the possibilist who casts being actual as the "harder" of two things, i.e., as the more robust of two fundamental ontological states. Actualism is simply the denial of the bifurcation, the denial that "is actual" signifies a "harder" thing. It is no knock against the actualists that their account renders being actual logically trivial; that is exactly how it should be if it is not after all the harder of two things, just as the actualist claims.21 Williamson's second salvo (ibid): 21Bennett (2005, pp. 298-9) also expresses a concern about the logical triviality of the "actualist slogan" Everything is actual. As she does not formalize the slogan, I found her precise concern difficult to pin down. However, the source of its alleged triviality is that, if the range of its quantifier is understood (in terms of Kripke semantics) to be world-relative (as I would say it is, albeit in a sense acceptable to actualists - see Menzel 1990), "its truth is just the straightforward result of the way that the quantifier interacts with the 'actually' operator". So, whatever exactly Bennett has in mind, the problem in question is similar to the one Williamson noted above when he attempted to render the slogan in terms of the "actually" operator. Hence, she is simply not addressing modern actualism Act∗; and as noted in the current paragraph, formalizing the slogan with an "is actual" predicate and understanding (the necessitation of) the slogan as a response to possibilism is critical to addressing concerns over logical triviality. 16 And why should the alternative to the view that everything actually does the harder thing be a view on which everything could do the harder thing? Why cannot something be impossible, in the sense that it could not do the harder thing? Here, however, Williamson is attacking a straw man, as the denial of impossibilia - things that necessarily fail to be actual - is an artifact of his own definition of actualism ActW . As noted in §2 above, impossibilia are entirely consistent with basic actualism Act, ∀x(^E!x → E!x); they are only ruled out explicitly by the additional principle ^E! that was invoked to force abstracta into the actual but which has the side effect of ruling out more aggressively nonexistent objects like the round square. Since, as Williamson rightly suggests, the question of impossibilia is not philosophically trivial, it is a virtue of the subsistence conception that they are not in fact ruled out by definition. So Williamson's attacks on the P-A distinction - when understood in accordance with the subsistence conception - don't amount to much; he has not shown that the subsistence conception of the P-A distinction is problematic, let alone "hopelessly muddled".22 However, he does introduce a distinction of his own that he argues is far clearer and more useful than the P-A distinction. Let us see if that might be so. 22In chapter 7 of his book, Williamson casts further aspersions on the P-A distinction, claiming that "obscure disputes" over "systematic mappings from the talk of one side to the talk of the other [have] figured in [the debates between possibilists and actualists] significantly" (2013, p. 305). However, the disputes in question are small in number and, by my lights, play no significant role in the P-A debate as I have (fairly, I hope) portrayed it. Specifically, these discussions frame the P-A distinction in terms of translation schemes between so-called possibilist and actualist languages - a framing chiefly due to Fine (1977, 1985) and, to a lesser degree, Pollock (1985). (Williamson also cites Melia (1992) and Forbes (1992) in this regard, but their debate solely concerns the expressive adequacy of a modalist language that Forbes proposes; neither philosopher characterizes it as the P-A debate.) As Williamson notes, such a framing threatens to reduce the P-A debate to a mere "verbal disagreement". But if my characterization above is correct, that is simply not the proper framing. The P-A debate has nothing whatever to do with "systematic mappings" between distinct possibilist and actualist languages. To the contrary, possibilists and actualists share a basic quantified modal language that (thanks to the possibilist) includes an existence/actuality predicate E! (though of course each might extend this basic language in different ways) and their very real disagreement concerns the truth values of certain specific sentences in that language, notably, Poss and Act. For possibilist and actualist alike, the quantifiers of this common language necessarily range over everything there is, in the broadest sense. Where they differ, crucially, is over the ontological question of whether the range of those quantifiers could include possibilia, things that fail to be actual, and, hence, whether the existence predicate E! could be true of fewer things than are in the range of the quantifiers. (This is roughly Plantinga's take in his cogent 1985 replies to Fine (pp. 329-49) and Pollock (pp. 313-29).) 17 4 The Necessitism-Contingentism Distinction Williamson's now well-known alternative to the P-A distinction is his distinction between necessitism and contingentism (2013, 2): [N]ecessitism says that necessarily everything is necessarily something; still more long-windedly: it is necessary that everything is such that it is necessary that something is identical with it. In a slogan: ontology is necessary. Contingentism denies that necessarily everything is necessarily something. In a slogan: ontology is contingent. More formally, then, we have: Nec ∀x∃y y = x Cont ^∃x^∀y y , x An apparent virtue of Williamson's distinction is that it does not require a new predicate. But note that it is indeed a different distinction that is entirely orthoganal to the P-A distinction. Possibilists are indeed typically necessitists - all objects, whether actual or merely possible, are necessarily something. But there is nothing to prevent a possibilist from being a contingentist, i.e., from holding that some possibilia might not have been anything, ∃x(¬E!x ∧^E!x ∧^∀y y , x). Likewise - and, as we'll see in §5, very significantly - there is nothing to prevent an actualist from being a necessitist and holding that there couldn't have been anything that doesn't already exist. As we'll see now, however, in order to accommodate powerful contingentist intuitions, Williamson must appeal to notions that enable us to reconstruct the modern P-A distinction in terms of his preferred framework. 4.1 Concreteness and the Contingentist Challenge There are two simple arguments for contingentism based, respectively, upon two compelling modal propositions. First, intuitively, ContSome things might not have existed, i.e., might not have been identical with anything, ∃x^¬∃y y = x. 18 For example, the Pope (as of July 2018), Jorge Bergoglio, might have failed to exist. Hence, it could have been that nothing was identical to him, ^¬∃y y = j. Generalizing, we have ∃x^¬∃y y = x, and so by the modal principle T we have exactly Cont. Second, intuitively, Cont+ There might have been things other than those that actually exist, i.e., things that would not have been identical with any actually existing thing, ^∃x@¬∃y y = x. For example, assuming his lifelong chastity, Bergoglio is in fact childless but certainly might not have been, ^∃xCxj; he could have, say, foregone the priesthood and raised a family in Argentina instead. Given widely accepted views on the essentiality of origins, nothing that actually exists could have been Bergoglio's child, i.e., ∀x(Cxj→@¬∃y y = x). Hence, by some simple modal reasoning, there could have been something - a child of Bergoglio - that would have been distinct from everything that actually exists, ^∃x@¬∃y y = x, and, hence, more generally, that could have been distinct from everything that might have existed, which is exactly Cont.23 Subsistence possibilists, of course, will agree with the basic intuition underlying Contbut express it in terms of the existence/actuality predicate E!: E!Some existing things might not have existed, ∃x(E!x∧^¬E!x). What they will dispute is the contingentist's (for them) illicit identification ∃E! of being with existence that enables the inference from E!to Cont-; substituting ∃y y = x for E!x in the former yields the latter immediately. For, while necessitism is true for the (subsistence) possibilist - everything there is is necessarily something - not everything necessarily exists. Had Bergoglio's parents never met, for example, he would not have existed, but there still would have been such a thing as Bergoglio - though, of course, qua subsistent being, he would not have been human (or a he, for that matter), or conscious, or spatio-temporal, or named 'Bergoglio', etc. Likewise, while Bergoglio in fact has no children, there are (given the essentiality of origin) non-existent things that are not actually his children but could have 23Thought of semantically, this last step here requires that accessibility be symmetric (as it is in Williamson's S5-based logic). 19 been. Hence, the possibilist will agree with the basic intuition underlying Cont+, so long as it is again expressed in terms of the existence predicate E!: ^E!+ There might have existed things other than those that actually exist, ^∃x(E!x∧@¬E!x). However, for the possibilist, ^E!+ is not basic but, rather, a direct consequence of the more substantive (possibilist) truth that E!+ There are things that don't exist but which could have existed, ∃x(¬E!x∧^E!x). Bergoglio's merely possible children, for example, do not in fact exist but could have. What the possibilist will resist, once again, is ∃E!, the identification of being with existence that enables the inference from^E!+ to Cont+; as above, substituting ∃y y = x for E!x in the former yields the latter immediately. Drawing upon a move first made by Linsky and Zalta (1994; 1996) in their wellknown defense of necessitism, Williamson's response parallels the possibilist's. Like the actualist, Williamson purports to reject the bifurcation of being; to be is to exist. What he claims, however, is that the contingentist confuses existence - at least, with regard to ordinary individuals like us - with concreteness. Necessitism is true; everything - hence, trivially, for Williamson, everything that exists - is necessarily something. However, not everything is necessarily concrete. Had Bergoglio's parents never met, for example, he would not have been concrete, but there still would have been such a thing as Bergoglio - though, of course, qua non-concrete being, he would not have been human (or a he, for that matter), or conscious, or spatio-temporal, or named 'Bergoglio', etc. Thus, more generally, according to Williamson, the intuition underpinning Cont− is, not that some things might not have existed, but that (introducing a predicate C! for concreteness): C!Some concrete things might not have been concrete, ∃x(C!x∧^¬C!x). Likewise, while Bergoglio in fact has no children, there are (given the essentiality of origin) non-concrete things that are not actually his children but could have been. Thus, Williamson will agree with the basic intuition underlying Cont+, so long as it is again expressed in terms of the concreteness predicate C!: ^C!+ There might have been concrete things other than those that are actually concrete, ^∃x(C!x∧@¬C!x). 20 And, again paralleling possibilism, this intuition is a direct consequence of the more substantive (Williamsonian) truth that C!+ There are non-concrete things that could have been concrete, ∃x(¬C!x∧^C!x). However, C!and C!+ are not really sufficiently general to serve as the metaphysical principles underlying Williamson's response to the contingentist challenge, as such principles should (as far as possible) be necessarily true and independent of what is actually the case. Arguably, C!and C!+ are neither. C!is true in virtue of the (arguably) contingent fact that there are concrete things and, likewise, C!+ in virtue of the (arguably) contingent Williamsonian fact that there are contingently non-concrete things. By generalizing C!and C!+ so they are independent of what is actually the case, we have the metaphysical principles underlying Williamson's response to the contingentist challenge, which we might call contingent non-concretism: CnC− ^∃x(C!x∧^¬C!x) CnC+ ^∃x(¬C!x∧^C!x). Given Williamson's S5-based framework, both principles are necessary and, moreover, easily shown to be logically equivalent.24 Hence, we will identify Williamson's contingent non-concretism simply with the principle CnC+, i.e., with the the principle that, possibly, there are things that are not concrete, but could have been - henceforth, simply "CnC". 4.2 Return of the P-A Distinction The observant, or even not-so-observant, reader cannot help but notice the structural similarity between the basic subsistence conception Poss of possibilism and Williamson's contingent non-concretism, CnC - CnC simply replaces the existence predicate E! with a concreteness predicate C!. Likewise, one cannot fail to 24Suppose CnC+ is true, i.e., true in the actual world @. Then there is a world w1 (accessible from @) where C!+ is true, i.e., where an individual a is non-concrete and possibly concrete. Let w2 be a world accessible from w1 where a is concrete. Then, since accessibility is symmetric, w1 is accessible fromw2 and so it's true inw2 that there is something (viz., a) that is concrete but possibly non-concrete, i.e., C!true w2. Since accessibility is transitive, w2 is accessible from @, so CnC− is true. Exactly parallel reasoning demonstrates the converse. 21 notice the structural similarity between the ontologies of possibilism and contingent non-concretism. The reason for this structural similarity should be clear: contingently non-concrete objects like Bergoglio's possible children - contingent non-concreta, for short(ish) - are nothing other than the mere possibilia of the subsistence conception.25 For there is not one (non-question-begging26) property of possibilia not shared by contingent non-concreta and vice versa. Williamson's contingent non-concretism, then, is essentially just a repackaging of the subsistence conception of possibilism in terms of concreteness rather than existence. However, in light of the discussion of abstracta in §2, we need to spell this claim out rather carefully. Recall that the basic issue in §2 was whether to consider abstracta to be subsisting or existing things, and we found strong reasons for actualists and possibilists alike on the subsistence conception to opt for the latter and, hence, to adopt the modern conception of the P-A distinction, as depicted in Figure 2. Under that conception, the concreteness predicate C! is obviously not synonymous with the actuality/existence predicate E! since, pretty much by definition, no abstract entity could be concrete, Given that assumption, the existence predicate, as it occurs in the modern P-A distinction, can still be defined in terms of the concreteness predicate as follows:27 DfE! E!x =df C!x∨¬C!x. And under this definition, the principles Act, Poss, and ^E! of the modern subsistence conception emerge directly out of Williamson's framework: unpacking E!x according to DfE!, the formal expression Poss of the subsistence conception of possibilism - ^∃x(¬E!x∧^E!x) - becomes PossC! ^∃x[¬(C!x∨¬C!x)∧^(C!x∨¬C!x)]. But PossC! is easily shown to be logically equivalent to CnC, ^∃x(¬C!x∧^C!x). Recall also that the subsistence actualist carves out their position in contrast to possibilism - it is to deny that there are possibilia. But, as I've argued, the 25This claim might require minor modification if there are contingent abstracta of the sort mentioned in note 17. Terminological note: "non-concreta" is admittedly barbarous but a suitable Latin-ish correlate to "possibilia" seems desirable. My thanks to Alex Dressler for his counsel regarding the Latin plural. He will appreciate my noting that he is not responsible for my choice of the term. 26E.g., possibilia have the property nonexistence while contingent non-concreta do not. 27Williamson himself introduces the notion of chunkiness (p. 313), which corresponds pretty much exactly to the definition of 'E!' here. 22 possibilia of the subsistence conception are exactly Williamson's contingent nonconcreta and, I claim, it is the purported existence of exactly such things that the typical contingentist objects to. That is, while contingentism is not defined as the denial of CnC, the typical contingentist will certainly consider its denial to be definitive of their view; that is, they will take as definitive the thesis that there could be no contingent non-concreta, i.e., that, necessarily, anything that could be concrete already is: SC ∀x(^C!x→ C!x). But (under S5) SC is exactly equivalent to ActC! ∀x(^(C!x∨¬C!x)→ (C!x∨¬C!x)) i.e., to the result of unpacking E!x according to DfE! in the formal expression Act - ∀x(^E!x→ E!x) - of the basic subsistence conception of actualism. Finally, under DfE!, the principle ^E! that yields the modern P-A distinction from the basic distinction becomes ^E!C! ∀x^(C!x∨¬C!x) which is easily seen to be a logical truth of Williamson's quantified modal logic. Given ^E!C!, it follows immediately from ActC! - hence SC - that Act∗C! ∀x(C!x∨¬C!x) which, under DfE!, is exactly the formulation of modern actualism Act∗, ∀xE!x. Under DfE!, then, the expressions of both Williamson's contingent non-concretism CnC and its denial, strict concretism SC, are exactly the result of replacing the actuality predicate E! in their basic P-A counterparts Poss and Act with the concreteness predicate C!. Since, once again, the possibilia of the subsistence conception are exactly Williamson's contingent non-concreta, it follows (together with Act∗C!) that the modern P-A distinction simply reappears within Williamson's preferred framework, albeit repackaged as the CnC-SC distinction. Hence, by relabeling appropriately, our depiction of the modern P-A distinction in Figure 2 transforms directly into a depiction of the CnC-SC distinction in Figure 3, and vice versa.28 28For reasons discussed in note 17, the relabeling may not yield identical ontological categories. Notably, if there are "mixed" abstracta like {∅,Obama}, they belong in the upper left quadrant of, 23 Contingently Non-concrete Necessarily Concrete/ Necessarily not Concrete Contingently Concrete Contingently Non-concrete Contingently Concrete Contingent Non-concretism Strict Concretism Concrete Not Concrete Being Being Concrete Not Concrete Necessarily Concrete/ Necessarily not Concrete Figure 3: The Modern P-A Distinction under its Williamsonian Repackaging So whatever confusions or unclarities infect the P-A distinction will reside in equal measure in Williamson's own framework in the guise of the CnC-SC distinction. Of course, I've argued at lengthy that the P-A distinction is entirely coherent and I would allow the same for the CnC-SC distinction - because they are at root tracking exactly the same broad ontological divide: the possibility or impossibility of the contingently non-actual/non-concrete. 5 A New Definition of the P-A Distinction In fact, Williamson's necessitism does raise a significant problem for friends of the P-A distinction. The problem, first identified by Linsky and Zalta (1994, pp. 445ff) is not that it's confused; rather, its characterization in terms of the existence/actuality predicate E! is, in a sense, too weak. To elaborate. Intuitively, contingent non-concreta certainly seem to be in an extraordinarily thin ontological state. As noted above, they are basically points in logical space that are indistinguishable with regard to their (mostly negative) non-modal qualitative properties. Moreover, unlike traditional abstract entities like sets, numbers, and propositions, they bear no structural or constitutive relaat least, the circle representing modern actualism in Figure 2. But since, necessarily, it is not the case that such abstracta are concrete, they belong in the lower left quadrant of the circles in Figure 3. 24 tions to one another. These observations lie at the heart of the actualist's charge that contingent non-concreta exhibit exactly the quality of being - i.e., subsistence - characteristic of classic possibilia. But necessitists can simply deny it! Instead, they can reject the definition DfE! of the existence predicate E! that consigns contingent non-concreta to the subsistent as question-begging, and blithely declare themselves to be actualists. As such, they will insist that being and existence/actuality are one and the same and, hence, that E! simply expresses the full range of the existential quantifier, as formalized in the definition ∃E!. There are no possibilia, they can affirm; being is unbifurcated; necessarily, whatever is, is actual, contingent non-concreta included, their lack of "thick" qualitative properties notwithstanding. The actualist's table-banging, foot-stamping protestations that contingent non-concreta are the very model of subsistent, mere possibilia are impassively dismissed.29 The problem is galling for the modern actualist: if Williamson and his ilk cannot be forced into the possibilist box where (the actualist believes) they belong, then that does indeed appear to reveal a serious shortcoming in the modern P-A distinction. For, clear and intuitive though the idea of bifurcated being may be as a way of expressing the P-A distinction, it is not itself sufficiently robust to forestall the necessitist's gambit; if the necessitist rejects the bifurcation of being and insists their contingent non-concreta exist as robustly as we, nothing can be done to demonstrate that they are wrong. One has to accept the idea of bifurcation at the outset as the proper characterization of contingent non-concreta in order for the modern P-A distinction, as represented by Poss and Act, to have any punch. However, I believe there is another way to mark the distinction that doesn't rely on bifurcation. Specifically, I believe we can also locate the source of the disagreement between actualists and possibilists in a substantive difference regarding the exemplification of essential properties. Most everyone with reasonably robust modal intuitions - actualist, possibilist, and necessitist alike - agrees that there are such properties. Exactly how the notion of an essential property is defined (if it's definable at all) is not critical to my proposal. But an important element of the notion is captured in 29Linsky and Zalta (ibid.) themselves only spell out this necessitist gambit without explicitly committing to it. See also Cameron 2016. 25 the familiar traditional modal account30 on which an object a is essentially F (and that F is essential to a) if and only if, necessarily, a exists only if it is F, (E!a→ Fa), and a is accidentally F if it is F but not essentially F. As a definition, this account of essentiality has, with good reason,31 fallen out of favor. But as a necessary condition it captures an important insight - call it the essentialist intuition - for both modern actualists and modern possibilists: we look to the properties an individual has while existing to identify its essential properties - it is in existence, actuality, that a thing's essence is made manifest; the properties it may have while nonexistent (if any) are irrelevant to its nature. Of course, necessitists who would claim the actualist label (would-be actualists, for short) will not express the essentialist intuition as above since, for them, E! signifies a metaphysically trivial property: everything necessarily exists and, hence, (E!a → Fa) is simply equivalent to Fa, and that clearly cannot be the general logical form of essentiality for things that are or could be concrete: a tiger, for example, though essentially a tiger, is not necessarily a tiger, since it would fail to be one if it were non-concrete. However, as Zalta (2006, §3) points out, the would-be actualist can preserve the essentialist intuition for tigers and the like simply by replacing existence with concreteness: a property F is essential to (possibly concrete) object a only if, necessarily, if a is concrete, it has F, (C!a→ Fa). The acceptance of essential properties enables us to construct an alternative definition of the P-A distinction upon some common ground. Note, first, that contingentists and necessitists alike all do agree that there can be merely possible Fs, for many properties F:32 MPF x is a merely possible F iff x is not an F but could have been. For example, I am a merely possible plumber; Barack Obama is a merely possible Kenyan; and so on. And here, I think, is where we can drive a permanent wedge between actualism and Williamsonian necessitism. For, assuming Zalta's necessitist revision of the essentialist intuition, necessitists of Williamson's ilk, no less than subsistence possibilists, believe that, for many properties F, there are merely possible Fs - hence things that contingently fail to be F - that are nonetheless 30Cf., e.g., Plantinga 1974, pp. 55-6. 31See, e.g., Fine 1994 and Zalta 2006 for criticisms of the definition and Robertson and Atkins 2018 for an overview of various alternatives. 32See in particular Williamson 2013, pp. 11ff. 26 essentially F; otherwise put, that there are things that fail to exemplify some of their essential properties. Thus, for subsistence possibilists and Williamsonian necessitists alike, merely possible tigers are essentially tigers; Bergoglio's merely possible children are essentially human. Though essentially tigers and essentially human, respectively, they subsist/exist in fact, not as tigers or humans but, as noted above, beyond space and time, qualitatively indistinguishable from all other possibilia/contingent non-concreta, failing, in particular, to exemplify at least some, if not all, of their essential properties. This failure, I claim, is a central distinguishing feature of possibilia on the subsistence conception. Accordingly, for those who question the bifurcation of being, we can alternatively characterize the P-A distinction in terms of the acceptance or rejection of things that fail to examplify all of their essential properties. More specifically: POSS Possibly, for some property F, there are merely possible Fs that are essentially F. ACT Necessarily, for every property F, if something is essentially F, it is F. Call this the essentialist conception of the P-A distinction. Instead of invoking the subsistence/existence distinction, the POSS-ACT distinction gets at the root of the intuition that has grounded the disagreement between actualists and possibilists in terms of concepts that are clear and (for the relevant stakeholders, anyway) uncontroversial.33 And it does so in a way that, in accordance with our analysis above, rightly categorizes Williamsonian necessitism as a species of possibilism. How might the would-be actualist respond? Recall that Zalta suggested that the necessitist can preserve the essentialist intuition by taking F to be essential 33In particular, like the original distinction, it makes no reference to possible worlds. Williamson claims (2013, p. 333) that "[m]uch of the debate between actualists and possibilists revolve[s] around the legitimacy or illegitimacy of quantification over possible worlds", such quantification being "seen as far more problematic for actualists than for possibilists." But, very little if anything in the debate has revolved around the legitimacy of such quantification; as should be clear from the principles Poss/Act and POSS/ACT, the question of possibilia on the subsistence conception is entirely orthogonal to it. There are, in particular, actualists who embrace worlds (e.g., Plantinga (1974) and R. Adams (1981)) and those that do not (e.g., Menzel (1990)). Moreover, while the project of defining worlds as abstract objects of some ilk is usually associated with actualism (though see Zalta 1993), the problems involved in the project are largely independent of one's commitment to possibilia (see, e.g., Grim 1984 and 1986; Menzel 1986, 1989, and 2012). It's also worth noting that similar problems arise for the worlds of Lewisian reductionism (see, e.g., Forrest and Armstrong 1984 and Lewis 1986). 27 to a only if necessarily, a has F if concrete, (C!a→ Fa). Williamson (2013, p. 8) himself suggests instead that the necessitist identify the form of essential properties (for possibly concrete beings) with that of the reified condition here. For any property F, let FC! be the property being F if concrete, [λxC!x→ Fx]; then, as per Williamson's suggestion, for any property F, FC! is essential to a only if, necessarily, a has FC!, i.e., only if [λxC!x → Fx]a. Thus, a tiger is not essentially a tiger but, rather, essentially a tiger if concrete, and Bergoglio's possible children are not essentially human but essentially human if concrete. On this understanding of essentiality, the would-be actualist is indeed an actualist on the POSS-ACT distinction: because, for example, both actual and merely possible tigers are necessarily tigers if concrete, TC!, if something is essentially TC!, it is TC!, in accordance with ACT. But the proposal is a bit odd, for a couple reasons. First, building the concreteness condition into essential properties themselves makes it the case that, for natural kinds K , the distinguishing essential property of Ks, viz., KC!, is shared by every non-concrete (hence non-K) object. Thus, in particular, the number 7, God, and Bergoglio's merely possible children are all alike tigers if concrete. At the least, this feature of Williamsonian essentiality seems at odds with modern conceptions of essence. Second, the move seems entirely unnecessary. For it is logically true for the necessitist that, for any property F and individual a, necessarily, a is F if concrete if and only if a is F if concrete, ([λxC!x → Fx]a ↔ (C!a → Fa)). Why not, then, follow Zalta and preserve the essentialist intuition by taking being F if concrete simply to be a necessary condition for F's being essential to a rather than identifying it as the logical form of a's essential properties? After all, the logical form of Williamson's account, no less than Zalta's, in accord with the essentialist intuition, reveals that certain properties a thing a must have while concrete mark its essence, even if we don't define them as a's essential properties. However, should would-be actualists nonetheless dig in their heels and insist that Williamson's suggestion is the correct account of essentiality, we can modify POSS and ACT accordingly: POSS* Possibly, for some property F, there are merely possible Fs that are essentially FC!. 28 ACT* Necessarily, for every property F, if something is essentially FC!, it is F.34 On these modified definitions, the would-be actualists are back in the possibilist box - all and only possibilists think there could be things that are essentially FC! but not F, notably, merely possible tigers and merely possible people. Actualists, by contrast, deny there are any such things.35 Only two options appear to remain for the would-be actualist: abandon CnC or abandon essentialism. The former is surely untenable as, not only is CnC the means by which the necessitist turns back the contingentist challenge discussed in §4.1, the denial of CnC is obviously false in the context of necessitism + essentialism - it entails, for example, that every actually existing human being exists necessarily (hence, in particular, eternally) as a human being. So in fact the only coherent option that could render Williamsonian necessitism consistent with actualism is the denial of essentialism (thereby rendering ACT* trivial). It is true that necessitism per se and essentialism are orthogonal. One can certainly hold that everything exists necessarily but that nothing, or at least no possibly concrete thing, has an essence; one can, without contradiction, be a necessitist and believe as well that a merely possible human, for example, could also be a mosquito, or that an actual block of wood might have been a bar of gold. But to adopt such a stance is to abandon one of the liveliest and most fundamental of the modal intuitions that would typically drive necessitism in the first place - certainly a necessitism 34If one wishes to insist that numbers and other abstracta are (contrary to most any modern conception of essence) essentially F if concrete, ACT* could be restricted to things that are possibly F. 35It's important not to get the scoping wrong here. Formally, where Σ(G,x) means that G is essential to x, ACT* says that ∀F∀x(Σ(FC!,x) → Fx). Thus, the actualist can accept that Toni is essentially, hence necessarily, a tiger if concrete, TC!, but Toni won't be in the range of the quantifier at worlds where she doesn't exist and, hence, though not a tiger at those worlds, she won't be a value of the variable x for which Σ(FC!,x) is true at those worlds and, hence, won't serve as a counterexample to ACT*. An objection to these modifications of POSS and ACT might be heard from so-called serious actualists, who hold that property exemplification entails existence (Prior 1957 (p. 31), Plantinga 1983 and 1985, Hudson 1997, Caplan 2007, Stephanou 2007). For, on the account of essential properties that the actualist is conceding to Williamson here, contingent beings have their essential properties necessarily. But if exemplification entails existence - i.e., if (Fx→ E!x), for any property F and entity x - then no contingent being has any essential properties; Toni, in particular, will not be a tiger if concrete essentially. However, in Menzel 1993 (pp. 136-142) it is argued in detail that a simple change of semantic perspective allows the actualist to agree that Toni is necessarily a tiger if concrete, i.e., that [λxC!x→ T x]t, without abandoning the metaphysical intuitions that underlie serious actualism. See also Fine 1985, §4, esp. pp. 163ff, Pollock 1985, §2, Hinchliff 1989, and Yagisawa 2005 29 as rich and robust as Williamson's. Given that one of the central talking points of the Williamsonian necessitist is that the view leaves all of our fundamental modal intuitions in place, abandoning essentialism is also untenable. So the categorization of Williamsonian necessitism as a species of possibilism on the essentialist conception appears to stand. Finally, it is worth elaborating briefly on the point noted three paragraphs back that, on either necessitist account of essentiality, Zalta's or Williamson's, it is the properties a thing must have while concrete that mark its essence, even if they are not defined as essential as per Williamson. But in acknowledging this, the wouldbe actualist seems to give the game away. For both accounts acknowledge that concreteness is not simply one accidental property among others but, rather, a state that reveals a thing's essence, a state in which the nature of a possibly concrete thing is manifest in the "thick" properties it exhibits when actually in that state. Whether or not one wishes to categorize that state in terms of robustness of being, it is difficult to deny that a powerful redolence of the bifurcation of being remains even on the essentialist conception of the P-A distinction. 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