The theorems of the simplest and strongest sensible quantified modal logic include the Barcan Formula and its converse. Both formulas face strong intuitive objections. This paper develops a theory of possibilia to meet those objections.

Four questions are raised about the semantics of Quantified Modal Logic. Does QML admit possible objects, i.e. possibilia? Is it plausible to admit them? Can sense be made of such objects? Is QML committed to the existence of possibilia? The conclusions are that QML, generalized as in Kripke, would seem to accommodate possibilia, but they are rejected on philosophical and semantical grounds. Things must be encounterable, directly nameable and a part of the actual order before they may (...) plausibly enter into the identity relation. QML is not committed to possibilia in that the range of variables may be restricted to actual objects. Support of the conclusions requires some discussion of substitution puzzles; also, the semantical distinction between proper names which are directly referring, and descriptions even where the latter are "rigid designators". Views of W.V. Quine, B. Russell, K. Donnellan, D. Kaplan as well as S. Kripke are invoked or evaluated in conjunction with these issues. (shrink)

Are there, in addition to the various actual objects that make up the world, various possible objects? Are there merely possible people, for example, or merely possible electrons, or even merely possible kinds? We certainly talk as if there were such things. Given a particular sperm and egg, I may wonder whether that particular child which would result from their union would have blue eyes. But if the sperm and egg are never in fact brought together, then there is no (...) actual object that my thought is about. Or again, in the semantics for modal logic we presuppose an ontology of possibilia twice over. For first, we countenance various possible worlds, in addition to the actual world; and second, each of these worlds is taken to be endowed with its own domain of objects. These will be the actual objects of the world in question, but they need not be actual simpliciter, i.e., actual objects of our world. What are we to make of such discourse? There are four options: (i) the discourse is taken to be unintelligible; (ii) it is taken to be intelligible but nonfactual, i.e. as not in the business of stating facts; (iii) it is taken to be factual but reducible to discourse involving no reference to possibilia; (iv) it is taken to be both factual and irreducible. These options range from a full-blooded form of actualism at one extreme to a full-blooded form of possibilism at the other. The two intermediate positions are possibilist in that they accept the intelligibility of possibilist discourse but actualist in that they attempt to dispense with its prima facie commitment to possibilia. All four positions have found advocates in the literature. Quine, in his less irenic moments, favours option (i); Forbes advocates option (ii), at least for certain parts of possibilist discourse; many philosophers, including Adams and myself, opt for (iii); while Lewis and Stalnaker have endorsed versions of (iv), that differ in how full-blooded they take the possible objects to be.. (shrink)

1. The problemLewis identifies the monadic property being F with the set of all actual and possible Fs; the dyadic relation R is identified with the set of actual and possible pairs of things that are related by R; and so on . 1 Egan has argued that the fact that some properties have some of their properties contingently leads to trouble: " Let @ be the actual world, in which being green is [someone's] favourite property, and let w be (...) a world in which being green is [nobody's] favourite property. Since being green is somebody's favourite property in @, it must be a member of … being somebody's favourite property. Since being green is not anybody's favourite property in w, it must not be a member of being somebody's favourite property. Contradiction. " Egan suggests identifying properties with functions from worlds to extensions. However, as Lewis and others have complained, this has the drawback of turning monadic properties into relations . 2 In this article, we shall show that the Lewisian has the resources to block the above argument while simultaneously respecting the adicity of the relevant property and the contingency of the predication without changing his theory of properties. However, our analysis reveals a hidden ambiguity in the Lewisian conception of properties, and on either disambiguation the resulting account of properties seems inadequate.2. On ‘being someone's favourite property’The phrase ‘ being someone's favourite property’ is ambiguous. Given Lewis's ontology of possibilia, where the phrase picks out a monadic property it is not one that is possessed contingently; where it picks out a property that is possessed contingently it is not one that is monadic. But the argument works only if being someone's favourite property is both monadic and possessed contingently.Why should …. (shrink)

Timothy Williamson supports the thesis that every possible entity necessarily exists and so he needs to explain how a possible son of Wittgenstein’s, for example, exists in our world:he exists as a merely possible object, a pure locus of potential. Williamson presents a short argument for the existence of MPOs: how many knives can be made by fitting together two blades and two handles? Four: at the most two are concrete objects, the others being merely possible knives and merely possible (...) objects. This paper defends the idea that one can avoid reference and ontological commitment to MPOs. My proposal is that MPOs can be dispensed with by using the notion of rules of knife-making. I first present a solution according to which we count lists of instructions - selected by the rules - describing physical combinations between components. This account, however, has its own difficulties and I eventually suggest that one can find a way out by admitting possible worlds, entities which are more commonly accepted - at least by philosophers - than MPOs. I maintain that, in answering Williamson’s questions, we count classes of physically possible worlds in which the same instance of a general rule is applied. (shrink)

Are there, in addition to the various actual objects that make up the world, various possible objects? Are there merely possible people, for example, or merely possible electrons, or even merely possible kinds? We certainly talk as if there were such things. Given a particular sperm and egg, I may wonder whether that particular child which would result from their union would have blue eyes. But if the sperm and egg are never in fact brought together, then there is no (...) actual object that my thought is about.1 Or again, in the semantics for modal logic we presuppose an ontology of possibilia twice over.2 For first, we countenance various possible worlds, in addition to the actual world; and second, each of these worlds is taken to be endowed with its own domain of objects. These will be the actual objects of the world in question, but they need not be actual simpliciter, i.e., actual objects of our world. What are we to make of such discourse? There are four options: (i) the discourse is taken to be unintelligible; (ii) it is taken to be intelligible but nonfactual, i.e. as not in the business of stating facts; (iii) it is taken to be factual but reducible to discourse involving no reference to possibilia; (iv) it is taken to be both factual and irreducible.3 These options range from a fullblooded form of actualism at one extreme to a full-blooded form of possibilism at the other. The two intermediate positions are possibilist in that they accept the intelligibility of possibilist discourse but actualist in that they attempt to dispense with its prima facie commitment to possibilia. All four positions have found advocates in the literature. Quine, in his less irenic moments, favors option (i); Forbes ([85], p. 94) advocates option (ii), at least for certain parts of possibilist discourse; many philosophers, including Adams [74] and myself, opt for (iii); while Lewis [86] and Stalnaker [75] have endorsed versions of (iv), that differ in how full-blooded they take the possible objects to be. My focus in the present article is on the third option.. (shrink)

In this article I shall first and foremost attempt to show that the semantic requirements of Wittgenstein’s Tractatus logico-philosophicus intend the objects of the Tractatus to be conceived of as possibilia in the Russellian sense of 1903, i.e., as objects that may exist or may not exist; secondly, that the general ontology of the Tractatus suggests integrating this onto-semantic conception with a conception of these objects not properly as qualia but as sensibilia in the Russellian sense of 1914, i.e., (...) as sense-data that may exist or may not exist. (shrink)

Many things can be other than they are. Many other things cannot. But what are statements like these about? One answer to this question is that we are speaking of possible worlds: if something can be other than it is, then it actually is that way in some possible world. If something cannot be otherwise, it is not otherwise in any world. This answer is presently dominant in analytical philosophy of language and logic. What are these worlds? David Lewis famously (...) claimed that every world exists, just like ours does: there is no difference between the other worlds and ours. In contrast, the medieval thinker John Buridan understands modal logic in terms of objects and causal powers in this world: if something can be other than it is, then there is a causal power that can make it that way. If it cannot, then no causal power—not even God—can alter it, at least without destroying its nature. As we’ll see, the Lewisian plurality is not possible on Buridan’s account; accordingly, a basic tenet of classical theism is untenable on Lewis’s metaphysics. In short, either the Lewisian plurality is incoherent, or a core monotheistic tenet is impossible. (shrink)

This paper aims to provide hyperintensional foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by (...) Hale and Wright and examined in Hale (2013), and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest that observational type theory can be applied to first-order abstraction principles in order to make abstraction principles recursively enumerable. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics. (shrink)

It seems to be an obvious truth that There could be something that doesn't actually exist. That is, it seems to be obiously true that ◊∃×). It is sufficient for the truth of that there could be more people, or trees, or cars, than there actually are. It is also sufficient for the truth of that there could be some pepole, or trees, or cars that are distinct from all those that actually exist. Do and suchlike statements involve a commitment (...) to possibilia, to things that possibly exist, but do not actually exist? If not, why not? And if so, what is the nature of the possibilia to which and its ilk commit us? These simple little questions are at the tip of an iceberg. (shrink)

Frank Jackson; VIII*—Conditionals and Possibilia, Proceedings of the Aristotelian Society, Volume 81, Issue 1, 1 June 1981, Pages 125–138, https://doi.org/10.10.

It seems to be an obvious truth that There could be something that doesn't actually exist.That is, it seems to be obiously true that ◊∃×).It is sufficient for the truth of that there could be more people, or trees, or cars, than there actually are. It is also sufficient for the truth of that there could be some pepole, or trees, or cars that are distinct from all those that actually exist. Do and suchlike statements involve a commitment to (...) class='Hi'>possibilia, to things that possibly exist, but do not actually exist? If not, why not? And if so, what is the nature of the possibilia to which and its ilk commit us? These simple little questions are at the tip of an iceberg. (shrink)

Frank Jackson; VIII*—Conditionals and Possibilia, Proceedings of the Aristotelian Society, Volume 81, Issue 1, 1 June 1981, Pages 125–138, https://doi.org/10.10.

Pace Necessitism – roughly, the view that existence is not contingent – essential properties provide necessary conditions for the existence of objects. Sufficiency properties, by contrast, provide sufficient conditions, and individual essences provide necessary and sufficient conditions. This paper explains how these kinds of properties can be used to illuminate the ontological status of merely possible objects and to construct a respectable possibilist ontology. The paper also reviews two points of interaction between essentialism and modal logic. First, we will briefly (...) see the challenge that arises against S4 from flexible essential properties; as well as the moves available to block it. After this, the emphasis is put on the Barcan Formula (BF), and on why it is problematic for essentialists. As we will see, Necessitism can accommodate both (BF) and essential properties. What necessitists cannot do at the same time is to continue to understanding essential properties as providing necessary conditions for the existence of individuals; against what might be for some a truism. (shrink)

This paper reconsiders Leibniz’s conception of the nature of possible things and offers a novel interpretation of the actualization of possible substances. This requires analyzing a largely neglected notion, the reality of individual essences. Thus far scholars have tended to construe essences as representational items in God’s intellect. We acknowledge that finite essences have being in the divine intellect but insist that they are also grounded in the infinite essence of God, as limitations of it. Indeed, we show that it (...) is critical to understand that this dependence on God’s essence is prior to the dependence on God through divine ideas. Here it is crucial to distinguish questions concerning the ontological status of essences from questions concerning their reality. This yields a fresh view of Leibniz’s theory of creation, which takes seriously his claim that the same thing is first a mere possibility but after creation an actually existent substance. (shrink)

Although both belong to the domain of the nonexistent, there is an ontological distinction between ficta and possibilia. Ficta are a particular kind of abstract objects, namely constructed abstract objects which generically depend on authors for their subsistence. Moreover, they are essentially incomplete entities, in that they are correlates of finite sets of properties. - On the other hand, possibilia are concrete objects. Being a possible object is indeed being an entity that might have existed, that is, that (...) might have been involved in the causal order. Besides, as an object existent in this sense may legitimately be qualified as complete, the incompleteness which pertains to possible objects is contingent, in that it regards them only with respect to the possible worlds in which they do not exist. This ontological distinction has a semantic correlate: whereas names for possibilia are full-fledged directly referential terms, names for ficta are synonymous with de facto rigid descriptions of a complex sort. (shrink)

Leibniz denies Spinoza’s claim that all possible things actually exist. He also denies necessitarianism, Spinoza’s claim that all truths are necessary truths. Both denials seem plausible. What is surprising, however, is Leibniz’s view that the first claim entails the second, i.e., that the existence of all possible things implies necessitarianism. Why think this? Couldn’t it be that, as a matter of contingent fact, all possible things actually exist? There seems to be no incoherency in claiming both that all possible things (...) actually exist and that fewer things could have existed. In this paper, I explain why Leibniz thought that such a position is indeed inconsistent. My thesis is that the Principle of Sufficient Reason plays a decisive role in his reasoning. Leibniz claims that the non-existence of a thing requires a sufficient reason. He also holds that if all possible things can coexist, such a reason cannot be given. Together these claims rule out a scenario in which all possible things actually exist, but only contingently so. (shrink)

Although both belong to the domain of the nonexistent, there is an ontological distinction between ficta and possibilia. Ficta are a particular kind of abstract objects, namely constructed abstract objects which generically depend on authors for their subsistence. Moreover, they are essentially incomplete entities, in that they are correlates of finite sets of properties. - On the other hand, possibilia are concrete objects. Being a possible object is indeed being an entity that might have existed, that is, that (...) might have been involved in the causal order. Besides, as an object existent in this sense may legitimately be qualified as complete, the incompleteness which pertains to possible objects is contingent, in that it regards them only with respect to the possible worlds in which they do not exist. This ontological distinction has a semantic correlate: whereas names for possibilia are full-fledged directly referential terms, names for ficta are synonymous with de facto rigid descriptions of a complex sort. (shrink)

In the Nouveaux Essais, Leibniz famously declared that he once had “begun to lean towards” Spinozist necessitarianism. In this article, I argue that this remark refers to his modal philosophy anterior to 1677. Leibniz’s mature refutation of Spinoza’s necessitarianism relies on the notion that pure possibility has some sort of reality in God’s mind, because only this allows for a strong notion of divine choice. But I believe that Leibniz only developed this ontology of possibility after 1677. Before this date, (...) he inclined towards the view that non existing possibilities are mere logical abstractions that God never actually conceives. In order to show this, I analyze a series of early texts written between 1668 and 1676. Next, I consider a series of texts from 1677-1678, where Leibniz developed his ontology of possibility and put it to use against Spinozist necessitarianism for the first time. (shrink)

In the Nouveaux Essais, Leibniz famously declared that he once had “begun to lean towards” Spinozist necessitarianism. In this article, I argue that this remark refers to his modal philosophy anterior to 1677. Leibniz’s mature refutation of Spinoza’s necessitarianism relies on the notion that pure possibility has some sort of reality in God’s mind, because only this allows for a strong notion of divine choice. But I believe that Leibniz only developed this ontology of possibility after 1677. Before this date, (...) he inclined towards the view that non existing possibilities are mere logical abstractions that God never actually conceives. In order to show this, I analyze a series of early texts written between 1668 and 1676. Next, I consider a series of texts from 1677-1678, where Leibniz developed his ontology of possibility and put it to use against Spinozist necessitarianism for the first time. (shrink)

In the Nouveaux Essais, Leibniz famously declared that he once had “begun to lean towards” Spinozist necessitarianism. In this article, I argue that this remark refers to his modal philosophy anterior to 1677. Leibniz’s mature refutation of Spinoza’s necessitarianism relies on the notion that pure possibility has some sort of reality in God’s mind, because only this allows for a strong notion of divine choice. But I believe that Leibniz only developed this ontology of possibility after 1677. Before this date, (...) he inclined towards the view that non existing possibilities are mere logical abstractions that God never actually conceives. In order to show this, I analyze a series of early texts written between 1668 and 1676. Next, I consider a series of texts from 1677-1678, where Leibniz developed his ontology of possibility and put it to use against Spinozist necessitarianism for the first time. (shrink)

In the Nouveaux Essais, Leibniz famously declared that he once had “begun to lean towards” Spinozist necessitarianism. In this article, I argue that this remark refers to his modal philosophy anterior to 1677. Leibniz’s mature refutation of Spinoza’s necessitarianism relies on the notion that pure possibility has some sort of reality in God’s mind, because only this allows for a strong notion of divine choice. But I believe that Leibniz only developed this ontology of possibility after 1677. Before this date, (...) he inclined towards the view that non existing possibilities are mere logical abstractions that God never actually conceives. In order to show this, I analyze a series of early texts written between 1668 and 1676. Next, I consider a series of texts from 1677-1678, where Leibniz developed his ontology of possibility and put it to use against Spinozist necessitarianism for the first time. (shrink)

In this paper I present a novel view of the ontological status of possible objects for Descartes. Specifically, I claim that possible objects just are innate ideas considered objectively. In the act of creation, God creates possibilities—in all its richness—in the form of innate ideas. Thus, in acts of thinking, one may clearly and distinctly perceive, via one’s innate ideas, that such and such is possible. To argue this, I first analyze and critique two competing views—one from Calvin Normore who (...) claims that innate ideas represent an independent realm of possibilia, and another from David Cunning and Alan Nelson who claim that Descartes had no theory of modality. I then move on to the defense of my view, both giving a positive account of my argument and noting how my interpretation enjoys certain advantages over my interlocutors. (shrink)

In this paper I present a novel view of the ontological status of possible objects for Descartes. Specifically, I claim that possible objects just are innate ideas considered objectively. In the act of creation, God creates possibilities—in all its richness—in the form of innate ideas. Thus, in acts of thinking, one may clearly and distinctly perceive, via one’s innate ideas, that such and such is possible. To argue this, I first analyze and critique two competing views—one from Calvin Normore who (...) claims that innate ideas represent an independent realm of possibilia, and another from David Cunning and Alan Nelson who claim that Descartes had no theory of modality. I then move on to the defense of my view, both giving a positive account of my argument and noting how my interpretation enjoys certain advantages over my interlocutors. (shrink)

According to modal realism formulated by David Lewis, there exist concrete possible worlds. As he argues the hypothesis is serviceable and that is a sufficient reason to think it is true. On the other side, Lewis does not consider the pragmatic reasons to be conclusive. He admits that the theoretical benefits of modal realism can be illusory or that the acceptance of controversial ontology for the sake of theoretical benefits might be misguided in the first place. In the first part (...) of the paper, I consider the worry and conclude that although the worry is justified, there can be an epistemological justification for his theory. Next, I outline the so-called indispensability argument for the legitimacy of mathematical Platonism. Finally, I argue that the argument, if accepted, can be applied to metaphysics in general, to the arguing for the existence of concrete (im)possibilia in particular. (shrink)

Establishing Dispositionalism as a viable theory of modality requires the successful fulfilment of two tasks: showing that all modal truths can be derived from truths about actual powers, and offering a suitable metaphysics of powers. These two tasks are intertwined: difficulties in one can affect the chances of success in the other. In this paper, I generalise an objection to Dispositionalism by Jessica Leech and argue that the theory in its present form is ill-suited to account for de re truths (...) about merely possible entities. I argue that such difficulty is rooted in a problem in the metaphysics of powers. In particular, I contend that the well-known tension between two key principle of powers ontology, namely Directedness and Independence has received an unsatisfactory solution so far, and that it is this unsatisfactory solution concerning the status of “unmanifested manifestations” that makes it hard for Dispositionalism to account for mere possibilia. I develop a novel account of the status of unmanifested manifestations and an overall metaphysics of powers which allows to better respond to Leech's objection and handle mere possibilia. The central idea of the proposal is that unmanifested manifestations are akin to mere logical existents, and are best characterised as non-essentially non-located entities. (shrink)

According to genuine modal realism, some things (including numbers and properties) lack distinct counterparts in different worlds. So how can they possess any of their properties contingently? Egan (2004) argues that to explain such accidental property possession, the genuine modal realist must depart from Lewis and identify properties with functions, rather than with sets of possibilia. We disagree. The genuine modal realist already has the resources to handle Egan's proposed counterexamples. As we show, she does not need to amend (...) her analysis of possibility statements, or her theory of what properties are. (shrink)

In On What Matters, Derek Parfit enters the debate between actualists and possibilists. This debate concerns mere possibilia, possible but non-actual things such as golden mountains and talking donkeys. Roughly, possibilism says that there are such things, and actualism says that there are not. Parfit not only argues for possibilism but also argues that some self-proclaimed actualists are, in fact, unwitting possibilists. -/- I argue that although Parfit’s arguments do not fully succeed, they do highlight a tension within the (...) frameworks of many actualists. Many actualists conscript abstract objects into the role of "possible worlds" to avoid quantifying over mere possibilia. But, in doing so, actualists must quantify over mere possibilia anyway. When we alleviate this tension, a Parfit-friendly form of actualism arguably remains. This form of actualism says that while everything that exists is actual, it is also true in some sense that there are mere possibilia. (shrink)