Necessitism and Contingentism

This paper offers a modification of Fabrice Correia's and Alexander Skiles' ("Grounding, Essence, and Identity") definition of grounding in terms of generalized identity that extends it to zero-grounding. This definition promises to improve our understanding of zero-grounding by capturing it within the framework of generalized identity and allows an essentialist theory of modality based on Correia's and Skiles' account to resist a recent challenge by Jessica Leech. The latter is achieved by combining the following two ideas: (1) Some necessities are (...) grounded in truths about zero-grounding, and (2) at least some identity truths are zero-grounded. Finally, some advantages of the zero-grounding approach over Correia's and Skiles' recent definition of necessity in terms of generalized identity and logical consequence are argued for. (shrink)

This paper aims to provide modal 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. 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)

This paper aims to provide two abductive considerations adducing in favor of the thesis of Necessitism in modal ontology. I demonstrate how instances of the Barcan formula can be witnessed, when the modal operators are interpreted 'naturally' -- i.e., as including geometric possibilities -- and the quantifiers in the formula range over a domain of natural, or concrete, entities and their contingently non-concrete analogues. I argue that, because there are considerations within physics and metaphysical inquiry which corroborate modal relationalist claims (...) concerning the possible geometric structures of spacetime, and dispositional properties are actual possible entities, the condition of being grounded in the concrete is consistent with the Barcan formula; and thus -- in the geometric setting -- merits adoption by the Necessitist. (shrink)

Let us distinguish two kinds of contingentism: entity contingentism and metaphysical contingentism. Here, I use ‘entity’ very broadly to include anything over which we can quantify—objects (abstract and concrete), properties, and relations. Then entity contingentism about some entity, E, is the view that E exists contingently: that is, that E exists in some possible worlds and not in others. By contrast, entity necessitarianism about E is the view that E exists of necessity: that is, that E exists in all possible (...) worlds. We can distinguish two views: global entity contingentism and global entity necessitarianism. Global entity contingentism is the view that for any possible E, E exists contingently. Global entity necessitarianism is the view that for any possible E, E exists necessarily. While entity contingentism and entity necessitarianism are views about the modal status of entities, metaphysical contingentism and necessitarianism are views about the modal status of metaphysical principles. Metaphysical contingentism about some metaphysical principle, P, is the view that P is contingent: it is true in some worlds, and false in others. Metaphysical necessitarianism about P is the view that P is necessary: either P is true in every world, or false in every world. We can then distinguish two views: global metaphysical contingentism and global metaphysical necessitarianism. Global metaphysical contingentism is the view that for any internally coherent metaphysical principle P, P is contingent: P is true in some worlds and false in others. Global metaphysical necessitarianism is the view that for any internally coherent metaphysical principle, P, P is necessary: it is either true in every world, or false in every world. This chapter principally focuses on metaphysical rather than entity contingentism, though §2 briefly discusses the latter. As we will see, (§2), both global entity contingentism and global entity necessitarianism are controversial views, and most philosophers fall somewhere between these two extremes, holding that some, but not all, entities exist necessarily—a view we can call entity moderatism. By contrast, global metaphysical necessitarianism has, until recently, largely been the default view. It is only recently that some philosophers have argued that we should be metaphysical contingentists about at least some metaphysical principles—a view we can call metaphysical moderatism. §3 considers why global metaphysical necessitarianism has hitherto been so persuasive, then evaluates (§3.1) some arguments for the view before considering more recent arguments in favour of the contingency of (at least some) metaphysical principles (§3.2). (shrink)

Indispensability arguments are used as a way of working out what there is: our best science tells us what things there are. Some philosophers think that indispensability arguments can be used to show that we should be committed to the existence of mathematical objects. Do indispensability arguments also deliver conclusions about the modal properties of these mathematical entities? Colyvan Mathematical knowledge, OUP, Oxford, 109-122, 2007) and Hartry Field each suggest that a consequence of the empirical methodology of indispensability arguments is (...) that the resulting mathematical objects can only be said to exist contingently. Kristie Miller has argued that this line of thought doesn’t work, 335-359, 2012). Miller argues that indispensability arguments are in direct tension with contingentism about mathematical objects, and that they cannot tell us about the modal status of mathematical objects. I argue that Miller’s argument is crucially imprecise, and that the best way of making it clearer no longer shows that the indispensability strategy collapses or is unstable if it delivers contingentist conclusions about what there is. (shrink)

On its usual interpretation, the Barcan Formula—◊∃xB → ∃x◊B—says that, if there could have been something that is such and such a way, then there is something that could have been that way. It is traditionally held that contingentist actualists should—indeed, must—reject the Barcan Formula. I argue that contingentist actualists should—indeed, must—endorse the Barcan Formula, at least assuming a standard, Tarskian conception of truth and truth preservation. I end by proposing a logic for contingentist actualists that validates the Barcan Formula. (...) This logic has the surprising feature of also validating the Converse Barcan Formula, □∀xB → ∀x□B, while still invalidating related formulas—such as □∀x□∃y x = y —that contingentist actualists should reject. It does this by employing models with fixed domains but assignments to the identity predicate that vary across worlds. (shrink)

This paper develops an account of pluralities based on the following simple claim: some things are nothing over and above the individual things they comprise. For some, this may seem like a mysterious statement, perhaps even meaningless; for others, like a truism, trivial and inferentially inert. I show that neither reaction is correct: the claim is both tractable and has important consequences for a number of debates in philosophy.

Trevor Teitel has recently argued that combining the assumption that modality reduces to essence with the assumption that possibly some objects contingently exist leads to problems if one wishes to uphold that the logic of metaphysical modality is S5. In this paper I will argue that there is a way for the essentialist to evade the problem described by Teitel. The proposed solution crucially involves the assumption that some propositions possibly fail to exist. I will show how this assumption affords (...) a motivated contingentist response to Teitel’s argument. (shrink)

Necessitism is the controversial thesis that necessarily everything is necessarily something, namely that everything, everywhere, necessarily exists. What is controversial about necessitism is that, at its core, it claims that things could not have failed to exist, while we have a pre-theoretical intuition that not everything necessarily exists. Contingentism, in accordance with common sense, denies necessitism: it claims that some things could have failed to exist. Timothy Williamson is a necessitist and claims that David Lewis is a necessitist too. The (...) paper argues that, granted the assumptions that lead to interpret the Lewisian as a necessitist, she can preserve contingentist intuitions, by genuinely agreeing with the folk that existence is contingent. This is not just the uncontroversial claim that the Lewisian, as a result of the prevalence of restricted quantification in counterpart theoretic regimentations of natural language, can agree with the folk while disagreeing with them in the metaphysical room. Rather, this is the claim that it is in the metaphysical room that the Lewisian can endorse the intuitions lying behind contingentism. (shrink)

Hybrid contingentism combines first-order contingentism, the view that it is contingent what individuals there are, with higher-order necessitism, the view that it is non-contingent what properties and propositions there are (where these are conceived as entities in the range of appropriate higher-order quantifiers). This combination of views avoids the most delicate problems afflicting alternative contingentist positions while preserving the central contingentist claim that ordinary, concrete entities exist contingently. Despite these attractive features, hybrid contingentism is usually faced with rejection. The main (...) reason for this is an objection that crucially involves haecceitistic properties, properties such as being identical to Plato or being identical to Aristotle. The objection alleges that by accepting the necessary existence of such haecceities, hybrid contingentists incur an explanatory commitment that they are unable to discharge, namely that of explaining how it is that certain haecceities ‘lock onto’ their target individuals even when those individuals are absent. To defend hybrid contingentism against this charge, I first clarify the haecceities objection in several respects and consider, in particular, what notion of explanation the objection is operating with. After arguing that it can be fruitfully understood as a challenge to provide metaphysical grounds for certain haecceity facts, I develop a contingentist response to the objection that draws on recent work on the connection between ground and essence. (shrink)

In his book Modal Logic as Metaphysics, Williamson argues that the traditional actualist‐possibilist debate should be abandoned as hopelessly unclear and that we should get on with the clearer contingentism‐necessitism debate. We think that Williamson’s pessimism is not warranted by the brief arguments he gives. In this paper, we explain why and provide a clear formulation of the traditional actualist‐possibilist debate.

Philosophical Investigations, EarlyView.

The dissertation introduces new sequent-calculi for free first- and second-order logic, and a hyper-sequent calculus for modal logics K, D, T, B, S4, and S5; to attain the calculi for the stronger modal logics, only external structural rules need to be added to the calculus for K, while operational and internal structural rules remain the same. Completeness and cut-elimination are proved for all calculi presented.Philosophically, the dissertation develops an inferentialist, or proof-theoretic, theory of meaning. It takes as a starting point (...) that the sense of a sentence is determined by the rules governing its use. In particular, there are two features of the use of a sentence that jointly determine its sense, the conditions under which it is coherent to assert that sentence and the conditions under which it is coherent to deny that sentence. The dissertation develops a theory of quantification as marking coherent ways a language can be expanded and modality as the means by which we can reflect on the norms governing the assertion and denial conditions of our language. If the view of quantification that is argued for is correct, then there is no tension between second-order quantification and nominalism. In particular, the ontological commitments one can incur through the use of a quantifier depend wholly on the ontological commitments one can incur through the use of atomic sentences. The dissertation concludes by applying the developed theory of meaning to the metaphysical issue of necessitism and contingentism. Two objections to a logic of contingentism are raised and addressed. The resulting logic is shown to meet all the requirement that the dissertation lays out for a theory of meaning for quantifiers and modal operators.Abstract prepared by Andrew ParisiE-mail: [email protected]: https://opencommons.uconn.edu/dissertations/1480/. (shrink)

Subverting a once widely held Quinean paradigm, there is a growing consensus among philosophers of logic that higher-order quantifiers (which bind variables in the syntactic position of predicates and sentences) are a perfectly legitimate and useful instrument in the logico-philosophical toolbox, while neither being reducible to nor fully explicable in terms of first-order quantifiers (which bind variables in singular term position). This article discusses the impact of this quantificational paradigm shift on metaphysics, focussing on theories of properties, propositions, and identity, (...) as well as on the metaphysics of modality. (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)

In Modal Logic as Metaphysics, Timothy Williamson claims that the possibilism-actualism (P-A) distinction is badly muddled. In its place, he introduces a necessitism-contingentism (N-C) distinction that he claims is free of the confusions that purportedly plague the P-A distinction. In this paper I argue first that the P-A distinction, properly understood, is historically well-grounded and entirely coherent. I then look at the two arguments Williamson levels at the P-A distinction and find them wanting and show, moreover, that, when the N-C (...) distinction is broadened (as per Williamson himself) so as to enable necessitists to fend off contingentist objections, the P-A distinction can be faithfully reconstructed in terms of the N-C distinction. However, Williamson’s critique does point to a genuine shortcoming in the common formulation of the P-A distinction. I propose a new definition of the distinction in terms of essential properties that avoids this shortcoming. (shrink)

The grounding relation is routinely characterized by means of logical postulates. The aim of this paper is twofold. First, I show that a subset of those postulates is incompatible with a minimal characterization of metaphysical modality. Then I consider a number of ways for reconciling ground with modality. The simplest and most elegant solution consists in adopting serious actualism, which is best captured within a first-order modal language with predicate abstraction governed by negative free logic. I also explore a number (...) of alternative strategies by revising the ground-theoretic postulates, while keeping the modal ones fixed. As I argue, each of those strategies is either unviable, highly contentious, or insufficiently motivated. (shrink)

Recently, some authors – call them Reformists – have argued that the traditional Presentism-Eternalism and Actualism-Possibilism debates in the metaphysics of time and modality respectively are unclear or insubstantial, and should therefore give way to the newer Temporaryism-Permanentism and Contingentism- Necessitism debates. In ‘On characterising the presentism/eternalism and actualism/possibilism debates’ (2016, Analytic Philosophy 57: 110-140), Ross Cameron defends the Conservative position that the traditional debates are both substantial and distinct from the Temporaryism-Permanentism and Contingentism- Necessitism debates. In this paper I (...) provide a Reformist response to Cameron’s arguments. (shrink)

Serious actualism is the prima facie plausible thesis that things couldn’t have been related while being nothing. The thesis plays an important role in a number of arguments in metaphysics, e.g., in Plantinga’s argument for the claim that propositions do not ontologically depend on the things that they are about and in Williamson’s argument for the claim that he, Williamson, is necessarily something. Salmon has put forward that which is, arguably, the most pressing challenge to serious actualists. Salmon’s objection is (...) based on a scenario intended to elicit the judgment that merely possible entities may nonetheless be actually referred to, and so may actually have properties. It is shown that predicativism, the thesis that names are true of their bearers, provides the resources for replying to Salmon’s objection. In addition, an argument for serious actualism based on Stephanou, 219–250 2007) is offered. Finally, it is shown that once serious actualism is conjoined with some minimal assumptions, it implies property necessitism, the thesis that necessarily all properties are necessarily something, as well as a strong comprehension principle for higher-order modal logic according to which for every condition there necessarily is the property of being a thing satisfying that condition. (shrink)

This paper first argues that we can bring out a tension between the following three popular doctrines: (i) the canonical reduction of metaphysical modality to essence, due to Fine, (ii) contingentism, which says that possibly something could have failed to be something, and (iii) the doctrine that metaphysical modality obeys the modal logic S5. After presenting two such arguments (one from the theorems of S4 and another from the theorems of B), I turn to exploring various conclusions we might draw (...) in light of these results, and argue that none comes cost free. In the course of laying out possible responses to my arguments, we'll have a chance to evaluate various doctrines about the interplay between contingency and essence, as well as develop some alternative reductions of metaphysical modality to essence. I don't decisively come down in favor of one response over the others, though I say some things that point towards the conclusion that essence has no role to play in reducing metaphysical modality. (shrink)

I proffer a success argument for classical logical consequence. I articulate in what sense that notion of consequence should be regarded as the privileged notion for metaphysical inquiry aimed at uncovering the fundamental nature of the world. Classical logic breeds necessitism. I use necessitism to produce problems for both ontological naturalism and atheism.

The models of contingency in what propositions, properties and relations there are developed in Part 1 are related to models of contingency in what propositions there are due to Robert Stalnaker. It is shown that some but not all of the classes of models of Part 1 agree with Stalnaker’s models concerning the patterns of contingency in what propositions there are they admit. Further structural connections between the two kinds of models are explored.

Two expressive limitations of an infinitary higher-order modal language interpreted on models for higher-order contingentism – the thesis that it is contingent what propositions, properties and relations there are – are established: First, the inexpressibility of certain relations, which leads to the fact that certain model-theoretic existence conditions for relations cannot equivalently be reformulated in terms of being expressible in such a language. Second, the inexpressibility of certain modalized cardinality claims, which shows that in such a language, higher-order contingentists cannot (...) express what is communicated using various instances of talk of ‘possible things’, such as ‘there are uncountably many possible stars’. (shrink)

Resumen En una serie de escritos Timothy Williamson ha argumentado a favor del necesitismo, esto es, la tesis de que es necesario que todo exista necesariamente. Este trabajo discute el necesitismo de segundo orden, esto es, la tesis de que es necesario que toda propiedad exista necesariamente, considerando líneas de argumentación semejantes a las desplegadas en primer orden. Se examinan tres de estos argumentos: el carácter necesario de ser una propiedad, la aparición de las propiedades en proposiciones, y los compromisos (...) ontológicos del metalenguaje en el que se formula la semántica. Se argumenta que ninguno de ellos es realmente convincente. La justificación del necesitismo de segundo orden parece requerir más metafísica sustantiva que resultados formales, al menos si es que los resultados formales de que se trata son aquellos discutidos aquí.In a series of writings Timothy Williamson has argued for necessitism, i. e. the thesis that it is necessary that everything exists necessarily. This work discusses second-order necessitism, i. e. the thesis that it is necessary that every property exists necessarily, considering lines of argument similar to those displayed on first-order. Three of those arguments are examined. the necessary character ofbeing a property, the occurrence of properties in propositions, and the ontological commitments of the metalanguage where the semantics is formulated. It is argued that none of them are compelling. The justification for second-order necessitism seems to require more substantive metaphysics than formal results, at least if the formal results in view are those discussed here. (shrink)

A discussion of a view, defended by Robert Adams and Boris Kment, according to which contingent existence requires rejecting many standard principles of propositional modal logic involving iterated modal operators.

Robert Stalnaker has recently advocated propositional contingentism, the claim that it is contingent what propositions there are. He has proposed a philosophical theory of contingency in what propositions there are and sketched a possible worlds model theory for it. In this paper, such models are used to interpret two propositional modal languages: one containing an existential propositional quantifier, and one containing an existential propositional operator. It is shown that the resulting logic containing an existential quantifier is not recursively axiomatizable, as (...) it is recursively isomorphic to second-order logic, and a natural candidate axiomatization for the resulting logic containing an existential operator is shown to be incomplete. (shrink)

This article explores the connection between two theses: the principle of conditional excluded middle for the counterfactual conditional, and the claim that it is a contingent matter which (coarse grained) propositions there are. Both theses enjoy wide support, and have been defended at length by Robert Stalnaker. We will argue that, given plausible background assumptions, these two principles are incompatible, provided that conditional excluded middle is understood in a certain modalized way. We then show that some (although not all) arguments (...) for conditional excluded middle can in fact be extended to motivate this modalized version of the principle. (shrink)

We often speak as if there are merely possible people—for example, when we make such claims as that most possible people are never going to be born. Yet most metaphysicians deny that anything is both possibly a person and never born. Since our unreflective talk of merely possible people serves to draw non-trivial distinctions, these metaphysicians owe us some paraphrase by which we can draw those distinctions without committing ourselves to there being merely possible people. We show that such paraphrases (...) are unavailable if we limit ourselves to the expressive resources of even highly infinitary first-order modal languages. We then argue that such paraphrases are available in higher-order modal languages only given certain strong assumptions concerning the metaphysics of properties. We then consider alternative paraphrase strategies, and argue that none of them are tenable. If talk of merely possible people cannot be paraphrased, then it must be taken at face value, in which case it is necessary what individuals there are. Therefore, if it is contingent what individuals there are, then the demands of paraphrase place tight constraints on the metaphysics of properties: either (i) it is necessary what properties there are, or (ii) necessarily equivalent properties are identical, and having properties does not entail even possibly being anything at all. (shrink)

The most common first- and second-order modal logics either have as theorems every instance of the Barcan and Converse Barcan formulae and of their second-order analogues, or else fail to capture the actual truth of every theorem of classical first- and second-order logic. In this paper we characterise and motivate sound and complete first- and second-order modal logics that successfully capture the actual truth of every theorem of classical first- and second-order logic and yet do not possess controversial instances of (...) the Barcan and Converse Barcan formulae as theorems, nor of their second-order analogues. What makes possible these results is an understanding of the individual constants and predicates of the target languages as strongly Millian expressions, where a strongly Millian expression is one that has an actually existing entity as its semantic value. For this reason these logics are called ‘strongly Millian’. It is shown that the strength of the strongly Millian second-order modal logics here characterised afford the means to resist an argument by Timothy Williamson for the truth of the claim that necessarily, every property necessarily exists. (shrink)

In this paper we will argue that the ontology implicit in John Buridan’s modal octagon commits him to a form of contingentism. In particular, we will argue that Buridan is committed to denying the validity of the Barcan and converse Barcan formulae.

The paper deals with cases of counting things that could exist but do not actually exist that resist common strategies for actualist paraphrases and that play an important role in motivating Timothy Williamson's ontology of contingently concrete objects. It is argued that these cases should be understood as cases of quantification not over individual possible objects but rather over kinds of objects, some of which do not actually have instances. This claim is motivated by a comparison with other cases of (...) natural-language quantification with a similar logical form that, in any case, have to be interpreted as involving quantification over kinds of things even if their surface structure seems to suggest otherwise. (shrink)

Boring ontological realists hold that objects exist at times and persist over time without having substantive essences. Boring realism is a consequence of the minimal A-theory of time and the most sensible formulations of necessitism. This kind of realism is at odds with a ubiquitous realist thesis, which I call the persistenceessence link. This essay surveys some examples of the persistence-essence link and argues that it is best understood as a thesis about grounding. If we understand the link in terms (...) of grounding, there are new options for denying it—and for better understanding boring realism. (shrink)

Timothy Williamson is one of the most influential living philosophers working in the areas of logic and metaphysics. His work in these areas has been particularly influential in shaping debates about metaphysical modality, which is the topic of his recent provocative and closely-argued book *Modal Logic as Metaphysics* (2013). The present book comprises ten essays by metaphysicians and logicians responding to Williamson’s work on metaphysical modality. The authors include some of the most distinguished philosophers of modality in the world, as (...) well as several rising stars. Each essay is followed by a reply by Williamson. In addition, the book contains a major new essay by Williamson, ‘Modal science,’ concerning the role of modal claims in natural science. This book was originally published as a special issue of the *Canadian Journal of Philosophy.*. (shrink)

Timothy Williamson’s Modal Logic as Metaphysics is a book-length defense of necessitism about objects—roughly put, the view that, necessarily, any object that exists, exists necessarily. In more formal terms, Williamson argues for the validity of necessitism for objects (NO: ◻︎∀x◻︎∃y(x=y)). NO entails both the (first-order) Barcan formula (BF: ◇∃xΦ → ∃x◇Φ, for any formula Φ) and the (first-order) converse Barcan formula (CBF: ∃x◇Φ → ◇∃xΦ, for any formula Φ). The purpose of this essay is not to assess Williamson’s arguments either (...) for necessitism (although discussion of these arguments will play a central role in the dialectic) or for necessitism’s two famous corollaries. Instead, the focus shall be a general principle governing abstract objects—the abstract of principle (or AOP) —instances of which seems to be at work in some of Williamson’s central arguments for necessitism. The AOP can be straightforwardly formulated and applied within the neo-logicist framework—in fact, arguably the principle is most naturally formulated in neo-logicist terms. -/- After closely examining, and carefully formalizing, the AOP, the remainder of the paper focuses on arguments for necessitism-like claims (the exact meaning of “necessitism-like” will become clearer as the essay progresses) based on the AOP. In particular, we shall focus on the instance of the AOP that applies to the abstract objects governed by the most well-known and most fully studied abstraction principle: Hume’s Principle (HP). It turns out that, although we cannot reconstruct a valid argument for necessitism based on this numerical instance of the AOP, we can obtain valid arguments for weaker, but equally interesting conclusions. In particular, we shall show that, although HP combined with the AOP (and some additional, related assumptions) allows the contents of the domains of possible worlds to vary, the size of those domains must remain constant. The paper concludes by developing and critiquing some related arguments for necessitism based on applying relevant instances of the AOP to abstraction principles governing sets (or extensions), and to a simple objectual abstraction principle. (shrink)

Necessitists hold that, necessarily, everything is such that, necessarily, something is identical to it. Timothy Williamson has posed a number of challenges to contingentism, the negation of necessitism. One such challenge is an argument that necessitists can more wholeheartedly embrace possible worlds semantics than can contingentists. If this charge is correct, then necessitists, but not contingentists, can unproblematically exploit the technical successes of possible worlds semantics. I will argue, however, that the charge is incorrect: contingentists can embrace possible worlds semantics (...) as wholeheartedly as necessitists. Williamson offers a criterion for a class of models of quantified modal logic to be intended, and argues on its basis that contingentists must deny that there is an intended class of models. I argue that Williamson’s criterion is objectionable, supply an alternative that does not support Williamson’s argument, and adapt Williamson’s construction of an intended model structure to the needs of contingentist metaphysics. (shrink)

I attempt to meet some criticisms that Williamson makes of my attempt to carry out Prior's project of reducing possibility discourse to actualist discourse.

I consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes that only the (...) cardinalities of these sets matters, and that not all pairs of infinite sets determine the same logic. I use so-called two-cardinal theorems from model theory to investigate the space of logics and consequence relations determined by pairs of infinite sets, and show how to eliminate the assumption that worlds are individuals from Williamson’s argument. (shrink)

According to propositional contingentism, it is contingent what propositions there are. This paper presents two ways of modeling contingency in what propositions there are using two classes of possible worlds models. The two classes of models are shown to be equivalent as models of contingency in what propositions there are, although they differ as to which other aspects of reality they represent. These constructions are based on recent work by Robert Stalnaker; the aim of this paper is to explain, expand, (...) and, in one aspect, correct Stalnaker's discussion. (shrink)

This paper is a study of higher-order contingentism – the view, roughly, that it is contingent what properties and propositions there are. We explore the motivations for this view and various ways in which it might be developed, synthesizing and expanding on work by Kit Fine, Robert Stalnaker, and Timothy Williamson. Special attention is paid to the question of whether the view makes sense by its own lights, or whether articulating the view requires drawing distinctions among possibilities that, according to (...) the view itself, do not exist to be drawn. The paper begins with a non-technical exposition of the main ideas and technical results, which can be read on its own. This exposition is followed by a formal investigation of higher-order contingentism, in which the tools of variable-domain intensional model theory are used to articulate various versions of the view, understood as theories formulated in a higher-order modal language. Our overall assessment is mixed: higher-order contingentism can be fleshed out into an elegant systematic theory, but perhaps only at the cost of abandoning some of its original motivations. (shrink)

This paper presents a new argument for necessitism, the claim that necessarily everything is necessarily something. The argument appeals to principles about the metaphysics of quantification and predication which are best seen as constraints on reality’s fineness of grain. I give this argument in section 4; the impatient reader may skip directly there. Sections 1-3 set the stage by surveying three other arguments for necessitism. I argue that none of them are persuasive, but I think it is illuminating to consider (...) my argument in light of the others and vice versa. These interconnections should be of interest even to those who reject necessitism; of particular interest may be the new conception of validity proposed in section 5. (shrink)

I critically discuss some of the main arguments of Modal Logic as Metaphysics, present a different way of thinking about the issues raised by those arguments, and briefly discuss some broader issues about the role of higher-order logic in metaphysics.

According to Timothy Williamson, we should accept the simplest and most powerful second-order modal logic, and as a result accept an ontology of "bare possibilia". This general method for extracting ontology from logic is salutary, but its application in this case depends on a questionable assumption: that modality is a fundamental feature of the world.

This paper explains and defends the idea that metaphysical necessity is the strongest kind of objective necessity. Plausible closure conditions on the family of objective modalities are shown to entail that the logic of metaphysical necessity is S5. Evidence is provided that some objective modalities are studied in the natural sciences. In particular, the modal assumptions implicit in physical applications of dynamical systems theory are made explicit by using such systems to define models of a modal temporal logic. Those assumptions (...) arguably include some necessitist principles. -/- Too often, philosophers have discussed ‘metaphysical’ modality — possibility, contingency, necessity — in isolation. Yet metaphysical modality is just a special case of a broad range of modalities, which we may call ‘objective’ by contrast with epistemic and doxastic modalities, and indeed deontic and teleological ones (compare the distinction between objective probabilities and epistemic or subjective probabilities). Thus metaphysical possibility, physical possibility and immediate practical possibility are all types of objective possibility. We should study the metaphysics and epistemology of metaphysical modality as part of a broader study of the metaphysics and epistemology of the objective modalities, on pain of radical misunderstanding. Since objective modalities are in general open to, and receive, natural scientific investigation, we should not treat the metaphysics and epistemology of metaphysical modality in isolation from the metaphysics and epistemology of the natural sciences. -/- In what follows, Section 1 gives a preliminary sketch of metaphysical modality and its place in the general category of objective modality. Section 2 reviews some familiar forms of scepticism about metaphysical modality in that light. Later sections explore a few of the many ways in which natural science deals with questions of objective modality, including questions of quantified modal logic. (shrink)