The idea that justified modal belief can be accounted for in terms of empirically justified, non-modal belief is enjoying increasing popularity in the epistemology of modality. One alleged reason to prefer modal empiricism over more traditional, rationalist modal epistemologies is that empiricism avoids the problem with the integration challenge that arise for rationalism, assuming that we want to be realists about modal metaphysics. In this paper, I argue that given two very reasonable constraints on what it means to meet the (...) integration challenge for modality, empiricism is currently at best on a par with, but potentially worse off than, rationalist alternatives, with respect to the integration challenge. (shrink)

This is a symposium on my book, Writing the Book of the World, containing a precis from me, criticisms from Contessa, Merricks, and Schaffer, and replies by me.

This paper contains an argument to the effect that possible worlds semantics renders semantic knowledge impossible, no matter what ontological interpretation is given to possible worlds. The essential contention made is that possible worlds semantic knowledge is unsafe and this is shown by a parallel with the preface paradox.

The possibility of Junk is the possibility that something exists and everything is a proper part. Just as we might imagine that there are no simples—that everything has a proper part, all the way down—we might imagine that there are no caps—that everything is a proper part, all the way up. It is not obvious that this apparent possibility can be accommodated within a Lewisian modal framework. For Lewis, every possibility involves the existence of a possible world, and a possible (...) world is just is a maximal sum, and so a cap. But the Lewisian can accommodate Junk, if she wishes, by allowing parts of possible worlds to represent complete possibilities. (shrink)

The dogma that the propositional logic of metaphysical modality is S5 is rebutted. The author exposes fallacies in standard arguments supporting S5, arguing that propositional metaphysical modal logic is weaker even than both S4 and B, and is instead the minimal and weak metaphysical-modal logic T.

David Lewis holds that a single possible world can provide more than one way things could be. But what are possible worlds good for if they come apart from ways things could be? We can make sense of this if we go in for a metaphysical understanding of what the world is. The world does not include everything that is the case—only the genuine facts. Understood this way, Lewis's “cheap haecceitism” amounts to a kind of metaphysical anti-haecceitism: it says there (...) aren't any genuine facts about individuals over and above their qualitative roles. (shrink)

According to Quine, in any disagreement over basic logical laws the contesting parties must mean different things by the connectives or quantifiers implicated in those laws; when a deviant logician ‘tries to deny the doctrine he only changes the subject’. The standard semantics for intuitionism offers some confirmation for this thesis, for it represents an intuitionist as attaching quite different senses to the connectives than does a classical logician. All the same, I think Quine was wrong, even about the dispute (...) between classicists and intuitionists. I argue for this by presenting an account of consequence, and a cognate semantic theory for the language of the propositional calculus, which respects the meanings of the connectives as embodied in the familiar classical truth-tables, does not presuppose Bivalence, and with respect to which the rules of the intuitionist propositional calculus are sound and complete. Thus the disagreement between classicists and intuitionists, at least, need not stem from their attaching different senses to the connectives; one may deny the doctrine without changing the subject. The basic notion of my semantic theory is truth at a possibility, where a possibility is a way that things might be, but which differs from a possible world in that the way in question need not be fully specific or determinate. I compare my approach with a previous theory of truth at a possibility due to Lloyd Humberstone, and with a previous attempt to refute Quine’s thesis due to John McDowell. (shrink)

In a recent article Mark Ian Thomas Robson argues that there is a clear contradiction between the view that possible worlds are a part of God's nature and the theologically pivotal, but philosophically neglected, claim that God is perfectly beautiful. In this article I show that Robson's argument depends on several key assumptions that he fails to justify and as such that there is reason to doubt the soundness of his argument. I also demonstrate that if Robson's argument were sound (...) then this would be a problem for all classical theists and not just those who hold the possible worlds view. (shrink)

In a short exchange published in 2000, Richard Rorty and Robert Brandom differed over the status of “facts” in a world containing no speakers and, hence, no speech acts. While Brandom wanted to retain the meaningfulness of talk of “facts” or “truths” about things—in this case truths about photons —in a world in which there could be no claimings about such things, Rorty denied the existence of any such “worldly items” as “facts.” In this essay the difference between Rorty and (...) Brandom on this issue is used to explore their differing attitudes to modality. Brandom appeals to a Kantian approach of modal realism to support counterfactual claims. However, I argue that when his approach to modality is examined in the context of current debates over possible world semantics, his own “incompatibilist” semantics itself seems incompatible with a Kantian approach to modality. In turn, I suggest that this difference between Brandom and Rorty in their attitudes to modality reveals a difference in their respective attitudes to pragmatism’s relation to philosophy in general. (shrink)

Here, I suggest a hitherto relatively unexplored way beyond the opposed Aristotelian realist and Kantian idealist approaches that divide recent interpretations of the categories or “thought determinations” of Hegel’s Logic, by locating his idealism within the terrain of recent debates in modal metaphysics. In particular, I return to the outlook of the first philosopher to attempt to bring Hegel into the analytic conversation, John Niemeyer Findlay, and consider Hegel’s idealism as instantiating the metaphysical position that, following the work of Findlay’s (...) former student, Arthur Prior, has come to be called “modal actualism”. (shrink)

Drawing upon a conception of the metaphysics of conscious states and of first-person content, we can argue that Descartes's transition ‘Cogito ergo sum’ is both sound and one he is entitled to make. We can nevertheless formulate a version of Lichtenberg's objection that can still be raised after Bernard Williams's discussion. I argue that this form of Lichtenberg's revenge can also be undermined. In doing so it helps to compare the metaphysics of subjects, worlds and times. The arguments also apply (...) to Descartes's ‘second Cogito’, that it is one and the same subject that thinks, wills, imagines. (shrink)

This intuition may be contrasted with the incompatible intuitions that might support, say, average utilitarianism. According to average utilitarianism we should bring about that outcome which has the highest average utility. That someone would have a higher than average level of utility is, therefore, ceteris paribus a reason to act so that that person exists. Because of this, the basic intuition is a reason for rejecting average utilitarianism.

Reductionist realist accounts of certain entities, such as the natural numbers and propositions, have been taken to be fatally undermined by what we may call the problem of arbitrary identification. The problem is that there are multiple and equally adequate reductions of the natural numbers to sets (see Benacerraf, 1965), as well as of propositions to unstructured or structured entities (see, e.g., Bealer, 1998; King, Soames, & Speaks, 2014; Melia, 1992). This paper sets out to solve the problem by canvassing (...) what we may call the arbitrary reference strategy. The main claims of such strategy are 2. First, we do not know which objects are the referents of proposition and numerical terms since their reference is fixed arbitrarily. Second, our ignorance of which object is picked out as the referent does not entail that no object is referred to by the relevant expression. Different articulations of the strategy are assessed, and a new one is defended. (shrink)

David Lewis’s arguments against magical ersatzism are notoriously puzzling. Untangling different strands in those arguments is useful for bringing out what he thought was wrong with not just one style of theory about possible worlds, but with much of the contemporary metaphysics of abstract objects. After setting out what I take Lewis’s arguments to be and how best to resist them, I consider the application of those arguments to general theories of properties and relations. The constraints Lewis motivates turn out (...) to yield an argument for concretism about possible individuals that is quite different from the better-known Lewisian arguments for that position. The discussion also touches on the puzzling question of whether things are the way they are because of the properties they have, or are the properties and relations the way they are because of the things that have them. (shrink)

Russell's "new contradiction" about "the totality of propositions" has been connected with a number of modal paradoxes. M. Oksanen has recently shown how these modal paradoxes are resolved in the set theory NFU. Russell's paradox of the totality of propositions was left unexplained, however. We reconstruct Russell's argument and explain how it is resolved in two intensional logics that are equiconsistent with NFU. We also show how different notions of possible worlds are represented in these intensional logics.

Can we explain why some propositions are necessary? Blackburn (Fact, science, and value. Blackwell, Oxford, 1987) has presented a dilemma aimed at showing that the necessity of a proposition cannot be explained either in the case where the explanans is another necessary proposition (necessity horn) or in the case where the explanans is a contingent proposition (contingency horn). Blackburn’s dilemma is intended to show that necessary truth is an explanatorily irreducible kind of truth: there is nothing that explains why propositions (...) are necessary, nothing that makes necessary necessary truths. In this paper, I criticize the contingency horn of Blackburn’s dilemma. On the one hand, I show that the official reconstruction of the horn uses a principle that is incompatible with the notion of explanation plausibly needed to explain why propositions are necessary; on the other, I show that a simpler formulation of the horn, which does not make use of such a controversial principle, makes essential use of principles that are incompatible with the idea that possibilities can have explanatory roles. I then defend the view that possibilities can have explanatory roles, and that the explanatory role of possibilities is best represented, within possible worlds, as the existence of trans-world relations of explanation. (shrink)

This paper presents an argument against the A-Theory of time. Briefly, I shall contend that the A-Theorist has no explanation for why the present moment in particular has the metaphysical privilege she accords it, and that this puts the theory at a disadvantage. In what follows, I shall begin by presenting this argument. I will follow that with some potential explanations for why the present moment is privileged and reasons militating against them, in addition to some other possible objections to (...) my argument and my responses to them. The conclusion will be that the A-Theorist fails to provide either an obvious or a theoretical explanation of the present time’s privileged status and is thereby at a theoretical disadvantage to theories that do not posit a metaphysically privileged present time. Topics covered include the purported analogy between times and worlds, the possibility that times are individuated by what is true at them, and the semantic status of titles for date-times. (shrink)

There are many parallels between the role of possible worlds in modal logic and that of times in tense logic. But the similarities only go so far, and it is important to note where the two come apart. This paper argues that even though worlds and times play similar roles in the model theories of modal and tense logic, there is no tense analogue of the possible-worlds analysis of modal operators. An important corollary of this result is that presentism cannot (...) be the tense analogue of actualism. (shrink)

This paper defends three theses: that presentism is either trivial or untenable; that the debate between tensed and tenseless theories of time is not about the status of presentism; and that there is no temporal analogue of the modal thesis of actualism.

The fundamental principle of the theory of possible worlds is that a proposition p is possible if and only if there is a possible world at which p is true. In this paper we present a valid derivation of this principle from a more general theory in which possible worlds are defined rather than taken as primitive. The general theory uses a primitive modality and axiomatizes abstract objects, properties, and propositions. We then show that this general theory has very small (...) models and hence that its ontological commitments—and, therefore, those of the fundamental principle of world theory—are minimal. (shrink)

Assuming minimal fine-individuation--that there are some necessarily equivalent intensional objects (e.g. propositions) that are nonetheless distinct objects, on standard actualist frameworks, the answer to our title question is "No". First I specify a fully cognitively accessible, purely qualitative maximal consistent state of affairs (MCS). (That there is an MCS that is either fully graspable or purely qualitative is in itself quite contrary to conventional dogma.) Then I identify another MCS, one necessarily equivalent to the first. It follows that there could (...) have been more than one obtaining MCS. I then argue that there is more than one obtaining MCS. So there is nothing answering to "the actual world", and the set of worlds is not the set of MCSs. I explore various patch-ups. Finally, I compare the actualist and modal realist notions of worlds, and I argue that even if the realist were right about concrete world ensembles, our reflections indicate that necessary truth is not truth in all worlds anyway, which undercuts the rationale for the realist's program. (shrink)

The pressure to individuate propositions more finely than intensionally—that is, hyper-intensionally—has two distinct sources. One source is the philosophy of mind: one can believe a proposition without believing an intensionally equivalent proposition. The second source is metaphysics: there are intensionally equivalent propositions, such that one proposition is true in virtue of the other but not vice versa. I focus on what our theory of propositions should look like when it's guided by metaphysical concerns about what is true in virtue of (...) what. In this paper I articulate and defend a metaphysical theory of the individuation of propositions, according to which two propositions are identical just in case they occupy the same nodes in a network of invirtuation relations. Invirtuation is here taken to be a primitive relation of metaphysical explanation exemplified by propositions that, in conjunction with truth, defines the notion of true in virtue of. After formulating the theory, I compare it with a view.. (shrink)

Rubin and Pearl offered approaches to causal effect estimation and Lewis and Pearl offered theories of counterfactual conditionals. Arguments offered by Pearl and his collaborators support a weak form of equivalence such that notation from the rival theory can be re-purposed to express Pearl’s theory in a way that is equivalent to Pearl’s theory expressed in its native notation. Nonetheless, the many fundamental differences between the theories rule out any stronger form of equivalence. A renewed emphasis on comparative research can (...) help to guide applications, further develop each theory, and better understand their relative strengths and weaknesses. (shrink)

This article offers a novel solution to the problem of material constitution: by including non-concrete objects among the parts of material objects, we can avoid having a statue and its constituent piece of clay composed of all the same proper parts. Non-concrete objects—objects that aren’t concrete, but possibly are—have been used in defense of the claim that everything necessarily exists. But the account offered shows that non-concreta are independently useful in other domains as well. The resulting view falls under a (...) ‘nonmaterial partist’ class of views that includes, in particular, Laurie Paul’s and Kathrin Koslicki’s constitution views; ones where material objects have properties or structures as parts respectively. The article gives reasons for preferring the non-concretist solution over these other non-material partist views and defends it against objections. (shrink)

The views of David Lewis and the Meinongians are both often met with an incredulous stare. This is not by accident. The stunned disbelief that usually accompanies the stare is a natural first reaction to a large ontology. Indeed, Lewis has been explicitly linked with Meinong, a charge that he has taken great pains to deny. However, the issue is not a simple one. "Meinongianism" is a complex set of distinctions and doctrines about existence and predication, in addition to the (...) famously large ontology. While there are clearly non-Meinongian features of Lewis' views, it is our thesis that many of the characteristic elements of Meinongian metaphysics appear in Lewis' theory. Moreover, though Lewis rejects incomplete and inconsistent Meinongian objects, his ontology may exceed that of a Meinongian who doesn't accept his possibilia. Thus, Lewis explains the truth of "there might have been talking donkeys" by appealing to possibilia which are talking donkeys. But the Meinongian need not accept that there exist things which are talking donkeys. Indeed, we show that a Meinongian even need not accept that there are nonexistent things which are talking donkeys! (shrink)

This is a survey of contemporary work on ‘fictionalism in metaphysics’, a term that is taken to signify both the place of fictionalism as a distinctive anti‐realist metaphysics in which usefulness rather than truth is the norm of acceptance, and the fact that philosophers have given fictionalist treatments of a range of specifically metaphysical notions.

Open future is incompatible with realism about possible worlds. Since realistically conceived (concrete or abstract) possible worlds are maximal in the sense that they contain/represent the full history of a possible spacetime, past and future included, if such a world is actual now, the future is fully settled now, which rules out openness. The kind of metaphysical indeterminacy required for open future is incompatible with the kind of maximality which is built into the concept of possible worlds. The paper discusses (...) various modal realist responses and argues that they provide ersatz openness only, or they lead to incoherence, or they render the resulting theory inadequate as a theory of modality. The paper also considers various accounts of the open future, including rejection of bivalence, supervaluationism, and the ‘thin red line’ view (TRL), and claims that a version of (TRL) can avoid the incompatibility problem, but only at the cost of deflating the notion of openness. (shrink)

The Ramseyan thesis that the probability of an indicative conditional is equal to the corresponding conditional probability of its consequent given its antecedent is both widely confirmed and subject to attested counterexamples (e.g., McGee 2000, Kaufmann 2004). This raises several puzzling questions. For instance, why are there interpretations of conditionals that violate this Ramseyan thesis in certain contexts, and why are they otherwise very rare? In this paper, I raise some challenges to Stefan Kaufmann's account of why the Ramseyan thesis (...) sometimes fails, and motivate my own theory. On my theory, the proposition expressed by an indicative conditional is partially determined by a background partition, and hence its probability depends on the choice of such a partition. I hold that this background partition is contextually determined, and in certain conditions is set by a salient question under discussion in the context. I show how the resulting theory offers compelling answers to the puzzling questions raised by failures of the Ramseyan thesis. (shrink)

Semantic theories based on a hierarchy of types have prominently been used to defend the possibility of unrestricted quantification. However, they also pose a prima facie problem for it: each quantifier ranges over at most one level of the hierarchy and is therefore not unrestricted. It is difficult to evaluate this problem without a principled account of what it is for a quantifier to be unrestricted. Drawing on an insight of Russell’s about the relationship between quantification and the structure of (...) predication, we offer such an account. We use this account to examine the problem in three different type-theoretic settings, which are increasingly permissive with respect to predication. We conclude that unrestricted quantification is available in all but the most permissive kind of type theory. (shrink)

Propositions play a central role in contemporary semantics. On the Russellian account, propositions are structured entities containing particulars, properties and relations. This contrasts sharply with the sets-of-possible-worlds view of propositions. I’ll discuss how to extend the sets-of-worlds view to accommodate fine-grained hyperintensional contents. When this is done in a satisfactory way, I’ll argue, it makes heavy use of entities very much like Russellian tuples. The two notions of proposition become inter-definable and inter-substitutable: they are not genuinely distinct accounts of how (...) propositions represent what they represent. Semantic theorists may move freely between the two conceptions of what propositions are. Nevertheless, the two approaches give different accounts of the metaphysical nature of propositions. I argue that the sets-of-worlds view provides an adequate account of the nature of propositions, whereas the Russellian view cannot. (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)

Possible worlds, concrete or abstract as you like, are irrelevant to the truthmakers for modality—or so I shall argue in this paper. First, I present the neo-Humean picture of modality, and explain why those who accept it deny a common sense view of modality. Second, I present what I take to be the most pressing objection to the neo-Humean account, one that, I argue, applies equally well to any theory that grounds modality in possible worlds. Third, I present an alternative, (...) properties-based theory of modality and explore several specific ways to flesh the general proposal out, including my favored version, the powers theory. And, fourth, I offer a powers semantics for counterfactuals that each version of the properties-based theory of modality can accept, mutatis mutandis. Together with a definition of possibility and necessity in terms of counterfactuals, the powers semantics of counterfactuals generates a semantics for modality that appeals to causal powers and not possible worlds. (shrink)

I propose a way of formulating scientific laws and magnitude attributions which eliminates ontological commitment to mathematical entities. I argue that science only requires quantitative sentences as thus formulated, and hence that we ought to deny the existence of sets and numbers. I argue that my approach cannot plausibly be extended to the concrete "theoretical" entities of science.

Although the use of possible worlds in semantics has been very fruitful and is now widely accepted, there is a puzzle about the standard definition of validity in possible-worlds semantics that has received little notice and virtually no comment. A sentence of an intensional language is typically said to be valid just in case it is true at every world under every model on every model structure of the language. Each model structure contains a set of possible worlds, and models (...) are defined relative to model structures, assigning truth-values to sentences at each world countenanced by the model structure. The puzzle is why more than one model structure is used in the definition of validity. There is presumably just one class of all possible worlds and just one model structure defined on this class that does correctly the things that model structures are supposed to do. (These include, but need not be limited to, specifying the set of individuals in each world as well as various accessibility relations between worlds.) Why not define validity simply as truth at every world under every model on this one model structure? What is the point of bringing in more model structures than just this one?

We investigate these questions in some detail and conclude that for many intensional languages the puzzle points to a genuine difficulty: the standard definition of validity is insufficiently motivated. We begin (Section 1) by showing that a plausible and natural account of validity for intensional languages can be based on a single model structure, and that validity so defined is analogous in important respects to the standard account of validity for extensional languages. We call this notion of validity "validity!", and in Section 2 we contrast it with the standard notion, which we call "validity2". Several attempts are made to discover a rationale for the almost universal acceptance of validity2, but in most of these attempts we come up empty-handed. So in Section 3 we investigate validity! for some intensional languages. Our investigation includes providing axiomatizations for several propositional and predicate logics, most of which are provably complete. The completeness proofs are given in the Appendix, which also contains a sketch of a compactness proof for one of the predicate logics. (shrink)

Introspective knowledge by acquaintance is knowledge we have by being directly aware of our phenomenally conscious states. In this paper, I argue that introspective knowledge by acquaintance is a sui generis kind of knowledge: it is irreducible to any sort of propositional knowledge and is wholly constituted by a relationship of introspective acquaintance. My main argument is that this is the best explanation of some epistemic facts about phenomenal consciousness and introspection. In particular, it best explains the epistemic asymmetry between (...) a subject who has never had a certain phenomenal state and one who has. I also consider two theoretical objections to my claim: an objection from disunity and an objection from mysteriousness. I show that these objections can be answered and that introspective knowledge by acquaintance being sui generis remains a live option on the table. (shrink)

Theories of propositions as sets of truth-supporting circumstances are committed to the thesis that sentences or other representations true in all and only the same circumstances express the same proposition. Theories of propositions as complex, structured entities are not committed to this thesis. As a result, structured propositions can play a role in our theories of language and thought that sets of truth-supporting circumstances cannot play. To illustrate this difference, I sketch a theory of transparent, non-deflationary truth consistent with some (...) theories of structured propositions, but inconsistent with any theory of propositions as sets of truth-supporting circumstances. (shrink)

We intuitively make a distinction between _lying_ and _misleading_. On the explanation of this phenomenon favored here—the _adverbial_ account—the distinction tracks whether the content and its truth-committing force are literally conveyed. On an alternative _commitment_ account, the difference between lying and misleading is predicated instead on the strength of assertoric commitment. One lies when one presents with full assertoric commitment what one believes to be false; one merely misleads when one presents it without full assertoric commitment, by merely hinting or (...) otherwise implying it. Now, as predicted by the well-supported assumption that we can also assert with pictures, the lying/misleading distinction appears to intuitively show up there too. Here I’ll explain how the debate confronting the two accounts plays out both in general and in that case, aiming to provide support for the adverbial account. (shrink)

We present here the papers selected for the volume on the Unity of Propositions problems. After summarizing what the problems are, we locate them in a spectrum from those aiming to provide substantive, reductive explanations, to those with a more deflationary take on the problems.

David Lewis has shocked the philosophical community with his original version of extreme modal realism according to which “every way that a world could possibly be is a way that some world is”. Logical Space is a plenitude of isolated physical worlds, each being the actualization of some way in which a world could be, that bear neither spatiotemporal nor causal relations to each other. Lewis has given independent, converging arguments for this. One is the argument from the indexicality of (...) actuality, the other an elaborate cost-benefit argument of the inference-to-the-best explanation sort to the effect that a systematic analysis of a number of concepts, including modality, causality, propositions and properties, fares better under his theory than under any rival one that takes a possible world to be either a linguistic entity or an ersatz abstract entity such as a maximal compossible set of properties, propositions or states of affairs. Lewis' legion of critics have confined themselves mostly to attempts at a reductio ad absurdum of his theory or to objections to his various analyses. The indexical argument, on the other hand, has not been subject to careful critical scrutiny. It is the purpose of this paper to show that this argument cannot withstand such scrutiny. Its demise, however, leaves untouched his argument from the explanatory superiority for his extreme modal realism. (shrink)

Propositional quantifiers are added to a propositional modal language with two modal operators. The resulting language is interpreted over so-called products of Kripke frames whose accessibility relations are equivalence relations, letting propositional quantifiers range over the powerset of the set of worlds of the frame. It is first shown that full second-order logic can be recursively embedded in the resulting logic, which entails that the two logics are recursively isomorphic. The embedding is then extended to all sublogics containing the logic (...) of so-called fusions of frames with equivalence relations. This generalizes a result due to Antonelli and Thomason, who construct such an embedding for the logic of such fusions. (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)

Robert Stalnaker recently proposed a simple theory of propositions using the notion of a set of propositions being consistent, and conjectured that this theory is equivalent to the claim that propositions form a complete atomic Boolean algebra. This paper clarifies and confirms this conjecture. Stalnaker also noted that some of the principles of his theory may be given up, depending on the intended notion of proposition. This paper therefore also investigates weakened constraints on consistency and the corresponding classes of Boolean (...) algebras. (shrink)

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)

Modal dualism is the claim that there is a space of epistemically possible worlds that exceeds the space of metaphysically possible worlds. In the present paper, I argue that modal dualism is false. I do so via an argument that differs from most previous arguments against modal dualism in that it does not rely on controversial semantic or epistemological assumptions like descriptivism, internalism or modal rationalism. The point of my argument is, instead, that modal dualism is internally inconsistent because it (...) is the result of the failure to draw the proper conclusions from the abandonment of these semantic and epistemological assumptions. The relevant inconsistency manifests itself in the modal dualist notion of epistemic modality. For this notion to play the explanatory roles assigned to it by modal dualists, it has to be a notion of a genuinely epistemic kind of modality. But the only way to make sense of such a notion is via just those semantic or epistemological assumptions that the modal dualist is keen to avoid. Anyone willing to abandon these assumptions has to go further and detach the epistemic from the modal altogether. (shrink)

David Armstrong in his A Combinatorial Theory of Possibility proposes that non-actual possibilities may be treated as fictions grounded in instantiated universals. In this paper, I first provide some objections to his theory. Then I make the case for Foundational Nominalism, the Armstrong inspired thesis that the whole of ontology supervenes on particulars described much as in the Quinean Nominalism that Armstrong rejected as an ontological ostrich. Finally, I argue that Foundational Nominalism permits a fictional theory of possibilities similar to (...) Brian Skyrms’ Tractarian Nominalism. (shrink)