his paper provides a sound and complete axiomatisation for constant domain modal logics without Boolean negation. This is a simpler case of the difficult problem of providing a sound and complete axiomatisation for constant-domain quantified relevant logics, which can be seen as a kind of modal logic with a two-place modal operator, the relevant conditional. The completeness proof is adapted from a proof for classical modal predicate logic (I follow James Garson’s 1984 presentation of the completeness proof quite closely), but (...) with an important twist, to do with the absence of Boolean negation. (shrink)

Noneism a is form of Meinongianism, proposed by Richard Routley and developed and improved by Graham Priest in his widely discussed book Towards Non-Being. Priest's noneism is based upon the double move of building a worlds semantics including impossible worlds, besides possible ones, and admitting a new comprehension principle for objects, differerent from the ones proposed in other kinds of neo-Meinongian theories, such as Parsons' and Zalta's. The new principle has no restrictions on the sets of properties that can deliver (...) objects, but parameterizes the having of properties by objects to worlds. Modality is therefore explicitly built in - so the approach can be conveniently labeled as "modal noneism". In this paper, I put modal noneism to work by testing it against classical issues in modal logic and semantics. It turns out that - perhaps surprisingly - the theory performs well in problems of transworld identity, which are frequently considered to be the difficult ones in the literature; faces a limitation, albeit not a severe one, when one comes to transworld individuation, which is often taken as an easy issue, if not a pseudo-problem; and may stumble upon a real trouble when dealing with what I shall call 'extensionally indiscernible entities' - particular nonexistent objects modal noneism is committed to. (shrink)

From Leibniz to Krauss philosophers and scientists have raised the question as to why there is something rather than nothing. Why-questions request a type of explanation and this is often thought to include a deductive component. With classical logic in the background only trivial answers are forthcoming. With free logics in the background, be they of the negative, positive or neutral variety, only question-begging answers are to be expected. The same conclusion is reached for the modal version of the Question, (...) namely ‘Why is there something contingent rather than nothing contingent?’. The categorial version of the Question, namely ‘Why is there something concrete rather than nothing concrete?’, is also discussed. The conclusion is reached that deductive explanations are question-begging, whether one works with classical logic or positive or negative free logic. I also look skeptically at the prospects of giving causal-counterfactual or probabilistic answers to the Question, although the discussion of the options is less comprehensive and the conclusions are more tentative. The meta-question, viz. ‘Should we not stop asking the Question’, is accordingly tentatively answered affirmatively. (shrink)

Bernard Linsky and Edward Zalta have recently proposed a new form of actualism. I characterize the general form of their view and the motivations behind it. I argue that it is not quite new – it bears interesting similarities to Alvin Plantinga’s view – and that it definitely isn’t actualist.

When some objects are the parts of another object, they compose that object and that object is composite. This article is intended as an introduction to the central questions about composition and a highly selective overview of various answers to those questions. In §1, we review some formal features of parthood that are important for understanding the nature of composition. In §2, we consider some answers to the question: which pluralities of objects together compose something? As we will see, the (...) dominant answers are all of them and none of them. In §§3-4, we examine one of the main arguments that has driven philosophers to these extreme answers: the argument from vagueness. In §5, we turn to the question of whether composition is unique: is it sometimes the case that some things compose more than one thing? Finally, in §6, we turn from the question of which composites exist to the question of which composites exist fundamentally. (shrink)

This paper presents structural similarities and historical connections between Prior’s rejection of the Barcan formula and his critique of Berkeley’s master argument for idealism in his 1955 paper “Berkeley in Logical Form”. Making use of Mackie’s paper “Self-Refutation—A Formal Analysis”, it concludes with some suggestions concerning what is at stake in the debate between Prior and Berkeley and in structurally similar debates such as whether to accept the Barcan formula.

Bob Hale’s distinguished record of research places him among the most important and influential contemporary analytic metaphysicians. In his deep, wide ranging, yet highly readable book Necessary Beings, Hale draws upon, but substantially integrates and extends, a good deal his past research to produce a sustained and richly textured essay on — as promised in the subtitle — ontology, modality, and the relations between them. I’ve set myself two tasks in this review: first, to provide a reasonably thorough (if not (...) exactly comprehensive) overview of the structure and content of Hale’s book and, second, to a limited extent, to engage Hale’s book philosophically. I approach these tasks more or less sequentially: Parts I and 2 of the review are primarily expository; in Part 3 I adopt a somewhat more critical stance and raise several issues concerning one of the central elements of Hale’s account, his essentialist theory of modality. (shrink)

Can there be grounding without necessitation? Can a fact obtain wholly in virtue of metaphysically more fundamental facts, even though there are possible worlds at which the latter facts obtain but not the former? It is an orthodoxy in recent literature about the nature of grounding, and in first-order philosophical disputes about what grounds what, that the answer is no. I will argue that the correct answer is yes. I present two novel arguments against grounding necessitarianism, and show that grounding (...) contingentism is fully compatible with the various explanatory roles that grounding is widely thought to play. (shrink)

Se ha destacado recientemente que la Fórmula de Barcan y la Conversa de la Fórmula de Barcan para lógica modal cuantificacional de orden superior parecen válidas. Si se interpreta que los cuantificadores tienen como rango propiedades, la validez de y de orden superior parece implicar la existencia de universales trascendentes, esto es, universales que no requieren estar instanciados para existir en un mundo posible. Este trabajo discute esta línea de argumentación. En primer lugar, se sostiene que la semántica en la (...) que los resultados de validez se siguen no requiere que las ‘intensiones’ asignadas a las variables de orden superior estén instanciadas en un mundo posible para que la intensión exista ahí. El defensor de universales inmanentes objetaría esta suposición. En una semántica modificada, más neutral, y de orden superior ya no son válidas. En segundo lugar, se sostiene que, incluso si se concediese la validez de y de orden superior, no se obtendrían resultados metafísicos sustantivos, pues diferentes formas de nominalismo y diferentes teorías de tropos no tendrían dificultades en aceptar y de orden superior. (shrink)

According to one tradition in the philosophy of language and mind, the content of a psychological attitude can be characterized by a set of possibilities. On the classic version of this account, advocated by Hintikka (1962) and Stalnaker (1984) among others, the possibilities in question are possible worlds, ways the universe might be. Lewis (1979, 1983a) proposed an alternative to this account, according to which the possibilities in question are possible individuals or centered worlds, ways an individual might be. The (...) motivation for the centered worlds theory has primarily to do with self-locating – or de se – attitudes. The focus of this paper is on the less-discussed question of how other-locating – or de re – attitudes ought to be treated within this framework. Most advocates of what we might call the modal approach to attitudes, Stalnaker and Lewis included, offer some kind of descriptivist solution to the well-known problems that other-locating attitudes raise. There are intramural differences between Stalnaker, Lewis, and other modal theorists (e.g. two-dimensionalists) on a number of issues: on the precise nature of the descriptivism involved, how attitude content relates to the asserted content of the sentences we utter, and on the proper semantic treatment of attitude reports. I pass over these differences to focus on a problem common to these various approaches: all face a problem when it comes to characterizing the contents of counterfactual attitudes like imagining, dreaming, and wishing. (shrink)

The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as ∃x t=x; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been noted that in order (...) to specify the truth conditions of certain sentences involving constants or variables that don’t denote, one has to apparently quantify over things that are not identical to anything. In this paper I defend a contingentist, non-Meinongian metaphysics within a positive free logic. I argue that although certain names and free variables do not actually refer to anything, in each case there might have been something they actually refer to, allowing one to interpret the contingentist claims without quantifying over mere possibilia. (shrink)

There is a long-standing disagreement among Branching-Time theorists. Even though they all believe that the branching representation accurately grasps the idea that the future, contrary to the past, is open, they argue whether this representation is compatible with the claim that one among many possible futures is distinguished—the single future that will come to be. This disagreement is paralleled in an argument about the bivalence of future contingents. The single, privileged future is often called the Thin Red Line. I reconstruct (...) the history of the arguments for and against this idea. Then, I propose my own version of the Thin Red Line theory which is immune to the major objections found in the literature. I argue that the semantic disagreement is grounded in distinct metaphysical presuppositions. My solution is expressed in a conceptual framework proposed by John MacFarlane, who distinguishes semantics from postsemantics. I extend his distinction and introduce a new notion of presemantics to elucidate my idea. (shrink)

The Barcan formula (BF) is commonly paraphrased as the schematic conditional that if it is possible that there be a phi then something or other is possibly a phi. It is validated by the most straightforward systems of quantified modal logic. It is also widely considered to pose a threat to the commonsensical metaphysical view that there are no non-actual (or ‘merely possible’) things. I show how BF can be cleared of such a charge by construing it as a bridge (...) principle connecting modality de dicto and modality de re while retaining a Russellian robust sense of reality in modal matters. (shrink)

Over the past few years, the tree model of time has been widely employed to deal with issues concerning the semantics of tensed discourse. The thought that has motivated its adoption is that the most plausible way to make sense of indeterminism is to conceive of future possibilities as branches that depart from a common trunk, constituted by the past and the present. However, the thought still needs to be further articulated and defended, and several important questions remain open, such (...) as the question of how actuality can be understood and formally represented in a branching framework. The present volume is intended to be a 360 degree reflection on the tree model. The contributions is gathers concern the model and its alternatives, both from a semantic and from a metaphysical point of view. ​. (shrink)

I take up a question raised by David Kaplan at the very end of his 1990 paper "Words": Is it possible for a name that in fact names a given individual to have named a different individual? I argue for a negative answer to Kaplan's question via the essentialist claims that, first, it is of the nature of a referring token of a name to be produced by a particular referential intention, and, second, that it is of the nature of (...) a referential intention to specify the particular thing it specifies. (shrink)

A‐theorists of time postulate a deep distinction between the present, past and future. Settling on an appropriate logic for such a view is no easy matter. This Philosophy Compass article describes one of the most vexing formal problems facing A‐theorists. It is commonly thought that A‐theories can only be formally expressed in a tense logic: a logic with operators like P and F . And it seems natural to think that we live in a world where objects come to exist (...) and cease to exist as time passes. Indeed, this is typically a key component of the most prominent kind of A‐theory, presentism. But the temporary existence assumption cannot be upheld in any tense logic with a standard quantification theory. I will explain the problem and outline the philosophical and logical considerations that generate it. I will then consider two possible solutions to the problem – one that targets our logic of quantification and one that targets our assumptions about change. I survey the costs of each solution. (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.

Presentists face a challenge from truthmaker theory: if you hold both that the only existing objects are presently existing and that truth supervenes on being, then you will be hard pressed to identify some existent on which a given true but traceless claim about the past supervenes. One reconciliation strategy, advocated by Cameron (2011), is to appeal to distributional properties so to serve as presently existing truthmakers for past truths. I argue that a presentist ought to deny that distributional properties (...) can serve as truthmakers. (shrink)

According to Essentialism, an object’s properties divide into those that are essential and those that are accidental. While being human is commonly thought to be essential to Socrates, being a philosopher plausibly is not. We can motivate the distinction by appealing—as we just did—to examples. However, it is not obvious how best to characterize the notion of essential property, nor is it easy to give conclusive arguments for the essentiality of a given property. In this paper, I elaborate on these (...) issues and explore the way in which essential properties behave in relation to other related properties, like sufficient-for-existence properties and individual essences. (shrink)

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)

Necessitism is the view that necessarily everything is necessarily something; contingentism is the negation of necessitism. The dispute between them is reminiscent of, but clearer than, the more familiar one between possibilism and actualism. A mapping often used to ‘translate’ actualist discourse into possibilist discourse is adapted to map every sentence of a first-order modal language to a sentence the contingentist (but not the necessitist) may regard as equivalent to it but which is neutral in the dispute. This mapping enables (...) the necessitist to extract a ‘cash value’ from what the contingentist says. Similarly, a mapping often used to ‘translate’ possibilist discourse into actualist discourse is adapted to map every sentence of the language to a sentence the necessitist (but not the contingentist) may regard as equivalent to it but which is neutral in the dispute. This mapping enables the contingentist to extract a ‘cash value’ from what the necessitist says. Neither mapping is a translation in the usual sense, since necessitists and contingentists use the same language with the same meanings. The former mapping is extended to a second-order modal language under a plural interpretation of the second-order variables. It is proved that the latter mapping cannot be. Thus although the necessitist can extract a ‘cash value’ from what the contingentist says in the second-order language, the contingentist cannot extract a ‘cash value’ from some of what the necessitist says, even when it raises significant questions. This poses contingentism a serious challenge. (shrink)

David Lewis proposed to deal with the semantics of sentences that state what is possible for an individual in terms of possible individuals that are in ways the first individual might have been, so called counterparts of the individual. In this book, I defend counterpart semantics as an approach to the semantics of modality and natural language semantics in particular. Counterpart semantics has a rival, the standard Kripkean semantics that deals with the same sentences in terms of an accessibility relation (...) between possible worlds. While counterpart semantics appears to be more flexible and carries less metaphysical presuppositions (it does not presuppose that I myself exist in various possible worlds, e.g.), Kripkean semantics has some advantages of its own. Most importantly, it incorporates the core assumptions of what may be called standard possible-worlds semantics; i.e. the core assumptions of the most successful framework within linguistic semantics. Counterpart semantics, on the other hand, does not conform to these assumptions, or so I will argue. In this book I opt for a synthesis of these two approaches that allows to combine their advantages. In Chap.1 I introduce the basic idea of counterpart semantics. I defend counterparts against the charge, made by Kripke, that counterparts are irrelevant for the analysis of modality. In Chap. 2 I present the classical version of counterpart semantics, i.e. David Lewis's translation of the language of quantified modal logic into counterpart theory. I discuss some well-known problems and opt for a revision of that translation that is able to solve the problems. Lewis's translation indirectly defines semantical values for expressions of quantified modal logic. In Chap.3 I evaluate counterpart semantics with respect to basic features of possible-worlds semantics. I conclude that the semantical values indirectly assigned to sentences by Lewis's translation are not sets of possible worlds, and that they do not meet certain intuitive demands on notions of meaning and content. (The revisions proposed in Chap.2 do not change this.) In Chap.4 I discuss various versions of a combination of counterpart semantics with Kripkean semantics found in the literature. But I conclude that here, the benefits of the latter are achieved by forfeiting the advantages of the former. Chap.5 finally contains my own proposal how to combine the two approaches in a more satisfactory way. The core semantical notion is truth according to a maximal complete representation, where representations now play the role of worlds. It is an important feature of the counterpart relation that it is qualitative, i.e. a relation in which things stand in virtue how they are. In Chap.1 I point out why it is qualitative, and why it ought to be. In Chap.6 I show how to make the notion of a qualitative property or relation precise. Finally, in Chap.7 I show how to extend this and related notions to predicates and propositions. For counterpart semantics to work at all we have to assume that everything that can be said at all can in principle be expressed in a language with qualitative predicates only (and perhaps, additionally, names, treated directly referentially). In Chap.7 I show how this assumption allows to maintain that the representations of our semantics deserve their name. (shrink)

The paper presents a dilemma for both epistemic and non-epistemic versions of conceivability-based accounts of modal knowledge. On the one horn, non-epistemic accounts do not elucidate the essentialist knowledge they would be committed to. On the other, epistemic accounts do not elucidate everyday life de re modal knowledge. In neither case, therefore, do conceivability accounts elucidate de re modal knowledge.

A presentation of the Lewis-Sider argument from vagueness for unrestricted composition and possible responses.

We outline a neo-Meinongian framework labeled as Modal Meinongian Metaphysics (MMM) to account for the ontology and semantics of fictional discourse. Several competing accounts of fictional objects are originated by the fact that our talking of them mirrors incoherent intuitions: mainstream theories of fiction privilege some such intuitions, but are forced to account for others via complicated paraphrases of the relevant sentences. An ideal theory should resort to as few paraphrases as possible. In Sect. 1, we make this explicit via (...) two methodological principles, called the Minimal Revision and the Acceptability Constraint. In Sect. 2, we introduce the standard distinction between internal and external fictional discourse. In Sects. 3–5, we discuss the approaches of (traditional) Meinongianism, Fictionalism, and Realism—and their main troubles. In Sect. 6 we propose our MMM approach. This is based upon (1) a modal semantics including impossible worlds (Subsect. 6.1); (2) a qualified Comprehension Principle for objects (Subsect. 6.2); (3) a notion of existence-entailment for properties (Subsect. 6.3). In Sect. 7 we present a formal semantics for MMM based upon a representation operator. And in Sect. 8 we have a look at how MMM solves the problems of the three aforementioned theories. (shrink)

Consider the kinds of macroscopic concrete objects that common sense and the sciences allege to exist: tables, raindrops, tectonic plates, galaxies, and the rest. Are there any such things? Opinions differ. Ontological liberals say they do; ontological radicals say they don't. Liberalism seems favored by its plausible acquiescence to the dictates of common sense abetted by science; radicalism by its ontological parsimony. Priority theorists claim we can have the virtues of both views. They hold that tables, raindrops, etc., exist, but (...) they aren't fundamental. The ontological liberal's ontology provides the correct inventory of existent individuals. The ontological radical's more restricted ontology provides the correct inventory of fundamental individuals. The priority theorist claims that the derivative individuals are "no addition in being" to the fundamental ones, so we can have our cake and eat it too. It would be nice if priority theorists were right. In this paper I argue, with regret, that they are not. One upshot is that the sort of explanations which underwrite the priority theorist's distinction between fundamental and derivative individuals do not mitigate our ontological commitments. Another is that we still have to choose between the charms of liberalism and radicalism. (shrink)

This paper investigates the form a modal realist analysis of possibility and necessity should take. It concludes that according to the best version of modal realism, the notion of a world plays no role in the analysis of modal claims. All contingent claims contain some de re element; the effect of modal operators on these elements is described by a counterpart theory which takes the same form whether the de re reference is to a world or to something else. This (...) fully general counterpart theory can validate orthodox modal logic, including the logic of 'actually'. (shrink)

This note is to show that a well-known point about David Lewis’s (1986) modal realism applies to Timothy Williamson’s (1998; 2002) theory of necessary existents as well.1 Each theory, together with certain “recombination” principles, generates individuals too numerous to form a set. The simplest version of the argument comes from Daniel Nolan (1996).2 Assume the following recombination principle: for each cardinal number, ν, it’s possible that there exist ν nonsets. Then given Lewis’s modal realism it follows that there can be (...) no set of all (that is, Absolutely All) the nonsets. For suppose for reductio that there were such a set, A; let ν be A’s cardinality; and let µ be any cardinal number larger than ν. By the recombination principle, it’s possible that there exist µ nonsets; by modal realism, there exists a possible world containing, as parts, µ nonsets; each of these nonsets is a member of A. (shrink)

David Lewis’s counterpart-theoretic semantics for quantified modal logic is motivated originally by worries about identifying objects across possible worlds; the counterpart relation is grounded more cautiously on comparative similarity. The possibility of contingent identity is an unsought -- and in some eyes, unwelcome -- consequence of this approach. In this paper I motivate a Kripkean counterpart theory by way of defending the prior, pre-theoretical, coherence of contingent directness. Contingent identity follows for free. The theory is Kripkean in that the counterpart (...) relation is in a sense stipulated rather than grounded on similarity, and is such that no object has more than one counterpart at a world. This avoids a number of objections Fara and Williamson have recently levelled against counterpart theory generally; their other objections are addressed by enriching the theory with special quantifiers and actuality operators. (shrink)

Are there nonexistent objects, i.e., objects that do not exist? Some examples often cited are: Zeus, Pegasus, Sherlock Holmes, Vulcan (the hypothetical planet postulated by the 19th century astronomer Le Verrier), the perpetual motion machine, the golden mountain, the fountain of youth, the round square, etc. Some important philosophers have thought that the very concept of a nonexistent object is contradictory (Hume) or logically ill-formed (Kant, Frege), while others (Leibniz, Meinong, the Russell of Principles of Mathematics) have embraced it wholeheartedly. (...) This entry is an examination of the many questions which arise in connection with the view that there are nonexistent objects. The following are particularly salient: What reasons are there (if any) for thinking that there are nonexistent objects? If there are nonexistent objects, then what kind of objects are they? How can they be characterized? Is it possible to provide a consistent theory of nonexistent objects? What is the explanatory force of a consistent theory of nonexistent objects (if such a thing is possible)? (shrink)

To understand the thesis of actualism, consider the following example. Imagine a race of beings — call them ‘Aliens’ — that is very different from any life-form that exists anywhere in the universe; different enough, in fact, that no actually existing thing could have been an Alien, any more than a given gorilla could have been a fruitfly. Now, even though there are no Aliens, it seems intuitively the case that there could have been such things. After all, life might (...) have evolved very differently than the way it did in fact. So in virtue of what is it true that there could have been Aliens when in fact there are none, and when, moreover, nothing that exists in fact could have been an Alien? So-called "possibilists" offer the following answer: ‘It is possible that there are Aliens’ is true because there are in fact individuals that could have been Aliens. At first blush, this might appear directly to contradict the premise that no existing thing could possibly have been an Alien. The possibilist's thesis, however, is that existence, or actuality, encompasses only a subset of the things that, in the broadest sense, are. So for the possibilist, ‘It is possible that there are Aliens’ is true simply in virtue of the fact that there are possible-but-nonactual Aliens, i.e., things that could have existed (but do not) and which would have been Aliens if they had. Actualists reject this answer; they deny that there are any nonactual individuals. Thus, actualism is the philosophical position that everything there is — everything that can in any sense be said to be — exists, or is actual. (shrink)

The full-text of this article is not currently available in ORA, but the original publication is available at springerlink.com . Citation: Williamson, T. . 'The necessary framework of objects', Topoi 19, 201-208. N.B. Tim Williamson is now based at the Faculty of Philosophy, University of Oxford.

Many philosophers, following David Lewis, believe that we should look to counterpart theory, not quantified modal logic, as a means of understanding modal discourse. We argue that this is a mistake. Significant parts of modal discourse involve either implicit or explicit reference to what is actually the case, raising the question of how talk about actuality is to be represented counterpart-theoretically. By considering possible modifications of Lewis's counterpart theory, including actual modifications due to Graeme Forbes and Murali Ramachandran, we argue (...) that no coherent version of counterpart theory can provide a plausible representation of talk about actuality, and so, we conclude, counterpart theory should be rejected. (shrink)

Actualists routinely characterize their view by means of the slogan, “Everything is actual.” They say that there aren’t any things that exist but do not actually exist—there aren’t any “mere possibilia.” If there are any things that deserve the label ‘possible world’, they are just actually existing entities of some kind—maximally consistent sets of sentences, or maximal uninstantiated properties, or maximal possible states of affairs, or something along those lines. Possibilists, in contrast, do think that there are mere possibilia, that (...) there are things that are not actual. They think that more exists than what actually exists. All I have done so far, though, is rephrase the slogan in various ways. To say that everything is actual is precisely to say that there are no things that do not actually exist, which is precisely to say that there are no mere possibilia, and which is also precisely to say that we cannot sep- arately quantify over what exists and what is actual. These claims all amount to the same thing. But what is that, exactly? What on earth does it mean to say that everything is actual, that there are no mere possibilia, and so on? What does the actualist slogan really come to? I think the literature is far from clear on this point, and that people work themselves into unnecessary muddles because of it. Indeed, certain confusions that I shall discuss in the first half of this article seem to be on the rise. It is high time to lay out the issues and the choice points as clearly as possible. There are two primary choices to be made; there are two axes along which versions of actualism can vary. One choice has to do with how to treat claims about things that merely could exist. The other choice has to do with the modal status of the view and of how we should think about the “actual” in actualism. I make no claim that the positions I will eventually endorse are star- tlingly new. I think that most people will agree with the decisions I make at both choice points and will in fact find some bits of this essay obvious. But not everyone agrees with my decisions, and it has been my experience that people differ remarkably about which bits they find obvious—a fact I find rather telling. My goal, then, is to show that the two axes are there and to clarify the consequences of the choices. (shrink)

Some recently-proposed counterexamples to the traditional definition of essential property do not require a separate logic of essence. Instead, the examples can be analysed in terms of the logic and theory of abstract objects. This theory distinguishes between abstract and ordinary objects, and provides a general analysis of the essential properties of both kinds of object. The claim ‘x has F necessarily’ becomes ambiguous in the case of abstract objects, and in the case of ordinary objects there are various ways (...) to make the definition of ‘F is essential to x’ more fine-grained. Consequently, the traditional definition of essential property for abstract objects in terms of modal notions is not correct, and for ordinary objects the relationship between essential properties and modality, once properly understood, addresses the counterexample. (shrink)

Karen Bennett has recently argued that the views articulated by Linsky and Zalta (Philos Perspect 8:431–458, 1994) and (Philos Stud 84:283–294, 1996) and Plantinga (The nature of necessity, 1974) are not consistent with the thesis of actualism, according to which everything is actual. We present and critique her arguments. We first investigate the conceptual framework she develops to interpret the target theories. As part of this effort, we question her definition of ‘proxy actualism’. We then discuss her main arguments that (...) the theories carry a commitment to actual entities that do not exist. We end by considering and addressing a worry that might have been the driving force behind Bennett’s claim that Linsky and Zalta’s view is not fully actualistic. (shrink)

In this paper, we investigate (1) what can be salvaged from the original project of "logicism" and (2) what is the best that can be done if we lower our sights a bit. Logicism is the view that "mathematics is reducible to logic alone", and there are a variety of reasons why it was a non-starter. We consider the various ways of weakening this claim so as to produce a "neologicism". Three ways are discussed: (1) expand the conception of logic (...) used in the reduction, (2) allow the addition of analytic-sounding principles to logic so that the reduction is not to "logic alone" but to logic and truths knowable a priori, and (3) revise the conception of "reducible". We show how the current versions of neologicism fit into this classification scheme, and then focus on a kind of neologicism which we take to have the most potential for achieving the epistemological goals of the original logicist project. We argue that that the "weaker" the form of neologicism, the more likely it is to be a new form of logicism, and show how our preferred system, though mathematically weak, is metaphysically and epistemogically strong, and can "reduce" arbitrary mathematical theories to logic and analytic truths, if given a legitimate new sense of "reduction". (shrink)

It is sometimes said that no living philosopher is a genuine modal realist. This is no doubt an exaggeration. But at least this much is true: while we all partake of possible world talk when philosophizing, most of us regard this talk as incurring no commitment to a plurality of concrete worlds.

In this paper, the author develops a theory of concepts and shows that it captures many of the ideas about concepts that Leibniz expressed in his work. Concepts are first analyzed in terms of a precise background theory of abstract objects, and once concept summation and concept containment are defined, the axioms and theorems of Leibniz's calculus of concepts (in his logical papers) are derived. This analysis of concepts is then seamlessly connected with Leibniz's modal metaphysics of complete individual concepts. (...) The fundamental theorem of Leibniz's modal metaphysics of concepts is proved, namely, whenever an object x has F contingently, then (i) the individual concept of x contains the concept F and (ii) there is a (counterpart) complete individual concept y which doesn't contain the concept F and which `appears' at some other possible world. Finally, the author shows how the concept containment theory of truth can be made precise and made consistent with a modern conception of truth. (shrink)

In this paper I present a formalization of the theory of ideal concepts applied to the concept of God. It is done within a version of the Simplest Quantified Modal Logic (SQML) and attempts to solve three meta-problems related to the concept of God: the unicity of extension problem, the homogeneity/heterogeneity problem and the problem of conceptual unity.

One important challenge for contingentists is that they seem to be unable to account for the meaning of some apparently meaningful modal discourse that is perfectly intelligible for necessitists. This worry is particularly pressing for higher-order contingentists, contingentists who hold that it is not only contingent which objects there are, but also contingent which semantic values there are for higher-order variables to quantify over. Objections against higher-order contingentism along these lines have been presented in Williamson (Mind 119(475):657–748, 2010; Modal logic (...) as metaphysics, Oxford University Press, 2013, ch. 7), and Fritz and Goodman (Mind 126(504):1063–1108, 2017). This paper presents a way for contingentists to respond to these challenges. The upshot is that the contingentist can account for the meaningfulness of the problematic modal claims by pretending necessitism to be true, but in some cases it turns out to be indeterminate whether they are true. I defend this strategy against the objections against pretence-strategies presented in Fritz and Goodman (Mind 126(504):1063–1108, 2017, §4). Furthermore, I defend the plausibility of the resulting indeterminacy from the contingentist’s perspective. (shrink)

Time and modality show remarkable similarities. Each of the most discussed theories in philosophy of time finds an analogous counterpart in modal metaphysics, suggesting that the parallel between the two notions is metaphysically deep. This chapter offers a brief overview of their analogies. Section 1 addresses the analogy between presentism and actualism. Section 2 explores the analogy between non-presentist theories and possibilism. Section 3 discusses the analogy between temporal and modal persistence.

Philosophers distinguish between having a property essentially and having it accidentally. The way the distinction has been drawn suggests that it is modal in character, and so that it can be captured in terms of necessity, or cognate notions. The present chapter takes the suggestion at face value by considering a number of modal characterizations of the essential/accidental distinction that have been articulated and discussed since the early 20th century, as well as some of the challenges that they face.