It is argued that a number of important, and seemingly disparate, types of representation are species of a single relation, here called structural representation, that can be described in detail and studied in a way that is of considerable philosophical interest. A structural representation depends on the existence of a common structure between a representation and that which it represents, and it is important because it allows us to reason directly about the representation in order to draw conclusions about the (...) phenomenon that it depicts. The present goal is to give a general and precise account of structural representation, then to use that account to illuminate several problems of current philosophical interest — including some that do not initially seem to involve representation at all. In particular, it is argued that ontological reductions (like that of the natural numbers to sets), compositional accounts of semantics, several important sorts of mental representation, and (perhaps) possible worlds semantics for intensional logics are all species of structural representation and are fruitfully studied in the framework developed here. (shrink)

We need to understand the impossible. Francesco Berto and Mark Jago start by considering what the concepts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition have in common. They are all concepts which divide the world up more finely than logic does. Logically equivalent sentences may carry different meanings and information and may differ in how they're believed. Fictions can be inconsistent yet meaningful. We can suppose impossible things without collapsing into total incoherence. Yet for the leading philosophical (...) theories of meaning, these phenomena are an unfathomable mystery. To understand these concepts, we need a metaphysical, logical, and conceptual grasp of situations that could not possibly exist: Impossible Worlds. This book discusses the metaphysics of impossible worlds and applies the concept to a range of central topics and open issues in logic, semantics, and philosophy. It considers problems in the logic of knowledge, the meaning of alternative logics, models of imagination and mental simulation, the theory of information, truth in fiction, the meaning of conditional statements, and reasoning about the impossible. In all these cases, impossible worlds have an essential role to play. (shrink)

The simplest quantified modal logic combines classical quantification theory with the propositional modal logic K. The models of simple QML relativize predication to possible worlds and treat the quantifier as ranging over a single fixed domain of objects. But this simple QML has features that are objectionable to actualists. By contrast, Kripke-models, with their varying domains and restricted quantifiers, seem to eliminate these features. But in fact, Kripke-models also have features to which actualists object. Though these philosophers have introduced variations (...) on Kripke-models to eliminate their objectionable features, the most well-known variations all have difficulties of their own. The present authors reexamine simple QML and discover that, in addition to having a possibilist interpretation, it has an actualist interpretation as well. By introducing a new sort of existing abstract entity, the contingently nonconcrete, they show that the seeming drawbacks of the simplest QML are not drawbacks at all. Thus, simple QML is independent of certain metaphysical questions. (shrink)

This paper defends a theory of fictional truth. According to this theory, there is a fact of the matter concerning the number of hairs on Sherlock Holmes' head, and likewise for any other meaningful question one could ask about what's true in a work of fiction. We argue that a theory of this form is needed to account for the patterns in our judgments about attitude reports that embed fictional claims. We contrast our view with one of the dominant approaches (...) to fictional truth, which originates with David Lewis. Along the way we explore the relationship between fiction, counterfactuals, and vagueness. (shrink)

This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the (...) predicate logic of the system. The propositional logic of HYPE is shown to contain first-degree entailment, to have the Finite Model Property, to be decidable, to have the Disjunction Property, and to extend intuitionistic propositional logic conservatively when intuitionistic negation is defined appropriately by HYPE’s logical connectives. Furthermore, HYPE’s first-order logic is a conservative extension of intuitionistic logic with the Constant Domain Axiom, when intuitionistic negation is again defined appropriately. The system allows for simple model constructions and intuitive Euler-Venn-like diagrams, and its logical structure matches structures well-known from ordinary mathematics, such as from optimization theory, combinatorics, and graph theory. HYPE may also be used as a general logical framework in which different systems of logic can be studied, compared, and combined. In particular, HYPE is found to relate in interesting ways to classical logic and various systems of relevance and paraconsistent logic, many-valued logic, and truthmaker semantics. On the philosophical side, if used as a logic for theories of type-free truth, HYPE is shown to address semantic paradoxes such as the Liar Paradox by extending non-classical fixed-point interpretations of truth by a conditional as well-behaved as that of intuitionistic logic. Finally, HYPE may be used as a background system for modal operators that create hyperintensional contexts, though the details of this application need to be left to follow-up work. (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)

Higher-order logic, with its type-theoretic apparatus known as the simple theory of types (STT), has increasingly come to be employed in theorizing about properties, relations, and states of affairs—or ‘intensional entities’ for short. This paper argues against this employment of STT and offers an alternative: ordinal type theory (OTT). Very roughly, STT and OTT can be regarded as complementary simplifications of the ‘ramified theory of types’ outlined in the Introduction to Principia Mathematica (on a realist reading). While STT, understood as (...) a theory of intensional entities, retains the Fregean division of properties and relations into a multiplicity of categories according to their adicities and ‘input types’ and discards the division of intensional entities into different ‘orders’, OTT takes the opposite approach: it retains the hierarchy of orders (though with some modifications) and discards the categorisation of properties and relations according to their adicities and input types. In contrast to STT, this latter approach avoids intensional counterparts of the Epimenides and related paradoxes. Fundamental intensional entities lie at the base of the proposed hierarchy and are also given a prominent part to play in the individuation of non-fundamental intensional entities. (shrink)

Peter Ludlow presents the first book on the philosophy of generative linguistics, including both Chomsky's government and binding theory and his minimalist ...

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

Since 2002 we have been testing and refining a methodology for ontology development that is now being used by multiple groups of researchers in different life science domains. Gary Merrill, in a recent paper in this journal, describes some of the reasons why this methodology has been found attractive by researchers in the biological and biomedical sciences. At the same time he assails the methodology on philosophical grounds, focusing specifically on our recommendation that ontologies developed for scientific purposes should be (...) constructed in such a way that their terms are seen as referring to what we call universals or types in reality. As we show, Merrill’s critique is of little relevance to the success of our realist project, since it not only reveals no actual errors in our work but also criticizes views on universals that we do not in fact hold. However, it nonetheless provides us with a valuable opportunity to clarify the realist methodology, and to show how some of its principles are being applied, especially within the framework of the OBO (Open Biomedical Ontologies) Foundry initiative. (shrink)

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)

This is the most comprehensive book ever published on philosophical methodology. A team of thirty-eight of the world's leading philosophers present original essays on various aspects of how philosophy should be and is done. The first part is devoted to broad traditions and approaches to philosophical methodology. The entries in the second part address topics in philosophical methodology, such as intuitions, conceptual analysis, and transcendental arguments. The third part of the book is devoted to essays about the interconnections between philosophy (...) and neighbouring fields, including those of mathematics, psychology, literature and film, and neuroscience. (shrink)

Natural languages generally distinguishes among different existence predicates for different types of entities, such as English 'exist', 'occur', and 'obtain'. The paper gives an in-depth discussion and analysis of a range of existence predicates in natural language within the general project of descriptive metaphysics, or more specifically ‘natural language ontology’.

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)

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)

In "Actualism or Possibilism?" (Philosophical Studies, 84 (2-3), December 1996), James Tomberlin develops two challenges for actualism. The challenges are to account for the truth of certain sentences without appealing to merely possible objects. After canvassing the main actualist attempts to account for these phenomena, he then criticizes the new conception of actualism that we described in our paper "In Defense of the Simplest Quantified Modal Logic" (Philosophical Perspectives 8: Philosophy of Logic and Language, Atascadero, CA: Ridgeview, 1994). We respond (...) to Tomberlin's criticism by showing that we wouldn't analyze the problematic claim (e.g., "Ponce de Leon searched for the fountain of youth") in the way he suggests. (shrink)

According to the traditional bundle theory, particulars are bundles of compresent universals. I think we should reject the bundle theory for a variety of reasons. But I will argue for the thesis at the core of the bundle theory: that all the facts about particulars are grounded in facts about universals. I begin by showing how to meet the main objection to this thesis (which is also the main objection to the bundle theory): that it is inconsistent with the possibility (...) of distinct qualitative indiscernibles. Here, the key idea appeals to a non-standard theory of haecceities as non-well-founded properties of a certain sort. I will then defend this theory from a number of objections, and finally argue that we should accept it on the basis of considerations of parsimony about the fundamental. (shrink)

The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, (...) a trilattice of truth values – a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi. (shrink)

This article includes a basic overview of possible world semantics and a relatively comprehensive overview of three central philosophical conceptions of possible worlds: Concretism (represented chiefly by Lewis), Abstractionism (represented chiefly by Plantinga), and Combinatorialism (represented chiefly by Armstrong).

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 distinction between a type and its tokens is a useful metaphysical distinction. In §1 it is explained what it is, and what it is not. Its importance and wide applicability in linguistics, philosophy, science and everyday life are briefly surveyed in §2. Whether types are universals is discussed in §3. §4 discusses some other suggestions for what types are, both generally and specifically. Is a type the sets of its tokens? What exactly is a word, a symphony, a species? (...) §5 asks what a token is. §6 considers the relation between types and their tokens. Do the type and all its tokens share the same properties? Must all the tokens be alike in some or all respects? §7 explains some problems for the view that types exist, and some problems for the view that they don't. §8 elucidates a distinction often confused with the type-token distinction, that between a type (or token) and an occurrence of it. It also discusses some problems that occurrences might be thought to give rise to, and one way to resolve them. (shrink)

This paper is concerned with two concepts of qualitativeness that apply to intensional entities. I propose an account of pure qualitativeness that largely follows the traditional understanding established by Carnap, and try to shed light on its ontological presuppositions. On this account, an intensional entity is purely qualitative iff it does not ‘involve’ any particular. An alternative notion of qualitativeness—which I propose to refer to as a concept of strict qualitativeness—has recently been introduced by Chad Carmichael. However, Carmichael’s definition presupposes (...) a highly fine-grained conception of properties and relations. To eliminate this presupposition, I tentatively suggest a different definition that rests on a concept of perspicuous denotation. In the penultimate section, both concepts of qualitativeness are put to work in distinguishing between different ‘grades’ of qualitative discriminability. (shrink)

Rather infamously, Kit Fine provided a series of counter-examples which purport to show that the modalist program of analysing essence in terms of metaphysical necessity is fundamentally misguided. Several would-be modalists have since responded, attempting to save the position from this Finean Challenge. This paper evaluates and rejects a trio of such responses, from Della Rocca, Zalta, and Gorman. But I’m not here arguing for Fine’s conclusion – ultimately, this is a fight amongst friends, with Della Rocca, Zalta, Gorman, and (...) I all wanting to be modalists, but disagreeing on the details. As such, while my primary aim is to show what’s wrong with this trio, the secondary aim is demonstrating how what’s right about them in fact pushes one towards my own sparse modalist account. So while the primary conclusion of this paper is negative, the secondary, positive, conclusion is that modalists shouldn’t give up hope – plausible responses to Fine are still out there. (shrink)

The standard view of truth-conditional semantics is that it is world-involving in the sense that a theory that specifies truth conditions eo ipso is a theory that specifies the way the world must be if the target sentences are to be true. It would appear to follow that the semantic properties of expressions, such as nominals, specify the very worldly objects that make true or false the sentences that host the nominals. Chomsky and others have raised a fundamental complaint against (...) this thought: perfectly quotidian nominals, such as London or book, may occur copredicatively as a single argument of categorically mismatched predicates, which prima facie preclude a coherent uniform construal of the nominal argument. The argument has hitherto been presented via examples that challenge the standard view. My aim here is to present the argument explicitly, defend it against some likely counterclaims, and resolve what might appear to be a decisive consideration against the conclusion of the argument, viz., if nominals as copredicatively occurring do not contribute uniform worldly entities, then how can the copredicative constructions be counted as true? (shrink)

The foregoing set of theorems forms an effective foundation for the theory of situations and worlds. All twenty-five theorems seem to be basic, reasonable principles that structure the domains of properties, relations, states of affairs, situations, and worlds in true and philosophically interesting ways. They resolve 15 of the 19 choice points defined in Barwise (1989) (see Notes 22, 27, 31, 32, 35, 36, 39, 43, and 45). Moreover, important axioms and principles stipulated by situation theorists are derived (see Notes (...) 33, 37, and 38). This is convincing evidence that the foregoing constitutes a theory of situations. Note that worlds are just a special kind of situation, and that the basic theorems of world theory, which were derived in previous work, can still be derived in this situation-theoretic setting. So there seems to be no fundamental incompatibility between situations and worlds — they may peacably coexist in the foundations of metaphysics. The theory may therefore reconcile two research programs that appeared to be heading off in different directions. And we must remind the reader that the general metaphysical principles underlying our theory were not designed with the application to situation theory in mind. This suggests that the general theory and the underlying distinction have explanatory power, for they seem to relate and systematize apparently unrelated phenomena. (shrink)

Presenting the first comprehensive, in-depth study of hyperintensionality, this book equips readers with the basic tools needed to appreciate some of current and future debates in the philosophy of language, semantics, and metaphysics. After introducing and explaining the major approaches to hyperintensionality found in the literature, the book tackles its systematic connections to normativity and offers some contributions to the current debates. The book offers undergraduate and graduate students an essential introduction to the topic, while also helping professionals in related (...) fields get up to speed on open research-level problems. (shrink)

In this paper, we compare two theories, modal Meinongianism and object theory, with respect to several issues that have been discussed recently in the literature. In particular, we raise some objections for MM, undermine some of the objections that its defenders raise for OT, and we point out some virtues of the latter with respect to the former.

This paper deals with the identity problems of fictional objects, focusing on Anthony Everett's and Stuart Brock's leading criticisms against fictional creationism, the view that fictional objects are abstract objects created by our acts involving literary practices. My primary aim is to argue that creationism based on referentialism has enough resources to individuate fictional objects and hence can address the alleged identity problems: every alleged problematic case regarding the identity of fictional objects is well explained in terms of the notions (...) of authorial intention, gappy proposition, inadvertent creation, and reference shift. (shrink)

Philosophy Compass, Volume 1. Oxford: Blackwell, 2006.

This paper is about intentional identity, the phenomenon of intentional attitudes having a common focus. I present an argument against an approach to explaining intentional identity, defended by Nathan Salmon, Terence Parsons and others, that involves positing exotic objects. For example, those who adopt this sort of view say that when two astronomers had beliefs about Vulcan, their attitudes had a common focus because there is an exotic object that both of their beliefs were about. I argue that countenancing these (...) exotic objects does not help us explain intentional identity. (shrink)

What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on (...) Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem. (shrink)

The complement of intensional transitive verbs, like any nonreferential complement, can be replaced by a ‘special quantifier’ or ‘special pronoun’ such as 'something', 'the same thing', or 'what'. In this paper, I will defend the ‘Nominalization Theory’ of special quantifiers against a range of apparent counterexamples involving intensional transitive verbs.

According to a well-known argument, originally due to David Armstrong, powers theory is objectionable, as it leads to a ‘Meinongian’ ontology on which some entities are real but do not actually exist. I argue here that the right conclusion to draw from this argument has thus far not been identified and that doing so has significant implications for powers theory. Specifically, I argue that the key consequence of the argument is that it provides substantial grounds for trope powers theorists, but (...) not other powers theorists, to accept one version of the view that properties are powerful qualities. In particular, they have grounds to favour the view that powerful properties are properties with exclusively qualitative natures that ground modal facts. (shrink)

Identity is arguably one of the most fundamental concepts in metaphysics. There are several reasons why this is the case: Identity is presupposed in every conceptual system: without identity, it is unclear that any conceptual system can be formulated. Identity is required to characterize an individual: nothing can be an individual unless it has well-specified identity conditions. Identity cannot be defined: even in systems that allegedly have the resources to define identity. Identity is required for quantification: the intelligibility of quantification (...) presupposes the identity of the objects that are quantified over. These are only four considerations in support of identity's fundamental role. In this paper, I examine and defend them. I then examine a challenge that has been raised against identity's fundamentality: one from the metaphysics of physics—based on a significant interpretation of non-relativist quantum mechanics—according to which certain quantum particles lack identity conditions. After responding to this challenge, I consider the nature of the commitment to identity, and argue that it turns out to be very minimal. In fact, a very deflationary form of metaphysics can accommodate it. In arguing that identity is fundamental, one need not overstep the boundaries of even a very minimal empiricist metaphysics. Or so I argue. (shrink)

We investigate the form of mathematical structuralism that acknowledges the existence of structures and their distinctive structural elements. This form of structuralism has been subject to criticisms recently, and our view is that the problems raised are resolved by proper, mathematics-free theoretical foundations. Starting with an axiomatic theory of abstract objects, we identify a mathematical structure as an abstract object encoding the truths of a mathematical theory. From such foundations, we derive consequences that address the main questions and issues that (...) have arisen. Namely, elements of different structures are different. A structure and its elements ontologically depend on each other. There are no haecceities and each element of a structure must be discernible within the theory. These consequences are not developed piecemeal but rather follow from our definitions of basic structuralist concepts. (shrink)

In this paper we reply to arguments of Kroon (“Characterization and Existence in Modal Meinongianism”. Grazer Philosophische Studien 86, 23–34) to the effect that Modal Meinongianism cannot do justice to Meinongian claims such as that the golden mountain is golden, and that it does not exist.

This paper provides an analysis of the intrinsic/extrinsic distinction, as applied both to properties and to relations. In contrast to other accounts, the approach taken here locates the source of a property’s intrinsicality or extrinsicality in the manner in which that property is ‘logically constituted’, and thus – plausibly – in its nature or essence, rather than in e.g. its modal profile. Another respect in which the present proposal differs from many extant analyses lies in the fact that it does (...) not seek to analyse the ‘global’ distinction between intrinsic and extrinsic properties on the basis of the ‘local’ distinction between having a property intrinsically and having it extrinsically. Instead, the latter distinction is explicated on the basis of the former. (shrink)

Bare particularism is a constituent ontology according to which substances—concrete, particular objects like people, tables, and tomatoes—are complex entities constituted by their properties and their bare particulars. Yet, aside from this description, much about bare particularism is fundamentally unclear. In this paper, I attempt to clarify this muddle by elucidating the key metaphysical commitments underpinning any plausible formulation of the position. So the aim here is primarily catechismal rather than evangelical—I don’t intend to convert anyone to bare particularism, but, by (...) looking at a series of questions, to instead specify what, if one is a bare particularist, one is committed to. Along the way, I address three major objections: a classic objection about whether bare particulars have properties, a new objection raised by Bailey, and an understanding objection that questions some of the position’s resources. (shrink)

In this paper, the author derives the Dedekind-Peano axioms for number theory from a consistent and general metaphysical theory of abstract objects. The derivation makes no appeal to primitive mathematical notions, implicit definitions, or a principle of infinity. The theorems proved constitute an important subset of the numbered propositions found in Frege's *Grundgesetze*. The proofs of the theorems reconstruct Frege's derivations, with the exception of the claim that every number has a successor, which is derived from a modal axiom that (...) (philosophical) logicians implicitly accept. In the final section of the paper, there is a brief philosophical discussion of how the present theory relates to the work of other philosophers attempting to reconstruct Frege's conception of numbers and logical objects. (shrink)

This paper considers two issues raised by the claim that fictional characters are abstract artifacts. First, given that artifacts normally have functions, what is the function of a fictional character? Second, given that, in experiencing works of fictions, we usually treat fictional characters as concrete individuals, how can such a phenomenology fit with an ontology according to which fictional characters are abstract artifacts? I will indirectly address the second issue by directly addressing the first one. For this purpose, I will (...) rely on the notion of a mental file. I will argue that the function of fictional characters is the generation of mental files of a special kind. I will show that our experience of fictional characters as concrete individuals depends on the kind of mental files that are generated by fictional characters as abstract artifacts. I will conclude that an appreciator of a work of fiction can open two files about a certain fictional character; one about the character as an individual in the fictional world, and the other about the character as an abstract artifact in the actual world. In this sense, our relation to a fictional character is characterized by a duality of files or ‘twofileness’. (shrink)

The specification and implementation of computational artefacts occurs throughout the discipline of computer science. Consequently, unpacking its nature should constitute one of the core areas of the philosophy of computer science. This paper presents a conceptual analysis of the central role of specification in the discipline.

Beach's Gaelic Symphony is plausibly an abstract object that Beach created. The view that people create some abstract objects is called abstract creationism. There are abstract creationists about many kinds of objects, including musical works, fictional characters, arguments, words, internet memes, installation artworks, bitcoins, and restaurants. Alternative theories include materialism and Platonism. This paper discusses some of the most serious objections against abstract creationism. Arguably, these objections have ramifications for questions in metaphysics pertaining to the abstract/concrete distinction, time, causation, vague (...) existence, vague identity, and inadvertent creation. (shrink)

A paradox about sets of properties is presented. The paradox, which invokes an impredicatively defined property, is formalized in a free third-order logic with lambda-abstraction, through a classically proof-theoretically valid deduction of a contradiction from a single premise to the effect that every property has a unit set. Something like a model is offered to establish that the premise is, although classically inconsistent, nevertheless consistent, so that the paradox discredits the logic employed. A resolution through the ramified theory of types (...) is considered. Finally, a general scheme that generates a family of analogous paradoxes and a generally applicable resolution are proposed. (shrink)