Abstract Objects

This paper elaborates distinctions between a core and a periphery in the ontological and the conceptual domain associated with natural language. The ontological core-periphery distinction is essential for natural language ontology and is the basis for the central thesis of my 2013 book Abstract Objects and the Semantics of Natural Language, namely that natural language permits reference to abstract objects in its periphery, but not its core.

This paper attempts to develop an ethico-aesthetic framework for enriching one's life and ethical outlook. Drawing primarily from Nietzsche, Foucault, and Heidegger, an argument is made that Heidegger's understanding of this issue was mistaken. The ontological crisis of modernity is not the overt influence of mathematics as a worldview over poetics and more traditionally aesthetic approaches. It is the rampant mis-and over-application of abstraction within one's view of the world while denying the material realities of life as we live it. (...) This runaway abstractive worldview leads to the misapplication of mathematics and other sciences which in turn facilitate the dehumanization of life and those within it. When we try to solve the real problems of our material human lives through overly abstractive means, then we arrive at inauthentic arguments that fuel popular disdain for philosophy as irrelevant and nothing more than the purview of the elite. The goal is a recalibration of the argument toward addressing the denial of materiality within Modernism. (shrink)

This paper investigates the question of how to correctly capture the scope of singular thinking. The first part of the paper identifies a scope problem for the dominant view of singular thought maintaining that, in order for a thinker to have a singular thought about an object o, the thinker has to bear a special epistemic relation to o. The scope problem has it is that this view cannot make sense of the singularity of our thoughts about objects to which (...) we do not or cannot bear any special epistemic relation. The paper focuses on a specific instance of the scope problem by addressing the case of thoughts about the natural numbers. Various possible solutions to the scope problem within the dominant framework are assessed and rejected. The second part of the paper develops a new theory of singular thought which hinges on the contention that the constraints that need to be met in order to think singularly vary depending on the kind of object we are thinking about. This idea is developed in detail by discussing the difference between the somewhat standard case of thoughts about spatio-temporal medium-sized inanimate objects and the case of thoughts about the natural numbers. It is contended that this new Pluralist theory of singular thought can successfully solve the scope problem. (shrink)

This chapter develops a semantics for 'reifying terms' of the sort 'the proposition that S', 'the fact that S', 'the property of being P', 'the number eight', 'the concept horse', 'the truth value true', 'the kind humane being'. This semantics is developed within the broader perspective of the ontology of natural language involving abstract objects only at its periphery, not its core.

Frege famously held that numbers play the role of objects in our language and thought, and that this role is on display when we use sentences like "The number of Jupiter's moons is four". I argue that this role is an example of a general pattern that also encompasses persons, times, locations, reasons, causes, and ways of appearing or acting. These things are 'objects' simply in the sense that they are answers to questions: they are the sort of thing we (...) search for and specify during investigation or inquiry. I support this epistemological conception of objects by studying specificational sentences, a class of sentences which includes Frege's original example. I defend an analysis of such sentences as question-answer pairs, and show how to formally represent this analysis using game-theoretical semantics. (shrink)

Can we feel emotions about abstract objects, assuming that abstract objects exist? I argue that at least some emotions can have abstract objects as their intentional objects and discuss why this conclusion is not just trivially true. Through critical engagement with the work of Dacher Keltner and Jonathan Haidt, I devote special attention to awe, an emotion that is particularly well suited to show that some emotions can be about either concrete or abstract objects. In responding to a possible objection, (...) according to which we can only feel emotions about things that we take to matter to our flourishing, and thus cannot feel emotions about causally inefficacious abstract objects, I explore how abstract objects can be relevant to human flourishing and discuss someemotions other than awe that can be about abstract objects. I finish by explaining somereasons why my conclusion matters, including the fact that it presents a challenge to perceptual theories of emotion and causal theories of intentionality. (shrink)

One of the philosophical uses of Dedekind’s categoricity theorem for Peano Arithmetic is to provide support for semantic realism. To this end, the logical framework in which the proof of the theorem is conducted becomes highly significant. I examine different proposals regarding these logical frameworks and focus on the philosophical benefits of adopting open-ended schemas in contrast to second order logic as the logical medium of the proof. I investigate Pederson and Rossberg’s critique of the ontological advantages of open-ended arithmetic (...) when it comes to establishing the categoricity of Peano Arithmetic and show that the critique is highly problematic. I argue that Pederson and Rossberg’s ontological criterion deliver the bizarre result that certain first order subsystems of Peano Arithmetic have a second order ontology. As a consequence, the application of the ontological criterion proposed by Pederson and Rossberg assigns a certain type of ontology to a theory, and a different, richer, ontology to one of its subtheories. (shrink)

How can a metaphysics of abstract entities be built upon a metaphysics of time? In this paper, I address the question of how to accommodate abstract entities in a presentist world. I consider both the traditional metaontological approach of unrestricted fundamental quantification and then ontological pluralism. I argue that under the former we need to impose two constraints in the characterization of presentism in order to avoid undesired commitments to abstract entities: we have to characterize presentism as a thesis only (...) about the concrete, and we also need to avoid the widely held distinction between tensed and tenseless senses of existence. Under ontological pluralism, instead, I argue that we can naturally accommodate any view of abstract objects in a presentist world. (shrink)

Theistic activism and theistic conceptual realism attempt to relieve the tension between transcendent realism about universals and a strong aseity-sovereignty doctrine. Paradoxically, both theories seem to imply that God is metaphysically prior and metaphysically posterior to his own nature. In this paper I critique one attempt to respond to this worry and offer a neo-Augustinian solution in its place. I demonstrate that Augustine’s argument for forms as ideas in the mind of God strongly suggests that only created beings need universals (...) to ground their character. For them, divine concepts can do all of the work that universals are typically invoked to do in the contemporary literature. An uncreated being’s character needs no such grounding and can be accounted for in terms of his own concepts. If this is correct, theists may be realists about universals while maintaining the traditional read of God’s aseity and sovereignty. (shrink)

Aquinas’s process of abstraction of the particular thing into a universal concept is of pivotal importance for grounding his philosophy and theology in a natural framework. Much has been said and written regarding Aquinas’s doctrine of abstraction, yet recent studies still consider it to be ‘nothing more than a kind of magic.’ This problematic claim is not without foundation, for in trying to understand exactly how this process works, we are constantly faced with an unbridgeable abyss and the repeated vague (...) explanations made by Aquinas. The plain truth is that Aquinas explains what abstraction ought to do and yet, most of the time, he does not explain how it is to be done. This paper intends to show that although Aquinas does not present us with a mechanism for the theory of abstraction, we are nevertheless able to construct a viable mechanism which accords with Aquinas’s guidelines. The aim of constructing a working mechanism that corresponds to what Aquinas demands of the process of abstraction is twofold: First, it attempts to extricate Aquinas’s doctrine of abstraction from the claims of being a quasi-natural doctrine. Second, a viable process of abstraction which is derived from Aquinian-Aristotelian sources can approach contemporary cognitive problems from a fresh point of view. (shrink)

Creationism about fictional entities requires a principle connecting what fictions say exist with which fictional entities really exist. The most natural way of spelling out such a principle yields inconsistent verdicts about how many fictional entities are generated by certain inconsistent fictions. Avoiding inconsistency without compromising the attractions of creationism will not be easy.

O problema no qual se inserem nominalismo e realismo, diz-nos MacBride, é o de como explicar as características repetidas das coisas. Enquanto o realista nos diz que as características repetidas se explicam por serem universais, ou seja, por serem as naturezas comuns que várias coisas compartilham, o nominalista nos diz que é possível explicar essas características repetidas com apenas particulares concretos (sem universais).

Neste capítulo, Loux apresenta alguns problemas com relação às modalidades e algumas das relações entre elas e o vocabulário dos mundos possíveis, expondo as duas principais posições ontológicas com relação a tais mundos e às modalidades e com relação à natureza das modalidades, a saber, o possibilismo e o actualismo, defendidos respectivamente por Lewis e Plantinga. Essas são teorias inconsistentes entre si, que intentam nos dizer se os mundos possíveis são concretos ou abstratos e se existe algo além do que (...) é actual. (shrink)

In this paper, I defend an indexical analysis of the abstract-concrete distinction within the framework of modal realism. This analysis holds the abstract-concrete distinction to be conceptually inseparable from the distinction between the actual and the merely possible, which is assumed to be indexical in nature. The resulting view contributes to the case for modal realism by demonstrating how its distinctive resources provide a reductive analysis of the abstract-concrete distinction. This indexical analysis also provides a solution to a sceptical problem (...) regarding our concreteness, which parallels the sceptical problem that motivates indexicalism about actuality. (shrink)

In this paper, two concepts of completing an infinite number of tasks are considered. After discussing supertasks, equisupertasks are introduced. I suggest that equisupertasks are logically possible.

This paper discusses the question whether it is possible to explain the notion of a singular term without invoking the notion of an object or other ontological notions. The framework here is that of Michael Dummett's discussion in Frege: Philosophy of Language. I offer an emended version of Dummett's conditions, accepting but modifying some suggestions made by Bob Hale, and defend the emended conditions against some objections due to Crispin Wright. This paper dates from about 1989. It originally formed part (...) of a very early draft of what became my Ph.D. dissertation. I rediscovered it and began scanning it, when I had nothing better to do, in Fall 2001, making some minor editing changes along the way. Suffice it to say that it no longer represents my current views. I hope, however, that it remains of some small interest. (shrink)

The essays collected in this volume are all concerned with the connection between fiction and truth. This question is of utmost importance to metaphysics, philosophy of language, philosophical logic and epistemology, raising in each of these areas and at their intersections a large number of issues related to creation, existence, reference, identity, modality, belief, assertion, imagination, pretense, etc. All these topics and many more are addressed in this collection, which brings together original essays written from various points of view by (...) philosophers of diverse trends. These essays constitute major contributions to the current debates that the connection between truth and fiction continually enlivens, and give a sense of the directions in which research on this question is heading. Contributors: Fred Adams, Frederick Kroon, Robert Howell, Brendan Murday, Terence Parsons, Graham Priest, Erich Rast, Manuel Rebuschi, Marion Renauld, R.M. Sainsbury, Grant Tavinor, Alberto Voltolini. (shrink)

Abstract In this paper I criticise a recent account of fictional discourse proposed by Nathan Salmon. Salmon invokes abstract artifacts as the referents of fictional names in both object- and meta-fictional discourse alike. He then invokes a theory of pretence to forge the requisite connection between object-fictional sentences and meta-fictional sentences, in virtue of which the latter can be assigned appropriate truth-values. I argue that Salmon's account of pretence renders his appeal to abstract artifacts as the referents of fictional names (...) in object-fictional discourse explanatorily redundant. I further argue that his account is therefore no improvement over those he criticises, thus leaving his own account unmotivated. (shrink)

Th ere is much controversy surrounding the nature of the relation between fictional individuals and possible individuals. Some have argued that no fictional individual is a possible individual; others have argued that (some) fictional individuals just are (merely) possible individuals. In this paper, I off er further grounds for believing the theory of fictional individuals defended by Amie Thomasson,viz., Artifactualism, by arguing that her view best allows one to make sense of this puzzling relation. More specifically, when we realize that (...) the view allows for an identification of merely possible individuals with fictional individuals, we seethat the utility, and hence the level of credence lent to Artifactualism, is increased. After arguing for this thesis, I respond to three of the most pressing worries. (shrink)

Chomsky and others have denied the relevance of external linguistic entities, such as E-languages, to linguistic explanation, and have questioned their coherence altogether. I discuss a new approach to understanding the nature of linguistic entities, focusing in particular on making sense of the varieties of kinds of “words” that are employed in linguistic theorizing. This treatment of linguistic entities in general is applied to constructing an understanding of external linguistic entities.

This paper argues for an ontological distinction between two kinds of universals, 'kinds of tropes' such as 'wisdom' and properties such as 'the property of being wise'. It argues that the distinction is parallel to that between two kinds of collections, pluralities such as 'the students' and collective objects such as 'the class'. The paper argues for the priortity of distributive readings with pluralities on the basis of predicates of extent or shape, such 'large' or 'long'.

In this paper I examine critically the relationship between the realist and nominalist views of abstract objects. I begin by pointing out some differences between the usage of existential statements in metaphysics and the usage of such statements in disciplines outside of philosophy. Then I propose an account of existence that captures the characteristic intuitions underlying the latter kind of usage. This account implies that abstract object existence claims are not as ontologically extravagant as they seem, and that such claims (...) are immune to certain standard nominalistic criticisms. (shrink)

In this paper I examine a new variant of the well-known idea that the self is an abstract object. I propose a simple model of the self as a property of temporal slices of a body's history. I argue that this model, when combined with even a modest realism with regard to properties, implies that the self has many of the chief features traditionally attributed to selves. I conclude that this model allows one to reconcile the full reality of the (...) self with even the most deflationary materialistic theories of consciousness. (shrink)

In this note I examine the two main differences between Plato's and Dennett's views of the self as an abstract object. I point out that in the presence of certain forms of ontological realism, abstract-object theories of the self are compatible with the full reality of the self. I conclude with some remarks on the relationship between ontology and ethics.

‘Nominalism’ refers to a family of views about what there is. The objects we are familiar with (e.g. hands, laptops, cookies, and trees) can be characterized as concrete and particular. Nominalists agree that there are such things. But one group of nominalists denies that anything is non-particular and another group denies that anything is non-concrete. These two sorts of nominalism, referred to as ‘nominalism about universals’ and ‘nominalism about abstract objects’, have common motivations in contemporary philosophy.

I present two puzzles about the metaphysics of establishments (e.g., stores and restaurants). The first puzzle is that, while there is good reason to think that they are constituted by the buildings they occupy, there also is good reason to think that they can exist without being constituted by anything and that nothing that’s constituted can ever become unconstituted. The second is that, while there is good reason to think that they are material objects, there also is good reason to (...) think they exhibit a certain kind of mind-dependence that no material object can have. I defend a solution to the puzzles according to which establishments are neither constituted nor material objects. (shrink)

Musical works change. Bruckner revised his Eighth Symphony. Ella Fitzgerald and many other artists have made it acceptable to sing the jazz standard “All the Things You Are” without its original verse. If we accept that musical works genuinely change in these ways, a puzzle arises: why can’t I change Bruckner’s Eighth Symphony? More generally, why are some individuals in a privileged position when it comes to changing musical works and other artifacts, such as novels, films, and games? I give (...) a view of musical works that helps to answer these questions. Musical works, on this view, are created abstract objects with no parts. The paradigmatic changes that musical works undergo are socially determined normative changes in how they should be performed. Due to contingent social practices, Bruckner, but not I, can change how his symphony should be performed. Were social practices radically different, I would be able to change his symphony. This view extends to abstract artifacts beyond music, including novels, films, words, games, and corporations. (shrink)

Peter van Inwagen has given an answer to the question ‘Why is there something rather than nothing?’. His answer is: Because there being nothing is as improbable as anything can be: it has probability 0. Here I shall examine his argument for this answer and I shall argue that it does not work because no good reasons have been given for two of the argument’s premises and that the conclusion of the argument does not constitute an answer to the question (...) van Inwagen wanted to answer. (shrink)

Some see concrete foundationalism as providing the central task for sparse ontology, that of identifying which concreta ground other concreta but aren’t themselves grounded by concreta. There is, however, potentially much more to sparse ontology. The thesis of abstract foundationalism, if true, provides an additional task: identifying which abstracta ground other abstracta but aren’t themselves grounded by abstracta. We focus on two abstract foundationalist theses—abstract atomism and abstract monism—that correspond to the concrete foundationalist theses of priority atomism and priority monism. (...) We show that a consequence of an attractive package of views is that abstract reality has a particular mereological structure, one capable of underwriting both theses. We argue that, of abstract foundationalist theses formulated in mereological terms, abstract atomism is the most plausible. (shrink)

Alexius Meinong developed a notion of defective objects in order to account for various logical and psychological paradoxes. The notion is of historical interest, since it presages recent work on the logical paradoxes by Herzberger and Kripke. But it fails to do the job it was designed for. However, a technique implicit in Meinong's investigation is more successful and can be adapted to resolve a similar paradox discovered by Romane Clark in a revised version of Meinong's Theory of Objects due (...) to Rapaport. One family of paradoxes remains, but it is argued that they are unavoidable and relatively harmless. (shrink)

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u_{F}={x|F(x)} for a property F() could never be self-predicative in the sense of u_{F}∈u_{F}. But the mathematical theory of categories, (...) dating from the mid-twentieth century, includes a theory of always-self-predicative universals--which can be seen as forming the "other bookend" to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. (shrink)

There is a widely shared account of the distinction between types and tokens, which might be termed the standard account. However, it has some surprising consequences that are not always realized. According to the standard account, a type is a contingent abstract object that can be created by us, but it does not allow any change and can never be destroyed once it is created, because it is an abstract object. I would like to present an alternative account of types (...) and tokens, according to which types are concrete objects that are located in space and time. This new account is based on a concept that I call a "token generator", which is something that specifies in detail how to produce the tokens. (shrink)

In this paper I confront what I take to be the crucial challenge for fictional realism, i.e. the view that fictional characters exist. This is the problem of accounting for the intuition that corresponding negative existentials such as ‘Sherlock Holmes does not exist’ are true (when, given fictional realism, taken literally they seem false). I advance a novel and detailed form of the response according to which we take them to mean variants of such claims as: there is no concrete (...) x such that x is Sherlock Holmes. (shrink)

I here defend a theory consisting of four claims about ‘property’ and properties, and argue that they form a coherent whole that can solve various serious problems. The claims are (1): ‘property’ is defined by the principles (PR): ‘F-ness/Being F/etc. is a property of x iff F’ and (PA): ‘F-ness/Being F/etc. is a property’; (2) the function of ‘property’ is to increase the expressive power of English, roughly by mimicking quantification into predicate position; (3) property talk should be understood at (...) face value: apparent commitments are real and our apparently literal use of ‘property’ is really literal; (4) there are no properties. In virtue of (1)–(2), this is a deflationist theory and in virtue of (3)–(4), it is an error theory. (1) is fleshed out as a claim about understanding conditions, and it is argued at length, and by going through a number of examples, that it satisfies a crucial constraint on meaning claims: all facts about ‘property’ can be explained, together with auxiliary facts, on its basis. Once claim (1) has been expanded upon, I argue that the combination of (1)–(3) provides the means for handling several problems: they help giving a happy-face solution to what I call the paradox of abstraction , they form part of a plausible account of the correctness of committive sentences, and, most importantly, they help respond to various indispensability arguments against nominalism. (shrink)

I address two related questions. First: what value is there in visiting a museum and becoming acquainted with the objects on display? For art museums the answer seem obvious: we go to experience valuable works of art, and experiencing valuable works of art is itself valuable. In this paper I focus on non-art museums, and while these may house aesthetically valuable objects, that is not their primary purpose, and at least some of the objects they house might not be particularly (...) aesthetically valuable at all. Second: to what ontological type or category do museum objects belong? What type of item that should be featured on an inventory of a museum collection? I distinguish between typical objects and special objects. While these are different types of object, both, I argue, are abstracta, not concreta. The answer to the second question, concerning the ontological category of special objects, throws new light on various philosophical questions about museums and their collections, including the question about the value of museum experiences. But it also throws light on important questions concerning the preservation and restoration of museum objects. (shrink)

I here investigate whether there is any version of the principle of charity both strong enough to conflict with an error-theoretic version of nominalism (EN) about abstract objects, and supported by the considerations adduced in favour of interpretive charity in the literature. I argue that in order to be strong enough, the principle, which I call (Charity), would have to read, “For all expressions e, an acceptable interpretation must make true a sufficiently high ratio of accepted sentences containing e”. I (...) next consider arguments based on Davidson's intuitive cases for interpretive charity, the reliability of perceptual beliefs, and the reliability of “non-abstractive inference modes”, and conclude that none support (Charity). I then propose a diagnosis of the view that there must be some universal principle of charity ruling out (EN). Finally, I present a reason to think (Charity) is false, namely, that it seems to exclude the possibility of such disagreements as that between nominalists and realists. (shrink)

Awareness is a two-place determinable relation some determinates of which are seeing, hearing, etc. Abstract objects are items such as universals and functions, which contrast with concrete objects such as solids and liquids. It is uncontroversial that we are sometimes aware of concrete objects. In this paper I explore the more controversial topic of awareness of abstract objects. I distinguish two questions. First, the Existence Question: are there any experiences that make their subjects aware of abstract objects? Second, the Grounding (...) Question: if an experience makes its subject aware of an abstract object, in virtue of what does it do so? I defend the view that intuitions, specifically mathematical intuitions, sometimes make their subjects aware of abstract objects. In defending this view, I develop an account of the ground of intuitive awareness. (shrink)

En la filosofía de Aristóteles y en la filosofía escolástica de cuño aristotélico, la abstracción constituía un acto fundamental del proceso cognitivo: marcaba el salto o ascenso de la sensibilidad a la inteligibilidad, del conocimiento del individuo al conocimiento de su esencia. En la teoría del conocimiento de Hegel, por el contrario, el concepto abstracto o, como Hegel prefiere llamarlo, la “representación abstracta” o “representación universal” es tan sólo un momento intermedio en el proceso fluido que va del conocimiento del (...) objeto como algo sensible -en la forma de la intuición y la subforma de la imagen- al conocimiento de su naturaleza intrínseca -en la forma del pensar. Sobre la base, por un lado, de los escasos textos en los que Hegel se ocupa expresamente del tema, y, por el otro, de la contextualización de estos textos en un análisis general de la filosofía del espíritu subjetivo teórico, el presente trabajo busca reconstruir las tesis fundamentales de Hegel sobre la abstracción y esclarecer con ello el sentido y función que la misma tiene en su teoría del conocimiento. The concept of abstraction in Hegel's theory of knowledgeIn both Aristotelian philosophy and the scholastic philosophy that bears its stamp, the concept of abstraction constitutes a fundamental act in the cognitive process; it signaled the leap or ascent from the realm of the senses to the realm of intellection, from knowledge of the individual to knowledge of his essence. By way of contrast, in Hegel's theory of knowledge, the abstract concept -or, as Hegel himself preferred to call it, “abstract representation” or “universal representation”­- is nothing but an intermediate moment in the fluid process of going from knowing the object as something given to the senses -in the form of intuition and the subform of image- to knowing its intrinsic nature -in the form of thought. Based on the scant writings by Hegel wherein he expressly addresses the matter, and by subsequently placing these texts into the broader context of an analysis of Hegel's philosophy of theoretical subjective spirit, this paper attempts to reconstruct Hegel's most significant ideas on abstraction. Hopefully, this will serve to clarify both the meaning and the role of that notion in Hegelian theory of knowledge. (shrink)

I consider the field of aesthetics to be at its most productive and engaging when adopting a broadly philosophically informative approach to its core issues (e.g., shaping and testing putative art theoretic commitments against the relevant standard models employed in philosophy of language, metaphysics, and philosophy of mind) and to be at its most impotent and bewildering when cultivating a philosophically insular character (e.g., selecting interpretative, ontological, or conceptual models solely for fit with pre-fixed art theoretic commitments). For example, when (...) philosophical aesthetics tends toward insularity, we shouldn’t be surprised to find standard art-ontological categories incongruous with those standardly employed in contemporary metaphysics. Of course, when contemporary metaphysics tends to ignore aesthetic and art theoretic concerns, perhaps we likewise shouldn’t be surprised to find the climate of contemporary metaphysics inhospitable for a theory of art. While this may seem to suggest at least a prima facie tension between our basic art theoretic commitments considered from within philosophical aesthetics and our standard ontological commitments considered from without, I think any perceived tension or antagonism largely due to metaphysicians and aestheticians (at least implicitly) assuming there to be but two available methodological positions with respect to the relationship between contemporary metaphysics and philosophical aesthetics (in the relevant overlap areas). I call these two opposing views the Deference View and the Independence View. I argue that either view looks to lead to what I call the Paradox of Standards. (shrink)

The paper is about the relationship between Scotus’s notion of ‘natura communis,’ for an examination of the main features that Scotus ascribes to ‘common natures’ can shed substantial light on the nature of metaphysics in itself. Some preliminary observations on historiography are also deemed to be in order.

Much attention has been given to the question of ontic vagueness, and the issues usually center around whether certain paradigmatically concrete entities – cats, clouds, mountains, etc. – are vague in the sense of having indeterminate spatial boundaries. In this paper, however, I wish to focus on a way in which some abstracta seem to be locationally vague. To begin, I will briefly cover some territory already covered regarding certain types of “traditional” abstracta and the ways they are currently alleged (...) to be vague. I then wish to discuss two types of “nontraditional” abstracta and the sense in which I think some of these objects are locationally vague. I will next reexamine some of the traditional abstracta and discuss whether any of these objects are locationally vague in the novel way suggested for the nontraditional sorts. I’ll finish by discussing objections, and conclude with some remarks about characterizing the abstract/concrete distinction. (shrink)