It is widely supposed that every entity falls into one of twocategories: Some are concrete; the rest abstract. The distinction issupposed to be of fundamental significance for metaphysics andepistemology. This article surveys a number of recent attempts to sayhow it should be drawn.

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 book pursues the question of how and whether natural language allows for reference to abstract objects in a fully systematic way. By making full use of contemporary linguistic semantics, it presents a much greater range of linguistic generalizations than has previously been taken into consideration in philosophical discussions, and it argues for an ontological picture is very different from that generally taken for granted by philosophers and semanticists alike. Reference to abstract objects such as properties, (...) numbers, propositions, and degrees is considerably more marginal than generally held. (shrink)

In this book, Zalta attempts to lay the axiomatic foundations of metaphysics by developing and applying a (formal) theory of abstract objects. The cornerstones include a principle which presents precise conditions under which there are abstract objects and a principle which says when apparently distinct such objects are in fact identical. The principles are constructed out of a basic set of primitive notions, which are identified at the end of the Introduction, just before the theorizing (...) begins. The main reason for producing a theory which defines a logical space of abstract objects is that it may have a great deal of explanatory power. It is hoped that the data explained by means of the theory will be of interest to pure and applied metaphysicians, logicians and linguists, and pure and applied epistemologists. (shrink)

This book offers an historically-informed critical assessment of Dummett's account of abstract objects, examining in detail some of the Fregean presuppositions whilst also engaging with recent work on the problem of abstract entities.

objects are standardly taken to be causally inert, but this claim is rarely explicitly argued for. In the context of his platonism about musical works, in order for musical works to be audible, Julian Dodd argues that abstracta are causally efficacious in virtue of their concrete tokens participating in events. I attempt to provide a principled argument for the causal inertness of abstracta by first rejecting Dodd’s arguments from events, and then extending and generalizing the causal exclusion argument to (...) the abstract/concrete distinction. For reasons of parsimony, if concrete tokens or instantiations of abstract objects account for all causal work, then there is no reason to attribute causal efficacy to abstracta, and thus reason to maintain their causal inertness. I then consider how one of the main arguments against causal exclusion, namely Stephen Yablo’s notion of “proportionality”, could be modified to support the causal efficacy of abstracta. I argue that from a few simple premises Yablo’s account in fact supports their causal inertness. Having a principled reason for the causal inertness of abstracta appears to entail that the musical platonist must admit that we never literally hear the musical work, but only its performances. I sketch a solution to this problem available to Dodd, so that the musical platonist can maintain that musical works are abstract objects and are causally inert while retaining their audibility. (shrink)

Art and Abstract Objects presents a lively philosophical exchange between the philosophy of art and the core areas of philosophy. The standard way of thinking about non-repeatable (single-instance) artworks such as paintings, drawings, and non-cast sculpture is that they are concrete (i.e., material, causally efficacious, located in space and time). Da Vinci's Mona Lisa is currently located in Paris. Richard Serra's Tilted Arc is 73 tonnes of solid steel. Johannes Vermeer's The Concert was stolen in 1990 and remains (...) missing. Michaelangelo's David was attacked with a hammer in 1991. By contrast, the standard way of thinking about repeatable (multiple-instance) artworks such as novels, poems, plays, operas, films, symphonies is that they must be abstract (i.e., immaterial, causally inert, outside space-time): consider the current location of Melville's Moby Dick, the weight of Yeats' "Sailing to Byzantium", or how one might go about stealing Puccini's La Boheme or vandalizing Mozart's Piano Concerto No. 9. Although novels, poems, and symphonies may appear radically unlike stock abstract objects such as numbers, sets, and propositions, most philosophers of art think that for the basic intuitions, practices, and conventions surrounding such works to be preserved, repeatable artworks must be abstracta. -/- This volume examines how philosophical enquiry into art might itself productively inform or be productively informed by enquiry into abstracta taking place within not just metaphysics but also the philosophy of mathematics, epistemology, philosophy of science, and philosophy of mind and language. While the contributors chiefly focus on the relationship between philosophy of art and contemporary metaphysics with respect to the overlap issue of abstracta, they provide a methodological blueprint from which scholars working both within and beyond philosophy of art can begin building responsible, mutually informative, and productive relationships between their respective fields. (shrink)

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)

This volume is about abstract objects and the ways we refer to them in natural language. Asher develops a semantical and metaphysical analysis of these entities in two stages. The first reflects the rich ontology of abstract objects necessitated by the forms of language in which we think and speak. A second level of analysis maps the ontology of natural language metaphysics onto a sparser domain--a more systematic realm of abstract objects that are fully (...) analyzed. This second level reflects the commitments of real metaphysics. The models for these commitments assign truth conditions to natural language discourse. Annotation copyright by Book News, Inc., Portland, OR. (shrink)

The aim of the paper is to answer some arguments raised against mathematical structuralism developed by Michael Resnik. These arguments stress the abstractness of mathematical objects, especially their causal inertness, and conclude that mathematical objects, the structures posited by Resnik included, are inaccessible to human cognition. In the paper I introduce a distinction between abstract and ideal objects and argue that mathematical objects are primarily ideal. I reconstruct some aspects of the instrumental practice of mathematics, (...) such as symbolic manipulations or ruler-and-compass constructions, and argue that instrumental practice can secure epistemic access to ideal objects of mathematics. (shrink)

Resumo O autor defenderá, por um lado, a existência dos objectos abstractos e, por outro, o seu papel causal, numa ontologia platónica, tal como enquadrada por Roderick Chisholm. Se plausível, a natureza e o papel dos abstracta sob a forma de estados de coisas, oferecem-nos razões para acreditar em uma descrição bem-sucedida e explicativa da intencionalidade humana e animal que não está encerrada no mundo físico. Palavras-chave : causalidade, encerramento causal, fisicalismo, objectos abstractos, platonismo, Roderick ChisholmA defense of the existence (...) and causal role of abstract objects in a Platonic ontology as influenced by the work of Roderick Chisholm. If plausible, the nature and role of abstracta in the form of states of affairs gives us some reason to believe that a successful description and explanation of human and animal intentionality that is not closed to the physical world. Keywords : abstract objects, causal closure, causation, physicalism, platonism, Roderick Chisholm. (shrink)

This is my main contribution to P. Gould (ed.) Beyond the Control of God?: Six Views on the Problem of God and Abstract Objects Bloomsbury. (The other contibutors to this work are: Keith Yandell; Paul Gould and Rich Davis; Greg Welty; William Lane Craig; and Scott Shalkowski.) I argue that, when it comes to a comparative assessment of the merits of theism and atheism, it makes no difference whether one opts for realism or fictionalism concerning abstract (...) class='Hi'>objects. (shrink)

What sorts of things are there in the world? Clearly enough, there are concrete, material things; but are there other things too, perhaps nonconcrete or non-material things? Some people believe that there are such things, which are often called abstract ; purported examples of such objects include numbers, properties, possible but non-actual states of affairs, propositions, and sets. Following a long-standing tradition, I shall describe persons who believe that there are abstract objects as ‘platonists’. In this (...) paper, I shall not directly address the plausibility of platonism, as compared with its rivals; instead, I shall confine my attention to one way in which some people have tried to combine platonism and theism. More specifically, I shall concentrate upon the claim that abstract objects depend upon God ontologically ; I shall argue that platonistic theists should reject DEP in favour of the claim that abstract objects exist independently of God . In order to evaluate the relative merits of DEP versus IND, it will be helpful to examine in some detail a particular articulation of DEP. When it comes to recent work on DEP, we can do no better in this regard than to examine the recent work of Thomas V. Morris and Christopher H. Menzel. According Morris and Menzel, there is a sense in which God literally creates such abstracta through engaging in intellective activities. (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)

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 (...) class='Hi'>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)

This book is an exploration and defense of the coherence of classical theism’s doctrine of divine aseity in the face of the challenge posed by Platonism with respect to abstract objects. A synoptic work in analytic philosophy of religion, the book engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology. It addresses absolute creationism, non-Platonic realism, fictionalism, neutralism, and alternative logics and semantics, among other topics. The book offers a helpful taxonomy of the wide range (...) of options available to the classical theist for dealing with the challenge of Platonism. It probes in detail the diverse views on the reality of abstract objects and their compatibility with classical theism. It contains a most thorough discussion, rooted in careful exegesis, of the biblical and patristic basis of the doctrine of divine aseity. Finally, it challenges the influential Quinean metaontological theses concerning the way in which we make ontological commitments. (shrink)

In recent discussions concerning the definition of argument, it has been maintained that the word ‘argument’ exhibits the process-product ambiguity, or an act/object ambigu-ity. Drawing on literature on lexical ambiguity we argue that ‘argument’ is not ambiguous. The term ‘argu-ment’ refers to an object, not to a speech act. We also examine some of the important implications of our argument by considering the question: what sort of abstract objects are arguments?

SummaryBenacerraf challenges us to account for the reliability of our mathematical beliefs given that there appear to be no natural connections between mathematical believers and mathematical ontology. In this paper I try to do two things. I argue that the interactionist view underlying this challenge renders inexplicable not only the reliability of our mathematical beliefs, construed either platonistically or naturalistically , but also the reliability of most of our beliefs in physics. I attempt to counter Benacerraf's challenge by sketching an (...) alternative conception of reliability explanations which renders explicable the reliability of our beliefs in physics and in mathematics but in which mathematical and formal considerations themselves play a central role. My main thesis is that abstract objects do not strike us, but that this is irrelevant to the reliability of our mathematical and physical beliefs. (shrink)

What is a concept? Philosophers have given many different answers to this question, reflecting a wide variety of approaches to the study of mind and language. Nonetheless, at the most general level, there are two dominant frameworks in contemporary philosophy. One proposes that concepts are mental representations, while the other proposes that they are abstract objects. This paper looks at the differences between these two approaches, the prospects for combining them, and the issues that are involved in the (...) dispute. We argue that powerful motivations have been offered in support of both frameworks. This suggests the possibility of combining the two. Unlike Frege, we hold that the resulting position is perfectly coherent and well worth considering. Nonetheless, we argue that it should be rejected along with the view that concepts are abstract objects. (shrink)

In this book, Linda Wetzel examines the distinction between types and tokens and argues that types exist (as abstract objects, since they lack a unique ...

According to Frege, the introduction of a new sort of abstract object is methodologically sound only if its identity conditions have been satisfactorily explained. Ironically, this ontological restriction has come to be known by Quine's criticism of Frege's intensional semantics, as the precept "No entity without identity." The aim of the paper is to reconstruct Frege's methodology of the introduction of abstract objects in detail, and to defend it against the more restrictive methodology underlying Quine's criticism of (...) the recognition of intensional objects. The main thesis is that Quine's criterion of non-circularity for the satisfactory individuation of abstract objects must be rejected. (shrink)

I reconcile the spatiotemporal location of repeatable artworks and impure sets with the non-location of natural numbers despite all three being varieties of abstract objects. This is possible because, while the identity conditions for all three can be given by abstraction principles, in the former two cases spatiotemporal location is a congruence for the equivalence relation featuring in the relevant principle, whereas in the latter it is not. I then generalize this to other ‘physical’ properties like shape, mass, (...) and causal powers. (shrink)

ABSTRACT Michael Rescorla has argued that it makes sense to compute directly with numbers, and he faulted Turing for not giving an analysis of number-theoretic computability. However, in line with a later paper of his, it only makes sense to compute directly with syntactic entities, such as strings on a given alphabet. Computing with numbers goes via notation. This raises broader issues involving de re propositional attitudes towards numbers and other non-syntactic abstract entities.

Philosophers frequently draw on natural language to motivate properties, numbers, and propositions as objects, and it is generally taken for granted that abstract objects of this sort are well-reflected in natural language and in fact that reference to them in natural language is pervasive In this paper, I will review and modify in a certain way the view I had advanced in Abstract Objects and the Semantics of Natural Language (Moltmann 2013a). This is the view (...) that natural language permits reference to abstract objects only in its periphery, not in its core. Even though reference to abstract objects of the sort of properties, propositions, and numbers is available only in the periphery of language, natural language permits reference to other sorts of abstract objects in its core, in particular abstract artifacts of various sorts. (shrink)

Before Duns Scotus, most philosophers agreed that God is identical with His necessary intrinsic attributes--omnipotence, omniscience, etc. This Identity Thesis was a component of widely held doctrines of divine simplicity, which stated that God exemplifies no metaphysical distinctions, including that between subject and attribute. The Identity Thesis seems to render God an attribute, an abstract object. This paper shows that the Identity Thesis follows from a basic theistic belief and does not render God abstract. If also discusses how (...) one might move from the Identity Thesis to the full doctrine of divine simplicity and shows that the Identity Thesis generates a new ontological argument. (shrink)

I explicate and defend the claim that, fundamentally speaking, there are no numbers, sets, properties or relations. The clarification consists in some remarks on the relevant sense of ‘fundamentally speaking’ and the contrasting sense of ‘superficially speaking’. The defence consists in an attempt to rebut two arguments for the existence of such entities. The first is a version of the indispensability argument, which purports to show that certain mathematical entities are required for good scientific explanations. The second is a speculative (...) reconstruction of Armstrong's version of the One Over Many argument, which purports to show that properties and relations are required for good philosophical explanations, e.g. of what it is for one thing to be a duplicate of another. (shrink)

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Abstract objects are standardly taken to be causally inert, however principled arguments for this claim are rarely given. As a result, a number of recent authors have claimed that abstract objects are causally efficacious. These authors take abstracta to be temporally located in order to enter into causal relations but lack a spatial location. In this paper, I argue that such a position is untenable by showing first that causation requires its relata to have a temporal (...) location, but second, that if an entity is temporally located then it is spatiotemporally located since this follows from the theory of Relativity. Since abstract objects lack a spatiotemporal location, then if something is causally efficacious, it is not abstract. (shrink)

Central to classical theism is the conception of God as the sole ultimate reality, the creator of all things apart from Himself. Such a doctrine is rooted in Hebrew-Christian scripture and unfolded by the ante-Nicene church fathers. Platonism, which postulates the existence of uncreated abstract objects, is therefore theologically objectionable. In order to overcome the presumption which anti-Platonism enjoys theologically, the Platonist would have to show that all other positions, both realist and nonrealist, are rationally untenable. No one (...) has even attempted so audacious a project, nor is there any reasonable expectation that it could be carried out. (shrink)