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)

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)

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)

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)

Trope theory is a leading metaphysical theory in analytic ontology. One of its classic statements is found in the work of Donald C. Williams who argued that tropes qua abstract particulars are the very alphabet of being. The concept of an abstract particular has been repeatedly attacked in the literature. Opponents and proponents of trope theory alike have levelled their criticisms at the abstractness of tropes and the associated act of abstraction. In this paper I defend the concept (...) of a trope qua abstract particular by rejecting arguments that purport to show that tropes should not be understood as abstract and by arguing that the abstractness of tropes plays an indispensable role in one of our more promising trope-theoretic analyses of universals and of concrete objects. (shrink)

In this contribution, I defend two claims. First, theological problems do not arise, because there are insufficient grounds for thinking that there are abstract objects. Second, theological problems do not arise because even if abstract objects do exist as platonists think they do, they pose no problem for God’s sovereignty or aseity. The argument for the second has two components. First, there are limits and then there are limits. The so-called limits platonism would place upon God (...) are merely notional and none any should care about. Second, it is not mandatory for at least Christian theists to think that the doctrine of creation requires that abstract object are created and it is not mandatory to think that the kind of sovereignty or aseity that a theologian should care about is impugned by the existence of abstracta. (shrink)

This paper is concerned with neo-Fregean accounts of reference to abstract objects. It develops an objection to the most familiar such accounts, due to Bob Hale and Crispin Wright, based upon what I call the 'proliferation problem': Hale and Wright's account makes reference to abstract objects seem too easy, as is shown by the fact that any equivalence relation seems as good as any other. The paper then develops a response to this objection, and offers an (...) account of what it is for abstracta to exist that is Fregean in spirit but more robust than familiar views. (shrink)

In this paper I explore a position on which it is possible to eliminate the need for postulating abstract objects through abstraction principles by treating terms for abstracta as ‘incomplete symbols’, using Russell's no-classes theory as a template from which to generalize. I defend views of this stripe against objections, most notably Richard Heck's charge that syntactic forms of nominalism cannot correctly deal with non-first-orderizable quantifcation over apparent abstracta. I further discuss how number theory may be developed in (...) a system treating apparent terms for numbers using these definitions. (shrink)

On the horizon between metaphysics and philosophy of religion stands the question of God’s relation to various abstracta. Like other contemporary philosophical debates, this one has resulted in a broadly dichotomous stalemate between Platonic realists on the one hand and varieties of nominalism/antirealism on the other. In this paper, I offer Aquinas’s moderaterealism as a true middle ground between realist or nominalist solutions. What Platonists take to be abstracta are actually the result of intellect’s abstractive work on sensible objects. (...) Further, the Christian philosopher should be concerned as much, if not more so, by nominalism than by Platonism. Given the problems associated with either Platonist or nominalist solutions, one should be open to a Thomistic moderate-realist solution to the problem of God and abstracta. (shrink)

Many philosophers think all abstract objects are causally inert. Here, focusing on novels, I argue that some abstracta are causally efficacious. First, I defend a straightforward argument for this view. Second, I outline an account of object causation—an account of how objects cause effects. This account further supports the view that some abstracta are causally efficacious.

This paper aims to provide hyperintensional foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by (...) Hale and Wright and examined in Hale (2013), and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest that observational type theory can be applied to first-order abstraction principles in order to make abstraction principles recursively enumerable. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics. (shrink)

This essay uses a mental files theory of singular thought—a theory saying that singular thought about and reference to a particular object requires possession of a mental store of information taken to be about that object—to explain how we could have such thoughts about abstract mathematical objects. After showing why we should want an explanation of this I argue that none of three main contemporary mental files theories of singular thought—acquaintance theory, semantic instrumentalism, and semantic cognitivism—can give it. (...) I argue for two claims intended to advance our understanding of singular thought about mathematical abstracta. First, that the conditions for possession of a file for an abstract mathematical object are the same as the conditions for possessing a file for an object perceived in the past—namely, that the agent retains information about the object. Thus insofar as we are able to have memory-based files for objects perceived in the past, we ought to be able to have files for abstract mathematical objects too. Second, at least one recently articulated condition on a file’s being a device for singular thought—that it be capable of surviving a certain kind of change in the information it contains—can be satisfied by files for abstract mathematical objects. (shrink)

In my “Creatures of Fiction, Objects of Myth” (2014), I present and defend an argument for thinking that mythical creationism—the view that mythical objects like phlogiston and Vulcan are abstract artifacts—is false. One intriguing sort of objection to my argument has been recently put forth by Zvolenszky (2016); she claims that a crucial premise is seen to be unjustified once one considers the phenomena of inadvertently created abstracta—specifically, inadvertently created fictional characters. I argue here that even if (...) we admit inadvertently created abstracta into our ontology, my argument survives. I ultimately defend a view on which fictional characters (if real) may be countenanced as created abstracta whether purposefully created or not, yet mythical objects are best taken to be discoverable, Platonic abstracta (if real). We can see that such a hybrid ontology is justified once we take proper note of the nature of the sorts of authorial activities involved in fictional storytelling and scientific hypothesizing. (shrink)

This essay uses a mental files theory of singular thought—a theory saying that singular thought about and reference to a particular object requires possession of a mental store of information taken to be about that object—to explain how we could have such thoughts about abstract mathematical objects. After showing why we should want an explanation of this I argue that none of three main contemporary mental files theories of singular thought—acquaintance theory, semantic instrumentalism, and semantic cognitivism—can give it. (...) I argue for two claims intended to advance our understanding of singular thought about mathematical abstracta. First, that the conditions for possession of a file for an abstract mathematical object are the same as the conditions for possessing a file for an object perceived in the past—namely, that the agent retains information about the object. Thus insofar as we are able to have memory-based files for objects perceived in the past, we ought to be able to have files for abstract mathematical objects too. Second, at least one recently articulated condition on a file’s being a device for singular thought—that it be capable of surviving a certain kind of change in the information it contains—can be satisfied by files for abstract mathematical objects. (shrink)

The idea that some objects are metaphysically “cheap” has wide appeal. An influential version of the idea builds on abstractionist views in the philosophy of mathematics, on which numbers and other mathematical objects are abstracted from other phenomena. For example, Hume’s Principle states that two collections have the same number just in case they are equinumerous, in the sense that they can be correlated one-to-one: (HP) #xx=#yy iff xx≈yy. The principal aim of this article is to use the (...) notion of grounding to develop this sort of abstractionism. The appeal to grounding enables a unified response to the two main challenges that confront abstractionism. First, we must explicate the metaphor of meta- physical “cheapness.” Second, we must rebut the “bad company” objection, which rejects abstraction principles like (HP) as tarnished by their similarity to inconsistent principles like Frege’s Basic Law V. By enforcing a simple requirement that all abstraction be properly grounded, we propose a unified solution to these two hard, and prima facie unrelated, problems. On our view, grounded abstraction simultaneously ensures “cheap” abstracta and permissible abstraction. (shrink)

In this paper, I present a polar concept argument for the existence of abstract objects. After recalling the fundamentals concerning the debate about the existence of abstracta, I present in a detailed way the argument for the existence of abstracta. I offer two different variations of the argument: one, deductive and the other, inductive. The argument rests primarily on the fact that our universe is well-balanced. This well-balanced property results from the fact that all instantiable polar dualities are (...) instantiated. Hence, the abstract pole of the abstract/concrete duality must also be exemplified. Lastly, I review several objections that can be raised against this latter argument. (shrink)

One common attitude toward abstract objects is a kind of platonism: a view on which those objects are mind-independent and causally inert. But there's an epistemological problem here: given any naturalistically respectable understanding of how our minds work, we can't be in any sort of contact with mind-independent, causally inert objects. So platonists, in order to avoid skepticism, tend to endorse epistemological theories on which knowledge is easy, in the sense that it requires no such contact—appeals (...) to Boghossian’s notion of epistemic analyticity are particularly common here, as are appeals to some broadly pragmatic account of the good standing of basic beliefs. I argue, though, that these appeals are hopeless: an argument adapted from the Benacerraf–Field challenge shows that, even if some such theory can deliver the verdict that our beliefs about abstract objects have some prima facie good standing, this good standing will inevitably be defeated. (shrink)

This paper presents a formalization of first-order arithmetic characterizing the natural numbers as abstracta of the equinumerosity relation. The formalization turns on the interaction of a nonstandard cardinality quantifier with an abstraction operator assigning objects to predicates. The project draws its philosophical motivation from a nonreductionist conception of logicism, a deflationary view of abstraction, and an approach to formal arithmetic that emphasizes the cardinal properties of the natural numbers over the structural ones.

Abstract artifacts such as musical works and fictional entities are human creations; they are intentional products of our actions and activities. One line of argument against abstract artifacts is that abstract objects are not the kind of objects that can be created. This is so, it is argued, because abstract objects are causally inert. Since creation requires being caused to exist, abstract objects cannot be created. One common way to refute this (...) argument is to reject the causal inefficacy of abstracta. I argue that creationists should rather reject the principle that creation requires causation. Creation, in my view, is a non-causal relation that can be explained using an appropriate notion of ontological dependence. The existence and the creation of abstract artifacts depend on certain individuals with appropriate intentions, along with events of a certain kind that include but are not limited to creations of certain concrete objects. (shrink)

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)

I argue that thoughts and concepts are mental representations rather than abstracta. I propose that the most important difference between the two views is that the mentalist believes that there are concept and thought tokens as well as types; this reveals that the dispute is not terminological but ontological. I proceed to offer an argument for mentalism. The key step is to establish that concepts and thoughts have lexical as well as semantic properties. I then show that this entails that (...) concepts and thoughts are susceptible to the type/token distinction. I finish by considering some objections to the argument. (shrink)

Many mathematicians are platonists: they believe that the axioms of mathematics are true because they express the structure of a nonspatiotemporal, mind independent, realm. But platonism is plagued by a philosophical worry: it is unclear how we could have knowledge of an abstract, realm, unclear how nonspatiotemporal objects could causally affect our spatiotemporal cognitive faculties. Here I aim to make room in our metaphysical picture of the world for the causal relevance of abstracta.

ABSTRACTAccording to Yablo, in uttering sentences that imply the existence of abstract objects, we do not assert their literal content. Instead, we only make a weaker conditional claim that does not have the controversial implication. In this commentary I argue that the conditional claims Yablo suggests we are making are true only if abstract objects exist and, thus, also carry the controversial implication.

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 paper takes up a recent challenge to mechanistic approaches to computational implementation, the view that computational implementation is best explicated within a mechanistic framework. The challenge, what has been labelled “the abstraction problem”, claims that one of MAC’s central pillars – medium independence – is deeply confused when applied to the question of computational implementation. The concern is that while it makes sense to say that computational processes are abstract (i.e. medium-independent), it makes considerably less sense to say (...) that they are also concrete processes of a mechanism. After outlining the problem and its effect on MAC, I examine a recent response from Kuokkanen and Rusanen [2018. “Making Too Many Enemies: Hutto and Myin’s Attack on Computationalism.” Philosophical Explorations 21 (2): 282–294. doi:10.1080/13869795.2018.1477980]. I argue that Kuokkanen and Rusanen’s response comes up short insofar as it makes problematic trade-offs among various desiderata we have for a theory of implementation. This leads to a general dilemma for MAC: either give up being an objective theory of implementation or concede the abstraction problem and so reintroduce triviality concerns. In response, I argue that conceiving of computations as abstracta rather than illata provides a way to avoid the proposed dilemma and articulate a notion of medium independence that addresses the abstraction problem. (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)

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)

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)