Think of a number, any number, or properties like fragility and humanity. These and other abstract entities are radically different from concrete entities like electrons and elbows. While concrete entities are located in space and time, have causes and effects, and are known through empirical means, abstract entities like meanings and possibilities are remarkably different. They seem to be immutable and imperceptible and to exist "outside" of space and time. This book provides a comprehensive (...) critical assessment of the problems raised by abstract entities and the debates about existence, truth, and knowledge that surround them. It sets out the key issues that inform the metaphysical disagreement between platonists who accept abstract entities and nominalists who deny abstract entities exist. Beginning with the essentials of the platonist–nominalist debate, it explores the key arguments and issues informing the contemporary debate over abstract reality: arguments for platonism and their connections to semantics, science, and metaphysical explanation the abstract–concrete distinction and views about the nature of abstract reality epistemological puzzles surrounding our knowledge of mathematical entities and other abstract entities. arguments for nominalism premised upon concerns about paradox, parsimony, infinite regresses, underdetermination, and causal isolation nominalist options that seek to dispense with abstract entities. Including chapter summaries, annotated further reading, and a glossary, _Entities_ is essential reading for anyone seeking a clear and authoritative introduction to the problems raised by abstract entities. (shrink)

This article discusses the argument we cannot have knowledge of abstract entities because they are not part of the causal order. The claim of this article is that the argument fails because of equivocation. Assume that the “causal order” is concerned with contingent facts involving time and space. Even if the existence of abstract entities is not contingent and does not involve time or space it does not follow that no truths about abstract entities (...) are contingent or involve time or space. I argue that it is the latter which is required to obtain the desired conclusion. (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)

Now the thesis that the universal redness is the linguistic type ⋅red⋅ has the ring of absurdity. There are several ways in which this discomfort can be expressed I shall open my argument by formulating an objection which, by cutting deeper than most, leads to a firm foundation for a restatement and defense of the thesis.

Modal Platonism utilizes "weak" logical possibility, such that it is logically possible there are abstract entities, and logically possible there are none. Modal Platonism also utilizes a non-indexical actuality operator. Modal Platonism is the EASY WAY, neither reductionist nor eliminativist, but embracing the Platonistic language of abstract entities while eliminating ontological commitment to them. Statement of Modal Platonism. Any consistent statement B ontologically committed to abstract entities may be replaced by an empirically equivalent modalization, (...) MOD(B), not so ontologically committed. This equivalence is provable using Modal/Actuality Logic S5@. Let MAX be a strong set theory with individuals. Then the following Schematic Bombshell Result (SBR) can be shown: MAX logically yields [T is true if and only if MOD(T) is true], for scientific theories T. The proof utilizes Stephen Neale's clever model-theoretic interpretation of Quantified Lewis S5, which I extend to S5@. (shrink)

(1988). Platonic explanation: Or, what abstract entities can do for you. International Studies in the Philosophy of Science: Vol. 3, No. 1, pp. 51-67. doi: 10.1080/02698598808573324.

Platonism, considered as a philosophy of mathematics, can be formulated in two interestingly different ways. Strong platonism holds that numerals, for example, refer to certain non-physical, non-mental entities. Weak platonism holds only that numerals uniquely apply to certain non-physical, non-mental entities. (Of course, there may even be weaker views that deserve to be called ‘platonistic.’The distinction between referring to an object and uniquely applying to an object may be illustrated as follows. If there is a tallest person and (...) I say, ‘the tallest person is over seven feet tall,’ without knowing who that person is, then my use of ‘the tallest person’ uniquely applies to someone, but it does not refer to anyone. The distinction is at least as old as Russell, for we might put his views in our terms by saying that for Russell only logically proper names refer to things, while ordinary proper names and definite descriptions at best uniquely apply to things. (shrink)

I argue that the most popular versions of naturalism imply nominalism in philosophy of mathematics. In particular, there is a conflict in Quine's philosophy between naturalism and realism in mathematics. The argument starts from a consequence of naturalism on the nature of human cognitive subjects, physicalism about cognitive subjects, and concludes that this implies a version of nominalism, which I will carefully characterize. The indispensability of classical mathematics for the sciences and semantic/confirmation holism does not affect the argument. The disquotational (...) theory of reference and truth is discussed but rejected. This argument differs from the Benacerrafian arguments against realism, because it does not rely on any specific assumption about the nature of knowledge or reference. It differs from the popular objections to the indispensability argument for realism as well, because it can admit both indispensability and holism. This argument motivates a new, radically naturalistic and nominalistic approach to philosophy of mathematics. (shrink)

I shall use upper case "Ki" to form the abstract singular term which stands to lower case "ki" as " fi-ness" stands to " fi." In other words, I shall drop the use of the suffix "-kind" in favor of this new device. Thus the platonistic counterpart of.

This paper argues that many so-called digital technologies can be construed as notational technologies, explored through the example of Monegraph, an art and digital asset management platform built on top of the blockchain system originally developed for the cryptocurrency bitcoin. As the paper characterizes it, a notational technology is the performance of syntactic notation within a field of reference, a technologized version of what Nelson Goodman called a “notational system.” Notational technologies produce abstracted entities through positive and reliable, or (...) constitutive, tests of socially acceptable meaning. Accordingly, this account deviates from typical narratives of blockchains, instead demonstrating that blockchain technologies are effective at managing digital assets because they produce abstracted identities through the performance of notation. Since notational technologies rely on configurations of socially acceptable meaning, this paper also provides a philosophical account of how blockchain technologies are socially embedded. (shrink)

ABSTRACT: Sellars formulated his thesis of 'psychological nominalism' in two very different ways: (1) most famously as the thesis that 'all awareness of sorts…is a linguistic affair', but also (2) as a certain thesis about the 'psychology of the higher processes'. The latter thesis denies the standard view that relations to abstract entities are required in order to explain human thought and intentionality, and asserts to the contrary that all such mental phenomena can in principle ‘be accounted (...) for causally' without any use of normative terms in the explanation. Recent 'Hegelian Sellarsians' such as Rorty, McDowell, and Brandom have argued that the holistic, normative themes in (1) support various non-realist or rather (German) 'idealist but common-sense realist' outlooks. By contrast, Sellars' own defenses of (2) reveal psychological nominalism itself to be a naturalistic empiricism intended to sustain the normative-holistic themes in (1) within an exhaustively scientific naturalist conception of reality. (shrink)

Alonzo Church has repeatedly argued that the semantic analysis of certain contexts requires reference to abstract entities of various kinds. The problem, arising from this argument for nominalists, will be examined first. Then we shall attempt to meet Church’s challenge by constructing and informally describing a semantics which was inspired by Nelson Goodman’s distinction between primary and secondary extensions. According to that semantics, no expression of the object language will make reference to any abstract or non-actual entity (...) while the system is strong enough to lend itself to semantic analysis in Church’s sense. (shrink)

In this paper, I articulate and solve a puzzle originally presented by Gideon Rosen. The puzzle challenges us to produce a causal criterion that distinguishes concrete objects from abstract objects, even though it seems like abstract objects are constituents of events that enter into causal relations. My solution is to identify concrete objects with objects that have dispositions to manifest causal powers.

Carnap’s ‘Empiricism, Semantics, and Ontology’ (Carnap (1950a), ESO hereafter) is certainly a classic of twentieth century analytic philosophy. For decades now, most undergraduates are expected to read it at some point in their studies. Lately, it is being seen as the inspiration for a host of positions in the field of metaontology. Despite the widespread agreement on the importance of the paper, there is a lack of agreement on what Carnap attempts to do in the paper. My main aim in (...) this chapter is to defend an interpretation of ESO by displaying its relation to Carnap’s earlier works. My secondary goal will be to draw a lesson from this discussion for Carnap’s later work on unobservable entities in science. (shrink)

The distinction between norms and norm-formulations commits legal theorists to treating legal norms as entities. In this article, I first explore the path from meaning to entities built by some analytical philosophers of language. Later, I present a set of problems produced by treating norms as entities. Whatever type of entities we deal with calls for a clear differentiation between the identification and individuation criteria of such entities. In the putative case of abstract (...) class='Hi'>entities, the differentiation collapses. By changing the notions of the intension and extension of words by extensional and intensional aspects of what we talk about, I outline a methodological programme for Law and Legal Theory. That programme is based in the identification of normativity. (shrink)

Quine has persuasively shown that the empiricist "dogma of reductionism", which is the belief that each meaningfiil statement of science can be reduced to statements about immediate sense experience, must be abandoned. However, Quine's methodology of ontology seems to incorporate an analogous physicalistic dogma according to which the identity conditions of each scientifically respectable sort of abstract objects can be reduced to the identity conditions of physical objects. This paper aims to show that the latter dogma must be abandoned, (...) too. In section 1, the reductionist methodology underlying Quine's prescript "No Entity without Identity" is reconstructed in detail. In section 2 and 3, this methodology is criticized on the ground that Quine's individuation of sets offendsagainst the reductive Criteria of adequacy for individuations that are presupposed by his criticism of the ontological recognition of intensional objects. Finally, in section 4 an alternative holistic conception of individuation is outlined. (shrink)

Belief in propositions no longer brings about the sorts of looks it did when Quine's affinity for desert landscapes held sway in the Anglo-American philosophical scene. People are doing work in the metaphysics of propositions, trying to figure out what sorts of creatures propositions are. In philosophers like Frege, Russell, and Moore we have strong shoulders upon which to stand. But, there is much more work that needs to be done. I will try to do a bit of that work (...) here. In the paper, I will probe the notion that propositions are structured entities, and that it is useful to think of their structure as resembling the structure of the sentences which express them. First, I will speak briefly to the issue of why one might find it rational to believe that propositions exist. In the second part of the paper, I will argue that we should think of propositions as having structure. In the last section, I will examine the nature of the structure of propositions. I will consider a recent account given by Jeffrey King of the nature of the relation that unifies constituents. I conclude by sketching my own view of the relation that holds between propositional constituents in virtue of which they compose a proposition. 1 I Why Believe in Propositions? Propositions are taken to be abstract entities that are a) the primary bearers of truth and falsity, b) the objects of our propositional attitudes, and c) the referents of "that-. (shrink)

Quine has persuasively shown that the empiricist "dogma of reductionism", which is the belief that each meaningfiil statement of science can be reduced to statements about immediate sense experience, must be abandoned. However, Quine's methodology of ontology seems to incorporate an analogous physicalistic dogma according to which the identity conditions of each scientifically respectable sort of abstract objects can be reduced to the identity conditions of physical objects. This paper aims to show that the latter dogma must be abandoned, (...) too. In section 1, the reductionist methodology underlying Quine's prescript "No Entity without Identity" is reconstructed in detail. In section 2 and 3, this methodology is criticized on the ground that Quine's individuation of sets offendsagainst the reductive Criteria of adequacy for individuations that are presupposed by his criticism of the ontological recognition of intensional objects. Finally, in section 4 an alternative holistic conception of individuation is outlined. (shrink)

In this paper, I give an argument for the view that non-fact entities – such as physical objects, abstract objects, events and so on – can ground other entities. Roughly put, the argument is as follows: those who accept this view can provide a more plausible account of the grounds of identity facts than those who deny this view.

Abstract: This chapter discusses speakers’ conceptions of reported entities as evident in reporting practices. Pragmatic analyses will be offered to explain the diversity of permissible reporting practices. Several candidate theses on speakers’ conceptions of reported entities will be introduced. The possibility that there can be a unified analysis of direct and indirect reporting practices will be considered. Barriers to this unification will be discussed with an emphasis on the cognitive abilities speakers use in discerning the entities (...) referred to in reporting contexts. (shrink)

Abstract: This chapter discusses speakers’ conceptions of reported entities as evident in reporting practices. Pragmatic analyses will be offered to explain the diversity of permissible reporting practices. Several candidate theses on speakers’ conceptions of reported entities will be introduced. The possibility that there can be a unified analysis of direct and indirect reporting practices will be considered. Barriers to this unification will be discussed with an emphasis on the cognitive abilities speakers use in discerning the entities (...) referred to in reporting contexts. (shrink)

A natural way to think of models is as abstract entities. If theories employ models to represent the world, theories traffic in abstract entities much more widely than is often assumed. This kind of thought seems to create a problem for a scientific realist approach to theories. Scientific realists claim theories should be understood literally. Do they then imply the reality of abstract entities? Or are theories simply—and incurably—false? Or has the very idea of (...) literal understanding to be abandoned? Is then fictionalism towards scientific theories inevitable? This paper argues that scientific realism can happily co-exist with models qua abstracta. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Preface: Virtual Entities in ScienceRobert Harlander, Jean-Philippe Martinez, Friedrich Steinle, and Adrian WüthrichIt is not only since the sudden increase of online communication due to the COVID-19 situation that the concept of the “virtual” has made its way into everyday language. In this context, it mostly denotes a digital substitute for a real object or process. Virtual reality is perhaps the best-known term in this respect. With (...) these digital connotations, “virtuality” has also been used in science and research: Chemists use virtual laboratories, biologists do virtual scanning of molecular structures, and geologists engage in virtual field trips. But the concept of the virtual has a much longer tradition, dating back to long before the dawn of the digital age. Virtual images and virtual displacements were introduced in classical physics already in the late seventeenth and eighteenth centuries, respectively. They represent auxiliary objects or processes without instantiation, with the purpose of efficiently describing specific physical systems. In today’s physics, the term “virtual” is mostly associated with the quantum world, first and foremost with the “virtual particle” of quantum field theory. It has become such an integral part of modern high energy physics that its ontological character may be considered to go beyond the purely auxiliary, which is typically associated with the virtual. [End Page 263]In other disciplines, however, use of the term virtual without a digital connotation is much rarer. While concepts like “virtual adrenaline” show up in physiological research around 1940s, and Charles Darwin, in a private note in January 1840,1 spoke of “virtual change” in the context of embryology, these examples seem to be singular occurrences of entities that were explicitly called “virtual.” The basic idea behind the terminology of the virtual, however, might be much more common, even outside of physics. The “invisible hand” in economics, or the “vital force” in biology, for instance, may carry aspects of a virtual entity, even if they have not been referred to that way.These different observations raise several questions about the status of virtual entities in science. What has led scientists to call one entity “virtual” and not another? Do all virtual entities in science have the same roots and meet the same characteristics? Are they more than auxiliary objects or processes? Why does physics seem to occupy a specific position with respect to the use of the notion of virtuality? These are some points that led us to discuss virtual entities in science during a workshop, out of which grew the present collection. We invited contributions that addressed the historical formation and philosophical interpretation of concepts of virtual entities in physics and other disciplines—in whatever terms they may come. The main goal of the workshop was to bring to the fore similarities and differences in the meanings and functions of these concepts, so as to be able to precisely characterize why certain entities are considered virtual in specific contexts, why a different terminology was often used in each individual case, and in what sense the virtual entities relate to the real world.The organization of the workshop was part of our project “The formation and development of the concept of virtual particles,” a subproject of the Research Unit “The Epistemology of the Large Hadron Collider,” funded by the Deutsche Forschungsgemeinschaft (DFG) and Der Wissenschaftsfonds (FWF). The workshop took place online on four consecutive Fridays in March 2021. It brought together contributors who discussed the role of the concept of the virtual in theoretical as well as experimental activities, and investigated into the origins of the terminology of the virtual as it was applied to the various disciplines of natural science. Dealing with historical, philosophical, but also methodological questions, the presentations covered a wide time range, from the Middle Ages to the present day. While physics naturally emerged as the dominant field, natural philosophy, computer science and biology were also addressed. The papers in this volume were contributed by participants in this workshop and approach the subject from different angles. [End Page 264]First, Friedrich Steinle provides us with an introductory piece that reflects on the specific meaning of the use of the term ‘virtual’ in science. He highlights and... (shrink)

We present a maximum-entropy based system for identifying Named Entities (NEs) in biomedical abstracts and present its performance in the only two biomedical Named Entity Recognition (NER) comparative evaluations that have been held to date, namely BioCreative and Coling BioNLP. Our system obtained an exact match f-score of 83.2% in the BioCreative evaluation and 70.1% in the BioNLP evaluation. We discuss our system in detail including its rich use of local features, attention to correct boundary identification, innovative use of (...) external knowledge resources including parsing and web searches, and rapid adaptation to new NE sets. We also discuss in depth problems with data annotation in the evaluations which caused the final performance to be lower than the optimal. (shrink)