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.

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)

(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.

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.

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)

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)

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)

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.

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)

Software is a ubiquitous artifact, yet not much has been done to understand its ontological nature. There are a few accounts offered so far about the nature of software. I argue that none of those accounts give a plausible picture of the nature of software. I draw attention to the striking similarities between software and musical works. These similarities motivate to look more closely on the discussions regarding the nature of the musical works. With the lessons drawn from the ontology (...) of musical works I offer a novel account of the nature of software. In this account, software is an abstract artifact. I elaborate the conditions under which software comes into existence; how it persists; how and on which entities its existence depends. (shrink)

This article focuses on a case that expert practitioners count as an explanation: a mathematical account of Plateau’s laws for soap films. I argue that this example falls into a class of explanations that I call abstract explanations.explanations involve an appeal to a more abstract entity than the state of affairs being explained. I show that the abstract entity need not be causally relevant to the explanandum for its features to be explanatorily relevant. However, it remains unclear (...) how to unify abstract and causal explanations as instances of a single sort of thing. I conclude by examining the implications of the claim that explanations require objective dependence relations. If this claim is accepted, then there are several kinds of objective dependence relations. 1 Introduction2 A Case3 Abstract and Causal Explanations4 Recent Work on Mathematical Explanation5 Explanation and Dependence6 Conclusion. (shrink)

concepts typically are defined in terms of lacking physical or perceptual referents. We argue instead that they are not devoid of perceptual information because knowledge of real-world situations is an important component of learning and using many abstract concepts. Although the relationship between perceptual information and abstract concepts is less straightforward than for concrete concepts, situation-based perceptual knowledge is part of many abstract concepts. In Experiment 1, participants made lexical decisions to abstract words that were preceded (...) by related and unrelated pictures of situations. For example, share was preceded by a picture of two girls sharing a cob of corn. When pictures were presented for 500 ms, latencies did not differ. However, when pictures were presented for 1,000 ms, decision latencies were significantly shorter for abstract words preceded by related versus unrelated pictures. Because the abstract concepts corresponded to the pictured situation as a whole, rather than a single concrete object or entity, the necessary relational processing takes time. In Experiment 2, on each trial, an abstract word was presented for 250 ms, immediately followed by a picture. Participants indicated whether or not the picture showed a normal situation. Decision latencies were significantly shorter for pictures preceded by related versus unrelated abstract words. Our experiments provide evidence that knowledge of events and situations is important for learning and using at least some types of abstract concepts. That is, abstract concepts are grounded in situations, but in a more complex manner than for concrete concepts. Although people's understanding of abstract concepts certainly includes knowledge gained from language describing situations and events for which those concepts are relevant, sensory and motor information experienced during real-life events is important as well. (shrink)

Ziel dieses Aufsatzes ist es zu zeigen, daß das ontologische Grundschema von Leibniz eine eigenstandige Erneuerung der Aristotelischen Einteilung des Seienden ist. Die Erklärung der genauen Entsprechung zwischen beiden kategorialen Systemen soil dazu dienen, gewisse, heute weit verbreitete MiBverstandnisse zu korrigieren. Die Originalität von Leibniz in dieser Sache liegt darin, daß die von Aristoteles am Anfang der Kategorien aufgestellte vierfache Gliederung des Seienden im Lichte einer doppelten Unterscheidung zu sehen ist: in der ontologischen Unterscheidung zwischen konkreten und abstrakten Sachen und (...) in der logischgrammatikalischen Unterscheidung zwischen konkreten und abstrakten Termini. Als Konsequenz dieser Neuheit kann die Leibnizsche Klassifikation der Dinge einige Ungenauigkeiten vermeiden, in welche die Aristotelische Kategorienlehre verfällt. (shrink)

This paper examines the potential for abstracting propositions – an as yet untested way of defending the realist thesis that propositions as abstract entities exist. I motivate why we should want to abstract propositions and make clear, by basing an account on the neo-Fregean programme in arithmetic, what ontological and epistemological advantages a realist can gain from this. I then raise a series of problems for the abstraction that ultimately have serious repercussions for realism about propositions in (...) general. I first identify problems about the number of entities able to be abstracted using these techniques. I then focus on how issues of language relativity result in problems akin to the Caesar problem in arithmetic by exposing circularity and modal concern over the status of the criterion of identity for propositions. (shrink)

In this article, I articulate and defend an account of corporations motivated by John Searle’s discussion of them in his Making the Social World. According to this account, corporations are abstract entities that are the products of status function Declarations. They are also connected with, though not reducible to, various people and certain of the power relations among them. Moreover, these connections are responsible for corporations having features that stereotypical abstract entities lack (e.g., the abilities to (...) take actions and make profits). (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)