Abstract Objects, Misc

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

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

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

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

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)

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

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

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

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

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

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

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

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

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

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)