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  1. Twofold Pictorial Experience.René Jagnow - 2019 - Erkenntnis (4):1-22.
    Richard Wollheim famously argued that figurative pictures depict their scenes, in part, in virtue of their ability to elicit a unique type of visual experience in their viewers, which he called seeing-in. According to Wollheim, experiences of seeing-in are necessarily twofold, that is, they involve two aspects of visual awareness: when a viewer sees a scene in a picture, she is simultaneously aware of certain visible features of the picture surface, the picture’s design, and the scene depicted by the picture. (...)
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  • Outline of a Theory of Scientific Aesthetics.Gustavo E. Romero - 2018 - Foundations of Science 23 (4):795-807.
    I offer a theory of art that is based on science. I maintain that, as any other human activity, art can be studied with the tools of science. This does not mean that art is scientific, but aesthetics, the theory of art, can be formulated in accord with our scientific knowledge. I present elucidations of the concepts of aesthetic experience, art, work of art, artistic movement, and I discuss the ontological status of artworks from the point of view of scientific (...)
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  • The Aesthetics of the Scientific Image.Clive Cazeaux - 2015 - Journal of Aesthetics and Phenomenology 2 (2):187-209.
    Images in science are often beautiful but their beauty cannot be explained using traditional aesthetic theories. Available theories either rely upon concepts antithetical to science, e.g. regularity as an index of God’s design, or they omit concepts intrinsic to scientific imaging, e.g. the image is taken as a representation of “beautiful nature.” I argue that the scientific image is not a representation but a construction: a series of mutually defining intra-actions, where “intra-action” signifies that the object depicted cannot be extricated (...)
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  • An Ontology of Words.Nurbay Irmak - 2019 - Erkenntnis 84 (5):1139-1158.
    Words are indispensable linguistic tools for beings like us. However, there is not much philosophical work done about what words really are. In this paper, I develop a new ontology for words. I argue that words are abstract artifacts that are created to fulfill various kinds of purposes, and words are abstract in the sense that they are not located in space but they have a beginning and may have an end in time given that certain conditions are met. What (...)
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  • Property Theory of Musical Works.Philip Letts - 2018 - Journal of Aesthetics and Art Criticism 76 (1):57-69.
    The property theory of musical works says that each musical work is a property that is instantiated by its occurrences, that is, the work's performances and playings. The property theory provides ontological explanations very similar to those given by its popular cousin, the type/token theory of musical works, but it is both simpler and stronger. However, type/token theorists often dismiss the property theory. In this essay, I formulate a version of the property theory that identifies each type (thus, each musical (...)
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  • Revisiting Arnheim and Gombrich in Social Scientific Perspective.Ian Verstegen - 2018 - Journal of Aesthetics and Art Criticism 76 (1):45-55.
    This article revisits an earlier social scientific analysis of the thought of Rudolf Arnheim and E. H. Gombrich. Adding to the earlier analysis in terms of social ontology and historical development is an analysis of the sufficiency of perception to yield information about the world, both in ordinary and in artistic contexts. Gombrich held to an idea of perception as hypothesis testing, and it joins with Popper's philosophy in the deferred warrant of the perceptual image. Arnheim, instead, followed the Gestalt (...)
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  • Frauds, Posers And Sheep: A Virtue Theoretic Solution To The Acquaintance Debate.Madeleine Ransom - 2017 - Philosophy and Phenomenological Research 98 (2):417-434.
    The acquaintance debate in aesthetics has been traditionally divided between pessimists, who argue that testimony does not provide others with aesthetic knowledge of artworks, and optimists, who hold that acquaintance with an artwork is not a necessary precondition for acquiring aesthetic knowledge. In this paper I propose a reconciliationist solution to the acquaintance debate: while aesthetic knowledge can be had via testimony, aesthetic judgment requires acquaintance with the artwork. I develop this solution by situating it within a virtue aesthetics framework (...)
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  • Types, Tokens, and Talk about Musical Works.Julian Dodd & Philip Letts - 2017 - Journal of Aesthetics and Art Criticism 75 (3):249-263.
    It has recently been suggested that the type/token theorist concerning musical works cannot come up with an adequate semantic theory of those sentences in which we purport to talk about such works. Specifically, it has been claimed that, since types are abstract entities, a type/token theorist can only account for the truth of sentences such as “The 1812 Overture is very loud” and “Bach's Two Part Invention in C has an F-sharp in its fourth measure” by adopting an untenable semantic (...)
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  • Relativism, Disagreement and Testimony.Alexander Dinges - 2017 - Pacific Philosophical Quarterly 98 (S1):497-519.
    This article brings together two sets of data that are rarely discussed in concert; namely, disagreement and testimony data. I will argue that relativism yields a much more elegant account of these data than its major rival, contextualism. The basic idea will be that contextualists can account for disagreement data only by adopting principles that preclude a simple account of testimony data. I will conclude that, other things being equal, we should prefer relativism to contextualism. In making this comparative point, (...)
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  • The uses of aesthetic testimony.C. Thi Nguyen - 2017 - British Journal of Aesthetics 57 (1):19-36.
    The current debate over aesthetic testimony typically focuses on cases of doxastic repetition — where, when an agent, on receiving aesthetic testimony that p, acquires the belief that p without qualification. I suggest that we broaden the set of cases under consideration. I consider a number of cases of action from testimony, including reconsidering a disliked album based on testimony, and choosing an artistic educational institution from testimony. But this cannot simply be explained by supposing that testimony is usable for (...)
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  • Vision, Action, and Make‐Perceive.Robert Eamon Briscoe - 2008 - Mind and Language 23 (4):457-497.
    In this paper, I critically assess the enactive account of visual perception recently defended by Alva Noë (2004). I argue inter alia that the enactive account falsely identifies an object’s apparent shape with its 2D perspectival shape; that it mistakenly assimilates visual shape perception and volumetric object recognition; and that it seriously misrepresents the constitutive role of bodily action in visual awareness. I argue further that noticing an object’s perspectival shape involves a hybrid experience combining both perceptual and imaginative elements—an (...)
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  • Aesthetic Testimony and the Test of Time.Jon Robson - 2018 - Philosophy and Phenomenological Research 96 (3):729-748.
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  • Depicting Depictions.René Jagnow - 2016 - Pacific Philosophical Quarterly 98 (S1):453-479.
    How is it possible for a picture to depict a picture? Proponents of perceptual theories of depiction, who argue that the content of a picture is determined, in part, by the visual state it elicits in suitable viewers, that is, by a state of seeing-in, have given a plausible answer to this question. They say that a picture depicts a picture, in part, because, under appropriate conditions of observation, a suitable viewer will be able to see a picture in the (...)
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  • Musical Perdurantism and the Problem of Intermittent Existence.Alexey Aliyev - 2017 - Grazer Philosophische Studien 94 (1-2):83-100.
    Recently, a number of philosophers have defended a novel, materialist view on the nature of musical works—musical perdurantism. According to this view, musical works are a peculiar kind of concreta, namely perduring mereological sums of performances and/or other concrete entities. One problem facing musical perdurantism stems from the thought that if this view is correct, then virtually no musical work can exist in a continuous, non-intermittent fashion. The aim of this paper is to expound this problem and show that it (...)
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  • A Kantian Hybrid Theory of Art Criticism: A Particularist Appeal to the Generalists.Emine Hande Tuna - 2016 - Journal of Aesthetics and Art Criticism 74 (4):397-411.
    Noël Carroll proposes a generalist theory of art criticism, which essentially involves evaluations of artworks on the basis of their success value, at the cost of rendering evaluations of reception value irrelevant to criticism. In this article, I argue for a hybrid account of art criticism, which incorporates Carroll's objective model but puts Carroll-type evaluations in the service of evaluations of reception value. I argue that this hybrid model is supported by Kant's theory of taste. Hence, I not only present (...)
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  • Painting, History, and Experience.Robert Hopkins - 2006 - Philosophical Studies 127 (1):19-35.
    Two themes run through Wollheim’s work: the importance of history to the practice and appreciation of the arts, and the centrality of experience in appreciation. Prima facie, these are in tension. Reconciling them requires two steps. First, we should follow Wollheim in adopting a notion of experience on which features can be experienced even if we must have experience-independent access to the fact that the work exhibits them. Second, we need to state what makes a particular experience appropriate to the (...)
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  • Improvisation in the Arts.Aili Bresnahan - 2015 - Philosophy Compass 10 (9):573-582.
    This article focuses primarily on improvisation in the arts as discussed in philosophical aesthetics, supplemented with accounts of improvisational practice by arts theorists and educators. It begins with an overview of the term improvisation, first as it is used in general and then as it is used to describe particular products and practices in the individual arts. From here, questions and challenges that improvisation raises for the traditional work-of-art concept, the type-token distinction, and the appreciation and evaluation of the arts (...)
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  • Aesthetic Adjectives: Experimental Semantics and Context-Sensitivity.Shen-yi Liao & Aaron Meskin - 2017 - Philosophy and Phenomenological Research 94 (2):371–398.
    One aim of this essay is to contribute to understanding aesthetic communication—the process by which agents aim to convey thoughts and transmit knowledge about aesthetic matters to others. Our focus will be on the use of aesthetic adjectives in aesthetic communication. Although theorists working on the semantics of adjectives have developed sophisticated theories about gradable adjectives, they have tended to avoid studying aesthetic adjectives—the class of adjectives that play a central role in expressing aesthetic evaluations. And despite the wealth of (...)
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  • Pictures, presence and visibility.Solveig Aasen - 2016 - Philosophical Studies 173 (1):187-203.
    This paper outlines a ‘perceptual account’ of depiction. It centrally contrasts with experiential accounts of depiction in that seeing something in a picture is understood as a visual experience of something present in the picture, rather than as a visual experience of something absent. The experience of a picture is in this respect akin to a veridical rather than hallucinatory perceptual experience on a perceptual account. Thus, the central selling-point of a perceptual account is that it allows taking at face (...)
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  • Seeing, visualizing, and believing: Pictures and cognitive penetration.John Zeimbekis - 2015 - In John Zeimbekis & Athanassios Raftopoulos (eds.), The Cognitive Penetrability of Perception: New Philosophical Perspectives. Oxford: Oxford University Press. pp. 298-327.
    Visualizing and mental imagery are thought to be cognitive states by all sides of the imagery debate. Yet the phenomenology of those states has distinctly visual ingredients. This has potential consequences for the hypothesis that vision is cognitively impenetrable, the ability of visual processes to ground perceptual warrant and justification, and the distinction between cognitive and perceptual phenomenology. I explore those consequences by describing two forms of visual ambiguity that involve visualizing: the ability to visually experience a picture surface as (...)
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  • Husserl’s struggle with mental images: imaging and imagining reconsidered.Andreea Smaranda Aldea - 2013 - Continental Philosophy Review 46 (3):371-394.
    Husserl’s extensive analyses of image consciousness (Bildbewusstsein) and of the imagination (Phantasie) offer insightful and detailed structural explications. However, despite this careful work, Husserl’s discussions fail to overcome the need to rely on a most problematic concept: mental images. The epistemological conundrums triggered by the conceptual framework of mental images are well known—we have only to remember the questions regarding knowledge acquisition that plagued British empiricism. Beyond these problems, however, a plethora of important questions arise from claiming that mental images (...)
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  • Why, as responsible for figurativity, seeing-in can only be inflected seeing-in.Alberto Voltolini - 2015 - Phenomenology and the Cognitive Sciences 14 (3):651-667.
    In this paper, I want to argue for two main and related points. First, I want to defend Richard Wollheim’s well-known thesis that the twofold mental state of seeing-in is the distinctive pictorial experience that marks figurativity. Figurativity is what makes a representation pictorial, a depiction of its subject. Moreover, I want to show that insofar as it is a mark of figurativity, all seeing-in is inflected. That is to say, every mental state of seeing-in is such that the characterisation (...)
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  • Image and ontology in Merleau-Ponty.Trevor Perri - 2013 - Continental Philosophy Review 46 (1):75-97.
    Although better known for his phenomenology of perception and the perceived world, Merleau-Ponty’s writings also contain the outlines of a rich and unique account of the imagination and the imaginary. In this paper, I explicate the phenomenology of the image that Merleau-Ponty develops throughout his work. I show how Merleau-Ponty develops this account of the image in critical response to Sartre and in a way that follows from his own descriptions of what painters do when they paint and of what (...)
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  • Aesthetic Testimony.Jon Robson - 2012 - Philosophy Compass 7 (1):1-10.
    It is frequently claimed that we can learn very little, if anything, about the aesthetic character of an artwork on the basis of testimony. Such disparaging assessments of the epistemic value of aesthetic testimony contrast markedly with our acceptance of testimony as an important source of knowledge in many other areas. There have, however, been a number of challenges to this orthodoxy of late; from those who seek to deny that such a contrast exists as well as attempts by those (...)
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  • Sculpture and Space.Robert Hopkins - 2003 - In Matthew Kieran & Dominic Lopes (eds.), Imagination, Philosophy and the Arts. New York: Routledge. pp. 272-290.
    What is distinctive about sculpture as an artform? I argue that it is related to the space around it as painting and the other pictorial arts are not. I expound and develop Langer's suggestive comments on this issue, before asking what the major strengths and weaknesses of that position might be.
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  • Videogames and aesthetics.Grant Tavinor - 2010 - Philosophy Compass 5 (8):624-634.
    Videogames are one of the most striking developments in recent popular arts. Many of the issues traditional to philosophical aesthetics find a new setting in videogames, and often take on a dramatic new form. Little has been written specifically on videogames in the philosophy of the arts, although they are often discussed in non-philosophical disciplines, such as media studies. A number of issues seem prominent, particularly those following from the interactive nature of videogames. This article is a survey of the (...)
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  • Reperforming and reforming art as performance: Responses. [REVIEW]David Davies - 2005 - Acta Analytica 20 (4):64-90.
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  • Musical works: Ontology and meta-ontology.Julian Dodd - 2008 - Philosophy Compass 3 (6):1113-1134.
    The ontological nature of works of music has been a particularly lively area of philosophical debate during the past few years. This paper serves to introduce the reader to some of the most fertile and interesting issues. Starting by distinguishing three questions – the categorial question, the individuation question, and the persistence question – the article goes on to focus on the first: the question of which ontological category musical works fall under. The paper ends by introducing, and briefly considering, (...)
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  • Comprehending speech.Guy Longworth - 2008 - Philosophical Perspectives 22 (1):339-373.
    What is the epistemological role of speech perception in comprehension? More precisely, what is its role in episodes or states of comprehension able to mediate the communication of knowledge? One answer, developed in recent work by Tyler Burge, has it that its role may be limited to triggering mobilizations of the understanding. I argue that, while there is much to be said for such a view, it should not be accepted. I present an alternative account, on which episodes of comprehension (...)
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  • The usefulness of 'aesthetic education'.Alan Simpson - 1985 - Journal of Philosophy of Education 19 (2):273–280.
    Alan Simpson; The Usefulness of ‘Aesthetic Education’, Journal of Philosophy of Education, Volume 19, Issue 2, 30 May 2006, Pages 273–280, https://doi.org/10.11.
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  • Pictorial representation.John Kulvicki - 2006 - Philosophy Compass 1 (6):535–546.
    Maps, notes, descriptions, diagrams, flowcharts, photographs, paintings, and prints, all, in one way or another, manage to be about things or stand for them. This article looks at three ways in which philosophers have explained the way that pictures represent the world. It starts by describing some leading perceptual accounts and then surveys contemporary content and structural alternatives.
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  • Sentimentalism and the Intersubjectivity of Aesthetic Evaluations.Fabian Dorsch - 2007 - Dialectica 61 (3):417-446.
    Within the debate on the epistemology of aesthetic appreciation, it has a long tradition, and is still very common, to endorse the sentimentalist view that our aesthetic evaluations are rationally grounded on, or even constituted by, certain of our emotional responses to the objects concerned. Such a view faces, however, the serious challenge to satisfactorily deal with the seeming possibility of faultless disagreement among emotionally based and epistemically appropriate verdicts. I will argue that the sentimentalist approach to aesthetic epistemology cannot (...)
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  • In support of content theories of art.John Dilworth - 2007 - Australasian Journal of Philosophy 85 (1):19 – 39.
    A content theory of art would identify an artwork with the meaningful or representational content of some concrete artistic vehicle, such as the intentional, expressive, stylistic, and subject matter-related content embodied in, or resulting from, acts of intentional artistic expression by artists. Perhaps surprisingly, the resultant view that an artwork is nothing but content seems to have been without theoretical defenders until very recently, leaving a significant theoretical gap in the literature. I present some basic arguments in defence of such (...)
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  • Debates about the Ontology of Art: What are We Doing Here?Amie L. Thomasson - 2006 - Philosophy Compass 1 (3):245-255.
    Philosophy Compass, Volume 1. Oxford: Blackwell, 2006.
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  • The Recent Renaissance of Acquaintance.Thomas Raleigh - 2019 - In Jonathan Knowles & Thomas Raleigh (eds.), Acquaintance: New Essays. Oxford, United Kingdom: Oxford University Press.
    This is the introductory essay to the collection of essays: 'Acquaintance: New Essays' (eds. Knowles & Raleigh, forthcoming, OUP). In this essay I provide some historical background to the concept of acquaintance. I examine various Russellian theses about acquaintance that contemporary acquaintance theorists may wish to reject. I consider a number of questions that acquaintance theorists face. I provide a survey of current debates in philosophy where acquaintance has recently been invoked. And I also provide brief summaries of the other (...)
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  • In Advance of the Broken Theory: Philosophy and Contemporary Art.Sherri Irvin & Julian Dodd - 2017 - Journal of Aesthetics and Art Criticism 75 (4):375-386.
    We discuss how analysis of contemporary artworks has shaped philosophical theories about the concept of art, the ontology of art, and artistic media. The rapid expansion, during the contemporary period, of the kinds of things that can count as artworks has prompted a shift toward procedural definitions, which focus on how artworks are selected, and away from definitions that focus exclusively on artworks’ features or effects. Some contemporary artworks challenge the traditional art–ontological dichotomy between physical particulars and repeatable entities whose (...)
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  • Descriptivism and Its Discontents.David Davies - 2017 - Journal of Aesthetics and Art Criticism 75 (2):117-129.
    Is ontologizing about art rightly held accountable to artistic practice, and, if so, how? Julian Dodd argues against such accountability. His target is “local descriptivism,” a meta-ontological principle that he contrasts with meta-ontological realism. The local descriptivist thinks that folk-theoretic beliefs implicit in our practices somehow determine the ontological characters of artworks. I argue, however, that according a grounding role to artistic practice in the ontology of art does not conflict with meta-ontological realism. Practice must ground our ontological inquiries because (...)
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  • Elucidating the Truth in Criticism.Stacie Friend - 2017 - Journal of Aesthetics and Art Criticism 75 (4):387-399.
    Analytic aesthetics has had little to say about academic schools of criticism, such as Freudian, Marxist, feminist, or postcolonial perspectives. Historicists typically view their interpretations as anachronistic; non-historicists assess all interpretations according to formalist criteria. Insofar as these strategies treat these interpretations as on a par, however, they are inadequate. For the theories that ground the interpretations differ in the claims they make about the world. I argue that the interpretations of different critical schools can be evaluated according to the (...)
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  • Beauty, The Social Network.Dominic McIver Lopes - 2017 - Canadian Journal of Philosophy 47 (4):437-453.
    Aesthetic values give agents reasons to perform not only acts of contemplation, but also acts like editing, collecting, and conserving. Moreover, aesthetic agents rarely operate solo: they conduct their business as integral members of networks of other aesthetic agents. The consensus theory of aesthetic value, namely that an item’s aesthetic value is its power to evoke a finally valuable experience in a suitable spectator, can explain neither the range of acts performed by aesthetic agents nor the social contexts in which (...)
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  • Artworks as dichotomous objects: implications for the scientific study of aesthetic experience.Robert Pepperell - 2015 - Frontiers in Human Neuroscience 9:146700.
    This paper addresses an issue that has been studied from both scientific and art theoretical perspectives, namely the dichotomous nature of representational artworks. Representational artworks are dichotomous in that they present us with two distinct aspects at once. In one aspect we are aware of what is represented while in the other we are aware of the material from which the representation is composed. The dichotomy arises due the incompatibility, indeed contradiction, between these aspects of awareness, both of which must (...)
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  • Institutional Ontology as an Ontology of Types.Lorenzo Passerini Glazel - 2012 - Phenomenology and Mind 3:78-91.
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  • Ambiguous figures and representationalism.Nicoletta Orlandi - 2011 - Phenomenology and the Cognitive Sciences 10 (3):307-323.
    Ambiguous figures pose a problem for representationalists, particularly for representationalists who believe that the content of perceptual experience is non-conceptual (MacPherson in Nous 40(1):82–117, 2006). This is because, in viewing ambiguous figures, subjects have perceptual experiences that differ in phenomenal properties without differing in non-conceptual content. In this paper, I argue that ambiguous figures pose no problem for non-conceptual representationalists. I argue that aspect shifts do not presuppose or require the possession of sophisticated conceptual resources and that, although viewing ambiguous (...)
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  • Mathematical Beauty and Perceptual Presence.Rob van Gerwen - 2011 - Philosophical Investigations 34 (3):249-267.
    This paper discusses the viability of claims of mathematical beauty, asking whether mathematical beauty, if indeed there is such a thing, should be conceived of as a sub-variety of the more commonplace kinds of beauty: natural, artistic and human beauty; or, rather, as a substantive variety in its own right. If the latter, then, per the argument, it does not show itself in perceptual awareness – because perceptual presence is what characterises the commonplace kinds of beauty, and mathematical beauty is (...)
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  • Works and performances in the performing arts.David Davies - 2009 - Philosophy Compass 4 (5):744-755.
    The primary purpose of the performing arts is to prepare and present 'artistic performances', performances that either are themselves the appreciative focuses of works of art or are instances of other things that are works of art. In the latter case, we have performances of what may be termed 'performed works', as is generally taken to be so with performances of classical music and traditional theatrical performances. In the former case, we have what may be termed 'performance-works', as, for example, (...)
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  • Music and metaphysics.Saam Trivedi - 2008 - Metaphilosophy 39 (1):124–143.
    In this article, I assume that musical works are abstract types, and I raise and address a new question concerning musical ontology that may take the types view at least a step further: When do musical works cease to exist? I then propound my view about musical works as types, which is somewhat like the Aristotelian Realist position concerning universals. Next, I address some objections to that view. Finally, I provide some grounds for rejecting alternative views that see Western classical (...)
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  • Created, Changeable, and Yet Acausal?Vanessa Carr - 2019 - Proceedings of the Aristotelian Society 119 (3):325-334.
    Amongst the entities that have been created by human agents, and can be changed by human agents, besides concrete particulars, such as tables and chairs, our intuitions suggest that there are repeatables—entities that can each have multiple concrete instances. And since there is reason to think that repeatables are acausal, there is reason to think that that there are entities that are created, changeable, repeatable and acausal. Then again, it might be supposed that if an entity is created then it (...)
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  • Depicting and seeing-in. The ‘Sujet’ in Husserl’s phenomenology of images.Patrick Eldridge - 2018 - Phenomenology and the Cognitive Sciences 17 (3):555-578.
    In this paper I investigate an underappreciated element of Husserl’s phenomenology of images: the consciousness of the depicted subject, which Husserl calls the Sujetintention, e.g. the awareness of the sitter of a portrait. Husserl claims that when a consciousness regards a figurative image, it is absorbed in the awareness of the depicted subject and yet this subject some how withholds its presence in the midst of its appearance in the image-object. Image-consciousness is an intuitive consciousness that intends a being that (...)
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  • The Ontology of Musical Works and the Role of Intuitions: An Experimental Study.Christopher Bartel - 2018 - European Journal of Philosophy 26 (1):348-367.
    Philosophers of music often appeal to intuition to defend ontological theories of musical works. This practice is worrisome as it is rather unclear just how widely shared are the intuitions that philosophers appeal to. In this paper, I will first offer a brief overview of the debate over the ontology of musical works. I will argue that this debate is driven by a conflict between two seemingly plausible intuitions—the repeatability intuition and the creatability intuition—both of which may be defended on (...)
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  • A Return to Musical Idealism.Wesley D. Cray & Carl Matheson - 2017 - Australasian Journal of Philosophy 95 (4):702-715.
    In disputes about the ontology of music, musical idealism—that is, the view that musical compositions are ideas—has proven to be rather unpopular. We argue that, once we have a better grip on the ontology of ideas, we can formulate a version of musical idealism that is not only defensible, but plausible and attractive. We conclude that compositions are a particular kind of idea: they are completed ideas for musical manifestation.
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  • Philosophy of the Matrix.A. C. Paseau - 2017 - Philosophia Mathematica 25 (2):246-267.
    A mathematical matrix is usually defined as a two-dimensional array of scalars. And yet, as I explain, matrices are not in fact two-dimensional arrays. So are we to conclude that matrices do not exist? I show how to resolve the puzzle, for both contemporary and older mathematics. The solution generalises to the interpretation of all mathematical discourse. The paper as a whole attempts to reinforce mathematical structuralism by reflecting on how best to interpret mathematics.
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