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  1. It’s Not a Game: Accurate Representation with Toy Models.James Nguyen - 2020 - British Journal for the Philosophy of Science 71 (3):1013-1041.
    Drawing on ‘interpretational’ accounts of scientific representation, I argue that the use of so-called ‘toy models’ provides no particular philosophical puzzle. More specifically; I argue that once one gives up the idea that models are accurate representations of their targets only if they are appropriately similar, then simple and highly idealized models can be accurate in the same way that more complex models can be. Their differences turn on trading precision for generality, but, if they are appropriately interpreted, toy models (...)
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  • Naming and Referring: Table of Contents.Heidi Savage - manuscript
    This book is about whether reference to an individual is the essential feature of a proper name -- a widely held view -- or whether referring to an individual is simply a contingent feature. Three questions need resolving, then. First, whether all names in particular contexts are themselves referring devices. Second, whether recognizing names types and the consequent issue of their ambiguity can be resolved simply by distinguishing between name types and tokens thereof. Last, whether names are ever referential in (...)
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  • Perceptual Pluralism.Jake Quilty-Dunn - 2019 - Noûs 54 (4):807-838.
    Perceptual systems respond to proximal stimuli by forming mental representations of distal stimuli. A central goal for the philosophy of perception is to characterize the representations delivered by perceptual systems. It may be that all perceptual representations are in some way proprietarily perceptual and differ from the representational format of thought (Dretske 1981; Carey 2009; Burge 2010; Block ms.). Or it may instead be that perception and cognition always trade in the same code (Prinz 2002; Pylyshyn 2003). This paper rejects (...)
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  • The Menard Case and the Identity of a Literary Work of Art.Tomas Hribek - 2013 - In Tomas Koblizek, Petr Kot'átko & Martin Pokorný (eds.), Text + Work: The Menard Case. Litteraria Pragensia. pp. 6-34.
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  • Poetic Opacity: How to Paint Things with Words.Jesse J. Prinz & Eric Mandelbaum - 2015 - In John Gibson (ed.), The Philosophy of Poetry. Oxford, GB: Oxford University Press. pp. 63-87.
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  • Seeing an Image- Being-in-the-World: The Interconnections between Visuality, Spatiality, and Agency in Philosophical Hermeneutics.Ilya Inishev & Yuliya Biedash - 2013 - Problemos 84:170-183.
    The article is dedicated to the revelation of heuristic potential of hermeneutic image conception within discussions on contemporary visual culture. H. G. Gadamer has analysed the image as the visual, spatial and social phenomenon expanding and thereby transforming the accustomed notion of iconic experience. The image is not primarily an object of research for aesthetics and art criticism, but a social phenomenon which has to be considered in its real and imagined character as well as in its interrelations with the (...)
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  • Models, models, models: a deflationary view.Jay Odenbaugh - 2018 - Synthese 198 (Suppl 21):1-16.
    In this essay, I first consider a popular view of models and modeling, the similarity view. Second, I contend that arguments for it fail and it suffers from what I call “Hughes’ worry.” Third, I offer a deflationary approach to models and modeling that avoids Hughes’ worry and shows how scientific representations are of apiece with other types of representations. Finally, I consider an objection that the similarity view can deal with approximations better than the deflationary view and show that (...)
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  • Blockchain Identities: Notational Technologies for Control and Management of Abstracted Entities.Quinn Dupont - 2017 - Metaphilosophy 48 (5):634-653.
    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, (...)
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  • Are computer simulations experiments? And if not, how are they related to each other?Claus Beisbart - 2018 - European Journal for Philosophy of Science 8 (2):171-204.
    Computer simulations and experiments share many important features. One way of explaining the similarities is to say that computer simulations just are experiments. This claim is quite popular in the literature. The aim of this paper is to argue against the claim and to develop an alternative explanation of why computer simulations resemble experiments. To this purpose, experiment is characterized in terms of an intervention on a system and of the observation of the reaction. Thus, if computer simulations are experiments, (...)
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  • Sound and Notation: Comparative Study on Musical Ontology.So Jeong Park - 2017 - Dao: A Journal of Comparative Philosophy 16 (3):417-430.
    Music is said to consist of melody, rhythm, and harmony. Sound is assumed to be something that automatically follows once musical structure is determined. Sound, which is what actually impinges on our eardrums, has been so long forgotten in the history of musical theory. It is ironic that we do not talk about the music which we hear every day but rather are exclusively concerned about the abstracted structure behind it. This is a legacy of ancient Greek ideas about music, (...)
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  • Ontologia da Arte.António Lopes - 2013 - Compêndio Em Linha de Problemas de Filosofia Analítica.
    Este artigo aborda as principais teorias sobre a natureza metafísica das obras de arte, cobrindo as propostas eliminativistas, monistas e pluralistas. Entre estas últimas, é dado destaque ao trabalho sobre a ontologia das artes performativas, e em particular, da música. Termina-se com uma referência à recente viragem da discussão para o campo da meta-ontologia e a polémica sobre a plausibilidade do revisionismo ontológico no caso de artefactos ou objectos sociais.
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  • Combining universal beauty and cultural context in a unifying model of visual aesthetic experience.Christoph Redies - 2015 - Frontiers in Human Neuroscience 9.
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  • THE TRANSCENDENTAL METAPHYSIC OF G.F. STOUT: HIS DEFENCE AND ELABORATION OF TROPE THEORY.Fraser Macbride - 2014 - In A. Reboul (ed.), Mind, Value and Metaphysics: Papers Dedicated to Kevin Mulligan. Springer. pp. 141-58.
    G. F. Stout is famous as an early twentieth century proselyte for abstract particulars, or tropes as they are now often called. He advanced his version of trope theory to avoid the excesses of nominalism on the one hand and realism on the other. But his arguments for tropes have been widely misconceived as metaphysical, e.g. by Armstrong. In this paper, I argue that Stout’s fundamental arguments for tropes were ideological and epistemological rather than metaphysical. He moulded his scheme to (...)
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  • Against the Additive View of Imagination.Nick Wiltsher - 2016 - Australasian Journal of Philosophy 94 (2):266-282.
    According to the additive view of sensory imagination, mental imagery often involves two elements. There is an image-like element, which gives the experiences qualitative phenomenal character akin to that of perception. There is also a non-image element, consisting of something like suppositions about the image's object. This accounts for extra- sensory features of imagined objects and situations: for example, it determines whether an image of a grey horse is an image of Desert Orchid, or of some other grey horse. The (...)
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  • Analogue Magnitude Representations: A Philosophical Introduction.Jacob Beck - 2015 - British Journal for the Philosophy of Science 66 (4):829-855.
    Empirical discussions of mental representation appeal to a wide variety of representational kinds. Some of these kinds, such as the sentential representations underlying language use and the pictorial representations of visual imagery, are thoroughly familiar to philosophers. Others have received almost no philosophical attention at all. Included in this latter category are analogue magnitude representations, which enable a wide range of organisms to primitively represent spatial, temporal, numerical, and related magnitudes. This article aims to introduce analogue magnitude representations to a (...)
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  • The Ubiquity of Humanity and Textuality in Human Experience.Daihyun Chung - 2015 - Humanities 4 (4):885-904.
    Abstract: The so-called “crisis of the humanities” can be understood in terms of an asymmetry between the natural and social sciences on the one hand and the humanities on the other. While the sciences approach topics related to human experience in quantificational or experimental terms, the humanities turn to ancient, canonical, and other texts in the search for truths about human experience. As each approach has its own unique limitations, it is desirable to overcome or remove the asymmetry between them. (...)
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  • The Cognitive Design of Tools of Thought.Barbara Tversky - 2015 - Review of Philosophy and Psychology 6 (1):99-116.
    When thought overwhelms the mind, the mind puts it into the world, notably in diagrams and gestures.Both use space and arrays of elements, depictive and non-depictive, to convey ideas, concrete and abstract,clear and sketchy. The arrays and the non-depictive elements like boxes and arrows serve to showrelationships and organizations, thematic, categorical, and more. on paper, in the air, in the diagrammedworld. Human actions organize space to convey abstractions: spraction.
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  • Pictures Have Propositional Content.Alex Grzankowski - 2015 - Review of Philosophy and Psychology 6 (1):151-163.
    Although philosophers of art and aesthetics regularly appeal to a notion of ‘pictorial content’, there is little agreement over its nature. The present paper argues that pictures have propositional contents. This conclusion is reached by considering a style of argument having to do with the phenomenon of negation intended to show that pictures must have some kind of non-propositional content. I first offer reasons for thinking that arguments of that type fail. Second, I show that when properly understood, such arguments (...)
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  • Improvisational Artistry in Live Dance Performance as Embodied and Extended Agency.Aili Bresnahan - 2014 - Dance Research Journal 46 (1):84-94.
    This paper provides an account of improvisational artistry in live dance performance that construes the contribution of the dance performer as a kind of agency. Andy Clark’s theory of the embodied and extended mind is used in order to consider how this account is supported by research on how a thinking-while-doing person navigates the world. I claim here that while a dance performer’s improvisational artistry does include embodied and extended features that occur outside of the brain and nervous system that (...)
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  • How brains make chaos in order to make sense of the world.Christine A. Skarda & Walter J. Freeman - 1987 - Behavioral and Brain Sciences 10 (2):161-173.
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  • Referring to the Qualitative Dimension of Consciousness: Iconicity instead of Indexicality.Marc Champagne - 2014 - Dialogue 53 (1):135-182.
    This paper suggests that reference to phenomenal qualities is best understood as involving iconicity, that is, a passage from sign-vehicle to object that exploits a similarity between the two. This contrasts with a version of the ‘phenomenal concept strategy’ that takes indexicality to be central. However, since it is doubtful that phenomenal qualities are capable of causally interacting with anything, indexical reference seems inappropriate. While a theorist like David Papineau is independently coming to something akin to iconicity, I think some (...)
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  • Representations gone mental.Alex Morgan - 2014 - Synthese 191 (2):213-244.
    Many philosophers and psychologists have attempted to elucidate the nature of mental representation by appealing to notions like isomorphism or abstract structural resemblance. The ‘structural representations’ that these theorists champion are said to count as representations by virtue of functioning as internal models of distal systems. In his 2007 book, Representation Reconsidered, William Ramsey endorses the structural conception of mental representation, but uses it to develop a novel argument against representationalism, the widespread view that cognition essentially involves the manipulation of (...)
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  • Misbehaving Machines: The Emulated Brains of Transhumanist Dreams.Corry Shores - 2011 - Journal of Evolution and Technology 22 (1):10-22.
    Enhancement technologies may someday grant us capacities far beyond what we now consider humanly possible. Nick Bostrom and Anders Sandberg suggest that we might survive the deaths of our physical bodies by living as computer emulations.­­ In 2008, they issued a report, or “roadmap,” from a conference where experts in all relevant fields collaborated to determine the path to “whole brain emulation.” Advancing this technology could also aid philosophical research. Their “roadmap” defends certain philosophical assumptions required for this technology’s success, (...)
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  • Words and Images in Argumentation.Axel Arturo Barceló Aspeitia - 2012 - Argumentation 26 (3):355-368.
    Abstract In this essay, I will argue that images can play a substantial role in argumentation: exploiting information from the context, they can contribute directly and substantially to the communication of the propositions that play the roles of premises and conclusion. Furthermore, they can achieve this directly, i.e. without the need of verbalization. I will ground this claim by presenting and analyzing some arguments where images are essential to the argumentation process. Content Type Journal Article Pages 1-14 DOI 10.1007/s10503-011-9259-y Authors (...)
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  • Identities of Artefacts.Christoph Baumberger & Georg Brun - 2011 - Theoria 78 (1):47-74.
    In non-philosophical discourse, “identity” is often used when the specific character of artefacts is described or evaluated. We argue that this usage of “identity” can be explicated as referring to the symbol properties of artefacts as they are conceptualized in the symbol theory of Goodman and Elgin. This explication is backed by an analysis of various uses of “identity”. The explicandum clearly differs from the concepts of numerical identity, qualitative identity and essence, but it has a range of similarities with (...)
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  • Lorraine Daston and Peter Galison * Objectivity. [REVIEW]Nick Jardine - 2012 - British Journal for the Philosophy of Science 63 (4):885-893.
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  • (1 other version)Seeing-in, seeing-as, seeing-with: Looking through pictures.Emmanuel Alloa - 2010 - In Elisabeth Nemeth, Richard Heinrich & Wolfram Pichler (eds.), Image and Imaging in Philosophy, Science, and the Arts. Preproceedings of the 33rd International Wittgenstein Symposium. Austrian Ludwig Wittgenstein Society. pp. 179-190.
    In the constitution of contemporary image theory, Ludwig Wittgenstein’s philosophy has undoubtedly become a major conceptual reference. Rather than trying to establish what Wittgenstein’s own image theory could possibly look like, this paper would like to critically assess some of the advantages as well as some of the quandaries that arise when using Wittgenstein’s concept of ‘seeing-as’ for addressing the plural realities of images. While putting into evidence the tensions that come into play when applying what was initially a theory (...)
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  • Proceedings of Sinn und Bedeutung 9.Emar Maier, Corien Bary & Janneke Huitink (eds.) - 2005 - Nijmegen Centre for Semantics.
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  • Why feynman diagrams represent.Letitia Meynell - 2008 - International Studies in the Philosophy of Science 22 (1):39 – 59.
    There are two distinct interpretations of the role that Feynman diagrams play in physics: (i) they are calculational devices, a type of notation designed to keep track of complicated mathematical expressions; and (ii) they are representational devices, a type of picture. I argue that Feynman diagrams not only have a calculational function but also represent: they are in some sense pictures. I defend my view through addressing two objections and in so doing I offer an account of representation that explains (...)
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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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  • The Iconic-Symbolic Spectrum.Gabriel Greenberg - 2023 - Philosophical Review 132 (4):579-627.
    It is common to distinguish two great families of representation. Symbolic representations include logical and mathematical symbols, words, and complex linguistic expressions. Iconic representations include dials, diagrams, maps, pictures, 3-dimensional models, and depictive gestures. This essay describes and motivates a new way of distinguishing iconic from symbolic representation. It locates the difference not in the signs themselves, nor in the contents they express, but in the semantic rules by which signs are associated with contents. The two kinds of rule have (...)
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  • From Metaphysical Representations to Aesthetic Life: Toward the Encounter with the Other in the Perspective of Daoism.Massimiliano Lacertosa - 2023 - Albany: SUNY Press.
    Reevaluates Western and Chinese philosophical traditions to question the boundaries of entrenched conceptual frameworks.
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  • Courageous Love: K. C. Bhattacharyya on the Puzzle of Painful Beauty.Emily Lawson & Dominic Mciver Lopes - 2024 - Journal of the American Philosophical Association 2024:1-16.
    In the 1930s, the Bengali philosopher K. C. Bhattacharyya proposed a new theory of rasa, or aesthetic emotion, according to which aesthetic emotions are feelings that have other feelings as their intentional objects. This paper articulates how Bhattacharyya’s theory offers a novel solution to the puzzle of how it is both possible and rational to enjoy the kind of negative emotions that are inspired by tragic and sorrowful tales. The new solution is distinct from the conversion and compensation views that (...)
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  • Understanding Structural Representations.Marc Artiga - forthcoming - British Journal for the Philosophy of Science.
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  • How Imagination Informs.Joshua Myers - forthcoming - Philosophical Quarterly.
    An influential objection to the epistemic power of the imagination holds that it is uninformative. You cannot get more out of the imagination than you put into it, and therefore learning from the imagination is impossible. This paper argues, against this view, that the imagination is robustly informative. Moreover, it defends a novel account of how the imagination informs, according to which the imagination is informative in virtue of its analog representational format. The core idea is that analog representations represent (...)
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  • Pictorial syntax.Kevin J. Lande - 2024 - Mind and Language 39 (4):518-539.
    It is commonly assumed that images, whether in the world or in the head, do not have a privileged analysis into constituent parts. They are thought to lack the sort of syntactic structure necessary for representing complex contents and entering into sophisticated patterns of inference. I reject this assumption. “Image grammars” are models in computer vision that articulate systematic principles governing the form and content of images. These models are empirically credible and can be construed as literal grammars for images. (...)
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  • Analytic Aesthetics in Mainland China.Liu Jiachen - 2023 - East Asian Journal of Philosophy 2 (3):29-49.
    Since its emergence in the 1950s, analytic aesthetics has become the mainstream approach to aesthetics in the English-speaking world, and it has subsequently spread throughout most of the world, including mainland China. Although it was introduced into the Chinese academic world at an early time, around the late 1950s, and has been disseminated and researched in China over the past three decades, analytic aesthetics remains underdeveloped in China. Chinese academics tend to have little familiarity with, and exposure to, analytic approaches (...)
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  • Musical works are mind-independent artifacts.Elzė Sigutė Mikalonytė - 2023 - Synthese 203 (1):1-28.
    Realism about musical works is often tied to some type of Platonism. Nominalism, which posits that musical works exist and that they are concrete objects, goes with ontological realism much less often than Platonism: there is a long tradition which holds human-created objects (artifacts) to be mind-dependent. Musical Platonism leads to the well-known paradox of the impossibility of creating abstract objects, and so it has been suggested that only some form of nominalism becoming dominant in the ontology of art could (...)
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  • Truth and directness in pictorial assertion.Lukas Lewerentz & Emanuel Viebahn - 2023 - Linguistics and Philosophy 46 (6):1441–1465.
    This paper develops an account of accuracy and truth in pictorial assertion. It argues that there are two ways in which pictorial assertions can be indirect: with respect to their content and with respect to their target. This twofold indirectness explains how accurate, unedited pictures can be used to make false pictorial assertions. It captures the fishiness of true pictorial assertions involving target-indirectness, such as true pictorial assertions involving outdated pictures. And it raises the question whether target-indirectness may also arise (...)
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  • Where Images Make Their Wonder: An Introduction.Alessandro Cavazzana & Francesco Ragazzi - 2021 - JOLMA - The Journal for the Philosophy of Language, Mind, and the Arts 2 (1):7-20.
    The paper is an introduction to the third issue of the Journal for the Philosophy of Language, Mind and the Arts. The authors give an account of the theories that have most enriched the study of images since the second half of the twentieth century: analytical philosophy and visual culture studies. A distinction is made between the two philosophical traditions. On the one hand, in particular within the context of analytic philosophy, images have been studied as single entities in relationship (...)
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  • Susanne Langer and the American Development of Analytic Philosophy.Sander Verhaegh - 2022 - In Jeanne Peijnenburg & Sander Verhaegh (eds.), Women in the History of Analytic Philosophy. Cham: Springer. pp. 219-245.
    Susanne K. Langer is best known as a philosopher of culture and student of Ernst Cassirer. In this chapter, however, I argue that this standard picture ignores her contributions to the development of analytic philosophy in the 1920s and 1930s. I reconstruct the reception of Langer’s first book *The Practice of Philosophy*—arguably the first sustained defense of analytic philosophy by an American philosopher—and describe how prominent European philosophers of science such as Moritz Schlick, Rudolf Carnap, and Herbert Feigl viewed her (...)
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  • Informational Equivalence but Computational Differences? Herbert Simon on Representations in Scientific Practice.David Waszek - 2024 - Minds and Machines 34 (1):93-116.
    To explain why, in scientific problem solving, a diagram can be “worth ten thousand words,” Jill Larkin and Herbert Simon (1987) relied on a computer model: two representations can be “informationally” equivalent but differ “computationally,” just as the same data can be encoded in a computer in multiple ways, more or less suited to different kinds of processing. The roots of this proposal lay in cognitive psychology, more precisely in the “imagery debate” of the 1970s on whether there are image-like (...)
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  • Is Jessie right to end her life?Iddo Landau - 2022 - Philosophical Forum 53 (3):163-174.
    Presupposing that our consideration of ethical issues can be enriched by examining literary works, this paper focuses on Marsha Norman's play ‘night, Mother. The play describes the last hour and a half in the life of Jessie, a young woman who decides to die by suicide. Before ending her life, Jessie explains to her mother her reasons for her suicide. In the context of the play, these are presented as quite weighty and as, perhaps, justifying her decision. Scholarly research on (...)
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  • On Resisting Art.James Harold - 2023 - Journal of Aesthetics and Art Criticism 81 (1):35-45.
    What responsibilities do audiences have in engaging with artworks? Certain audience responses seem quite clear: for example, audiences should not vandalize or destroy artworks; they should not disrupt performances. This paper examines other kinds of resisting responses that audiences sometimes engage in, including petitioning the artist to change their works, altering copies of artworks, and creating new artworks in another artist’s fictional world. I argue for five claims: (1) while these actions can sometimes infringe on the rights of artists, the (...)
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  • VI—Aesthetic Beautification.Andrew Huddleston - 2022 - Proceedings of the Aristotelian Society 122 (2):119-139.
    Aesthetic beautification is a familiar artistic phenomenon. Even as they face death, heroes and heroines in operas still sing glorious music. Characters in Shakespearean tragedies still deliver beautifully eloquent speeches in the throes of despair. Even when depicting suffering and horror, paintings can still remain a transfixing delight for the eyes. In such cases, the work of art represents or expresses something to which we would, in ordinary life, attribute a negative valence, but it does so beautifully. Doubtless there is (...)
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  • Panpsychism and AI consciousness.Marcus Arvan & Corey J. Maley - 2022 - Synthese 200 (3):1-22.
    This article argues that if panpsychism is true, then there are grounds for thinking that digitally-based artificial intelligence may be incapable of having coherent macrophenomenal conscious experiences. Section 1 briefly surveys research indicating that neural function and phenomenal consciousness may be both analog in nature. We show that physical and phenomenal magnitudes—such as rates of neural firing and the phenomenally experienced loudness of sounds—appear to covary monotonically with the physical stimuli they represent, forming the basis for an analog relationship between (...)
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  • The Role of Teleological Thinking in Judgments of Persistence of Musical Works.Elzė Sigutė Mikalonytė & Vilius Dranseika - 2022 - Journal of Aesthetics and Art Criticism 80 (1):42-57.
    In his article “The Ontology of Musical Versions: Introducing the Hypothesis of Nested Types,” Nemesio Puy raises a hypothesis that continuity of the purpose is both a necessary and a sufficient condition for musical work’s identity. Puy’s hypothesis is relevant to two topics in cognitive psychology and experimental philosophy. The first topic is the prevalence of teleological reasoning about various objects and its influence on persistence and categorization judgments. The second one is the importance of an artist’s intention in the (...)
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  • The Putnam-Goodman-Kripke Paradox.Robert Kowalenko - 2022 - Acta Analytica 37 (4):575-594.
    The extensions of Goodman’s ‘grue’ predicate and Kripke’s ‘quus’ are constructed from the extensions of more familiar terms via a reinterpretation that permutes assignments of reference. Since this manoeuvre is at the heart of Putnam’s model-theoretic and permutation arguments against metaphysical realism (‘Putnam’s Paradox’), both Goodman’s New Riddle of Induction and the paradox about meaning that Kripke attributes to Wittgenstein are instances of Putnam’s. Evidence cannot selectively confirm the green-hypothesis and disconfirm the grue-hypothesis, because the theory of which the green-hypothesis (...)
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  • Who's Afraid of Mathematical Diagrams?Silvia De Toffoli - 2023 - Philosophers' Imprint 23 (1).
    Mathematical diagrams are frequently used in contemporary mathematics. They are, however, widely seen as not contributing to the justificatory force of proofs: they are considered to be either mere illustrations or shorthand for non-diagrammatic expressions. Moreover, when they are used inferentially, they are seen as threatening the reliability of proofs. In this paper, I examine certain examples of diagrams that resist this type of dismissive characterization. By presenting two diagrammatic proofs, one from topology and one from algebra, I show that (...)
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  • Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics.Ulianov Montano - 2013 - Dordrecht, Netherland: Springer.
    This book develops a naturalistic aesthetic theory that accounts for aesthetic phenomena in mathematics in the same terms as it accounts for more traditional aesthetic phenomena. Building upon a view advanced by James McAllister, the assertion is that beauty in science does not confine itself to anecdotes or personal idiosyncrasies, but rather that it had played a role in shaping the development of science. Mathematicians often evaluate certain pieces of mathematics using words like beautiful, elegant, or even ugly. Such evaluations (...)
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