Results for 'scientific perspectivism'

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  1. Scientific perspectivism.Ronald N. Giere - 2006 - Chicago: University of Chicago Press.
    Many people assume that the claims of scientists are objective truths. But historians, sociologists, and philosophers of science have long argued that scientific claims reflect the particular historical, cultural, and social context in which those claims were made. The nature of scientific knowledge is not absolute because it is influenced by the practice and perspective of human agents. Scientific Perspectivism argues that the acts of observing and theorizing are both perspectival, and this nature makes scientific (...)
  2. Scientific perspectivism: A philosopher of science's response to the challenge of big data biology.Werner Callebaut - 2012 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 43 (1):69-80.
    Big data biology—bioinformatics, computational biology, systems biology (including ‘omics’), and synthetic biology—raises a number of issues for the philosophy of science. This article deals with several such: Is data-intensive biology a new kind of science, presumably post-reductionistic? To what extent is big data biology data-driven? Can data ‘speak for themselves?’ I discuss these issues by way of a reflection on Carl Woese’s worry that “a society that permits biology to become an engineering discipline, that allows that science to slip into (...)
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  3.  95
    Scientific perspectivism in the phenomenological tradition.Philipp Berghofer - 2020 - European Journal for Philosophy of Science 10 (3):1-27.
    In current debates, many philosophers of science have sympathies for the project of introducing a new approach to the scientific realism debate that forges a middle way between traditional forms of scientific realism and anti-realism. One promising approach is perspectivism. Although different proponents of perspectivism differ in their respective characterizations of perspectivism, the common idea is that scientific knowledge is necessarily partial and incomplete. Perspectivism is a new position in current debates but it (...)
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  4. Scientific Perspectivism and Its Foes.Michela Massimi - 2012 - Philosophica 84 (1):25-52.
    In this paper, I address a prominent realist challenge recently raised by Anjan Chakravartty (2010) against scientific perspectivism. I offer a response to the challenge, by rethinking scientific perspectivism as a view on how we form scientific knowledge, as opposed to a view about what sort of objects we have scientific knowledge of. My response follows Ernest Sosa’s perspectivism in epistemology by drawing a distinction between truth and justification for our knowledge claims. With (...)
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  5. Scientific perspectivism: behind the stage door.Ronald N. Giere - 2009 - Studies in History and Philosophy of Science Part A 40 (2):221-223.
    Adopting the stage metaphor suggested in Brown’s review, and treating Scientific perspectivism as a play in five acts, I respond to his review as a playwright might respond to a generally favorable review. Taking the reader behind the stage door, I discuss the playwright’s intentions for each act, paying special attention to the expected audience for the play as a whole. The result, therefore, supplements the review from the standpoint of the playwright. It also provides answers to some (...)
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  6.  22
    Scientific Perspectivism and psychiatric diagnoses: respecting history and constraining relativism.Sam Fellowes - 2020 - European Journal for Philosophy of Science 11 (1):1-24.
    Historians and sociologists of psychiatry often claim that psychiatric diagnoses are discontinuous. That is, a particular diagnoses will be described in one way in one era and described quite differently in a different era. Historians and sociologists often draw epistemic consequences from such discontinuities, claiming that truth is pluralistic, provisional and historicised. These arguments do not readily fit in with how analytical philosophers of science approach scientific realism. I show how the pessimistic meta induction does not capture the point (...)
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  7.  19
    Scientific perspectivism: A philosopher of science’s response to the challenge of big data biology.Werner Callebaut - 2012 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 43 (1):69-80.
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  8. Scientific perspectivism: realism, antirealism, or a new paradigm? / Научный перспективизм: реализм, антиреализм или новая парадигма?Vadim Chaly - 2022 - Tomsk State University Journal of Philosophy, Sociology and Political Science 70 (4):80-90.
    The current state of philosophy of science is characterized by stasis in the struggle between realism and antirealism. In recent years, a number of authors have come out with a program of scientific perspectivism that claims to sublate this great collision and gain the status of a new epistemological paradigm: “perspectivism, or, better, perspectival realism, is one of the newest attempts to find a middle ground between scientific realism and antirealism” [1. P. 2]. Important milestones of (...)
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  9.  36
    Scientific Perspectivism and the Methodology of Modern Mathematical Physics.Noah Stemeroff - 2022 - Philosophy of Science 89 (3):504-520.
    Perspectival realists often appeal to the methodology of science to secure a realist account of the retention and continued success of scientific claims through the progress of science. However, in the context of modern physics, the retention and continued success of scientific claims are typically only definable within a mathematical framework. In this article, I argue that this concern leaves the perspectivist open to Cassirer’s neo-Kantian critique of the applicability of mathematics in the natural sciences. To support this (...)
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  10.  67
    Review: Scientific Perspectivism[REVIEW]A. Kukla - 2007 - Mind 116 (464):1122-1125.
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    Scientific Perspectivism[REVIEW]Jude P. Dougherty - 2007 - Review of Metaphysics 61 (2):419-420.
  12. Models and perspectives on stage: remarks on Giere’s Scientific perspectivism.Matthew J. Brown - 2009 - Studies in History and Philosophy of Science Part A 40 (2):213-220.
    Ron Giere’s recent book Scientific perspectivism sets out an account of science that attempts to forge a via media between two popular extremes: absolutist, objectivist realism on the one hand, and social constructivism or skeptical anti-realism on the other. The key for Giere is to treat both scientific observation and scientific theories as perspectives, which are limited, partial, contingent, context-, agent- and purpose-dependent, and pluralism-friendly, while nonetheless world-oriented and modestly realist. Giere’s perspectivism bears significant similarity (...)
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  13.  29
    On the Structure and Function of Scientific Perspectivism in Categorical Quantum Mechanics.Vassilios Karakostas & Elias Zafiris - 2022 - British Journal for the Philosophy of Science 73 (3):811-848.
    Contemporary scientific perspectivism is primarily viewed as a methodological framework of how we obtain and form scientific knowledge of nature, through a broadly perspectivist process, especially, with reference to quantum mechanics. In the present study, this is implemented by representing categorically the global structure of a quantum algebra of events in terms of structured interconnected families of local Boolean probing frames, realized as suitable perspectives or contexts for measuring physical quantities. The essential philosophical meaning of the proposed (...)
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  14.  22
    Ronald N. Giere. Scientific Perspectivism. iv + 151 pp., illus., index. Chicago/London: University of Chicago Press, 2006. $30 .Stephen H. Kellert;, Helen E. Longino;, C. Kenneth Waters . Scientific Pluralism. xxix + 248 pp., figs., tables, index. Minneapolis/London: University of Minnesota Press, 2006. $50. [REVIEW]Gregory Radick - 2009 - Isis 100 (1):206-207.
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  15. Scientific Realism Within Perspectivism and Perspectivism Within Scientific Realism.Evandro Agazzi - 2016 - Axiomathes 26 (4):349-365.
    Perspectivism is often understood as a conception according to which subjective conditions inevitably affect our knowledge and, therefore, we are never confronted with reality and facts but only with interpretations. Hence, subjectivism and anti-realism are usually associated with perspectivism. The thesis of this paper is that, especially in the case of the sciences, perspectivism can be better understood as an appreciation of the cognitive attitude that consists in considering reality only from a certain ‘point of view’, in (...)
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  16. Understanding Perspectivism (Open Access): Scientific Challenges and Methodological Prospects.Michela Massimi & Casey D. McCoy - 2020 - New York, NY, USA: Routledge.
    This edited collection is the first of its kind to explore the view called perspectivism in philosophy of science. The book brings together an array of essays that reflect on the methodological promises and scientific challenges of perspectivism in a variety of fields such as physics, biology, cognitive neuroscience, and cancer research, just as a few examples. What are the advantages of using a plurality of perspectives in a given scientific field and for interdisciplinary research? Can (...)
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  17. Twenty-first century perspectivism: The role of emotions in scientific inquiry.Mark Alfano - 2017 - Studi di Estetica 7 (1):65-79.
    How should emotions figure in scientific practice? I begin by distinguishing three broad answers to this question, ranging from pessimistic to optimistic. Confirmation bias and motivated numeracy lead us to cast a jaundiced eye on the role of emotions in scientific inquiry. However, reflection on the essential motivating role of emotions in geniuses makes it less clear that science should be evacuated of emotion. I then draw on Friedrich Nietzsche’s perspectivism to articulate a twenty-first century epistemology of (...)
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  18.  44
    The paradox of scientific expertise: A perspectivist approach to knowledge asymmetries.Hugo Fjelsted Alrøe & Egon Noe - 2011 - Fachsprache - International Journal of Specialized Communication (3–4):152-167.
    Modern societies depend on a growing production of scientific knowledge, which is based on the functional differentiation of science into still more specialised scientific disciplines and subdisciplines. This is the basis for the paradox of scientific expertise: The growth of science leads to a fragmentation of scientific expertise. To resolve this paradox, the present paper investigates three hypotheses: 1) All scientific knowledge is perspectival. 2) The perspectival structure of science leads to specific forms of knowledge (...)
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  19.  44
    A perspectivist approach to the strategic planning of programmatic scientific research.William J. McGuire - 1989 - In Barry Gholson (ed.), Psychology of Science: Contributions to Metascience. Cambridge University Press. pp. 214--245.
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  20. Perspectivism and Special Relativity.Mahdi Khalili - 2021 - Teorie Vědy / Theory of Science 43 (2):191-217.
    The special theory of relativity holds significant interest for scientific perspectivists. In this paper, I distinguish between two related meanings of “perspectival,” and argue that reference frames are perspectives, provided that perspectival means “being conditional” rather than “being partial.” Frame-dependent properties such as length, time duration, and simultaneity, are not partially measured in a reference frame, but their measurements are conditional on the choice of frame. I also discuss whether the constancy of the speed of light depends on perspectival (...)
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  21.  21
    Some perspective on perspectivism: Michela Massimi and Casey D. McCoy (eds): Understanding perspectivism. Scientific challenges and methodological prospects. New York: Routledge, 2020, 200pp.Alexander Rueger - 2020 - Metascience 29 (2):193-196.
  22. Perspectivism, inconsistent models, and contrastive explanation.Anjan Chakravartty - 2010 - Studies in History and Philosophy of Science Part A 41 (4):405-412.
    It is widely recognized that scientific theories are often associated with strictly inconsistent models, but there is little agreement concerning the epistemic consequences. Some argue that model inconsistency supports a strong perspectivism, according to which claims serving as interpretations of models are inevitably and irreducibly perspectival. Others argue that in at least some cases, inconsistent models can be unified as approximations to a theory with which they are associated, thus undermining this kind of perspectivism. I examine the (...)
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  23.  16
    Perspectivism in current epigenetics.Karim Bschir - 2020 - European Journal for Philosophy of Science 10 (3):1-18.
    Discussions about perspectivism in the current philosophical literature often focus on questions concerning perspectival modeling or the compatibility between perspectivism and realism. In this paper, I propose to extend the debate on perspectivism by taking into account the social dimension of scientific perspectives. Scientific perspectives are always adopted and advocated for by individual scientists and groups of scientists with different epistemic affinities. I describe an example of a current and ongoing controversy in the field of (...)
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  24.  4
    Perspectivism: A Contribution to the Philosophy of the Social Sciences.Kenneth Smith - 2020 - New York, NY: The Bardwell Press.
    Perspectivism: A Contribution to the Philosophy of the Social Sciences advances the philosophy of perspectivism, showing how its capacity to assess competing views of a particular concept by approaching them as different 'sides' of a multi-dimensional object supports a concept of 'adequate' rather than 'absolute' truth. Presenting four case studies - of the social scientific concepts of power, equality, crime, and sex and gender - Smith demonstrates the manner in which the perspectivist approach does not take all (...)
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  25. Realism and Explanatory Perspectivism.Juha Saatsi - 2020 - In Michela Massimi & Casey D. McCoy (eds.), Understanding Perspectivism (Open Access): Scientific Challenges and Methodological Prospects. New York, NY, USA: Routledge.
    This chapter defends a (minimal) realist conception of progress in scientific understanding in the face of the ubiquitous plurality of perspectives in science. The argument turns on the counterfactual-dependence framework of explanation and understanding, which is illustrated and evidenced with reference to different explanations of the rainbow.
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  26.  57
    Realism, perspectivism, and disagreement in science.Michela Massimi - 2019 - Synthese 198 (Suppl 25):6115-6141.
    This paper attends to two main tasks. First, I introduce the notion of perspectival disagreement in science. Second, I relate perspectival disagreement in science to the broader issue of realism about science: how to maintain realist ontological commitments in the face of perspectival disagreement among scientists? I argue that often enough perspectival disagreement is not at the level of the scientific knowledge claims but rather of the methodological and justificatory principles. I introduce and clarify the notion of ‘agreeing-whilst-perspectivally-disagreeing’ with (...)
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  27.  27
    Realism, perspectivism, and disagreement in science.Michela Massimi - 2019 - Synthese 198 (Suppl 25):6115-6141.
    This paper attends to two main tasks. First, I introduce the notion of perspectival disagreement in science. Second, I relate perspectival disagreement in science to the broader issue of realism about science: how to maintain realist ontological commitments in the face of perspectival disagreement among scientists? I argue that often enough perspectival disagreement is not at the level of the scientific knowledge claims but rather of the methodological and justificatory principles. I introduce and clarify the notion of ‘agreeing-whilst-perspectivally-disagreeing’ with (...)
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  28.  23
    Review of "Understanding Perspectivism: Scientific Challenges and Methodological Prospects". [REVIEW]Lucas J. Matthews - 2019 - Notre Dame Philosophical Review 2019.
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  29.  16
    Realism, perspectivism, and disagreement in science.Michela Massimi - 2019 - Synthese 198 (Suppl 25):6115-6141.
    This paper attends to two main tasks. First, I introduce the notion of perspectival disagreement in science. Second, I relate perspectival disagreement in science to the broader issue of realism about science: how to maintain realist ontological commitments in the face of perspectival disagreement among scientists? I argue that often enough perspectival disagreement is not at the level of the scientific knowledge claims but rather of the methodological and justificatory principles. I introduce and clarify the notion of ‘agreeing-whilst-perspectivally-disagreeing’ with (...)
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  30.  37
    Perspectivism Versus a Completed Copernican Revolution.Thomas Nickles - 2016 - Axiomathes 26 (4):367-382.
    I discuss changes of perspective of four kinds in science and about science. Section 2 defends a perspectival nonrealism—something akin to Giere’s perspectival realism but not a realism—against the idea of complete, “Copernican” objectivity. Section 3 contends that there is an inverse relationship between epistemological conservatism and scientific progress. Section 4 casts doubt on strong forms of scientific realism by taking a long-term historical perspective that includes future history. Section 5 defends a partial reversal in the status of (...)
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  31.  25
    Natural Law, the modeling relation, and two roots of perspectivism.Markus Mikael Weckström - 2023 - Synthese 201 (3):1-35.
    Scientific perspectivism, or perspectival realism, is a view according to which scientific knowledge is neither utterly objective nor independent of the world “as it is”, but always tied to some particular ways of conceptualization and interaction with Nature. In the present paper, I employ Robert Rosen’s concept of the modeling relation for arguing that there are two basic reasons why our knowledge of natural systems is perspectival in this sense. The first of these pertains to the dualism (...)
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  32. From Phenomenological-Hermeneutical Approaches to Realist Perspectivism.Mahdi Khalili - 2022 - European Journal for Philosophy of Science 12 (4):1-26.
    This paper draws on the phenomenological-hermeneutical approaches to philosophy of science to develop realist perspectivism, an integration of experimental realism and perspectivism. Specifically, the paper employs the distinction between “manifestation” and “phenomenon” and it advances the view that the evidence of a real entity is “explorable” in order to argue that instrumentally-mediated robust evidence indicates real entities. Furthermore, it underpins the phenomenological notion of the horizonal nature of scientific observation with perspectivism, so accounting for scientific (...)
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  33. Giere’s instrumental Perspectivism.Kane Baker - 2020 - European Journal for Philosophy of Science 10 (3):1-19.
    When Ron Giere introduced perspectivism into philosophy of science, he provided a perspectivist analysis of both scientific instruments and scientific theorizing. Today, there is a burgeoning literature that extends Giere’s analysis of theorizing, with many philosophers examining the perspectivist approach to aspects of theorizing such as models, laws, explanations, and so on. However, relatively little attention has been paid to Giere’s analysis of instruments. In this article, I hope to fill this gap. I argue that the perspectivist (...)
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  34.  41
    Instrumental Perspectivism: Is AI Machine Learning Technology like NMR Spectroscopy?Sandra D. Mitchell - unknown
    The question, “Will science remain human?” expresses a worry that deep learning algorithms will replace scientists in making crucial judgments of classification and inference and that something crucial will be lost if that happens. Ever since the introduction of telescopes and microscopes humans have relied on technologies to “extend” beyond human sensory perception in acquiring scientific knowledge. In this paper I explore whether the ways in which new learning technologies “extend” beyond human cognitive aspects of science can be treated (...)
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  35. Symmetries, Indexicality and the Perspectivist Stance.Quentin Ruyant - 2021 - International Studies in the Philosophy of Science 34 (1):21-39.
    I critically examine the assumption that the theoretical structure that varies under theoretical symmetries is redundant and should be eliminated from a metaphysical picture of the universe, following a ‘symmetry to reality’ inference. I do so by analysing the status of coordinate change symmetries taking a pragmatic approach. I argue that coordinate systems function as indexical devices, and play an important pragmatic role for representing concrete physical systems. I examine the implications of considering this pragmatic role seriously, taking what I (...)
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  36.  43
    The Potential of Perspectivism for Science Education.Jacob V. Pearce - 2013 - Educational Philosophy and Theory 45 (5):531-545.
    Many science teachers are presented with the challenge of characterizing science as a dynamic, human endeavour. Perspectivism, as a hermeneutic philosophy of science, has the potential to be a learning tool for teachers as they elucidate the complex nature of science. Developed earlier by Nietzsche and others, perspectivism has recently re-emerged in the context of the philosophy of science in the work of Ronald Giere. Giere presents a compelling case that scientific theories and scientific observation are (...)
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  37.  19
    Perspectivism and truth in sociology: Bourdieu and Giddens.Jorge Gibert Galassi - 2015 - Cinta de Moebio 52:69-78.
    From the traditional point of view, power and truth are not related. Since 20th century there has been a social and historical breach in conventional assumptions about the relationship between power and truth. On one hand, it is generally accepted that scientific facts are considered artificial, in the sense of being constructed. This assumption neither implied any kind of fraud nor did it mean that they could be created ex-nihilo. But the interpretation of Kuhn as well as the subsequent (...)
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  38.  26
    Reductivism versus perspectivism versus holism: A key theme in philosophy of science, and its application to modern linguistics.Finn Collin & Per Durst-Andersen - 2023 - Theoria 90 (1):56-80.
    We use recent developments within philosophy of science and within certain strands of linguistic research to throw light on each other. According to Ronald Giere's perspectivist philosophy of science, the scientific understanding of reality must proceed along different, mutually irreducible lines of approach. Giere's proposal, however, leaves unresolved the problem of how to integrate the ever‐growing multitude of highly diverse scientific accounts of what is, after all, one and the same world. We propose a technique for the alignment (...)
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  39. Authors’ Response: A Perspectivist View on the Perspectivist View of Interdisciplinary Science.H. F. Alrøe & E. Noe - 2014 - Constructivist Foundations 10 (1):88-95.
    Upshot: In our response we focus on five questions that point to important common themes in the commentaries: why start in wicked problems, what kind of system is a scientific perspective, what is the nature of second-order research processes, what does this mean for understanding interdisciplinary work, and how may polyocular research help make real-world decisions.
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  40.  21
    Data identity and perspectivism.Franklin Jacoby - 2020 - Synthese 198 (12):11695-11711.
    This paper uses several case studies to suggest that (1) two prominent definitions of data do not on their own capture how scientists use data and (2) a novel perspectival account of data is needed. It then outlines some key features of what this account could look like. Those prominent views, the relational and representational, do not fully capture what data are and how they function in science. The representational view is insensitive to the scientific context in which data (...)
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  41.  56
    Perspectivismo na filosofia da ciência: um estudo de caso na física quântica / Perspectivism in philosophy of science: a case-study in quantum physics.Décio Krause & Jonas Rafael Becker Arenhart - 2013 - Scientiae Studia 11 (1):159-183.
    PORTUGUESE: Neste artigo, apresentaremos uma visão particular do desenvolvimento de teorias científicas que denominamos (inspirados em Ortega y Gasset) "perspectivismo". Discutiremos como, através desse enfoque, é possível compatibilizar diversas descrições aparentemente distintas e incompatíveis de uma suposta realidade que se investiga. Fazemos isso distinguindo entre a "realidade" (R) e a "descrição empírica da realidade" (Re). Aceitando que podemos ter diversas descrições empíricas de uma mesma realidade, discutimos o caso particular em que esse esquema é utilizado nos debates atuais acerca da (...)
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  42.  17
    Getting the Big Picture in Perspectivist Optics.A. Mark Smith - 1981 - Isis 72 (4):568-589.
    In the first section I outline the theory of abstraction, discussing first its con- ceptual basis, then its psychological-epistemological basis, and last its causal basis. My purpose throughout is to show how these bases, and thus the theory itself, were not only paramountly Aristotelian, but also eminently sensible. In the second section I draw the perspectivist account of vision within the bounds of the theory of abstraction and show stage by stage how that account unfolds coherently within those bounds. This (...)
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  43.  17
    Introduction to topical collection on perspectivism in science: metaphysical and epistemological reflections.Michela Massimi - 2021 - European Journal for Philosophy of Science 11 (2):1-2.
    This topical collection was an invitation to offer a better understanding of the philosophical view called “perspectivism” and its relevance to science by exploring a variety of metaphysical and epistemological issues arising from perspectivism in science. The papers here collected deliver on this two-fold goal. I will not try to summarise each of them, but suffice to say that they map onto three broad inter-related themes, which I shall call scientific practice, normativity, and history.
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  44.  37
    Physicists’ views on scientific realism.Céline Henne, Hannah Tomczyk & Christoph Sperber - 2024 - European Journal for Philosophy of Science 14 (1):1-27.
    Do physicists believe that general relativity is true, and that electrons and phonons exist, and if so, in what sense? To what extent does the spectrum of positions among physicists correspond to philosophical positions like scientific realism, instrumentalism, or perspectivism? Does agreement with these positions correlate with demographic factors, and are realist physicists more likely to support research projects purely aimed at increasing knowledge? We conducted a questionnaire study to scrutinize the philosophical stances of physicists. We received responses (...)
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  45.  3
    Scientific progress: a study concerning the nature of the relation between successive scientific theories.Craig Dilworth - 1981 - Hingham, MA, U.S.A.: Sold and distributed in the U.S.A. and Canada by Kluwer Academic.
    Featuring the Gestalt Model and the Perspectivist conception of science, this book is unusual in its non-relativistic development of the idea that successive scientific theories are logically incommensurable. This edition includes four new appendices in which the central ideas of the book are applied to subatomic physics, the distinction between laws and theories, the relation between absolute and relative conceptions of space, and the environmental issue of sustainable development.
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  46. Sandra B. Rosenthal Cultural Pluralism and the Issue of Relativism: The Significance of Pragmatic Perspectivism.Pragmatic Perspectivism - 2005 - In Friedrich Wallner, Martin J. Jandl & Kurt Greiner (eds.), Science, Medicine, and Culture: Festschrift for Fritz G. Wallner. Peter Lang. pp. 98.
     
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  47. Perspectival realism and norms of scientific representation.Quentin Ruyant - 2020 - European Journal for Philosophy of Science 10 (2):1-17.
    Perspectival realism combines two apparently contradictory aspects: the epistemic relativity of perspectives and the mind-independence of realism. This paper examines the prospects for a coherent perspectival realism, taking the literature on scientific representation as a starting point. It is argued that representation involves two types of norms, referred to as norms of relevance and norms of accuracy. Norms of relevance fix the domain of application of a theory and the way it categorises the world, and norms of accuracy give (...)
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  48. Essay Review Thinking Scientifically.Thinking Scientifically - 1995 - Annals of Science 52:615-618.
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  49. Randomness and Mathematical Proof.Scientific American - unknown
    Almost everyone has an intuitive notion of what a random number is. For example, consider these two series of binary digits: 01010101010101010101 01101100110111100010 The first is obviously constructed according to a simple rule; it consists of the number 01 repeated ten times. If one were asked to speculate on how the series might continue, one could predict with considerable confidence that the next two digits would be 0 and 1. Inspection of the second series of digits yields no such comprehensive (...)
     
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  50. Randomness in Arithmetic.Scientific American - unknown
    What could be more certain than the fact that 2 plus 2 equals 4? Since the time of the ancient Greeks mathematicians have believed there is little---if anything---as unequivocal as a proved theorem. In fact, mathematical statements that can be proved true have often been regarded as a more solid foundation for a system of thought than any maxim about morals or even physical objects. The 17th-century German mathematician and philosopher Gottfried Wilhelm Leibniz even envisioned a ``calculus'' of reasoning such (...)
     
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