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  1. The Internal Relatedness of All Things.J. Schaffer - 2010 - Mind 119 (474):341-376.
    The argument from internal relatedness was one of the major nineteenth century neo-Hegelian arguments for monism. This argument has been misunderstood, and may even be sound. The argument, as I reconstruct it, proceeds in two stages: first, it is argued that all things are internally related in ways that render them interdependent; second, the substantial unity of the whole universe is inferred from the interdependence of all of its parts. The guiding idea behind the argument is that failure of free (...)
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  • A Cognitive Approach to Benacerraf's Dilemma.Luke Jerzykiewicz - 2009 - Dissertation, University of Western Ontario
    One of the important challenges in the philosophy of mathematics is to account for the semantics of sentences that express mathematical propositions while simultaneously explaining our access to their contents. This is Benacerraf’s Dilemma. In this dissertation, I argue that cognitive science furnishes new tools by means of which we can make progress on this problem. The foundation of the solution, I argue, must be an ontologically realist, albeit non-platonist, conception of mathematical reality. The semantic portion of the problem can (...)
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  • The philosophy of information as a conceptual framework.Luciano Floridi - 2010 - Knowledge, Technology & Policy 23 (1-2):1-31.
    The article contains the replies to the collection of contributions discussing my research on the philosophy of information.
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  • The philosophy of mathematics and the independent 'other'.Penelope Rush - unknown
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  • David Bostock: Philosophy of Mathematics: An Introduction: Wiley-Blackwell, Oxford, 2009, 332 pp, BPD 55.00, ISBN: 978-1405189927 , BPD 20.99, ISBN: 978-1-4051-8991-0. [REVIEW]Holger A. Leuz - 2011 - Erkenntnis 74 (3):425-428.
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  • Deferentialism.Chris Daly & David Liggins - 2011 - Philosophical Studies 156 (3):321-337.
    There is a recent and growing trend in philosophy that involves deferring to the claims of certain disciplines outside of philosophy, such as mathematics, the natural sciences, and linguistics. According to this trend— deferentialism , as we will call it—certain disciplines outside of philosophy make claims that have a decisive bearing on philosophical disputes, where those claims are more epistemically justified than any philosophical considerations just because those claims are made by those disciplines. Deferentialists believe that certain longstanding philosophical problems (...)
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  • Nihilism without Self-Contradiction.David Liggins - 2008 - Royal Institute of Philosophy Supplement 62:177-196.
    in Robin Le Poidevin (ed.) Being: Developments in Contemporary Metaphysics. Cambridge: Cambridge University Press. Peter van Inwagen claims that there are no tables or chairs. He also claims that sentences such as ‘There are chairs here’, which seem to imply their existence, are often true. This combination of views opens van Inwagen to a charge of self-contradiction. I explain the charge, and van Inwagen’s response to it, which involves the claim that sentences like ‘There are tables’ shift their truth-conditions between (...)
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  • Number Concepts: An Interdisciplinary Inquiry.Richard Samuels & Eric Snyder - 2024 - Cambridge University Press.
    This Element, written for researchers and students in philosophy and the behavioral sciences, reviews and critically assesses extant work on number concepts in developmental psychology and cognitive science. It has four main aims. First, it characterizes the core commitments of mainstream number cognition research, including the commitment to representationalism, the hypothesis that there exist certain number-specific cognitive systems, and the key milestones in the development of number cognition. Second, it provides a taxonomy of influential views within mainstream number cognition research, (...)
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  • Rules to Infinity: The Normative Role of Mathematics in Scientific Explanation.Mark Povich - 2024 - Oxford University Press USA.
    One central aim of science is to provide explanations of natural phenomena. What role(s) does mathematics play in achieving this aim? How does mathematics contribute to the explanatory power of science? Rules to Infinity defends the thesis, common though perhaps inchoate among many members of the Vienna Circle, that mathematics contributes to the explanatory power of science by expressing conceptual rules, rules which allow the transformation of empirical descriptions. Mathematics should not be thought of as describing, in any substantive sense, (...)
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  • Modelling the psychological structure of reasoning.M. A. Winstanley - 2022 - European Journal for Philosophy of Science 12 (2):1-27.
    Mathematics and logic are indispensable in science, yet how they are deployed and why they are so effective, especially in the natural sciences, is poorly understood. In this paper, I focus on the how by analysing Jean Piaget’s application of mathematics to the empirical content of psychological experiment; however, I do not lose sight of the application’s wider implications on the why. In a case study, I set out how Piaget drew on the stock of mathematical structures to model psychological (...)
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  • Grammar, Numerals, and Number Words: A Wittgensteinian Reflection on the Grammar of Numbers.Dennis De Vera - 2014 - Social Science Diliman 10 (1):53-100.
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  • The Enhanced Indispensability Argument, the circularity problem, and the interpretability strategy.Jan Heylen & Lars Arthur Tump - 2019 - Synthese 198 (4):3033-3045.
    Within the context of the Quine–Putnam indispensability argument, one discussion about the status of mathematics is concerned with the ‘Enhanced Indispensability Argument’, which makes explicit in what way mathematics is supposed to be indispensable in science, namely explanatory. If there are genuine mathematical explanations of empirical phenomena, an argument for mathematical platonism could be extracted by using inference to the best explanation. The best explanation of the primeness of the life cycles of Periodical Cicadas is genuinely mathematical, according to Baker (...)
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  • Soul‐Making, Theosis, and Evolutionary History: An Irenaean Approach.James Henry Collin - 2019 - Zygon 54 (2):523-541.
    In Romans 5, St. Paul claims that death came into the world through Adam's sin. Many have taken this to foist on us a fundamentalist reading of Genesis. If death is the result of human sin, then, apparently, there cannot have been death in the world prior to human sin. This, however, is inconsistent with contemporary evolutionary biology, which requires that death predates the existence of modern humans. Although the relationship between Romans 5, Genesis, and contemporary science has been much (...)
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  • Independence of the Grossone-Based Infinity Methodology from Non-standard Analysis and Comments upon Logical Fallacies in Some Texts Asserting the Opposite.Yaroslav D. Sergeyev - 2019 - Foundations of Science 24 (1):153-170.
    This paper considers non-standard analysis and a recently introduced computational methodology based on the notion of ①. The latter approach was developed with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework and in all the situations requiring these notions. Non-standard analysis is a classical purely symbolic technique that works with ultrafilters, external and internal sets, standard and non-standard numbers, etc. In its turn, the ①-based methodology does not use any of these (...)
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  • Absence perception and the philosophy of zero.Neil Barton - 2020 - Synthese 197 (9):3823-3850.
    Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...)
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  • Towards a Fictionalist Philosophy of Mathematics.Robert Knowles - 2015 - Dissertation, University of Manchester
    In this thesis, I aim to motivate a particular philosophy of mathematics characterised by the following three claims. First, mathematical sentences are generally speaking false because mathematical objects do not exist. Second, people typically use mathematical sentences to communicate content that does not imply the existence of mathematical objects. Finally, in using mathematical language in this way, speakers are not doing anything out of the ordinary: they are performing straightforward assertions. In Part I, I argue that the role played by (...)
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  • Naturalizing Badiou: mathematical ontology and structural realism.Fabio Gironi - 2014 - New York: Palgrave-Macmillan.
    This thesis offers a naturalist revision of Alain Badiou’s philosophy. This goal is pursued through an encounter of Badiou’s mathematical ontology and theory of truth with contemporary trends in philosophy of mathematics and philosophy of science. I take issue with Badiou’s inability to elucidate the link between the empirical and the ontological, and his residual reliance on a Heideggerian project of fundamental ontology, which undermines his own immanentist principles. I will argue for both a bottom-up naturalisation of Badiou’s philosophical approach (...)
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  • On the Indispensability of (Im)Possibilia.Martin Vacek - 2013 - Humana Mente 6 (25).
    According to modal realism formulated by David Lewis, there exist concrete possible worlds. As he argues the hypothesis is serviceable and that is a sufficient reason to think it is true. On the other side, Lewis does not consider the pragmatic reasons to be conclusive. He admits that the theoretical benefits of modal realism can be illusory or that the acceptance of controversial ontology for the sake of theoretical benefits might be misguided in the first place. In the first part (...)
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  • Computing as a Science: A Survey of Competing Viewpoints. [REVIEW]Matti Tedre - 2011 - Minds and Machines 21 (3):361-387.
    Since the birth of computing as an academic discipline, the disciplinary identity of computing has been debated fiercely. The most heated question has concerned the scientific status of computing. Some consider computing to be a natural science and some consider it to be an experimental science. Others argue that computing is bad science, whereas some say that computing is not a science at all. This survey article presents viewpoints for and against computing as a science. Those viewpoints are analyzed against (...)
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  • Program Verification and Functioning of Operative Computing Revisited: How about Mathematics Engineering? [REVIEW]Uri Pincas - 2011 - Minds and Machines 21 (2):337-359.
    The issue of proper functioning of operative computing and the utility of program verification, both in general and of specific methods, has been discussed a lot. In many of those discussions, attempts have been made to take mathematics as a model of knowledge and certitude achieving, and accordingly infer about the suitable ways to handle computing. I shortly review three approaches to the subject, and then take a stance by considering social factors which affect the epistemic status of both mathematics (...)
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  • Spacetime, Ontology, and Structural Realism.Edward Slowik - 2005 - International Studies in the Philosophy of Science 19 (2):147 – 166.
    This essay explores the possibility of constructing a structural realist interpretation of spacetime theories that can resolve the ontological debate between substantivalists and relationists. Drawing on various structuralist approaches in the philosophy of mathematics, as well as on the theoretical complexities of general relativity, our investigation will reveal that a structuralist approach can be beneficial to the spacetime theorist as a means of deflating some of the ontological disputes regarding similarly structured spacetimes.
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  • A psychological theory of reasoning as logical evidence: a Piagetian perspective.M. A. Winstanley - 2021 - Synthese 199 (3-4):10077-10108.
    Many contemporary logicians acknowledge a plurality of logical theories and accept that theory choice is in part motivated by logical evidence. However, just as there is no agreement on logical theories, there is also no consensus on what constitutes logical evidence. In this paper, I outline Jean Piaget’s psychological theory of reasoning and show how he used it to diagnose and solve one of the paradoxes of material implication. I assess Piaget’s use of psychology as a source of evidence for (...)
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  • Physicalism Without the Idols of Mathematics.László E. Szabó - 2023 - Foundations of Science:1-20.
    I will argue that the ontological doctrine of physicalism inevitably entails the denial that there is anything conceptual in logic and mathematics. The elements of a formal system, even if they are tagged by suggestive names, are merely meaningless parts of a physically existing machinery, which have nothing to do with concepts, because they have nothing to do with the actual things. The only situation in which they can become meaning-carriers is when they are involved in a physical theory. But (...)
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  • Alethic Pluralism and the Role of Reference in the Metaphysics of Truth.Brian Ball - 2017 - Southern Journal of Philosophy 55 (1):116-135.
    In this paper, I outline and defend a novel approach to alethic pluralism, the thesis that truth has more than one metaphysical nature: where truth is, in part, explained by reference, it is relational in character and can be regarded as consisting in correspondence; but where instead truth does not depend upon reference it is not relational and involves only coherence. In the process, I articulate a clear sense in which truth may or may not depend upon reference: this involves (...)
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  • A General Theory of Objectivity: Contributions from the Reformational Philosophy Tradition.Richard M. Gunton, Marinus D. Stafleu & Michael J. Reiss - 2022 - Foundations of Science 27 (3):941-955.
    Objectivity in the sciences is a much-touted yet problematic concept. It is sometimes held up as characterising scientific knowledge, yet operational definitions are diverse and call for such paradoxical genius as the ability to see without a perspective, to predict repeatability, to elicit nature’s own self-revelation, or to discern the structure of reality with inerrancy. Here we propose a positive and general definition of objectivity based on work in the Reformational philosophy tradition. We recognise a suite of relation-frames–ways in which (...)
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  • Indispensability, causation and explanation.Sorin Bangu - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):219-232.
    When considering mathematical realism, some scientific realists reject it, and express sympathy for the opposite view, mathematical nominalism; moreover, many justify this option by invoking the causal inertness of mathematical objects. The main aim of this note is to show that the scientific realists’ endorsement of this causal mathematical nominalism is in tension with another position some of them also accept, the doctrine of methodological naturalism. By highlighting this conflict, I intend to tip the balance in favor of a rival (...)
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  • Relationism and the Problem of Order.Michele Paolini Paoletti - 2023 - Acta Analytica 38 (2):245-273.
    Relationism holds that objects entirely depend on relations or that they must be eliminated in favour of the latter. In this article, I raise a problem for relationism. I argue that relationism cannot account for the order in which non-symmetrical relations apply to their relata. In Section 1, I introduce some concepts in the ontology of relations and define relationism. In Section 2, I present the Problem of Order for non-symmetrical relations, after distinguishing it from the Problem of Differential Application. (...)
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  • (1 other version)Mathematical platonism meets ontological pluralism?Matteo Plebani - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy 63 (6):655-673.
    Mathematical platonism is the view that abstract mathematical objects exist. Ontological pluralism is the view that there are many modes of existence. This paper examines the prospects for plural platonism, the view that results from combining mathematical platonism and ontological pluralism. I will argue that some forms of platonism are in harmony with ontological pluralism, while other forms of platonism are in tension with it. This shows that there are some interesting connections between the platonism–antiplatonism dispute and recent debates over (...)
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  • Arrow’s impossibility theorem as a special case of Nash equilibrium: a cognitive approach to the theory of collective decision-making.Andrea Oliva & Edgardo Bucciarelli - 2020 - Mind and Society 19 (1):15-41.
    Metalogic is an open-ended cognitive, formal methodology pertaining to semantics and information processing. The language that mathematizes metalogic is known as metalanguage and deals with metafunctions purely by extension on patterns. A metalogical process involves an effective enrichment in knowledge as logical statements, and, since human cognition is an inherently logic–based representation of knowledge, a metalogical process will always be aimed at developing the scope of cognition by exploring possible cognitive implications reflected on successive levels of abstraction. Indeed, it is (...)
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  • Philosophy of mathematical practice: A primer for mathematics educators.Yacin Hamami & Rebecca Morris - 2020 - ZDM Mathematics Education 52:1113–1126.
    In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the philosophy of mathematical practice . In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice investigate as well as the philosophical methods they use to tackle them. We then provide a selective overview of work in the philosophy of mathematical practice covering topics including the (...)
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  • Philosophical pictures about mathematics: Wittgenstein and contradiction.Hiroshi Ohtani - 2018 - Synthese 195 (5):2039-2063.
    In the scholarship on Wittgenstein’s later philosophy of mathematics, the dominant interpretation is a theoretical one that ascribes to Wittgenstein some type of ‘ism’ such as radical verificationism or anti-realism. Essentially, he is supposed to provide a positive account of our mathematical practice based on some basic assertions. However, I claim that he should not be read in terms of any ‘ism’ but instead should be read as examining philosophical pictures in the sense of unclear conceptions. The contrast here is (...)
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  • Deductivism in the Philosophy of Mathematics.Alexander Paseau & Fabian Pregel - 2023 - Stanford Encyclopedia of Philosophy 2023.
    Deductivism says that a mathematical sentence s should be understood as expressing the claim that s deductively follows from appropriate axioms. For instance, deductivists might construe “2+2=4” as “the sentence ‘2+2=4’ deductively follows from the axioms of arithmetic”. Deductivism promises a number of benefits. It captures the fairly common idea that mathematics is about “what can be deduced from the axioms”; it avoids an ontology of abstract mathematical objects; and it maintains that our access to mathematical truths requires nothing beyond (...)
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  • Penrose on What Scientists Know.Rubén Herce - 2016 - Foundations of Science 21 (4):679-694.
    This paper presents an analysis and critique of Roger Penrose’s epistemological, methodological, and ontological positions. The analysis is relevant not only because Penrose is an influential scientist, but also because of the particular traits of his thought. These traits are directly connected with his background and approach to science: ontological and epistemological realism, mathematical Platonism, emphasis on the continuities of science, epistemological inclusiveness and essential openness of science, the role of common sense, emphasis on the connection between science, ethics, and (...)
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  • Labyrinth of Continua.Patrick Reeder - 2018 - Philosophia Mathematica 26 (1):1-39.
    This is a survey of the concept of continuity. Efforts to explicate continuity have produced a plurality of philosophical conceptions of continuity that have provably distinct expressions within contemporary mathematics. I claim that there is a divide between the conceptions that treat the whole continuum as prior to its parts, and those conceptions that treat the parts of the continuum as prior to the whole. Along this divide, a tension emerges between those conceptions that favor philosophical idealizations of continuity and (...)
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  • (1 other version)Mathematical platonism meets ontological pluralism?Matteo Plebani - 2017 - Inquiry: An Interdisciplinary Journal of Philosophy:1-19.
    Mathematical platonism is the view that abstract mathematical objects exist. Ontological pluralism is the view that there are many modes of existence. This paper examines the prospects for...
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  • Information, Meaning, and Error in Biology.Lucy A. K. Kumar - 2014 - Biological Theory 9 (1):89-99.
    Whether “information” exists in biology, and in what sense, has been a topic of much recent discussion. I explore Shannon, Dretskean, and teleosemantic theories, and analyze whether or not they are able to give a successful naturalistic account of information—specifically accounts of meaning and error—in biological systems. I argue that the Shannon and Dretskean theories are unable to account for either, but that the teleosemantic theory is able to account for meaning. However, I argue that it is unable to account (...)
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  • Pictures and Mathematics : Essays on Geometrical Representation, Pictorial Realism and Representational Abilities.Anna Stenkvist - 2014 - Dissertation, Kth Royal Institute of Technology
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  • Computers as a Source of A Posteriori Knowledge in Mathematics.Mikkel Willum Johansen & Morten Misfeldt - 2016 - International Studies in the Philosophy of Science 30 (2):111-127.
    Electronic computers form an integral part of modern mathematical practice. Several high-profile results have been proven with techniques where computer calculations form an essential part of the proof. In the traditional philosophical literature, such proofs have been taken to constitute a posteriori knowledge. However, this traditional stance has recently been challenged by Mark McEvoy, who claims that computer calculations can constitute a priori mathematical proofs, even in cases where the calculations made by the computer are too numerous to be surveyed (...)
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  • (1 other version)Motivating Wittgenstein's Perspective on Mathematical Sentences as Norms.Simon Friederich - 2011 - Philosophia Mathematica 19 (1):1-19.
    The later Wittgenstein’s perspective on mathematical sentences as norms is motivated for sentences belonging to Hilbertian axiomatic systems where the axioms are treated as implicit definitions. It is shown that in this approach the axioms are employed as norms in that they function as standards of what counts as using the concepts involved. This normative dimension of their mode of use, it is argued, is inherited by the theorems derived from them. Having been motivated along these lines, Wittgenstein’s perspective on (...)
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  • Formalism and Hilbert’s understanding of consistency problems.Michael Detlefsen - 2021 - Archive for Mathematical Logic 60 (5):529-546.
    Formalism in the philosophy of mathematics has taken a variety of forms and has been advocated for widely divergent reasons. In Sects. 1 and 2, I briefly introduce the major formalist doctrines of the late nineteenth and early twentieth centuries. These are what I call empirico-semantic formalism, game formalism and instrumental formalism. After describing these views, I note some basic points of similarity and difference between them. In the remainder of the paper, I turn my attention to Hilbert’s instrumental formalism. (...)
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  • C.S. Peirce on Mathematical Practice: Objectivity and the Community of Inquirers.Maria Regina Brioschi - 2022 - Topoi 42 (1):221-233.
    What understanding of mathematical objectivity is promoted by Peirce’s pragmatism? Can Peirce’s theory help us to further comprehend the role of intersubjectivity in mathematics? This paper aims to answer such questions, with special reference to recent debates on mathematical practice, where Peirce is often quoted, although without a detailed scrutiny of his theses. In particular, the paper investigates the role of intersubjectivity in the constitution of mathematical objects according to Peirce. Generally speaking, this represents one of the key issues for (...)
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