Results for 'Mathematical realism'

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  1. Numerical Cognition and Mathematical Realism.Helen De Cruz - 2016 - Philosophers' Imprint 16.
    Humans and other animals have an evolved ability to detect discrete magnitudes in their environment. Does this observation support evolutionary debunking arguments against mathematical realism, as has been recently argued by Clarke-Doane, or does it bolster mathematical realism, as authors such as Joyce and Sinnott-Armstrong have assumed? To find out, we need to pay closer attention to the features of evolved numerical cognition. I provide a detailed examination of the functional properties of evolved numerical cognition, and (...)
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  2. Two Criticisms Against Mathematical Realism.Seungbae Park - 2017 - Diametros 52:96-106.
    Mathematical realism asserts that mathematical objects exist in the abstract world, and that a mathematical sentence is true or false, depending on whether the abstract world is as the mathematical sentence says it is. I raise two objections against mathematical realism. First, the abstract world is queer in that it allows for contradictory states of affairs. Second, mathematical realism does not have a theoretical resource to explain why a sentence about a (...)
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  3. Inference to the Best Explanation and Mathematical Realism.Sorin Ioan Bangu - 2008 - Synthese 160 (1):13-20.
    Arguing for mathematical realism on the basis of Field’s explanationist version of the Quine–Putnam Indispensability argument, Alan Baker has recently claimed to have found an instance of a genuine mathematical explanation of a physical phenomenon. While I agree that Baker presents a very interesting example in which mathematics plays an essential explanatory role, I show that this example, and the argument built upon it, begs the question against the mathematical nominalist.
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  4. Rejecting Mathematical Realism While Accepting Interactive Realism.Seungbae Park - 2018 - Analysis and Metaphysics 17:7-21.
    Indispensablists contend that accepting scientific realism while rejecting mathematical realism involves a double standard. I refute this contention by developing an enhanced version of scientific realism, which I call interactive realism. It holds that interactively successful theories are typically approximately true, and that the interactive unobservable entities posited by them are likely to exist. It is immune to the pessimistic induction while mathematical realism is susceptible to it.
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  5. Mathematical Realism and Conceptual Semantics.Luke Jerzykiewicz - 2012 - In Oleg Prosorov & Vladimir Orevkov (eds.), Philosophy, Mathematics, Linguistics: Aspects of Interaction. Euler International Mathematical Institute.
    The dominant approach to analyzing the meaning of natural language sentences that express mathematical knowl- edge relies on a referential, formal semantics. Below, I discuss an argument against this approach and in favour of an internalist, conceptual, intensional alternative. The proposed shift in analytic method offers several benefits, including a novel perspective on what is required to track mathematical content, and hence on the Benacerraf dilemma. The new perspective also promises to facilitate discussion between philosophers of mathematics and (...)
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  6. Animal Cognition, Species Invariantism, and Mathematical Realism.Helen De Cruz - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury Academic. pp. 39-61.
    What can we infer from numerical cognition about mathematical realism? In this paper, I will consider one aspect of numerical cognition that has received little attention in the literature: the remarkable similarities of numerical cognitive capacities across many animal species. This Invariantism in Numerical Cognition (INC) indicates that mathematics and morality are disanalogous in an important respect: proto-moral beliefs differ substantially between animal species, whereas proto-mathematical beliefs (at least in the animals studied) seem to show more similarities. (...)
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  7. Talking About Numbers: Easy Arguments for Mathematical Realism[REVIEW]Richard Lawrence - 2017 - History and Philosophy of Logic 38 (4):390-394.
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  8. Mathematical and Moral Disagreement.Silvia Jonas - 2020 - Philosophical Quarterly 70 (279):302-327.
    The existence of fundamental moral disagreements is a central problem for moral realism and has often been contrasted with an alleged absence of disagreement in mathematics. However, mathematicians do in fact disagree on fundamental questions, for example on which set-theoretic axioms are true, and some philosophers have argued that this increases the plausibility of moral vis-à-vis mathematical realism. I argue that the analogy between mathematical and moral disagreement is not as straightforward as those arguments present it. (...)
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  9. Justification and Explanation in Mathematics and Morality.Justin Clarke-Doane - 2015 - Oxford Studies in Metaethics 10.
    In his influential book, The Nature of Morality, Gilbert Harman writes: “In explaining the observations that support a physical theory, scientists typically appeal to mathematical principles. On the other hand, one never seems to need to appeal in this way to moral principles.” What is the epistemological relevance of this contrast, if genuine? This chapter argues that ethicists and philosophers of mathematics have misunderstood it. They have confused what the chapter calls the justificatory challenge for realism about an (...)
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  10.  54
    Mathematical Anti-Realism and Explanatory Structure.Bruno Whittle - forthcoming - Synthese:1-15.
    Plausibly, mathematical claims are true, but the fundamental furniture of the world does not include mathematical objects. This can be made sense of by providing mathematical claims with paraphrases, which make clear how the truth of such claims does not require the fundamental existence of mathematical objects. This paper explores the consequences of this type of position for explanatory structure. There is an apparently straightforward relationship between this sort of structure, and the logical sort: i.e. logically (...)
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  11.  22
    Anti-Realism and Anti-Revisionism in Wittgenstein’s Philosophy of Mathematics.Anderson Nakano - 2020 - Grazer Philosophische Studien 97 (3):451-474.
    Since the publication of the Remarks on the Foundations of Mathematics, Wittgenstein’s interpreters have endeavored to reconcile his general constructivist/anti-realist attitude towards mathematics with his confessed anti-revisionary philosophy. In this article, the author revisits the issue and presents a solution. The basic idea consists in exploring the fact that the so-called “non-constructive results” could be interpreted so that they do not appear non-constructive at all. The author substantiates this solution by showing how the translation of mathematical results, given by (...)
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  12.  83
    Mathematics as a Science of Non-Abstract Reality: Aristotelian Realist Philosophies of Mathematics.James Franklin - 2021 - Foundations of Science 26:1-18.
    There is a wide range of realist but non-Platonist philosophies of mathematics—naturalist or Aristotelian realisms. Held by Aristotle and Mill, they played little part in twentieth century philosophy of mathematics but have been revived recently. They assimilate mathematics to the rest of science. They hold that mathematics is the science of X, where X is some observable feature of the (physical or other non-abstract) world. Choices for X include quantity, structure, pattern, complexity, relations. The article lays out and compares these (...)
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  13. Can Mathematical Objects Be Causally Efficacious?Seungbae Park - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 62 (3):247–255.
    Callard (2007) argues that it is metaphysically possible that a mathematical object, although abstract, causally affects the brain. I raise the following objections. First, a successful defence of mathematical realism requires not merely the metaphysical possibility but rather the actuality that a mathematical object affects the brain. Second, mathematical realists need to confront a set of three pertinent issues: why a mathematical object does not affect other concrete objects and other mathematical objects, what (...)
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  14. Mathematical Explanation by Law.Sam Baron - 2019 - British Journal for the Philosophy of Science 70 (3):683-717.
    Call an explanation in which a non-mathematical fact is explained—in part or in whole—by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this article, a theory of extra-mathematical explanation is developed. The theory is modelled on a deductive-nomological theory of scientific explanation. A basic DN account of extra-mathematical explanation is proposed and then redeveloped in the light of two difficulties that (...)
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  15. Mathematics and Explanatory Generality: Nothing but Cognitive Salience.Juha Saatsi & Robert Knowles - forthcoming - Erkenntnis:1-19.
    We demonstrate how real progress can be made in the debate surrounding the enhanced indispensability argument. Drawing on a counterfactual theory of explanation, well-motivated independently of the debate, we provide a novel analysis of ‘explanatory generality’ and how mathematics is involved in its procurement. On our analysis, mathematics’ sole explanatory contribution to the procurement of explanatory generality is to make counterfactual information about physical dependencies easier to grasp and reason with for creatures like us. This gives precise content to key (...)
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  16. Mathematical Explanations and the Piecemeal Approach to Thinking About Explanation.Gabriel Târziu - 2018 - Logique Et Analyse 61 (244):457-487.
    A new trend in the philosophical literature on scientific explanation is that of starting from a case that has been somehow identified as an explanation and then proceed to bringing to light its characteristic features and to constructing an account for the type of explanation it exemplifies. A type of this approach to thinking about explanation – the piecemeal approach, as I will call it – is used, among others, by Lange (2013) and Pincock (2015) in the context of their (...)
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  17. In Defense of Mathematical Inferentialism.Seungbae Park - 2017 - Analysis and Metaphysics 16:70-83.
    I defend a new position in philosophy of mathematics that I call mathematical inferentialism. It holds that a mathematical sentence can perform the function of facilitating deductive inferences from some concrete sentences to other concrete sentences, that a mathematical sentence is true if and only if all of its concrete consequences are true, that the abstract world does not exist, and that we acquire mathematical knowledge by confirming concrete sentences. Mathematical inferentialism has several advantages over (...)
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  18. Against Mathematical Convenientism.Seungbae Park - 2016 - Axiomathes 26 (2):115-122.
    Indispensablists argue that when our belief system conflicts with our experiences, we can negate a mathematical belief but we do not because if we do, we would have to make an excessive revision of our belief system. Thus, we retain a mathematical belief not because we have good evidence for it but because it is convenient to do so. I call this view ‘ mathematical convenientism.’ I argue that mathematical convenientism commits the consequential fallacy and that (...)
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  19. On the ‘Indispensable Explanatory Role’ of Mathematics.Juha Saatsi - 2016 - Mind 125 (500):1045-1070.
    The literature on the indispensability argument for mathematical realism often refers to the ‘indispensable explanatory role’ of mathematics. I argue that we should examine the notion of explanatory indispensability from the point of view of specific conceptions of scientific explanation. The reason is that explanatory indispensability in and of itself turns out to be insufficient for justifying the ontological conclusions at stake. To show this I introduce a distinction between different kinds of explanatory roles—some ‘thick’ and ontologically committing, (...)
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  20. The Applicability of Mathematics to Physical Modality.Nora Berenstain - 2017 - Synthese 194 (9):3361-3377.
    This paper argues that scientific realism commits us to a metaphysical determination relation between the mathematical entities that are indispensible to scientific explanation and the modal structure of the empirical phenomena those entities explain. The argument presupposes that scientific realism commits us to the indispensability argument. The viewpresented here is that the indispensability of mathematics commits us not only to the existence of mathematical structures and entities but to a metaphysical determination relation between those entities and (...)
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  21. Scientific Realism, the Semantic View and Evolutionary Biology.Fabio Sterpetti - 2016 - In Emiliano Ippoliti, Fabio Sterpetti & Thomas Nickles (eds.), Models and Inferences in Science. Springer. pp. 55-76.
    The semantic view of theories is normally considered to be an ac-count of theories congenial to Scientific Realism. Recently, it has been argued that Ontic Structural Realism could be fruitfully applied, in combination with the semantic view, to some of the philosophical issues peculiarly related to bi-ology. Given the central role that models have in the semantic view, and the relevance that mathematics has in the definition of the concept of model, the fo-cus will be on population genetics, (...)
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  22. Mathematical Representation: Playing a Role.Kate Hodesdon - 2014 - Philosophical Studies 168 (3):769-782.
    The primary justification for mathematical structuralism is its capacity to explain two observations about mathematical objects, typically natural numbers. Non-eliminative structuralism attributes these features to the particular ontology of mathematics. I argue that attributing the features to an ontology of structural objects conflicts with claims often made by structuralists to the effect that their structuralist theses are versions of Quine’s ontological relativity or Putnam’s internal realism. I describe and argue for an alternative explanation for these features which (...)
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  23. An Aristotelian Realist Philosophy of Mathematics by James Franklin. [REVIEW]Alex Koo - 2016 - Mathematical Intelligencer 38:81-84.
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  24. 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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  25. A Simpler and More Realistic Subjective Decision Theory.Haim Gaifman & Yang Liu - 2018 - Synthese 195 (10):4205--4241.
    In his classic book “the Foundations of Statistics” Savage developed a formal system of rational decision making. The system is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: Any preference relation that (...)
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  26. From Mathematics to Quantum Mechanics - On the Conceptual Unity of Cassirer’s Philosophy of Science.Thomas Mormann - 2015 - In Sebastian Luft & J. Tyler Friedman (eds.), The Philosophy of Ernst Cassirer: A Novel Assessment. De Gruyter. pp. 31-64.
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  27. Formalizing Darwinism, Naturalizing Mathematics.Fabio Sterpetti - 2015 - Paradigmi. Rivista di Critica Filosofica 33 (2):133-160.
    In the last decades two different and apparently unrelated lines of research have increasingly connected mathematics and evolutionism. Indeed, on the one hand different attempts to formalize darwinism have been made, while, on the other hand, different attempts to naturalize logic and mathematics have been put forward. Those researches may appear either to be completely distinct or at least in some way convergent. They may in fact both be seen as supporting a naturalistic stance. Evolutionism is indeed crucial for a (...)
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  28. Mathematics as Make-Believe: A Constructive Empiricist Account.Sarah Elizabeth Hoffman - 1999 - Dissertation, University of Alberta (Canada)
    Any philosophy of science ought to have something to say about the nature of mathematics, especially an account like constructive empiricism in which mathematical concepts like model and isomorphism play a central role. This thesis is a contribution to the larger project of formulating a constructive empiricist account of mathematics. The philosophy of mathematics developed is fictionalist, with an anti-realist metaphysics. In the thesis, van Fraassen's constructive empiricism is defended and various accounts of mathematics are considered and rejected. Constructive (...)
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  29. The Genetic Reification of 'Race'? A Story of Two Mathematical Methods.Rasmus Grønfeldt Winther - 2014 - Critical Philosophy of Race 2 (2):204-223.
    Two families of mathematical methods lie at the heart of investigating the hierarchical structure of genetic variation in Homo sapiens: /diversity partitioning/, which assesses genetic variation within and among pre-determined groups, and /clustering analysis/, which simultaneously produces clusters and assigns individuals to these “unsupervised” cluster classifications. While mathematically consistent, these two methodologies are understood by many to ground diametrically opposed claims about the reality of human races. Moreover, modeling results are sensitive to assumptions such as preexisting theoretical commitments to (...)
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  30.  72
    Importance and Explanatory Relevance: The Case of Mathematical Explanations.Gabriel Târziu - 2018 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 49 (3):393-412.
    A way to argue that something plays an explanatory role in science is by linking explanatory relevance with importance in the context of an explanation. The idea is deceptively simple: a part of an explanation is an explanatorily relevant part of that explanation if removing it affects the explanation either by destroying it or by diminishing its explanatory power, i.e. an important part is an explanatorily relevant part. This can be very useful in many ontological debates. My aim in this (...)
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  31. Objectivity in Ethics and Mathematics.Justin Clarke-Doane - 2015 - Proceedings of the Aristotelian Society: The Virtual Issue 3.
    How do axioms, or first principles, in ethics compare to those in mathematics? In this companion piece to G.C. Field's 1931 "On the Role of Definition in Ethics", I argue that there are similarities between the cases. However, these are premised on an assumption which can be questioned, and which highlights the peculiarity of normative inquiry.
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  32. Theism, naturalism, and scientific realism.Jeffrey Koperski - 2017 - Epistemology and Philosophy of Science 53 (3):152-166.
    Scientific knowledge is not merely a matter of reconciling theories and laws with data and observations. Science presupposes a number of metatheoretic shaping principles in order to judge good methods and theories from bad. Some of these principles are metaphysical and some are methodological. While many shaping principles have endured since the scientific revolution, others have changed in response to conceptual pressures both from within science and without. Many of them have theistic roots. For example, the notion that nature conforms (...)
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  33.  51
    Badiou’s Platonism: The Mathematical Ideas of Post-Cantorian Set-Theory.Simon B. Duffy - 2012 - In Sean Bowden & Simon B. Duffy (eds.), Badiou and Philosophy. Edinburgh University Press.
    Plato’s philosophy is important to Badiou for a number of reasons, chief among which is that Badiou considered Plato to have recognised that mathematics provides the only sound or adequate basis for ontology. The mathematical basis of ontology is central to Badiou’s philosophy, and his engagement with Plato is instrumental in determining how he positions his philosophy in relation to those approaches to the philosophy of mathematics that endorse an orthodox Platonic realism, i.e. the independent existence of a (...)
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  34. Realism: Metaphysical, Scientific, and Semantic.Panu Raatikainen - 2014 - In Kenneth R. Westphal (ed.), Realism, Science, and Pragmatism. Routledge. pp. 139-158.
    Three influential forms of realism are distinguished and interrelated: realism about the external world, construed as a metaphysical doctrine; scientific realism about non-observable entities postulated in science; and semantic realism as defined by Dummett. Metaphysical realism about everyday physical objects is contrasted with idealism and phenomenalism, and several potent arguments against these latter views are reviewed. -/- Three forms of scientific realism are then distinguished: (i) scientific theories and their existence postulates should be taken (...)
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  35. Realism, Objectivity, and Evaluation.Justin Clarke-Doane - forthcoming - In David Kaspar (ed.), Explorations in Ethics.
    I discuss Benacerraf's epistemological challenge for realism about areas like mathematics, metalogic, and modality, and describe the pluralist response to it. I explain why normative pluralism is peculiarly unsatisfactory, and use this explanation to formulate a radicalization of Moore's Open Question Argument. According to the argument, the facts -- even the normative facts -- fail to settle the practical questions at the center of our normative lives. One lesson is that the concepts of realism and objectivity, which are (...)
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  36.  75
    Historicity, Value and Mathematics.Barry Smith - 1975 - In A. T. Tymieniecka (ed.), Analecta Husserliana, vol. 4. Dordrecht: Reidel. pp. 219-239.
    At the beginning of the present century, a series of paradoxes were discovered within mathematics which suggested a fundamental unclarity in traditional mathemati­cal methods. These methods rested on the assumption of a realm of mathematical idealities existing independently of our thinking activity, and in order to arrive at a firmly grounded mathematics different attempts were made to formulate a conception of mathematical objects as purely human constructions. It was, however, realised that such formulations necessarily result in a mathematics (...)
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  37.  61
    Mathematical Application and the No Confirmation Thesis.Kenneth Boyce - 2020 - Analysis 80 (1):11-20.
    Some proponents of the indispensability argument for mathematical realism maintain that the empirical evidence that confirms our best scientific theories and explanations also confirms their pure mathematical components. I show that the falsity of this view follows from three highly plausible theses, two of which concern the nature of mathematical application and the other the nature of empirical confirmation. The first is that the background mathematical theories suitable for use in science are conservative in the (...)
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  38. Aristotelianism in the Philosophy of Mathematics.James Franklin - 2011 - Studia Neoaristotelica 8 (1):3-15.
    Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementary mathematics: the ratio of two heights, for example, is (...)
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  39.  34
    Mathematizing as a virtuous practice: different narratives and their consequences for mathematics education and society.Deborah Kant & Deniz Sarikaya - forthcoming - Synthese:1-25.
    There are different narratives on mathematics as part of our world, some of which are more appropriate than others. Such narratives might be of the form ‘Mathematics is useful’, ‘Mathematics is beautiful’, or ‘Mathematicians aim at theorem-credit’. These narratives play a crucial role in mathematics education and in society as they are influencing people’s willingness to engage with the subject or the way they interpret mathematical results in relation to real-world questions; the latter yielding important normative considerations. Our strategy (...)
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  40.  87
    Crunchy Methods in Practical Mathematics.Michael Wood - 2001 - Philosophy of Mathematics Education Journal 14.
    This paper focuses on the distinction between methods which are mathematically "clever", and those which are simply crude, typically repetitive and computer intensive, approaches for "crunching" out answers to problems. Examples of the latter include simulated probability distributions and resampling methods in statistics, and iterative methods for solving equations or optimisation problems. Most of these methods require software support, but this is easily provided by a PC. The paper argues that the crunchier methods often have substantial advantages from the perspectives (...)
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  41. Justifying and Exploring Realistic Monism.Paul Budnik - manuscript
    The foundations of mathematics and physics no longer start with fundamental entities and their properties like spatial extension, points, lines or the billiard ball like particles of Newtonian physics. Mathematics has abolished these from its foundations in set theory by making all assumptions explicit and structural. Particle physics has become completely mathematical, connecting to physical reality only through experimental technique. Applying the principles guiding the foundations of mathematics and physics to philosophical analysis underscores that only conscious experience has an (...)
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  42. Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism.Hasen Khudairi - 2019 - In Matteo Vincenzo D'Alfonso & Don Berkich (eds.), On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence. Springer. pp. 65-82.
    This essay examines the philosophical significance of Ω-logic in Zermelo-Fraenkel set theory with choice (ZFC). The dual isomorphism between algebra and coalgebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of Ω-logical validity can then be countenanced within a coalgebraic logic, and Ω-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of Ω-logical validity correspond to those of (...)
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  43. Retention Myths Vs. Well-Managed Resources: Promises and Failings of Structural Realism (2014).Jean-Michel Delhotel - 2014
    Turning away from entities and focusing instead exclusively on ‘structural’ aspects of scientific theories has been advocated as a cogent response to objections levelled at realist conceptions of the aim and success of science. Physical theories whose (predictive) past successes are genuine would, in particular, share with their successors structural traits that would ultimately latch on to ‘structural’ features of the natural world. Motives for subscribing to Structural Realism are reviewed and discussed. It is argued that structural retention claims (...)
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  44. Time and Space in Special Relativity a Critique of the Realist Interpretation.Fredrik Andersen - 2010 - Dissertation, University of Tromsø
    In this thesis the author focuses on the metaphysical implications of the realist interpretation of special relativity. The realist interpretation is found wanting in coherence as it utilizes metaphysical concepts (as causation) that are left unjustified if the theory is taken at face value. The author points at a possible re-interpretation of special relativity that allows for a coherent metaphysical basis while containing the mathematical structure of the theory.
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  45. Countable Additivity, Idealization, and Conceptual Realism.Yang Liu - 2020 - Economics and Philosophy 36 (1):127-147.
    This paper addresses the issue of finite versus countable additivity in Bayesian probability and decision theory -- in particular, Savage's theory of subjective expected utility and personal probability. I show that Savage's reason for not requiring countable additivity in his theory is inconclusive. The assessment leads to an analysis of various highly idealised assumptions commonly adopted in Bayesian theory, where I argue that a healthy dose of, what I call, conceptual realism is often helpful in understanding the interpretational value (...)
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  46. Modality and constitution in distinctively mathematical explanations.Mark Povich - 2020 - European Journal for Philosophy of Science 10 (3):1-10.
    Lange argues that some natural phenomena can be explained by appeal to mathematical, rather than natural, facts. In these “distinctively mathematical” explanations, the core explanatory facts are either modally stronger than facts about ordinary causal law or understood to be constitutive of the physical task or arrangement at issue. Craver and Povich argue that Lange’s account of DME fails to exclude certain “reversals”. Lange has replied that his account can avoid these directionality charges. Specifically, Lange argues that in (...)
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  47. A Possible Answer to Newman’s Objection From the Perspective of Informational Structural Realism.Lavinia Marin - 2015 - Revue Roumaine de Philosophie 59 (2):307-318.
    This paper aims to reconstruct a possible answer to the classical Newman’s objection which has been used countless times to argue against structural realism. The reconstruction starts from the new strand of structural realism – informational structural realism – authored by Luciano Floridi. Newman’s objection had previously stated that all propositions which comprise the mathematical structures are merely trivial truths and can be instantiated by multiple models. This paper examines whether informational structural realism can overcome (...)
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  48.  88
    Building on Sellars: Concept Formation and Scientific Realism[REVIEW]Tanya Kelley - 2008 - Metascience 17 (2):257-259.
    Harold Brown has written an ambitious work, which traces the formation of concepts in individuals and cultures, examines case studies of concepts in calculus, mathematics, biology and related fields, summarises important philosophical works on the theory of concepts, and seeks to reconcile scientific realism with conceptual change. Brown considers himself a scientific realist but concedes that this very label is one that depends on a long history of concepts that came before, and may indeed be superseded as conceptual change (...)
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  49. If There Were No Numbers, What Would You Think?Thomas Mark Eden Donaldson - 2014 - Thought: A Journal of Philosophy 3 (4):283-287.
    Hartry Field has argued that mathematical realism is epistemologically problematic, because the realist is unable to explain the supposed reliability of our mathematical beliefs. In some of his discussions of this point, Field backs up his argument by saying that our purely mathematical beliefs do not ‘counterfactually depend on the facts’. I argue that counterfactual dependence is irrelevant in this context; it does nothing to bolster Field's argument.
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  50. Some Recent Existential Appeals to Mathematical Experience.Michael J. Shaffer - 2006 - Principia: An International Journal of Epistemology 10 (2):143-170.
    Some recent work by philosophers of mathematics has been aimed at showing that our knowledge of the existence of at least some mathematical objects and/or sets can be epistemically grounded by appealing to perceptual experience. The sensory capacity that they refer to in doing so is the ability to perceive numbers, mathematical properties and/or sets. The chief defense of this view as it applies to the perception of sets is found in Penelope Maddy’s Realism in Mathematics, but (...)
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