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Naturalism in mathematics

New York: Oxford University Press (1997)

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  1. Quine's ‘needlessly strong’ holism.Sander Verhaegh - 2017 - Studies in History and Philosophy of Science Part A 61:11-20.
    Quine is routinely perceived as having changed his mind about the scope of the Duhem-Quine thesis, shifting from what has been called an 'extreme holism' to a more moderate view. Where the Quine of 'Two Dogmas of Empiricism' argues that “the unit of empirical significance is the whole of science” (1951, 42), the later Quine seems to back away from this “needlessly strong statement of holism” (1991, 393). In this paper, I show that the received view is incorrect. I distinguish (...)
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  • A Metasemantic Challenge for Mathematical Determinacy.Jared Warren & Daniel Waxman - 2020 - Synthese 197 (2):477-495.
    This paper investigates the determinacy of mathematics. We begin by clarifying how we are understanding the notion of determinacy before turning to the questions of whether and how famous independence results bear on issues of determinacy in mathematics. From there, we pose a metasemantic challenge for those who believe that mathematical language is determinate, motivate two important constraints on attempts to meet our challenge, and then use these constraints to develop an argument against determinacy and discuss a particularly popular approach (...)
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  • Realismo/Anti-Realismo.Eduardo Castro - 2014 - Compêndio Em Linha de Problemas de Filosofia Analítica.
    State of the art paper on the topic realism/anti-realism. The first part of the paper elucidates the notions of existence and independence of the metaphysical characterization of the realism/anti-realism dispute. The second part of the paper presents a critical taxonomy of the most important positions and doctrines in the contemporary literature on the domains of science and mathematics: scientific realism, scientific anti-realism, constructive empiricism, structural realism, mathematical Platonism, mathematical indispensability, mathematical empiricism, intuitionism, mathematical fictionalism and second philosophy.
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  • Maddy and Mathematics: Naturalism or Not.Jeffrey W. Roland - 2007 - British Journal for the Philosophy of Science 58 (3):423-450.
    Penelope Maddy advances a purportedly naturalistic account of mathematical methodology which might be taken to answer the question 'What justifies axioms of set theory?' I argue that her account fails both to adequately answer this question and to be naturalistic. Further, the way in which it fails to answer the question deprives it of an analog to one of the chief attractions of naturalism. Naturalism is attractive to naturalists and nonnaturalists alike because it explains the reliability of scientific practice. Maddy's (...)
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  • Conjoining Mathematical Empiricism with Mathematical Realism: Maddy’s Account of Set Perception Revisited.Alex Levine - 2005 - Synthese 145 (3):425-448.
    Penelope Maddy's original solution to the dilemma posed by Benacerraf in his 'Mathematical Truth' was to reconcile mathematical empiricism with mathematical realism by arguing that we can perceive realistically construed sets. Though her hypothesis has attracted considerable critical attention, much of it, in my view, misses the point. In this paper I vigorously defend Maddy's account against published criticisms, not because I think it is true, but because these criticisms have functioned to obscure a more fundamental issue that is well (...)
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  • The varieties of indispensability arguments.Marco Panza & Andrea Sereni - 2016 - Synthese 193 (2):469-516.
    The indispensability argument comes in many different versions that all reduce to a general valid schema. Providing a sound IA amounts to providing a full interpretation of the schema according to which all its premises are true. Hence, arguing whether IA is sound results in wondering whether the schema admits such an interpretation. We discuss in full details all the parameters on which the specification of the general schema may depend. In doing this, we consider how different versions of IA (...)
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  • (1 other version)Gödel’s Cantorianism.Claudio Ternullo - 2015 - In E.-M. Engelen (ed.), Kurt Gödel: Philosopher-Scientist. Presses Universitaires de Provence. pp. 417-446.
    Gödel’s philosophical conceptions bear striking similarities to Cantor’s. Although there is no conclusive evidence that Gödel deliberately used or adhered to Cantor’s views, one can successfully reconstruct and see his “Cantorianism” at work in many parts of his thought. In this paper, I aim to describe the most prominent conceptual intersections between Cantor’s and Gödel’s thought, particularly on such matters as the nature and existence of mathematical entities (sets), concepts, Platonism, the Absolute Infinite, the progress and inexhaustibility of mathematics.
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  • Must Naturalism Lead to a Deflationary Meta-Ontology?Matthew Haug - 2014 - Metaphysica 15 (2):347-367.
    Huw Price has argued that naturalistic philosophy inevitably leads to a deflationary approach to ontological questions. In this paper, I rebut these arguments. A more substantive, less language-focused approach to metaphysics remains open to naturalists. However, rebutting one of Price’s main arguments requires rejecting Quine’s criterion of ontological commitment. So, even though Price’s argument is unsound, it reveals that naturalists cannot rest content with broadly Quinean, “mainstream metaphysics,” which, I suggest, naturalists also have independent reasons to reject.
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  • A Deflationist Error Theory of Properties.Arvid Båve - 2015 - Dialectica 69 (1):23-59.
    I here defend a theory consisting of four claims about ‘property’ and properties, and argue that they form a coherent whole that can solve various serious problems. The claims are (1): ‘property’ is defined by the principles (PR): ‘F-ness/Being F/etc. is a property of x iff F’ and (PA): ‘F-ness/Being F/etc. is a property’; (2) the function of ‘property’ is to increase the expressive power of English, roughly by mimicking quantification into predicate position; (3) property talk should be understood at (...)
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  • Hilbert’s Finitism: Historical, Philosophical, and Metamathematical Perspectives.Richard Zach - 2001 - Dissertation, University of California, Berkeley
    In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...)
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  • In defence of existence questions.Chris Daly & David Liggins - 2014 - Monist 97 (7):460–478.
    Do numbers exist? Do properties? Do possible worlds? Do fictional characters? Many metaphysicians spend time and effort trying to answer these and other questions about the existence of various entities. These inquiries have recently encountered opposition: a group of philosophers, drawing inspiration from Aristotle, have argued that many or all of the existence questions debated by metaphysicians can be answered trivially, and so are not worth debating. Our task is to defend existence questions from the neo-Aristotelians' attacks.
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  • The normative structure of mathematization in systematic biology.Beckett Sterner & Scott Lidgard - 2014 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 46 (1):44-54.
    We argue that the mathematization of science should be understood as a normative activity of advocating for a particular methodology with its own criteria for evaluating good research. As a case study, we examine the mathematization of taxonomic classification in systematic biology. We show how mathematization is a normative activity by contrasting its distinctive features in numerical taxonomy in the 1960s with an earlier reform advocated by Ernst Mayr starting in the 1940s. Both Mayr and the numerical taxonomists sought to (...)
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  • The Bounds of Logic: A Generalized Viewpoint.Gila Sher - 1991 - MIT Press.
    The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her (...)
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  • The philosophy of mathematics and the independent 'other'.Penelope Rush - unknown
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  • Is the Continuum Hypothesis a definite mathematical problem?Solomon Feferman - manuscript
    The purpose of this article is to explain why I believe that the Continuum Hypothesis (CH) is not a definite mathematical problem. My reason for that is that the concept of arbitrary set essential to its formulation is vague or underdetermined and there is no way to sharpen it without violating what it is supposed to be about. In addition, there is considerable circumstantial evidence to support the view that CH is not definite.
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  • The Story About Propositions.Bradley Armour-Garb & James A. Woodbridge - 2010 - Noûs 46 (4):635-674.
    It is our contention that an ontological commitment to propositions faces a number of problems; so many, in fact, that an attitude of realism towards propositions—understood the usual “platonistic” way, as a kind of mind- and language-independent abstract entity—is ultimately untenable. The particular worries about propositions that marshal parallel problems that Paul Benacerraf has raised for mathematical platonists. At the same time, the utility of “proposition-talk”—indeed, the apparent linguistic commitment evident in our use of 'that'-clauses (in offering explanations and making (...)
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  • Modest Evolutionary Naturalism.Ronald N. Giere - 2006 - Biological Theory 1 (1):52-60.
    I begin by arguing that a consistent general naturalism must be understood in terms of methodological maxims rather than metaphysical doctrines. Some specific maxims are proposed. I then defend a generalized naturalism from the common objection that it is incapable of accounting for the normative aspects of human life, including those of scientific practice itself. Evolutionary naturalism, however, is criticized as being incapable of providing a sufficient explanation of categorical moral norms. Turning to the epistemological norms of science itself, particularly (...)
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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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  • Mirror Symmetry and Other Miracles in Superstring Theory.Dean Rickles - 2013 - Foundations of Physics 43 (1):54-80.
    The dominance of string theory in the research landscape of quantum gravity physics (despite any direct experimental evidence) can, I think, be justified in a variety of ways. Here I focus on an argument from mathematical fertility, broadly similar to Hilary Putnam’s ‘no miracles argument’ that, I argue, many string theorists in fact espouse in some form or other. String theory has generated many surprising, useful, and well-confirmed mathematical ‘predictions’—here I focus on mirror symmetry and the mirror theorem. These predictions (...)
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  • Of Numbers and Electrons.Cian Dorr - 2010 - Proceedings of the Aristotelian Society 110 (2pt2):133-181.
    According to a tradition stemming from Quine and Putnam, we have the same broadly inductive reason for believing in numbers as we have for believing in electrons: certain theories that entail that there are numbers are better, qua explanations of our evidence, than any theories that do not. This paper investigates how modal theories of the form ‘Possibly, the concrete world is just as it in fact is and T’ and ‘Necessarily, if standard mathematics is true and the concrete world (...)
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  • Probabilistic proofs and transferability.Kenny Easwaran - 2009 - Philosophia Mathematica 17 (3):341-362.
    In a series of papers, Don Fallis points out that although mathematicians are generally unwilling to accept merely probabilistic proofs, they do accept proofs that are incomplete, long and complicated, or partly carried out by computers. He argues that there are no epistemic grounds on which probabilistic proofs can be rejected while these other proofs are accepted. I defend the practice by presenting a property I call ‘transferability’, which probabilistic proofs lack and acceptable proofs have. I also consider what this (...)
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  • Just how controversial is evidential holism?Joe Morrison - 2010 - Synthese 173 (3):335-352.
    This paper is an examination of evidential holism, a prominent position in epistemology and the philosophy of science which claims that experiments only ever confirm or refute entire theories. The position is historically associated with W.V. Quine, and it is at once both popular and notorious, as well as being largely under-described. But even though there’s no univocal statement of what holism is or what it does, philosophers have nevertheless made substantial assumptions about its content and its truth. Moreover they (...)
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  • How applied mathematics became pure.Penelope Maddy - 2008 - Review of Symbolic Logic 1 (1):16-41.
    My goal here is to explore the relationship between pure and applied mathematics and then, eventually, to draw a few morals for both. In particular, I hope to show that this relationship has not been static, that the historical rise of pure mathematics has coincided with a gradual shift in our understanding of how mathematics works in application to the world. In some circles today, it is held that historical developments of this sort simply represent changes in fashion, or in (...)
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  • Against Fantology.Barry Smith - 2005 - In Johann C. Marek Maria E. Reicher (ed.), Experience and Analysis. HPT&ÖBV. pp. 153-170.
    The analytical philosophy of the last hundred years has been heavily influenced by a doctrine to the effect that the key to the correct understanding of reality is captured syntactically in the ‘Fa’ (or, in more sophisticated versions, in the ‘Rab’) of standard first order predicate logic. Here ‘F’ stands for what is general in reality and ‘a’ for what is individual. Hence “f(a)ntology”. Because predicate logic has exactly two syntactically different kinds of referring expressions—‘F’, ‘G’, ‘R’, etc., and ‘a’, (...)
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  • (1 other version)Abstract objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
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  • Thomson's lamp is dysfunctional.William I. McLaughlin - 1998 - Synthese 116 (3):281-301.
    James Thomson envisaged a lamp which would be turned on for 1 minute, off for 1/2 minute, on for 1/4 minute, etc. ad infinitum. He asked whether the lamp would be on or off at the end of 2 minutes. Use of “internal set theory” (a version of nonstandard analysis), developed by Edward Nelson, shows Thomson's lamp is chimerical; its copy within set theory yields a contradiction. The demonstration extends to placing restrictions on other “infinite tasks” such as Zeno's paradoxes (...)
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  • What perception is doing, and what it is not doing, in mathematical reasoning.Dennis Lomas - 2002 - British Journal for the Philosophy of Science 53 (2):205-223.
    What is perception doing in mathematical reasoning? To address this question, I discuss the role of perception in geometric reasoning. Perception of the shape properties of concrete diagrams provides, I argue, a surrogate consciousness of the shape properties of the abstract geometric objects depicted in the diagrams. Some of what perception is not doing in mathematical reasoning is also discussed. I take issue with both Parsons and Maddy. Parsons claims that we perceive a certain type of abstract object. Maddy claims (...)
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  • A Role for Mathematics in the Physical Sciences.Chris Pincock - 2007 - Noûs 41 (2):253-275.
    Conflicting accounts of the role of mathematics in our physical theories can be traced to two principles. Mathematics appears to be both (1) theoretically indispensable, as we have no acceptable non-mathematical versions of our theories, and (2) metaphysically dispensable, as mathematical entities, if they existed, would lack a relevant causal role in the physical world. I offer a new account of a role for mathematics in the physical sciences that emphasizes the epistemic benefits of having mathematics around when we do (...)
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  • Mathematics as a quasi-empirical science.Gianluigi Oliveri - 2004 - Foundations of Science 11 (1-2):41-79.
    The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call ‘set theory’ is not one theory which grows by simple addition of a theorem after the other, but a finite sequence of theories T1, ..., Tn in which Ti+1, for 1 ≤ i < n, supersedes Ti. This thesis has a great philosophical significance because it implies that there is a sense in which mathematical theories, (...)
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  • The last mathematician from Hilbert's göttingen: Saunders Mac Lane as philosopher of mathematics.Colin McLarty - 2007 - British Journal for the Philosophy of Science 58 (1):77-112.
    While Saunders Mac Lane studied for his D.Phil in Göttingen, he heard David Hilbert's weekly lectures on philosophy, talked philosophy with Hermann Weyl, and studied it with Moritz Geiger. Their philosophies and Emmy Noether's algebra all influenced his conception of category theory, which has become the working structure theory of mathematics. His practice has constantly affirmed that a proper large-scale organization for mathematics is the most efficient path to valuable specific results—while he sees that the question of which results are (...)
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  • Quine, Putnam, and the ‘Quine–Putnam’ Indispensability Argument.David Liggins - 2008 - Erkenntnis 68 (1):113 - 127.
    Much recent discussion in the philosophy of mathematics has concerned the indispensability argument—an argument which aims to establish the existence of abstract mathematical objects through appealing to the role that mathematics plays in empirical science. The indispensability argument is standardly attributed to W. V. Quine and Hilary Putnam. In this paper, I show that this attribution is mistaken. Quine's argument for the existence of abstract mathematical objects differs from the argument which many philosophers of mathematics ascribe to him. Contrary to (...)
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  • 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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  • Abstract Objects.David Liggins - 2024 - Cambridge: Cambridge University Press.
    Philosophers often debate the existence of such things as numbers and propositions, and say that if these objects exist, they are abstract. But what does it mean to call something 'abstract'? And do we have good reason to believe in the existence of abstract objects? This Element addresses those questions, putting newcomers to these debates in a position to understand what they concern and what are the most influential considerations at work in this area of metaphysics. It also provides advice (...)
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  • The explanatory and heuristic power of mathematics.Marianna Antonutti Marfori, Sorin Bangu & Emiliano Ippoliti - 2023 - Synthese 201 (5):1-12.
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  • Ontology of Divinity.Mirosław Szatkowski (ed.) - 2024 - Boston: De Gruyter.
    This volume announces a new era in the philosophy of God. Many of its contributions work to create stronger links between the philosophy of God, on the one hand, and mathematics or metamathematics, on the other hand. It is about not only the possibilities of applying mathematics or metamathematics to questions about God, but also the reverse question: Does the philosophy of God have anything to offer mathematics or metamathematics? The remaining contributions tackle stereotypes in the philosophy of religion. The (...)
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  • No Magic: From Phenomenology of Practice to Social Ontology of Mathematics.Mirja Hartimo & Jenni Rytilä - 2023 - Topoi 42 (1):283-295.
    The paper shows how to use the Husserlian phenomenological method in contemporary philosophical approaches to mathematical practice and mathematical ontology. First, the paper develops the phenomenological approach based on Husserl's writings to obtain a method for understanding mathematical practice. Then, to put forward a full-fledged ontology of mathematics, the phenomenological approach is complemented with social ontological considerations. The proposed ontological account sees mathematical objects as social constructions in the sense that they are products of culturally shared and historically developed practices. (...)
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  • Logical Realism: A Tale of Two Theories.Gila Sher - 2024 - In Sophia Arbeiter & Juliette Kennedy (eds.), The Philosophy of Penelope Maddy. Springer.
    The paper compares two theories of the nature of logic: Penelope Maddy's and my own. The two theories share a significant element: they both view logic as grounded not just in the mind (language, concepts, conventions, etc.), but also, and crucially, in the world. But the two theories differ in significant ways as well. Most distinctly, one is an anti-holist, "austere naturalist" theory while the other is a non-naturalist "foundational-holistic" theory. This methodological difference affects their questions, goals, orientations, the scope (...)
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  • Mathematics and Metaphilosophy.Justin Clarke-Doane - 2022 - Cambridge: Cambridge University Press.
    This book discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the problem of explaining the (defeasible) justification of our mathematical beliefs (‘the justificatory challenge’), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the problem of explaining their reliability (‘the reliability challenge’), arises to the extent that we could have easily had different beliefs. The book shows that mathematical facts are not, in general, empirically accessible, contra Quine, (...)
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  • Framing the Epistemic Schism of Statistical Mechanics.Javier Anta - 2021 - Proceedings of the X Conference of the Spanish Society of Logic, Methodology and Philosophy of Science.
    In this talk I present the main results from Anta (2021), namely, that the theoretical division between Boltzmannian and Gibbsian statistical mechanics should be understood as a separation in the epistemic capabilities of this physical discipline. In particular, while from the Boltzmannian framework one can generate powerful explanations of thermal processes by appealing to their microdynamics, from the Gibbsian framework one can predict observable values in a computationally effective way. Finally, I argue that this statistical mechanical schism contradicts the Hempelian (...)
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  • Mathematical Explanations in Evolutionary Biology or Naturalism? A Challenge for the Statisticalist.Fabio Sterpetti - 2021 - Foundations of Science 27 (3):1073-1105.
    This article presents a challenge that those philosophers who deny the causal interpretation of explanations provided by population genetics might have to address. Indeed, some philosophers, known as statisticalists, claim that the concept of natural selection is statistical in character and cannot be construed in causal terms. On the contrary, other philosophers, known as causalists, argue against the statistical view and support the causal interpretation of natural selection. The problem I am concerned with here arises for the statisticalists because the (...)
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  • Aspectos metafísicos na física de Newton: Deus.Bruno Camilo de Oliveira - 2011 - In Luiz Henrique de Araújo Dutra & Alexandre Meyer Luz (eds.), Coleção rumos da epistemologia. pp. 186-201.
    CAMILO, Bruno. Aspectos metafísicos na física de Newton: Deus. In: DUTRA, Luiz Henrique de Araújo; LUZ, Alexandre Meyer (org.). Temas de filosofia do conhecimento. Florianópolis: NEL/UFSC, 2011. p. 186-201. (Coleção rumos da epistemologia; 11). Através da análise do pensamento de Isaac Newton (1642-1727) encontramos os postulados metafísicos que fundamentam a sua mecânica natural. Ao deduzir causa de efeito, ele acreditava chegar a uma causa primeira de todas as coisas. A essa primeira causa de tudo, onde toda a ordem e leis (...)
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  • Explicação Matemática.Eduardo Castro - 2020 - Compêndio Em Linha de Problemas de Filosofia Analítica.
    Opinionated state of the art paper on mathematical explanation. After a general introduction to the subject, the paper is divided into two parts. The first part is dedicated to intra-mathematical explanation and the second is dedicated to extra-mathematical explanation. Each of these parts begins to present a set of diverse problems regarding each type of explanation and, afterwards, it analyses relevant models of the literature. Regarding the intra-mathematical explanation, the models of deformable proofs, mathematical saliences and the demonstrative structure of (...)
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  • Anti-Scientism, Conceptual Analysis, Naturalism.Filip Tvrdý - 2018 - Pro-Fil 19 (1):49-61.
    Filozofie ve 20. století ztratila velkou část svých kompetencí a pro svou údajnou neužitečnost se stala terčem kritiky ze strany přírodních vědců. Vztah mezi filozofií a vědou lze řešit pomocí tří stanovisek, kterými jsou antiscientismus, konceptuální analýza a naturalismus. Obsahem článku je charakteristika jednotlivých přístupů a identifikace problémů, s nimiž se musí jejich zastánci potýkat. Autorovi se jako nejslibnější jeví Quinem inspirovaný naturalismus, podle něhož má veškeré poznání povahu syntetických aposteriorních výroků, a filozofie je proto kontinuální s přírodní vědou. Není (...)
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  • Set-theoretic justification and the theoretical virtues.John Heron - 2020 - Synthese 199 (1-2):1245-1267.
    Recent discussions of how axioms are extrinsically justified have appealed to abductive considerations: on such accounts, axioms are adopted on the basis that they constitute the best explanation of some mathematical data, or phenomena. In the first part of this paper, I set out a potential problem caused by the appeal made to the notion of mathematical explanation and suggest that it can be remedied once it is noted that all the justificatory work is done by appeal to the theoretical (...)
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  • Proof, Explanation, and Justification in Mathematical Practice.Moti Mizrahi - 2020 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (4):551-568.
    In this paper, I propose that applying the methods of data science to “the problem of whether mathematical explanations occur within mathematics itself” (Mancosu 2018) might be a fruitful way to shed new light on the problem. By carefully selecting indicator words for explanation and justification, and then systematically searching for these indicators in databases of scholarly works in mathematics, we can get an idea of how mathematicians use these terms in mathematical practice and with what frequency. The results of (...)
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  • On Logical and Scientific Strength.Luca Incurvati & Carlo Nicolai - forthcoming - Erkenntnis:1-23.
    The notion of strength has featured prominently in recent debates about abductivism in the epistemology of logic. Following Williamson and Russell, we distinguish between logical and scientific strength and discuss the limits of the characterizations they employ. We then suggest understanding logical strength in terms of interpretability strength and scientific strength as a special case of logical strength. We present applications of the resulting notions to comparisons between logics in the traditional sense and mathematical theories.
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  • Explanatory Consolidation: From ‘Best’ to ‘Good Enough’.Finnur Dellsén - 2020 - Philosophy and Phenomenological Research 103 (1):157-177.
    In science and everyday life, we often infer that something is true because it would explain some set of facts better than any other hypothesis we can think of. But what if we have reason to believe that there is a better way to explain these facts that we just haven't thought of? Wouldn't that undermine our warrant for believing the best available explanation? Many philosophers have assumed that we can solve such underconsideration problems by stipulating that a hypothesis should (...)
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  • Computing, Modelling, and Scientific Practice: Foundational Analyses and Limitations.Philippos Papayannopoulos - 2018 - Dissertation,
    This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS model--, both claiming to formalise algorithmic (...)
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  • (1 other version)Maddy On The Multiverse.Claudio Ternullo - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 43-78.
    Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...)
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  • Mathematical surrealism as an alternative to easy-road fictionalism.Kenneth Boyce - 2020 - Philosophical Studies 177 (10):2815-2835.
    Easy-road mathematical fictionalists grant for the sake of argument that quantification over mathematical entities is indispensable to some of our best scientific theories and explanations. Even so they maintain we can accept those theories and explanations, without believing their mathematical components, provided we believe the concrete world is intrinsically as it needs to be for those components to be true. Those I refer to as “mathematical surrealists” by contrast appeal to facts about the intrinsic character of the concrete world, not (...)
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