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What is Mathematical Truth?

In Mathematics, Matter and Method. Cambridge University Press. pp. 60--78 (1975)

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  1. Konwencjonalizm a realizm: Poincaré i Duhem wobec statusu poznawczego nauk przyrodniczych.Mateusz Kotowski - 2016 - Przeglad Filozoficzny - Nowa Seria 99 (3):103-118.
    W pierwszej połowie XX wieku przyjęło się upatrywać w poglądach H. Poincarégo i P. Duhema przykładów antyrealistycznego stanowiska odnośnie do nauki i jej teorii. Etykietka ta przylgnęła do tych autorów tak mocno, że coraz częstszym dzisiaj głosom tych, którzy sprzeciwiają się takiemu szufladkowaniu ich filozofii, trudno jest przebić się do głównego nurtu dyskusji filozoficznych. W artykule wskazuję, że odczytywanie poglądów obu francuskich autorów jako antyrealistycznych nie znajduje potwierdzenia w ich własnych wypowiedziach. Przeciwnie, ich prace dostarczają mocnych świadectw na rzecz upatrywania (...)
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  • What’s voluntary in stance voluntarism?Bruno Malavolta E. Silva - 2021 - Manuscrito 44 (2):52-88.
    Stance voluntarism highlights the role of the will in epistemic agency, claiming that agents can control the epistemic stances they assume in forming beliefs. It claims that radical belief changes are not compelled by the evidence; they are rationally permitted choices about which epistemic stances to adopt. However, terms like “will”, “choice”, and “stance” play a crucial role while being left as vague notions. This paper investigates what kind of control rational agents can have over epistemic stances. I argue that (...)
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  • Realismo cient’ifico empirista.Sílvio Seno Chibeni - 1997 - Principia: An International Journal of Epistemology 1 (2):255--270.
    In his influential criticism of scientific realism, Bas van Fraassen assumes that this doctrine is incompatible with empiricism, according to which the sole ultimate basis of knowledge is experience. This claim has been generally accepted in the contemporary literature in philosophy of science. Thus, the very distinction between scientific realism and empiricism is often forgotten, the term 'empiricism' being now widely used to designate a range of anti-realist positions, such as van Fraassen's "construct ive empiricism". In this paper it is (...)
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  • Proofs and pictures.James Robert Brown - 1997 - British Journal for the Philosophy of Science 48 (2):161-180.
    Everyone appreciates a clever mathematical picture, but the prevailing attitude is one of scepticism: diagrams, illustrations, and pictures prove nothing; they are psychologically important and heuristically useful, but only a traditional verbal/symbolic proof provides genuine evidence for a purported theorem. Like some other recent writers (Barwise and Etchemendy [1991]; Shin [1994]; and Giaquinto [1994]) I take a different view and argue, from historical considerations and some striking examples, for a positive evidential role for pictures in mathematics.
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  • Wigner’s “Unreasonable Effectiveness of Mathematics”, Revisited.Roland Omnès - 2011 - Foundations of Physics 41 (11):1729-1739.
    A famous essay by Wigner is reexamined in view of more recent developments around its topic, together with some remarks on the metaphysical character of its main question about mathematics and natural sciences.
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  • A Proof of ‘1st/3rd Person Relativism’ and its Consequences to the Mind-Body Problem.João Fonseca - manuscript
    The suggestion of something akin to a ‘relativist solution to the Mind-Body problem’ has recently been held by some scientists and philosophers; either explicitly (Galadí, 2023; Lahav & Neemeh, 2022; Ludwig, 2015) or in more implicit terms (Solms, 2018; Velmans, 2002, 2008). In this paper I provide an argument in favor of a relativist approach to the Mind-Body problem, more specifically, an argument for ‘1st/3rd person relativism’, the claim that ‘The truth value of some sentences or propositions is relative to (...)
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  • Why Should Metaphysics be Systematic? Contemporary Answers and Kant’s.Nicholas Stang - forthcoming - In Aaron Segal & Nicholas Stang (eds.), Systematic Metaphysics: Historical and Contemporary Perspectives.
    The other chapters in this volume discuss the important, but neglected, topic of systematicity in metaphysics. In this chapter I begin by taking a step back and asking: why is systematicity important in metaphysics? Assuming that metaphysics should be systematic, why is this the case? I canvas some answers that emerge naturally within contemporary philosophy and argue that none of them adequately explains why metaphysics should be systematic. I then turn to Kant’s account of systematicity for his explanation. I argue (...)
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  • Do We Perceive Reality?John Klasios - 2022 - arXiv.
    The cognitive scientist Donald Hoffman argues that we don't perceive reality: spacetime, objects, colors, sounds, tastes, and so forth, are all merely an interface that we evolved to track evolutionary fitness rather than to perceive truths about external reality. In this paper, I expound on his argument, then I extend it, primarily, by looking at key ideas in physics that are quite germane to it. Among the topics in physics that I discuss are black holes, the holographic principle, string theory, (...)
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  • Remarks on the Gödelian Anti-Mechanist Arguments.Panu Raatikainen - 2020 - Studia Semiotyczne 34 (1):267–278.
    Certain selected issues around the Gödelian anti-mechanist arguments which have received less attention are discussed.
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  • Como Ser um Naturalista Filosófico Responsável?Luis R. G. Oliveira - 2017 - Revista Brasileira de Filosofia da Religião 4 (1):9-25.
    Um alinhamento responsável à alguma versão do naturalismo filosófico requer a articulação explicita e cuidadosa de um argumento em sua defesa. Em quatro passos, o texto que segue abaixo expande e examina a validade de um argumento que é frequentemente rascunhado em favor do naturalismo. Como veremos, contudo, a versão do naturalismo que esse argumento nos permite é um pouco diferente dos naturalismos filosóficos mais populares.
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  • Critiques of Axiological Realism and Surrealism.Seungbae Park - 2020 - Acta Analytica 35 (1):61-74.
    Lyons’s (2003, 2018) axiological realism holds that science pursues true theories. I object that despite its name, it is a variant of scientific antirealism, and is susceptible to all the problems with scientific antirealism. Lyons (2003, 2018) also advances a variant of surrealism as an alternative to the realist explanation for success. I object that it does not give rise to understanding because it is an ad hoc explanans and because it gives a conditional explanation. Lyons might use axiological realism (...)
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  • How to Overcome Antirealists’ Objections to Scientific Realism.Seungbae Park - 2020 - Axiomathes 30 (1):1-12.
    Van Fraassen contends that there is no argument that rationally compels us to disbelieve a successful theory, T. I object that this contention places upon him the burden of showing that scientific antirealists’ favorite arguments, such as the pessimistic induction, do not rationally compel us to disbelieve T. Van Fraassen uses the English view of rationality to rationally disbelieve T. I argue that realists can use it to rationally believe T, despite scientific antirealists’ favorite arguments against T.
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  • The Coherence of Evolutionary Theory with Its Neighboring Theories.Seungbae Park - 2019 - Acta Biotheoretica 67 (2):87-102.
    Evolutionary theory coheres with its neighboring theories, such as the theory of plate tectonics, molecular biology, electromagnetic theory, and the germ theory of disease. These neighboring theories were previously unconceived, but they were later conceived, and then they cohered with evolutionary theory. Since evolutionary theory has been strengthened by its several neighboring theories that were previously unconceived, it will be strengthened by infinitely many hitherto unconceived neighboring theories. This argument for evolutionary theory echoes the problem of unconceived alternatives. Ironically, however, (...)
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  • Extensional Scientific Realism vs. Intensional Scientific Realism.Seungbae Park - 2016 - Studies in History and Philosophy of Science Part A 59:46-52.
    Extensional scientific realism is the view that each believable scientific theory is supported by the unique first-order evidence for it and that if we want to believe that it is true, we should rely on its unique first-order evidence. In contrast, intensional scientific realism is the view that all believable scientific theories have a common feature and that we should rely on it to determine whether a theory is believable or not. Fitzpatrick argues that extensional realism is immune, while intensional (...)
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  • Is There a Compelling Argument for Ontic Structural Realism?Matteo Morganti - 2011 - Philosophy of Science 78 (5):1165-1176.
    Structural realism first emerged as an epistemological thesis aimed to avoid the socalled pessimistic metainduction on the history of science. Some authors, however, have suggested that the preservation of structure across theory change is best explained by endorsing the metaphysical thesis that structure is all there is. Although the possibility of this latter, ‘ontic’ form of structural realism has been extensively debated, not much has been said concerning its justification. In this article, I distinguish between two arguments in favor of (...)
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  • Editorial.[author unknown] - 2017 - Editorial 9 (44):1-4.
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  • Naturalism, Quietism, and the Threat to Philosophy.Thomas J. Spiegel - 2021 - Basel: Schwabe Verlagsgruppe.
    Two opposed movements of thought threaten philosophy as an autonomous practice from the inside: scientific naturalism and quietism. Naturalism (qua methodological thesis) threatens to turn philosophy into a mere ancilla of the sciences, quietism understood as the prescription to remain silent in philosophy would not countenance any more "positive" philosophy. This book reconstructs naturalism and quietism such that it becomes clear naturalism does have the potential to end philosophy as an autonomous practice and that quietism, correctly understood, does not. To (...)
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  • Putnam, Gödel, and Mathematical Realism Revisited.Alan Weir - 2023 - International Journal of Philosophical Studies 32 (1):146-168.
    I revisit my 1993 paper on Putnam and mathematical realism focusing on the indispensability argument and how it has fared over the years. This argument starts from the claim that mathematics is an indispensable part of science and draws the conclusion, from holistic considerations about confirmation, that the ontology of science includes abstract objects as well as the physical entities science deals with.
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  • An Evolutionary Sceptical Challenge to Scientific Realism.Christophe de Ray - 2022 - Erkenntnis 87 (3):969-989.
    Evolutionary scepticism holds that the evolutionary account of the origins of the human cognitive apparatus has sceptical implications for at least some of our beliefs. A common target of evolutionary scepticism is moral realism. Scientific realism, on the other hand, is much less frequently targeted, though the idea that evolutionary theory should make us distrustful of science is by no means absent from the literature. This line of thought has received unduly little attention. I propose to remedy this by advancing (...)
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  • Should Scientific Realists Embrace Theoretical Conservatism?Finnur Dellsén - 2018 - Studies in History and Philosophy of Science Part A:30-38.
    A prominent type of scientific realism holds that some important parts of our best current scientific theories are at least approximately true. According to such realists, radically distinct alternatives to these theories or theory-parts are unlikely to be approximately true. Thus one might be tempted to argue, as the prominent anti-realist Kyle Stanford recently did, that realists of this kind have little or no reason to encourage scientists to attempt to identify and develop theoretical alternatives that are radically distinct from (...)
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  • Explanatory Rivals and the Ultimate Argument.Finnur Dellsén - 2015 - Theoria 82 (3):217-237.
    Although many aspects of Inference to the Best Explanation have been extensively discussed, very little has so far been said about what it takes for a hypothesis to count as a rival explanatory hypothesis in the context of IBE. The primary aim of this article is to rectify this situation by arguing for a specific account of explanatory rivalry. On this account, explanatory rivals are complete explanations of a given explanandum. When explanatory rivals are conceived of in this way, I (...)
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  • Realism, Common Sense, and Science.Mario De Caro - 2015 - The Monist 98 (2):197-214.
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  • The Many Faces of Science and Technology Relationships.Ana Cuevas - 2005 - Essays in Philosophy 6 (1):54-75.
    In this paper, the different theories about science and technology relationships are analyzed. All of them have some virtues, but also one main defect: these theories do not take into account other well-founded possible relationships. The origin of this problem is the narrow view about science and technology. In this paper another characterization about technology based on Ronald Giere’s perspective is suggested. In the light of this new description, six different relationships between science and technology arise. Some of these relations (...)
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  • Epistemic truth and excluded middle.Cesare Cozzo - 1998 - Theoria 64 (2-3):243-282.
    Can an epistemic conception of truth and an endorsement of the excluded middle (together with other principles of classical logic abandoned by the intuitionists) cohabit in a plausible philosophical view? In PART I I describe the general problem concerning the relation between the epistemic conception of truth and the principle of excluded middle. In PART II I give a historical overview of different attitudes regarding the problem. In PART III I sketch a possible holistic solution.
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  • Scientific Realism Without Reality? What Happens When Metaphysics is Left Out.Alberto Corti - 2020 - Foundations of Science 28 (1):1-21.
    Scientific realism is usually presented as if metaphysical realism (i.e. the thesis that there is a structured mind-independent external world) were one of its essential parts. This paper aims to examine how weak the metaphysical commitments endorsed by scientific realists could be. I will argue that scientific realism could be stated without accepting any form of metaphysical realism. Such a conclusion does not go as far as to try to combine scientific realism with metaphysical antirealism. Instead, it amounts to the (...)
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  • Éxito predictivo y realismo.Manuel Comesaña - 2015 - Revista de filosofía (Chile) 71:23-30.
    El realismo científico enfrenta el problema de la subdeterminación de la teoría por los datos generada por la equivalencia empírica entre teorías rivales. Podría superarlo si fuera verdadero el predictivismo –el débil, ya que el fuerte tropieza con una dificultad que parece insuperable–. En tal caso, contribuiría además a refutar el escepticismo con respecto al mundo externo, pero no, como se ha sostenido, porque la experiencia dé más apoyo al realismo “ingenuo” del sentido común que a dicho escepticismo sino porque (...)
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  • Modal Dispositionalism and the (T) Axiom.Matthew James Collier - 2020 - Philosophia 49 (3):977-988.
    Yates has recently argued that modal dispositionalism invalidates the axiom. Both Yates and Allen have advanced responses to the objection: Yates’s response proposes installing truth into the possibility biconditional, and Allen’s response requires that all properties be construed as being essentially dispositional. I argue that supporters of Borghini and Williams’s modal dispositionalist theory cannot accept these responses, given critical tenets of their theory. But, since these responses to the objection are the most plausible in the literature, I conclude that the (...)
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  • Discussions Quinton’s Neglected Argument for Scientific Realism.Silvio Seno Chibeni - 2005 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 36 (2):393-400.
    This paper discusses an argument for scientific realism put forward by Anthony Quinton in The Nature of Things. The argument – here called the controlled continuity argument – seems to have received no attention in the literature, apparently because it may easily be mistaken for a better-known argument, Grover Maxwell’s “argument from the continuum”. It is argued here that, in point of fact, the two are quite distinct and that Quinton’s argument has several advantages over Maxwell’s. The controlled continuity argument (...)
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  • The new correspondence theory of truth without the concept of fact.Bo Chen - 2023 - Philosophical Forum 54 (4):261-286.
    Traditional correspondence theory of truth with the concept of fact encounters many serious difficulties, main one of which is that it is too difficult to explain clearly the concept of ‘fact’ and how propositions ‘correspond’ to facts. This does not mean that we should abandon the traditional correspondence theory of truth and turn to some other type theories of truth. In order to guarantee the objectivity of truth, any reasonable theory of truth must adhere to the core insight of the (...)
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  • Realism, antirealism, and theoretical conservatism.Luca Tambolo & Gustavo Cevolani - 2023 - Synthese 201 (1):1-18.
    This paper contributes to the debate on the question of whether a systematic connection obtains between one’s commitment to realism or antirealism and one’s attitude towards the possibility of radical theoretical novelty, namely, theory change affecting our best, most successful theories (see, e.g., Stanford in Synthese 196:3915–3932, 2019; Dellsén in Stud Hist Philos Sci 76:30–38, 2019). We argue that it is not allegiance to realism or antirealism as such that primarily dictates one’s response to the possibility of radical theoretical novelty: (...)
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  • Defending the Indispensability Argument: Atoms, Infinity and the Continuum.Eduardo Castro - 2013 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 44 (1):41-61.
    This paper defends the Quine-Putnam mathematical indispensability argument against two objections raised by Penelope Maddy. The objections concern scientific practices regarding the development of the atomic theory and the role of applied mathematics in the continuum and infinity. I present two alternative accounts by Stephen Brush and Alan Chalmers on the atomic theory. I argue that these two theories are consistent with Quine’s theory of scientific confirmation. I advance some novel versions of the indispensability argument. I argue that these new (...)
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  • Pragmatism about Truth-Makers.John Capps - 2022 - Contemporary Pragmatism 19 (4):350-370.
    Truth-makers are the dark matter of metaphysics. On the one hand, truth-makers seem obvious and necessary: if there are truths then there must be something that makes these truths true. On the other hand, it’s proven difficult to say exactly what these truth-makers are. Even defenders disagree about what sort of entity truth-makers are or whether all truths have truth-makers. Skeptics have questioned whether truth-makers are actually so obvious and necessary, or even whether they exist at all. Here I offer (...)
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  • Analyticity and Incorrigibility.Manuel Campos - 2003 - Philosophy and Phenomenological Research 66 (3):689-708.
    The traditional point of view on analyticity implies that truth in virtue only of meaning entails a priori acceptability and vice versa. The argument for this claim is based on the idea that meaning as it concerns truth and meaning as it concerns competence are one and the same thing. In this paper I argue that the extensions of these notions do not coincide. I hold that truth in virtue of meaning— truth for semantic reasons—doesn't imply a priori acceptability, and (...)
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  • Can there be a Bayesian explanationism? On the prospects of a productive partnership.Frank Cabrera - 2017 - Synthese 194 (4):1245–1272.
    In this paper, I consider the relationship between Inference to the Best Explanation and Bayesianism, both of which are well-known accounts of the nature of scientific inference. In Sect. 2, I give a brief overview of Bayesianism and IBE. In Sect. 3, I argue that IBE in its most prominently defended forms is difficult to reconcile with Bayesianism because not all of the items that feature on popular lists of “explanatory virtues”—by means of which IBE ranks competing explanations—have confirmational import. (...)
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  • On the Possibility of Quantum Informational Structural Realism.Terrell Ward Bynum - 2014 - Minds and Machines 24 (1):123-139.
    In The Philosophy of Information, Luciano Floridi presents an ontological theory of Being qua Being, which he calls “Informational Structural Realism”, a theory which applies, he says, to every possible world. He identifies primordial information (“dedomena”) as the foundation of any structure in any possible world. The present essay examines Floridi’s defense of that theory, as well as his refutation of “Digital Ontology” (which some people might confuse with his own). Then, using Floridi’s ontology as a starting point, the present (...)
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  • Can the new indispensability argument be saved from Euclidean rescues?Jacob Busch - 2012 - Synthese 187 (2):489-508.
    The traditional formulation of the indispensability argument for the existence of mathematical entities (IA) has been criticised due to its reliance on confirmational holism. Recently a formulation of IA that works without appeal to confirmational holism has been defended. This recent formulation is meant to be superior to the traditional formulation in virtue of it not being subject to the kind of criticism that pertains to confirmational holism. I shall argue that a proponent of the version of IA that works (...)
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  • Realismus in duhems naturgemässer klassifikation.Alex Burri - 1996 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 27 (2):203 - 213.
    Realism in Duhem's Natural Classification. Pierre Duhem is an outstanding exponent of empiricism. According to the empiricist view scientific laws and theories merely describe formal relations between observable phenomena. Duhems' important notion of natural classification is intended to explain the predictive success of science. I shall argue that it can only be interpreted realistically. Besides the success of science, two further arguments are put forward in favor of realism: (i) the fact that laws of nature are necessary, and (ii) the (...)
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  • The Rationality of Science.James Robert Brown - 1983 - Dialogue 22 (2):299-309.
    William Newton-Smith is a fine young Canadian philosopher of science who has spent the last decade in productive thought at Balliol, Oxford. His new work, The Rationality of Science, follows hot on the heels of his other book, The Structure of Time. And with them he establishes himself as a major force to be reckoned with in philosophical circles.
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  • Why inference to the best explanation doesn’t secure empirical grounds for mathematical platonism.Kenneth Boyce - 2018 - Synthese 198 (1):1-13.
    Proponents of the explanatory indispensability argument for mathematical platonism maintain that claims about mathematical entities play an essential explanatory role in some of our best scientific explanations. They infer that the existence of mathematical entities is supported by way of inference to the best explanation from empirical phenomena and therefore that there are the same sort of empirical grounds for believing in mathematical entities as there are for believing in concrete unobservables such as quarks. I object that this inference depends (...)
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  • The Coincidentalist Reply to the No-Miracles Argument.Kenneth Boyce - 2018 - Erkenntnis 83 (5):929-946.
    Proponents of the no-miracles argument contend that scientific realism is “the only philosophy that doesn’t make the success of science a miracle.” Bas van Fraassen argued, however, that the success of our best theories can be explained in Darwinian terms—by the fact they are survivors of a winnowing process in which unsuccessful theories are rejected. Critics of this selectionist explanation complain that while it may account for the fact we have chosen successful theories, it does not explain why any particular (...)
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  • 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 sense outlined by Hartry Field. (...)
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  • The Positive Argument Against Scientific Realism.Florian J. Boge - 2023 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 54 (4):535-566.
    Putnam coined what is now known as the no miracles argument “[t]he positive argument for realism”. In its opposition, he put an argument that by his own standards counts as negative. But are there no positive arguments against scientific realism? I believe that there is such an argument that has figured in the back of much of the realism-debate, but, to my knowledge, has nowhere been stated and defended explicitly. This is an argument from the success of quantum physics to (...)
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  • Did Bishop have a philosophy of mathematics?Helen Billinge - 2003 - Philosophia Mathematica 11 (2):176-194.
    When Bishop published Foundations of Constructive Analysis he showed that it was possible to do ordinary analysis within a constructive framework. Bishop's reasons for doing his mathematics constructively are explicitly philosophical. In this paper, I will expound, examine, and amplify his philosophical arguments for constructivism in mathematics. In the end, however, I argue that Bishop's philosophical comments cannot be rounded out into an adequate philosophy of constructive mathematics.
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  • Self-Fulfillment of Social Science Theories: Cooling the Fire.Carsten Bergenholtz & Jacob Busch - 2016 - Philosophy of the Social Sciences 46 (1):24-43.
    Self-fulfillment of theories is argued to be a threat to social science in at least two ways. First, a realist might worry that self-fulfillment constitutes a threat to the idea that social science is a proper science consistent with a realist approach that develops true and successful statements about the world. Second, one might argue that the potential self-fulfilling nature of social science theories potentially undermines the ethical integrity of social scientists. We argue that if one accepts that social science (...)
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  • Immunity to error through misidentification and past-tense memory judgements.J. L. Bermudez - 2013 - Analysis 73 (2):211-220.
    Autobiographical memories typically give rise either to memory reports (“I remember going swimming”) or to first person past-tense judgements (“I went swimming”). This article focuses on first person past-tense judgements that are (epistemically) based on autobiographical memories. Some of these judgements have the IEM property of being immune to error through misidentification. This article offers an account of when and why first person past-tense judgements have the IEM property.
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  • Evidence amalgamation, plausibility, and cancer research.Marta Bertolaso & Fabio Sterpetti - 2019 - Synthese 196 (8):3279-3317.
    Cancer research is experiencing ‘paradigm instability’, since there are two rival theories of carcinogenesis which confront themselves, namely the somatic mutation theory and the tissue organization field theory. Despite this theoretical uncertainty, a huge quantity of data is available thanks to the improvement of genome sequencing techniques. Some authors think that the development of new statistical tools will be able to overcome the lack of a shared theoretical perspective on cancer by amalgamating as many data as possible. We think instead (...)
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  • Reconstructing Probabilistic Realism: Re-enacting Syntactical Structures.Majid Davoody Beni - 2020 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (2):293-313.
    Probabilistic realism and syntactical positivism were two among outdated theories that Feigl criticised on account of their semantical poverty. In this paper, I argue that a refined version of probabilistic realism, which relies on what Feigl specified as the pragmatic description of the symbolic behaviour of scientists’ estimations and foresight, is defendable. This version of statistical realism does not need to make the plausibility of realist thesis dependent on the conventional acceptance of a constructed semantic metalanguage. I shall rely on (...)
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  • Ten Misconceptions from the History of Analysis and Their Debunking.Piotr Błaszczyk, Mikhail G. Katz & David Sherry - 2013 - Foundations of Science 18 (1):43-74.
    The widespread idea that infinitesimals were “eliminated” by the “great triumvirate” of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum (...)
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  • Optimisation and mathematical explanation: doing the Lévy Walk.Sam Baron - 2014 - Synthese 191 (3).
    The indispensability argument seeks to establish the existence of mathematical objects. The success of the indispensability argument turns on finding cases of genuine extra- mathematical explanation. In this paper, I identify a new case of extra- mathematical explanation, involving the search patterns of fully-aquatic marine predators. I go on to use this case to predict the prevalence of extra- mathematical explanation in science.
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  • Can Indispensability‐Driven Platonists Be (Serious) Presentists?Sam Baron - 2014 - Theoria 80 (2):153-173.
    In this article I consider what it would take to combine a certain kind of mathematical Platonism with serious presentism. I argue that a Platonist moved to accept the existence of mathematical objects on the basis of an indispensability argument faces a significant challenge if she wishes to accept presentism. This is because, on the one hand, the indispensability argument can be reformulated as a new argument for the existence of past entities and, on the other hand, if one accepts (...)
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