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Mathematical truth

Journal of Philosophy 70 (19):661-679 (1973)

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  1. Estructuralismo, ficcionalismo, y la aplicabilidad de las matemáticas en ciencia.Manuel Barrantes - 2019 - Areté. Revista de Filosofía 31 (1):7-34.
    “Structuralism, Fictionalism, and the Applicability of Mathematics in Science”. This article has two objectives. The first one is to review some of the most important questions in the contemporary philosophy of mathematics: What is the nature of mathematical objects? How do we acquire knowledge about these objects? Should mathematical statements be interpreted differently than ordinary ones? And, finally, how can we explain the applicability of mathematics in science? The debate that guides these reflections is the one between mathematical realism and (...)
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  • Can Indispensability‐Driven Platonists Be (Serious) Presentists?Sam Baron - 2013 - Theoria 79 (3):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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  • 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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  • A Truthmaker Indispensability Argument.Sam Baron - 2013 - Synthese 190 (12):2413-2427.
    Recently, nominalists have made a case against the Quine–Putnam indispensability argument for mathematical Platonism by taking issue with Quine’s criterion of ontological commitment. In this paper I propose and defend an indispensability argument founded on an alternative criterion of ontological commitment: that advocated by David Armstrong. By defending such an argument I place the burden back onto the nominalist to defend her favourite criterion of ontological commitment and, furthermore, show that criterion cannot be used to formulate a plausible form of (...)
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  • A reliability challenge to theistic Platonism.Dan Baras - 2017 - Analysis 77 (3):479-487.
    Many philosophers believe that when a theory is committed to an apparently unexplainable massive correlation, that fact counts significantly against the theory. Philosophical theories that imply that we have knowledge of non-causal mind-independent facts are especially prone to this objection. Prominent examples of such theories are mathematical Platonism, robust normative realism and modal realism. It is sometimes thought that theists can easily respond to this sort of challenge and that theism therefore has an epistemic advantage over atheism. In this paper, (...)
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  • Absence perception and the philosophy of zero.Neil Barton - 2020 - Synthese 197 (9):3823-3850.
    Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...)
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  • Indispensability, causation and explanation.Sorin Bangu - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):219-232.
    When considering mathematical realism, some scientific realists reject it, and express sympathy for the opposite view, mathematical nominalism; moreover, many justify this option by invoking the causal inertness of mathematical objects. The main aim of this note is to show that the scientific realists’ endorsement of this causal mathematical nominalism is in tension with another position some of them also accept, the doctrine of methodological naturalism. By highlighting this conflict, I intend to tip the balance in favor of a rival (...)
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  • Realistic rationalism [1998]: Can we know that platonism is true?Mark Balaguer - 2003 - Philosophical Forum 34 (3-4):459–476.
    Book reviewed:;Jerrold J. Katz, Realistic Rationalism;Book reviewed:;Jerrold J. Katz, Realistic Rationalism;Book reviewed:;Jerrold J. Katz, Realistic Rationalism;Book reviewed:;Jerrold J. Katz, Realistic Rationalism;Book reviewed:;Jerrold J. Katz, Realistic Rationalism;Book reviewed:;Jerrold J. Katz, Realistic Rationalism;Book reviewed:;Jerrold J. Katz, Realistic Rationalism;Book reviewed:;Jerrold J. Katz, Realistic Rationalism;Book reviewed:;Jerrold J. Katz, Realistic Rationalism;Book reviewed:;Jerrold J. Katz, Realistic Rationalism.
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  • Non-uniqueness as a non-problem.Mark Balaguer - 1998 - Philosophia Mathematica 6 (1):63-84.
    A response is given here to Benacerraf's (1965) non-uniqueness (or multiple-reductions) objection to mathematical platonism. It is argued that non-uniqueness is simply not a problem for platonism; more specifically, it is argued that platonists can simply embrace non-uniqueness—i.e., that one can endorse the thesis that our mathematical theories truly describe collections of abstract mathematical objects while rejecting the thesis that such theories truly describe unique collections of such objects. I also argue that part of the motivation for this stance is (...)
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  • Can we know that platonism is true?Mark Balaguer - 2003 - Philosophical Forum 34 (3):459-475.
    ? Mark BALAGUER Philosophical forum 34:3-43-4, 459-475, Blackwell, 2003.
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  • Alethic Pluralism and the Role of Reference in the Metaphysics of Truth.Brian Ball - 2017 - Southern Journal of Philosophy 55 (1):116-135.
    In this paper, I outline and defend a novel approach to alethic pluralism, the thesis that truth has more than one metaphysical nature: where truth is, in part, explained by reference, it is relational in character and can be regarded as consisting in correspondence; but where instead truth does not depend upon reference it is not relational and involves only coherence. In the process, I articulate a clear sense in which truth may or may not depend upon reference: this involves (...)
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  • A platonist epistemology.Mark Balaguer - 1995 - Synthese 103 (3):303 - 325.
    A response is given here to Benacerraf's 1973 argument that mathematical platonism is incompatible with a naturalistic epistemology. Unlike almost all previous platonist responses to Benacerraf, the response given here is positive rather than negative; that is, rather than trying to find a problem with Benacerraf's argument, I accept his challenge and meet it head on by constructing an epistemology of abstract (i.e., aspatial and atemporal) mathematical objects. Thus, I show that spatio-temporal creatures like ourselves can attain knowledge about mathematical (...)
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  • Against (maddian) naturalized platonism.Mark Balaguer - 1994 - Philosophia Mathematica 2 (2):97-108.
    It is argued here that mathematical objects cannot be simultaneously abstract and perceptible. Thus, naturalized versions of mathematical platonism, such as the one advocated by Penelope Maddy, are unintelligble. Thus, platonists cannot respond to Benacerrafian epistemological arguments against their view vias Maddy-style naturalization. Finally, it is also argued that naturalized platonists cannot respond to this situation by abandoning abstractness (that is, platonism); they must abandon perceptibility (that is, naturalism).
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  • A fictionalist account of the indispensable applications of mathematics.Mark Balaguer - 1996 - Philosophical Studies 83 (3):291 - 314.
    The main task of this paper is to defend anti-platonism by providing an anti-platonist (in particular, a fictionalist) account of the indispensable applications of mathematics to empirical science.
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  • Popper’s Theory of World 3 and the Evolution of the Internet.Peter Backes - 2016 - Philosophy of the Social Sciences 46 (3):265-287.
    While developing his theory of world 3, Popper rejects two claims made by Plato: first, that the inhabitants of world 3, ideas, are a source of ultimate explanation, a divine revelation of truth, and second, that these ideas are unchanging. I will rehabilitate the second claim. Man does not construct world 3 by creating his theories, nor is it a source of ultimate truth. Instead, world 3 is discovered by man, and it destroys some of his theories: destructive Platonism. I (...)
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  • Why deflationary nominalists shouldn’t be agnostics.Jody Azzouni - 2015 - Philosophical Studies 172 (5):1143-1161.
    A feature of agnostic views—views that officially express ignorance about the existence of something —is that they are widely perceived to be epistemically more cautious than views that are committed to the entities in question. This is often seen as giving agnostics a debating advantage: all things being equal, fence-sitters have smaller argumentative burdens. Otávio Bueno argues in this way for what he calls “agnostic nominalism,” the view that we don’t know whether ontologically-independent Platonic objects exist. I show that agnostic (...)
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  • Stipulation, logic, and ontological independence.Jody Azzouni - 2000 - Philosophia Mathematica 8 (3):225-243.
    A distinction between the epistemic practices in mathematics and in the empirical sciences is rehearsed to motivate the epistemic role puzzle. This is distinguished both from Benacerraf's 1973 epistemic puzzle and from sceptical arguments against our knowledge of an external world. The stipulationist position is described, a position which can address this puzzle. Methods of avoiding the stipulationist position by using pure logic to provide knowledge of mathematical abstracta are discussed and criticized.
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  • True Nominalism: Referring versus Coding.Jody Azzouni & Otávio Bueno - 2016 - British Journal for the Philosophy of Science 67 (3):781-816.
    One major motivation for nominalism, at least according to Hartry Field, is the desirability of intrinsic explanations: explanations that don’t invoke objects that are causally irrelevant to the phenomena being explained. There is something right about the search for such explanations. But that search must be carefully implemented. Nothing is gained if, to avoid a certain class of objects, one only introduces other objects and relations that are just as nominalistically questionable. We will argue that this is the case for (...)
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  • On "on what there is".Jody Azzouni - 1998 - Pacific Philosophical Quarterly 79 (1):1–18.
    All sides in the recent debates over the Quine‐Putnam Indispensability thesis presuppose Quine's criterion for determining what a discourse is ontologically committed to. I subject the criterion to scrutiny, especially in regard to the available competitor‐criteria, asking what means of evaluation there are for comparing alternative criteria against each other. Finding none, the paper concludes that ontological questions, in a certain sense, are philosophically indeterminate.
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  • Empty de re attitudes about numbers.Jody Azzouni - 2009 - Philosophia Mathematica 17 (2):163-188.
    I dub a certain central tradition in philosophy of language (and mind) the de re tradition. Compelling thought experiments show that in certain common cases the truth conditions for thoughts and public-language expressions categorically turn on external objects referred to, rather than on linguistic meanings and/or belief assumptions. However, de re phenomena in language and thought occur even when the objects in question don't exist. Call these empty de re phenomena. Empty de re thought with respect to numeration is explored (...)
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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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  • From Possibility to Properties? Or from Properties to Possibility?Sophie R. Allen - 2017 - Philosophy 92 (1):21-49.
    This paper contrasts two metaphysical accounts of modality and properties: Modal Realism which treats possible entities as primitive; and Strong Dispositionalism in which metaphysical possibility and necessity are determined by actually existing dispositions or powers. I argue that Strong Dispositionalism loses its initial advantages of simplicity and parsimony over Modal Realism as it is extended and amended to account for metaphysical rather than just causal necessity. Furthermore, to avoid objections to its material and formal adequacy, Strong Dispositionalism requires a richer (...)
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  • Can Metaphysical Structuralism Solve the Plurality Problem?Sophie R. Allen - 2018 - International Journal of Philosophical Studies 26 (5):722-746.
    ABSTRACTMetaphysics has a problem with plurality: in many areas of discourse, there are too many good theories, rather than just one. This embarrassment of riches is a particular problem for metaphysical realists who want metaphysics to tell us the way the world is and for whom one theory is the correct one. A recent suggestion is that we can treat the different theories as being functionally or explanatorily equivalent to each other, even though they differ in content. The aim of (...)
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  • Electromagnetic Theory: Some Philosophical and Mathematical Problems of the Wave and Helmholtz Equations.Vicente Aboites - 2022 - Open Journal of Philosophy 12 (3):489-503.
    In this article some intriguing aspects of electromagnetic theory and its relation to mathematics and reality are discussed, in particular those related to the suppositions needed to obtain the wave equations from Maxwell equations and from there Helmholtz equation. The following questions are discussed. How is that equations obtained with so many irreal or fictitious assumptions may provide a description that is in a high degree verifiable? Must everything that is possible to deduce from a theoretical mathematical model occur in (...)
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  • Indispensabilité et réalisme restreint : réponse à Nicolas Pain.Fabrice Pataut - 2012 - RÉPHA, revue étudiante de philosophie analytique 6:33-38.
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  • Deductivism in the Philosophy of Mathematics.Alexander Paseau & Fabian Pregel - 2023 - Stanford Encyclopedia of Philosophy 2023.
    Deductivism says that a mathematical sentence s should be understood as expressing the claim that s deductively follows from appropriate axioms. For instance, deductivists might construe “2+2=4” as “the sentence ‘2+2=4’ deductively follows from the axioms of arithmetic”. Deductivism promises a number of benefits. It captures the fairly common idea that mathematics is about “what can be deduced from the axioms”; it avoids an ontology of abstract mathematical objects; and it maintains that our access to mathematical truths requires nothing beyond (...)
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  • Getting a Moral Thing Into a Thought: Metasemantics for Non-Naturalists.Preston J. Werner - 2020 - In Russ Shafer-Landau (ed.), Oxford Studies in Metaethics. Oxford University Press. pp. 140-169.
    Non-naturalism is the view that normative properties are response-independent, irreducible to natural properties, and causally inefficacious. An underexplored question for non-naturalism concerns the metasemantics of normative terms. Ideally, the non-naturalist could remain ecumenical, but it appears they cannot. Call this challenge the metasemantic challenge. This chapter suggests that non-naturalists endorse an epistemic account of reference determination of the sort recently defended by Imogen Dickie, with some modifications. An important implication of this account is that, if correct, a fully fleshed out (...)
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  • Etiological Debunking Beyond Belief.Joshua Schechter - forthcoming - Oxford Studies in Metaethics.
    Learning information about the etiology of one's beliefs can reduce the justification a thinker has for those beliefs. Learning information about the etiology of one's desires, emotions, or concepts can similarly have a debunking effect. In this chapter, I develop a unified account of etiological debunking that applies across these different kinds of cases. According to this account, etiological debunking arguments work by providing reason to think that there is no satisfying explanation of how it is that some part of (...)
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  • Against Minimalist Responses to Moral Debunking Arguments.Daniel Z. Korman & Dustin Locke - 2020 - Oxford Studies in Metaethics 15:309-332.
    Moral debunking arguments are meant to show that, by realist lights, moral beliefs are not explained by moral facts, which in turn is meant to show that they lack some significant counterfactual connection to the moral facts (e.g., safety, sensitivity, reliability). The dominant, “minimalist” response to the arguments—sometimes defended under the heading of “third-factors” or “pre-established harmonies”—involves affirming that moral beliefs enjoy the relevant counterfactual connection while granting that these beliefs are not explained by the moral facts. We show that (...)
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  • International Handbook of Research in History, Philosophy and Science Teaching.Michael R. Matthews (ed.) - 2014 - Springer.
    This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...)
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  • modality and meaning.William G. Lycan - 1994 - Dordrecht: Kluwer Academic Publishers.
    MEANING POSTULATES REINSTATED If I am right in agreeing with Cresswell that the "logicarrlexicaT distinction is one of degree rather than one of kind, that in turn impugns the distinction between the official truth-rules that define logical ...
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  • Naturalizing Badiou: mathematical ontology and structural realism.Fabio Gironi - 2014 - New York: Palgrave-Macmillan.
    This thesis offers a naturalist revision of Alain Badiou’s philosophy. This goal is pursued through an encounter of Badiou’s mathematical ontology and theory of truth with contemporary trends in philosophy of mathematics and philosophy of science. I take issue with Badiou’s inability to elucidate the link between the empirical and the ontological, and his residual reliance on a Heideggerian project of fundamental ontology, which undermines his own immanentist principles. I will argue for both a bottom-up naturalisation of Badiou’s philosophical approach (...)
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  • Leśniewski's Systems of Logic and Foundations of Mathematics.Rafal Urbaniak - 2013 - Cham, Switzerland: Springer.
    With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great ...
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  • Rationality and the Structure of the Self Volume II: A Kantian Conception.Adrian M. S. Piper - 2013 - APRA Foundation.
    Adrian Piper argues that the Humean conception can be made to work only if it is placed in the context of a wider and genuinely universal conception of the self, whose origins are to be found in Kant’s Critique of Pure Reason. This conception comprises the basic canons of classical logic, which provide both a model of motivation and a model of rationality. These supply necessary conditions both for the coherence and integrity of the self and also for unified agency. (...)
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  • Phenomenology and mathematics.Mirja Hartimo (ed.) - 2010 - London: Springer.
    This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics.
  • Rationality and the Structure of the Self, Volume I: The Humean Conception.Adrian M. S. Piper - 2013 - APRA Foundation Berlin.
    The Humean conception of the self consists in the belief-desire model of motivation and the utility-maximizing model of rationality. This conception has dominated Western thought in philosophy and the social sciences ever since Hobbes’ initial formulation in Leviathan and Hume’s elaboration in the Treatise of Human Nature. Bentham, Freud, Ramsey, Skinner, Allais, von Neumann and Morgenstern and others have added further refinements that have brought it to a high degree of formal sophistication. Late twentieth century moral philosophers such as Rawls, (...)
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  • The Place of Probability in Science: In Honor of Ellery Eells (1953-2006).Ellery Eells & James H. Fetzer (eds.) - 2010 - Springer.
  • Logic, Logicism, and Intuitions in Mathematics.Besim Karakadılar - 2001 - Dissertation, Middle East Technical University
    In this work I study the main tenets of the logicist philosophy of mathematics. I deal, basically, with two problems: (1) To what extent can one dispense with intuition in mathematics? (2) What is the appropriate logic for the purposes of logicism? By means of my considerations I try to determine the pros and cons of logicism. My standpoint favors the logicist line of thought. -/- .
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  • Realism.Alexandern D. Miller - 2008 - Stanford Encyclopedia of Philosophy.
  • Pythagorean Powers.Colin Cheyne & Charles R. Pigden - unknown
    The Quine/Putnam indispensability argument is regarded by many as the chief argument for the existence of platonic objects. We argue that this argument cannot establish what its proponents intend. The form of our argument is simple. Suppose indispensability to science is the only good reason for believing in the existence of platonic objects. Either the dispensability of mathematical objects to science can be demonstrated and, hence, there is no good reason for believing in the existence of platonic objects, or their (...)
     
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  • Lógica, lenguajes formales y modalidad.Otávio Bueno & Melisa Vivanco - 2023 - Andamios 20 (53):45-60.
    This paper examines two alleged limitations in the use of formal languages: on the one hand, the trade-offs between expressive and inferential power, and on the other, the phenomenon of system imprisonment. After reconceptualizing the issue, we consider the role played by modality in the understanding of certain aspects of mathematical structures and argue for its centrality.
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  • Debunking Arguments in Metaethics and Metaphysics.Daniel Z. Korman - 2019 - In Alvin Goldman & Brian McLaughlin (eds.), Metaphysics and Cognitive Science. Oxford University Press. pp. 337-363.
    Evolutionary debunking arguments abound, but it is widely assumed that they do not arise for our perceptual beliefs about midsized objects, insofar as the adaptive value of our object beliefs cannot be explained without reference to the objects themselves. I argue that this is a mistake. Just as with moral beliefs, the adaptive value of our object beliefs can be explained without assuming that the beliefs are accurate. I then explore the prospects for other sorts of vindications of our object (...)
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  • Towards a Fictionalist Philosophy of Mathematics.Robert Knowles - 2015 - Dissertation, University of Manchester
    In this thesis, I aim to motivate a particular philosophy of mathematics characterised by the following three claims. First, mathematical sentences are generally speaking false because mathematical objects do not exist. Second, people typically use mathematical sentences to communicate content that does not imply the existence of mathematical objects. Finally, in using mathematical language in this way, speakers are not doing anything out of the ordinary: they are performing straightforward assertions. In Part I, I argue that the role played by (...)
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  • Nominalism.Zoltán Gendler Szabó - 2003 - In Michael J. Loux & Dean W. Zimmerman (eds.), The Oxford Handbook of Metaphysics. Oxford University Press.
    …entities? 2. How to be a nominalist 2.1. “Speak with the vulgar …” 2.2. “…think with the learned” 3. Arguments for nominalism 3.1. Intelligibility, physicalism, and economy 3.2. Causal..
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  • Applied Mathematics in the Sciences.Dale Jacquette - 2006 - Croatian Journal of Philosophy 6 (2):237-267.
    A complete philosophy of mathematics must address Paul Benacerraf’s dilemma. The requirements of a general semantics for the truth of mathematical theorems that coheres also with the meaning and truth conditions for non-mathematical sentences, according to Benacerraf, should ideally be coupled with an adequate epistemology for the discovery of mathematical knowledge. Standard approaches to the philosophy of mathematics are criticized against their own merits and against the background of Benacerraf’s dilemma, particularly with respect to the problem of understanding the distinction (...)
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  • Motivation and the Primacy of Perception.Peter Antich - 2017 - Dissertation, University of Kentucky
    In this dissertation, I provide an interpretation and defense of Merleau-Ponty's thesis of the primacy of perception, namely, the thesis that all knowledge is founded in perceptual experience. I take as an interpretative and argumentative key Merleau-Ponty's phenomenological conception of motivation. Whereas epistemology has traditionally accepted a dichotomy between reason and natural causality, I show that this dichotomy is not exhaustive of the forms of epistemic grounding. There is a third type of grounding, the one characteristic of the grounding relations (...)
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  • Conceivability and the Epistemology of Modality.Asger Bo Skjerning Steffensen - 2015 - Dissertation, Aarhus University
    The dissertation is in the format of a collection of several academic texts, composed of a two-part presentation and three papers on the topic of conceivability and the epistemology of modality. The presentation is composed of, first, a general introduction to conceivability theses and objections and, second, a discussion of two cases. Following the presentation, Asger provides three papers. The first paper, Pretense and Conceivability: A reply to Roca-Royes, presents a problem and a dilemma for Roca-Royes’ Non-Standard Dilemma for conceivability-based (...)
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  • Nominalism in metaphysics.Gonzalo Rodriguez-Pereyra - 2008 - Stanford Encyclopedia of Philosophy.
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  • Abstract objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
  • Dualism.Howard Robinson - 2008 - Stanford Encyclopedia of Philosophy.
    This entry concerns dualism in the philosophy of mind. The term ‘dualism’ has a variety of uses in the history of thought. In general, the idea is that, for some particular domain, there are two fundamental kinds or categories of things or principles. In theology, for example a ‘dualist’ is someone who believes that Good and Evil — or God and the Devil — are independent and more or less equal forces in the world. Dualism contrasts with monism, which is (...)
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