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  1. What anti-realism in philosophy of mathematics must offer.Feng Ye - 2010 - Synthese 175 (1):13 - 31.
    This article attempts to motivate a new approach to anti-realism (or nominalism) in the philosophy of mathematics. I will explore the strongest challenges to anti-realism, based on sympathetic interpretations of our intuitions that appear to support realism. I will argue that the current anti-realistic philosophies have not yet met these challenges, and that is why they cannot convince realists. Then, I will introduce a research project for a new, truly naturalistic, and completely scientific approach to philosophy of mathematics. It belongs (...)
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  • Abstract Objects: An Introduction to Axiomatic Metaphysics.Edward N. Zalta - 1983 - Dordrecht, Netherland: D. Reidel.
    In this book, Zalta attempts to lay the axiomatic foundations of metaphysics by developing and applying a (formal) theory of abstract objects. The cornerstones include a principle which presents precise conditions under which there are abstract objects and a principle which says when apparently distinct such objects are in fact identical. The principles are constructed out of a basic set of primitive notions, which are identified at the end of the Introduction, just before the theorizing begins. The main reason for (...)
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  • Problems and meaning today: What can we learn from Hattiangadi's failed attempt to explain them together?John Wettersten - 2002 - Philosophy of the Social Sciences 32 (4):487-536.
    Philosophers have tried to explain how science finds the truth by using new developments in logic to study scientific language and inference. R. G. Collingwood argued that only a logic of problems could take context into account. He was ignored, but the need to reconcile secure meanings with changes in context and meanings was seen by Karl Popper, W. v. O. Quine, and Mario Bunge. Jagdish Hattiangadi uses problems to reconcile the need for security with that for growth. But he (...)
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  • Kant on the Nature of Logical Laws.Clinton Tolley - 2006 - Philosophical Topics 34 (1-2):371-407.
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  • (1 other version)Abstract objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
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  • Philosophy of mathematics.Leon Horsten - 2008 - Stanford Encyclopedia of Philosophy.
    If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are located in space and time, it is not at all obvious that this is also the case (...)
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  • On Quine on Carnap on Ontology.Marc Alspector-Kelly - 2001 - Philosophical Studies 102 (1):93 - 122.
    W. V. Quine assumed that in _Empiricism, Semantics, and Ontology Rudolf Carnap was attempting to dodge commitment to abstract entities--without either renouncing quantification over them or demonstrating their dispensability--by wielding the analytic/synthetic distinction against ontological issues. Quine's interpretation of Carnap's intent--and his criticism of it--is widely endorsed. But Carnap objected, I argue, not to abstract entities, but to his critics' suggestion that empiricism implies nominalism. Quine's and Carnap's views are therefore more akin than Quine ever suspected. Unfortunately, Quine's misinterpretation of (...)
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  • What is constructive empiricism?Gideon Rosen - 1994 - Philosophical Studies 74 (2):143 - 178.
    Van Fraassen defines constructive empiricism as the view that science aims to produce empirically adequate theories. But this account has been misunderstood. Constructive empiricism in not, as it seems, a description of the intentional features of scientific practice, nor is it a normative prescription for their revision. It is rather a fiction about the practice of science that van Fraassen displays in the interests of a broader empiricism. The paper concludes with a series of arguments designed to show that constructive (...)
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  • How nominalist is Hartry field's nominalism?Michael D. Resnik - 1985 - Philosophical Studies 47 (2):163 - 181.
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  • Logic and Ontology.Nino B. Cocchiarella - 2001 - Axiomathes 12 (1-2):117-150.
    A brief review of the historicalrelation between logic and ontologyand of the opposition between the viewsof logic as language and logic as calculusis given. We argue that predication is morefundamental than membership and that differenttheories of predication are based on differenttheories of universals, the three most importantbeing nominalism, conceptualism, and realism.These theories can be formulated as formalontologies, each with its own logic, andcompared with one another in terms of theirrespective explanatory powers. After a briefsurvey of such a comparison, we argue (...)
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  • Monism.Jonathan Schaffer - 2008 - Stanford Encyclopedia of Philosophy.
    This entry focuses on two of the more historically important monisms: existence monism and priority monism . Existence monism targets concrete objects and counts by tokens. This is the doctrine that exactly one concrete object exists. Priority monism also targets concrete objects, but counts by basic tokens. This is the doctrine that exactly one concrete object is basic, which will turn out to be the classical doctrine that the whole is prior to its parts.
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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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  • Dummett on abstract objects.George Duke - 2012 - New York: Palgrave-Macmillan.
    This book offers an historically-informed critical assessment of Dummett's account of abstract objects, examining in detail some of the Fregean presuppositions whilst also engaging with recent work on the problem of abstract entities.
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  • Ockham's razor, encounterability, and ontological naturalism.J. M. Dieterle - 2001 - Erkenntnis 55 (1):51-72.
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  • Number Concepts: An Interdisciplinary Inquiry.Richard Samuels & Eric Snyder - 2024 - Cambridge University Press.
    This Element, written for researchers and students in philosophy and the behavioral sciences, reviews and critically assesses extant work on number concepts in developmental psychology and cognitive science. It has four main aims. First, it characterizes the core commitments of mainstream number cognition research, including the commitment to representationalism, the hypothesis that there exist certain number-specific cognitive systems, and the key milestones in the development of number cognition. Second, it provides a taxonomy of influential views within mainstream number cognition research, (...)
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  • Justified True Belief: The Remarkable History of Mainstream Epistemology.Sander Verhaegh - forthcoming - Journal of the History of Philosophy.
    This paper reconstructs the origins of Gettier-style epistemology, highlighting the philosophical and methodological debates that led to its development in the 1960s. Though present-day epistemologists assume that the search for necessary and sufficient conditions for knowledge began with Gettier’s 1963 argument against the JTB-definition, I show that this research program can be traced back to British discussions about knowledge and analysis in the 1940s and 1950s. I discuss work of, among others, Bertrand Russell, G. E. Moore, A. J. Ayer, Norman (...)
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  • Castles Built on Clouds: Vague Identity and Vague Objects.Benjamin L. Curtis & Harold W. Noonan - 2014 - In Ken Akiba & Ali Abasnezhad (eds.), Vague Objects and Vague Identity: New Essays on Ontic Vagueness. Dordrecht, Netherland: Springer. pp. 305-326.
    Can identity itself be vague? Can there be vague objects? Does a positive answer to either question entail a positive answer to the other? In this paper we answer these questions as follows: No, No, and Yes. First, we discuss Evans’s famous 1978 argument and argue that the main lesson that it imparts is that identity itself cannot be vague. We defend the argument from objections and endorse this conclusion. We acknowledge, however, that the argument does not by itself establish (...)
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  • Against Mereological Nominalism: Reply to Effingham.Javier Cumpa & Alexandre Declos - 2021 - Synthese 199 (3-4):8991-9011.
    Mereological Nominalism, as traditionally understood, states that properties are mereological wholes and that instantiation is mereological. Thus defined, this view faces a number of well-known issues, which make it virtually untenable. Recently, Effingham :160–185, 2020) has offered an alternative account of Mereological Nominalism, which intends to avoid these problems by accepting while rejecting. In this paper, we argue that this theory is not viable for two main reasons. First, it faces a threat of circularity. Second, the various non-mereological accounts of (...)
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  • Understandability: Greg Frost-Arnold: Carnap, Tarski, and Quine at Harvard: Conversations of Logic, Mathematics, and Science. Chicago: Open Court, 2013. xiv+257pp. $49.95PB.Richard Creath - 2015 - Metascience 25 (1):25-30.
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  • Susanne Langer and the American Development of Analytic Philosophy.Sander Verhaegh - 2022 - In Jeanne Peijnenburg & Sander Verhaegh (eds.), Women in the History of Analytic Philosophy. Cham: Springer. pp. 219-245.
    Susanne K. Langer is best known as a philosopher of culture and student of Ernst Cassirer. In this chapter, however, I argue that this standard picture ignores her contributions to the development of analytic philosophy in the 1920s and 1930s. I reconstruct the reception of Langer’s first book *The Practice of Philosophy*—arguably the first sustained defense of analytic philosophy by an American philosopher—and describe how prominent European philosophers of science such as Moritz Schlick, Rudolf Carnap, and Herbert Feigl viewed her (...)
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  • God and Abstract Objects: The Coherence of Theism: Aseity.William Lane Craig - 2017 - Cham: Springer.
    This book is an exploration and defense of the coherence of classical theism’s doctrine of divine aseity in the face of the challenge posed by Platonism with respect to abstract objects. A synoptic work in analytic philosophy of religion, the book engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology. It addresses absolute creationism, non-Platonic realism, fictionalism, neutralism, and alternative logics and semantics, among other topics. The book offers a helpful taxonomy of the wide range of options (...)
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  • Formal Ontology.Jani Hakkarainen & Markku Keinänen - 2023 - Cambridge: Cambridge University Press.
    Formal ontology as a main branch of metaphysics investigates categories of being. In the formal ontological approach to metaphysics, these ontological categories are analysed by ontological forms. This analysis, which we illustrate by some category systems, provides a tool to assess the clarity, exactness and intelligibility of different category systems or formal ontologies. We discuss critically different accounts of ontological form in the literature. Of ontological form, we propose a character- neutral relational account. In this metatheory, ontological forms of entities (...)
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  • Safety first: making property talk safe for nominalists.Jack Himelright - 2022 - Synthese 200 (3):1-26.
    Nominalists are confronted with a grave difficulty: if abstract objects do not exist, what explains the success of theories that invoke them? In this paper, I make headway on this problem. I develop a formal language in which certain platonistic claims about properties and certain nominalistic claims can be expressed, develop a formal language in which only certain nominalistic claims can be expressed, describe a function mapping sentences of the first language to sentences of the second language, and prove some (...)
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  • The Concept of Existence: History and Definitions by Leading Philosophers.Raul Corazzon - unknown
    "Philosophical discussion of the notion of existence, or being, has centered on two main problems which have not always been very clearly distinguished. First, there is the problem of what we are to say about the existence of fictitious objects, such as centaurs, dragons, and Pegasus; second, there is the problem of what we are t o say about the existence of abstract objects, such as qualities, relations, and numbers. Both problems have tempted philosophers to say that there are inferior (...)
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  • (Book Review) Ontological independence as the mark of the real. [REVIEW]Mark Colyvan - 2005 - Philosophia Mathematica 13 (2):216-225.
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  • Ontological Independence as the Mark of the Real. Jody Azzouni. Deflating Existential Consequence: A Case for Nominalism. New York: Oxford University Press, 2004. Pp. viii + 241. ISBN 0-19-515988-8. [REVIEW]Mark Colyvan - 2005 - Philosophia Mathematica 13 (2):216-225.
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  • Strict Finitism and the Logic of Mathematical Applications.Feng Ye - 2011 - Dordrecht, Netherland: Springer.
    This book intends to show that radical naturalism, nominalism and strict finitism account for the applications of classical mathematics in current scientific theories. The applied mathematical theories developed in the book include the basics of calculus, metric space theory, complex analysis, Lebesgue integration, Hilbert spaces, and semi-Riemann geometry. The fact that so much applied mathematics can be developed within such a weak, strictly finitistic system, is surprising in itself. It also shows that the applications of those classical theories to the (...)
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  • The ontology of a theory.Lorenzo Cocco - unknown
    This paper defends two claims about the criterion of commitment of W.V.O Quine. The first claim is that the criterion can be made extensional. The second is that a proper formulation becomes an analytic truth. We spend a few preliminary sections clarifying our intended notion of ontological commitment. We will not go very far in our investigation of the criterion if we do not distinguish the things a theory postulates, what its adherents, or anybody else, believe in, and which of (...)
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  • Formal Ontology and Conceptual Realism.Nino Barnabas Cocchiarella - 2007 - Dordrecht, Netherland: Springer.
    Theories about the ontological structure of the world have generally been described in informal, intuitive terms. This book offers an account of the general features and methodology of formal ontology. The book defends conceptual realism as the best system to adopt based on a logic of natural kinds. By formally reconstructing an intuitive, informal ontological scheme as a formal ontology we can better determine the consistency and adequacy of that scheme.
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  • Why Can’t There Be Numbers?David Builes - forthcoming - The Philosophical Quarterly.
    Platonists affirm the existence of abstract mathematical objects, and Nominalists deny the existence of abstract mathematical objects. While there are standard arguments in favor of Nominalism, these arguments fail to account for the necessity of Nominalism. Furthermore, these arguments do nothing to explain why Nominalism is true. They only point to certain theoretical vices that might befall the Platonist. The goal of this paper is to formulate and defend a simple, valid argument for the necessity of Nominalism that seeks to (...)
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  • Carnapian frameworks.Gabriel L. Broughton - 2021 - Synthese 199 (1-2):4097-4126.
    Carnap’s seminal ‘Empiricism, Semantics and Ontology’ makes important use of the notion of a framework and the related distinction between internal and external questions. But what exactly is a framework? And what role does the internal/external distinction play in Carnap’s metaontology? In an influential series of papers, Matti Eklund has recently defended a bracingly straightforward interpretation: A Carnapian framework, Eklund says, is just a natural language. To ask an internal question, then, is just to ask a question in, say, English. (...)
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  • A simple type theory without platonic domains.Charles S. Chihara - 1984 - Journal of Philosophical Logic 13 (3):249 - 283.
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  • Plurals and Mereology.Salvatore Florio & David Nicolas - 2020 - Journal of Philosophical Logic 50 (3):415-445.
    In linguistics, the dominant approach to the semantics of plurals appeals to mereology. However, this approach has received strong criticisms from philosophical logicians who subscribe to an alternative framework based on plural logic. In the first part of the article, we offer a precise characterization of the mereological approach and the semantic background in which the debate can be meaningfully reconstructed. In the second part, we deal with the criticisms and assess their logical, linguistic, and philosophical significance. We identify four (...)
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  • There is overlap in letters: a mereological definition of word types.Massimiliano Carrara & Jeroen Smid - 2022 - Synthese 200 (2):1-17.
    Classical mereology seems unable to characterise the identity conditions of word types. For example, the same letter types ordered differently result in different word types; but mereological fusions of the same letters are identical, regardless of the order of the letters. We show, however, that by combining classical mereology with plural logic one can give a definition of word types that satisfies the identity criteria of word types. This means that it is not necessary to abandon classical mereology in order (...)
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  • The ontology of words: Realism, nominalism, and eliminativism.J. T. M. Miller - 2020 - Philosophy Compass 15 (7):e12691.
    What are words? What makes two token words tokens of the same word-type? Are words abstract entities, or are they (merely) collections of tokens? The ontology of words tries to provide answers to these, and related questions. This article provides an overview of some of the most prominent views proposed in the literature, with a particular focus on the debate between type-realist, nominalist, and eliminativist ontologies of words.
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  • ¿De qué se trata la matemática?Gustavo Esteban Romero - 2020 - Scientia in Verba Magazine 6 (1):60-64.
    Las teorías que usamos para representar el mundo pueden ser extremadamente complejas. Abordan temas tales como electrones, campos cuánticos, estrellas de neutrones, materia oscura, redes neuronales, mercados económicos, la atmósfera y muchas otras entidades que suponemos existen en el universo. Al formular nuestras teorías, recurrimos a lenguajes exactos que nos permiten minimizar la vaguedad y expresarnos lo más precisa y cuantitativamente posible. Recurrimos a la matemática. Cuando formulamos nuestras teorías fácticas en lenguaje matemático, estas se refieren no solamente a objetos (...)
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  • A Bundle Theory of Words.J. T. M. Miller - 2021 - Synthese 198 (6):5731–5748.
    It has been a common assumption that words are substances that instantiate or have properties. In this paper, I question the assumption that our ontology of words requires posting substances by outlining a bundle theory of words, wherein words are bundles of various sorts of properties (such as semantic, phonetic, orthographic, and grammatical properties). I argue that this view can better account for certain phenomena than substance theories, is ontologically more parsimonious, and coheres with claims in linguistics.
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  • Accessibility of reformulated mathematical content.Stefan Buijsman - 2017 - Synthese 194 (6).
    I challenge a claim that seems to be made when nominalists offer reformulations of the content of mathematical beliefs, namely that these reformulations are accessible to everyone. By doing so, I argue that these theories cannot account for the mathematical knowledge that ordinary people have. In the first part of the paper I look at reformulations that employ the concept of proof, such as those of Mary Leng and Ottavio Bueno. I argue that ordinary people don’t have many beliefs about (...)
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  • Putnam’s indispensability argument revisited, reassessed, revived.Otávio Bueno - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):201-218.
    Crucial to Hilary Putnam’s realism in the philosophy of mathematics is to maintain the objectivity of mathematics without the commitment to the existence of mathematical objects. Putnam’s indispensability argument was devised as part of this conception. In this paper, I reconstruct and reassess Putnam’s argument for the indispensability of mathematics, and distinguish it from the more familiar, Quinean version of the argument. Although I argue that Putnam’s approach ultimately fails, I develop an alternative way of implementing his form of realism (...)
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  • The Enhanced Indispensability Argument, the circularity problem, and the interpretability strategy.Jan Heylen & Lars Arthur Tump - 2019 - Synthese 198 (4):3033-3045.
    Within the context of the Quine–Putnam indispensability argument, one discussion about the status of mathematics is concerned with the ‘Enhanced Indispensability Argument’, which makes explicit in what way mathematics is supposed to be indispensable in science, namely explanatory. If there are genuine mathematical explanations of empirical phenomena, an argument for mathematical platonism could be extracted by using inference to the best explanation. The best explanation of the primeness of the life cycles of Periodical Cicadas is genuinely mathematical, according to Baker (...)
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  • (1 other version)Quine, Ontology, and Physicalism.Frederique Janssen-Lauret - 2019 - In Robert Sinclair (ed.), Science and Sensibilia by W. V. Quine: The 1980 Immanuel Kant Lectures. Cham: Palgrave Macmillan. pp. 181-204.
    Quine's views on ontology and naturalism are well-known but rarely considered in tandem. According to my interpretation the connection between them is vital. I read Quine as a global epistemic structuralist. Quine thought we only ever know objects qua solutions to puzzles about significant intersections in observations. Objects are always accessed descriptively, via their roles in our best theory. Quine's Kant lectures contain an early version of epistemic structuralism with uncharacteristic remarks about the mental. Here Quine embraces mitigated anomalous monism, (...)
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  • Worlds and Propositions: The Structure and Ontology of Logical Space.Phillip Bricker - 1983 - Dissertation, Princeton University
    In sections 1 through 5, I develop in detail what I call the standard theory of worlds and propositions, and I discuss a number of purported objections. The theory consists of five theses. The first two theses, presented in section 1, assert that the propositions form a Boolean algebra with respect to implication, and that the algebra is complete, respectively. In section 2, I introduce the notion of logical space: it is a field of sets that represents the propositional structure (...)
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  • The Menard Case and the Identity of a Literary Work of Art.Tomas Hribek - 2013 - In Tomas Koblizek, Petr Kot'átko & Martin Pokorný (eds.), Text + Work: The Menard Case. Litteraria Pragensia. pp. 6-34.
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  • Willard Van Orman Quine's Philosophical Development in the 1930s and 1940s.Frederique Janssen-Lauret - 2018 - In Willard Van Orman Quine, Walter Carnielli, Frederique Janssen-Lauret & William Pickering (eds.), The Significance of the New Logic. Cambridge: Cambridge University Press.
    As analytic philosophy is becoming increasingly aware of and interested in its own history, the study of that field is broadening to include, not just its earliest beginnings, but also the mid-twentieth century. One of the towering figures of this epoch is W.V. Quine (1908-2000), champion of naturalism in philosophy of science, pioneer of mathematical logic, trying to unite an austerely physicalist theory of the world with the truths of mathematics, psychology, and linguistics. Quine's posthumous papers, notes, and drafts revealing (...)
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  • Prioritizing platonism.Kelly Trogdon & Sam Cowling - 2019 - Philosophical Studies 176 (8):2029-2042.
    Discussion of atomistic and monistic theses about abstract reality.
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  • Working from Within: The Nature and Development of Quine's Naturalism.Sander Verhaegh - 2018 - New York: Oxford University Press.
    During the past few decades, a radical shift has occurred in how philosophers conceive of the relation between science and philosophy. A great number of analytic philosophers have adopted what is commonly called a ‘naturalistic’ approach, arguing that their inquiries ought to be in some sense continuous with science. Where early analytic philosophers often relied on a sharp distinction between science and philosophy—the former an empirical discipline concerned with fact, the latter an a priori discipline concerned with meaning—philosophers today largely (...)
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  • Sign and Object : Quine’s forgotten book project.Sander Verhaegh - 2019 - Synthese 196 (12):5039-5060.
    W. V. Quine’s first philosophical monograph, Word and Object, is widely recognized as one of the most influential books of twentieth century philosophy. Notes, letters, and draft manuscripts at the Quine Archives, however, reveal that Quine was already working on a philosophical book in the early 1940s; a project entitled Sign and Object. In this paper, I examine these and other unpublished documents and show that Sign and Object sheds new light on the evolution of Quine’s ideas. Where “Two Dogmas (...)
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  • In defense of quine’s ostrich nominalism.Guido Imaguire - 2014 - Grazer Philosophische Studien 89 (1):185-203.
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  • Truth and Scientific Change.Gila Sher - 2017 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 48 (3):371-394.
    The paper seeks to answer two new questions about truth and scientific change: What lessons does the phenomenon of scientific change teach us about the nature of truth? What light do recent developments in the theory of truth, incorporating these lessons, throw on problems arising from the prevalence of scientific change, specifically, the problem of pessimistic meta-induction?
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  • Boarding Neurath's Boat: The Early Development of Quine's Naturalism.Sander Verhaegh - 2017 - Journal of the History of Philosophy 55 (2):317-342.
    W. V. Quine is arguably the intellectual father of contemporary naturalism, the idea that there is no distinctively philosophical perspective on reality. Yet, even though Quine has always been a science-minded philosopher, he did not adopt a fully naturalistic perspective until the early 1950s. In this paper, I reconstruct the genesis of Quine’s ideas on the relation between science and philosophy. Scrutinizing his unpublished papers and notebooks, I examine Quine’s development in the first decades of his career. After identifying three (...)
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