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  1. On Specifying Truth-Conditions.Agustín Rayo - 2008 - Philosophical Review 117 (3):385-443.
    This essay is a study of ontological commitment, focused on the special case of arithmetical discourse. It tries to get clear about what would be involved in a defense of the claim that arithmetical assertions are ontologically innocent and about why ontological innocence matters. The essay proceeds by questioning traditional assumptions about the connection between the objects that are used to specify the truth-conditions of a sentence, on the one hand, and the objects whose existence is required in order for (...)
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  • John P. Burgess. Rigor and Structure. Oxford: Oxford University Press, 2015. ISBN: 978-0-19-872222-9 ; 978-0-19-103360-5 . Pp. xii + 215. [REVIEW]Richard Pettigrew - 2016 - Philosophia Mathematica 24 (1):129-136.
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  • The Oxford Handbook of Philosophical Methodology.Herman Cappelen, Tamar Gendler & John Hawthorne (eds.) - 2016 - Oxford, United Kingdom: Oxford University Press.
    This is the most comprehensive book ever published on philosophical methodology. A team of thirty-eight of the world's leading philosophers present original essays on various aspects of how philosophy should be and is done. The first part is devoted to broad traditions and approaches to philosophical methodology. The entries in the second part address topics in philosophical methodology, such as intuitions, conceptual analysis, and transcendental arguments. The third part of the book is devoted to essays about the interconnections between philosophy (...)
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  • Can Semantics Guide Ontology?Katherine Ritchie - 2016 - Australasian Journal of Philosophy 94 (1):24-41.
    Since the linguistic turn, many have taken semantics to guide ontology. Here, I argue that semantics can, at best, serve as a partial guide to ontological commitment. If semantics were to be our guide, semantic data and semantic treatments would need to be taken seriously. Through an examination of plurals and their treatments, I argue that there can be multiple, equally semantically adequate, treatments of a natural language theory. Further, such treatments can attribute different ontological commitments to a theory. Given (...)
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  • Necessarily Maybe. Quantifiers, Modality and Vagueness.Alessandro Torza - 2015 - In Quantifiers, Quantifiers, and Quantifiers. Themes in Logic, Metaphysics, and Language. (Synthese Library vol. 373). Springer. pp. 367-387.
    Languages involving modalities and languages involving vagueness have each been thoroughly studied. On the other hand, virtually nothing has been said about the interaction of modality and vagueness. This paper aims to start filling that gap. Section 1 is a discussion of various possible sources of vague modality. Section 2 puts forward a model theory for a quantified language with operators for modality and vagueness. The model theory is followed by a discussion of the resulting logic. In Section 3, the (...)
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  • (1 other version)Platonism in the Philosophy of Mathematics.Øystein Linnebo - forthcoming - Stanford Encyclopedia of Philosophy.
    Platonism about mathematics (or mathematical platonism) isthe metaphysical view that there are abstract mathematical objectswhose existence is independent of us and our language, thought, andpractices. Just as electrons and planets exist independently of us, sodo numbers and sets. And just as statements about electrons and planetsare made true or false by the objects with which they are concerned andthese objects' perfectly objective properties, so are statements aboutnumbers and sets. Mathematical truths are therefore discovered, notinvented., Existence. There are mathematical objects.
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  • If engineering function is a family resemblance concept: Assessing three formalization strategies.Massimiliano Carrara, Pawel Garbacz & Pieter E. Vermaas - 2011 - Applied ontology 6 (2):141-163.
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  • Fundamental and Derivative Truths.J. R. G. Williams - 2010 - Mind 119 (473):103 - 141.
    This article investigates the claim that some truths are fundamentally or really true — and that other truths are not. Such a distinction can help us reconcile radically minimal metaphysical views with the verities of common sense. I develop an understanding of the distinction whereby Fundamentality is not itself a metaphysical distinction, but rather a device that must be presupposed to express metaphysical distinctions. Drawing on recent work by Rayo on anti-Quinean theories of ontological commitments, I formulate a rigourous theory (...)
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  • The Way of Actuality.Sam Cowling - 2014 - Australasian Journal of Philosophy 92 (2):231-247.
    In this paper, I defend an indexical analysis of the abstract-concrete distinction within the framework of modal realism. This analysis holds the abstract-concrete distinction to be conceptually inseparable from the distinction between the actual and the merely possible, which is assumed to be indexical in nature. The resulting view contributes to the case for modal realism by demonstrating how its distinctive resources provide a reductive analysis of the abstract-concrete distinction. This indexical analysis also provides a solution to a sceptical problem (...)
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  • Plato's Problem: An Introduction to Mathematical Platonism.Marco Panza & Andrea Sereni - 2013 - New York: Palgrave-Macmillan. Edited by Andrea Sereni & Marco Panza.
    What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on (...)
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  • The Iterative Conception of Set: a (Bi-)Modal Axiomatisation.J. P. Studd - 2013 - Journal of Philosophical Logic 42 (5):1-29.
    The use of tensed language and the metaphor of set ‘formation’ found in informal descriptions of the iterative conception of set are seldom taken at all seriously. Both are eliminated in the nonmodal stage theories that formalise this account. To avoid the paradoxes, such accounts deny the Maximality thesis, the compelling thesis that any sets can form a set. This paper seeks to save the Maximality thesis by taking the tense more seriously than has been customary (although not literally). A (...)
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  • In the Mental Fiction, Mental Fictionalism is Fictitious.T. Parent - 2013 - The Monist 96 (4):605-621.
    Here I explore the prospects for fictionalism about the mental, modeled after fictionalism about possible worlds. Mental fictionalism holds that the mental states posited by folk psychology do not exist, yet that some sentences of folk psychological discourse are true. This is accomplished by construing truths of folk psychology as “truths according to the mentalistic fiction.” After formulating the view, I identify five ways that the view appears self-refuting. Moreover, I argue that this cannot be fixed by semantic ascent or (...)
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  • Musil’s Imaginary Bridge.Achille C. Varzi - 2014 - The Monist 97 (1):30-46.
    In a calculation involving imaginary numbers, we begin with real numbers that represent concrete measures and we end up with numbers that are equally real, but in the course of the operation we find ourselves walking “as if on a bridge that stands on no piles”. How is that possible? How does that work? And what is involved in the as-if stance that this metaphor introduces so beautifully? These are questions that bother Törless deeply. And that Törless is bothered by (...)
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  • Composition as Identity: A Study in Ontology and Philosophical Logic.Einar Bohn - 2009 - Dissertation, University of Massachusetts, Amherst
    In this work I first develop, motivate, and defend the view that mereological composition, the relation between an object and all its parts collectively, is a relation of identity. I argue that this view implies and hence can explain the logical necessity of classical mereology, the formal study of the part-whole relation. I then critically discuss four contemporary views of the same kind. Finally, I employ my thesis in a recent discussion of whether the world is fundamentally one in number.
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  • Existence as a Real Property: The Ontology of Meinongianism.Francesco Berto - 2012 - Dordrecht: Synthèse Library, Springer.
    This book is both an introduction to and a research work on Meinongianism. “Meinongianism” is taken here, in accordance with the common philosophical jargon, as a general label for a set of theories of existence – probably the most basic notion of ontology. As an introduction, the book provides the first comprehensive survey and guide to Meinongianism and non-standard theories of existence in all their main forms. As a research work, the book exposes and develops the most up-to-date Meinongian theory (...)
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  • Pragmatic antirealism: a new antirealist strategy.Michael Scott & Philip Brown - 2012 - Philosophical Studies 161 (3):349-366.
    In everyday speech we seem to refer to such things as abstract objects, moral properties, or propositional attitudes that have been the target of metaphysical and/or epistemological objections. Many philosophers, while endorsing scepticism about some of these entities, have not wished to charge ordinary speakers with fundamental error, or recommend that the discourse be revised or eliminated. To this end a number of non-revisionary antirealist strategies have been employed, including expressivism, reductionism and hermeneutic fictionalism. But each of these theories faces (...)
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  • Stevin Numbers and Reality.Karin Usadi Katz & Mikhail G. Katz - 2012 - Foundations of Science 17 (2):109-123.
    We explore the potential of Simon Stevin’s numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.
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  • Naturalism in the Philosophy of Mathematics.Alexander Paseau - 2012 - In Ed Zalta (ed.), Stanford Encyclopedia of Philosophy. Stanford Encyclopedia of Philosophy.
    Contemporary philosophy’s three main naturalisms are methodological, ontological and epistemological. Methodological naturalism states that the only authoritative standards are those of science. Ontological and epistemological naturalism respectively state that all entities and all valid methods of inquiry are in some sense natural. In philosophy of mathematics of the past few decades methodological naturalism has received the lion’s share of the attention, so we concentrate on this. Ontological and epistemological naturalism in the philosophy of mathematics are discussed more briefly in section (...)
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  • (1 other version)Ontologia.Achille C. Varzi - 2005 - Rome: Laterza.
    An introduction to analytic ontology. Part 1 deals with the question, What is ontology?, focusing on (i) the interplay between ontological and broadly metaphysical concerns, and (ii) the difference between material ontology and formal ontology. Part 2 deals with the question, How is ontology done?, focusing on (i) the delicate interplay between ontology and truth-making (or: between meaning and existence), and (ii) the differences between revolutionary vs. hermeneutic, prescriptive vs. descriptive, and absolute vs. relative approaches to ontology. Part 3 surveys (...)
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  • Knowledge of Meaning, Conscious and Unconscious.Steven Gross - 2010 - The Baltic International Yearbook of Cognition, Logic and Communication.
    This paper motivates two bases for ascribing propositional semantic knowledge (or something knowledgelike): first, because it’s necessary to rationalize linguistic action; and, second, because it’s part of an empirical theory that would explain various aspects of linguistic behavior. The semantic knowledge ascribed on these two bases seems to differ in content, epistemic status, and cognitive role. This raises the question: how are they related, if at all? The bulk of the paper addresses this question. It distinguishes a variety of answers (...)
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  • Deferentialism.Chris Daly & David Liggins - 2011 - Philosophical Studies 156 (3):321-337.
    There is a recent and growing trend in philosophy that involves deferring to the claims of certain disciplines outside of philosophy, such as mathematics, the natural sciences, and linguistics. According to this trend— deferentialism , as we will call it—certain disciplines outside of philosophy make claims that have a decisive bearing on philosophical disputes, where those claims are more epistemically justified than any philosophical considerations just because those claims are made by those disciplines. Deferentialists believe that certain longstanding philosophical problems (...)
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  • (1 other version)Nominalism, Naturalism, Epistemic Relativism.Gideon Rosen - 2001 - Noûs 35 (s15):69 - 91.
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  • The applicability of mathematics as a scientific and a logical problem.Feng Ye - 2010 - Philosophia Mathematica 18 (2):144-165.
    This paper explores how to explain the applicability of classical mathematics to the physical world in a radically naturalistic and nominalistic philosophy of mathematics. The applicability claim is first formulated as an ordinary scientific assertion about natural regularity in a class of natural phenomena and then turned into a logical problem by some scientific simplification and abstraction. I argue that there are some genuine logical puzzles regarding applicability and no current philosophy of mathematics has resolved these puzzles. Then I introduce (...)
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  • Mathematical Explanation in Science.Alan Baker - 2009 - British Journal for the Philosophy of Science 60 (3):611-633.
    Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various philosophers, and I discuss (...)
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  • Eliminativism and the challenge from folk belief.Daniel Z. Korman - 2009 - Noûs 43 (2):242-264.
    Virtually everyone agrees that, even after having presented the arguments for their positions, proponents of revisionary philosophical theories are required to provide some sort of account of the conflict between their theories and what the folk believe. I examine various strategies for answering the challenge from folk belief. The examination proceeds as a case study, whose focus is eliminativism about ordinary material objects. I critically assess eliminativist attempts to explain folk belief by appeal to paraphrase, experience, and intuition.
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  • On Naturalizing the Epistemology of Mathematics.Jeffrey W. Roland - 2009 - Pacific Philosophical Quarterly 90 (1):63-97.
    In this paper, I consider an argument for the claim that any satisfactory epistemology of mathematics will violate core tenets of naturalism, i.e. that mathematics cannot be naturalized. I find little reason for optimism that the argument can be effectively answered.
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  • 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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  • Fictionalism in the philosophy of mathematics.Mark Balaguer - 2008 - Stanford Encyclopedia of Philosophy.
    Mathematical fictionalism (or as I'll call it, fictionalism) is best thought of as a reaction to mathematical platonism. Platonism is the view that (a) there exist abstract mathematical objects (i.e., nonspatiotemporal mathematical objects), and (b) our mathematical sentences and theories provide true descriptions of such objects. So, for instance, on the platonist view, the sentence ‘3 is prime’ provides a straightforward description of a certain object—namely, the number 3—in much the same way that the sentence ‘Mars is red’ provides a (...)
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  • (1 other version)On what grounds what.Jonathan Schaffer - 2009 - In Ryan Wasserman, David Manley & David Chalmers (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford, England: Oxford University Press. pp. 347-383.
    On the now dominant Quinean view, metaphysics is about what there is. Metaphysics so conceived is concerned with such questions as whether properties exist, whether meanings exist, and whether numbers exist. I will argue for the revival of a more traditional Aristotelian view, on which metaphysics is about what grounds what. Metaphysics so revived does not bother asking whether properties, meanings, and numbers exist (of course they do!) The question is whether or not they are fundamental.
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  • (1 other version)Modal fictionalism.Daniel Nolan - 2008 - Stanford Encyclopedia of Philosophy.
    Questions about necessity (or what has to be, or what cannot be otherwise) and possibility (or what can be, or what could be otherwise) are questions about modality. Fictionalism is an approach to theoretical matters in a given area which treats the claims in that area as being in some sense analogous to fictional claims: claims we do not literally accept at face value, but which we nevertheless think serve some useful function. However, despite its name, “Modal Fictionalism” in its (...)
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  • (1 other version)Platonism in metaphysics.Mark Balaguer - 2008 - Stanford Encyclopedia of Philosophy.
    Platonism is the view that there exist such things as abstract objects — where an abstract object is an object that does not exist in space or time and which is therefore entirely non-physical and nonmental. Platonism in this sense is a contemporary view. It is obviously related to the views of Plato in important ways, but it is not entirely clear that Plato endorsed this view, as it is defined here. In order to remain neutral on this question, the (...)
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  • Tenses, changes, and space-time.Jan Faye - 2008 - In Time in the Different Scientific Approaches. Genova: Tilgher. pp. 89-104.
    Here I develop the idea, which I have presented elsewhere, that time instants are abstract entities existing tenselessly and therefore that events and changes likewise may be said to exist tenselessly in virtue of their place at a certain space-time point.
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  • Finitary and infinitary mathematics, the possibility of possibilities and the definition of probabilities.Matthew J. Donald - unknown
    Some relations between physics and finitary and infinitary mathematics are explored in the context of a many-minds interpretation of quantum theory. The analogy between mathematical ``existence'' and physical ``existence'' is considered from the point of view of philosophical idealism. Some of the ways in which infinitary mathematics arises in modern mathematical physics are discussed. Empirical science has led to the mathematics of quantum theory. This in turn can be taken to suggest a picture of reality involving possible minds and the (...)
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  • Words and Objects.Achille C. Varzi - 2002 - In Andrea Bottani, Massimiliano Carrara & Daniele Giaretta (eds.), Individuals, Essence, and Identity. Themes of Analytic Metaphysics. Kluwer Academic Publishers. pp. 49–75.
    A lot of work in metaphysics relies on linguistic analysis and intuitions. Do we want to know what sort of things there are or could be? Then let’s see what sort of things there must be in order for what we truthfully say to be true. Do we want to see whether x is distinct from y? Then let’s see whether there is any statement that is true of x but not of y. And so on. In this paper I (...)
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  • Nihilism without Self-Contradiction.David Liggins - 2008 - Royal Institute of Philosophy Supplement 62:177-196.
    in Robin Le Poidevin (ed.) Being: Developments in Contemporary Metaphysics. Cambridge: Cambridge University Press. Peter van Inwagen claims that there are no tables or chairs. He also claims that sentences such as ‘There are chairs here’, which seem to imply their existence, are often true. This combination of views opens van Inwagen to a charge of self-contradiction. I explain the charge, and van Inwagen’s response to it, which involves the claim that sentences like ‘There are tables’ shift their truth-conditions between (...)
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  • Indispensability argument and anti-realism in philosophy of mathematics.Feng Ye - 2007 - Frontiers of Philosophy in China 2 (4):614-628.
    The indispensability argument for abstract mathematical entities has been an important issue in the philosophy of mathematics. The argument relies on several assumptions. Some objections have been made against these assumptions, but there are several serious defects in these objections. Ameliorating these defects leads to a new anti-realistic philosophy of mathematics, mainly: first, in mathematical applications, what really exist and can be used as tools are not abstract mathematical entities, but our inner representations that we create in imagining abstract mathematical (...)
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  • Fictionalism.Matti Eklund - 2010 - Stanford Encyclopedia of Philosophy.
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  • Speaking with Shadows: A Study of Neo‐Logicism.Fraser MacBride - 2003 - British Journal for the Philosophy of Science 54 (1):103-163.
    According to the species of neo-logicism advanced by Hale and Wright, mathematical knowledge is essentially logical knowledge. Their view is found to be best understood as a set of related though independent theses: (1) neo-fregeanism-a general conception of the relation between language and reality; (2) the method of abstraction-a particular method for introducing concepts into language; (3) the scope of logic-second-order logic is logic. The criticisms of Boolos, Dummett, Field and Quine (amongst others) of these theses are explicated and assessed. (...)
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  • Survey article. Listening to fictions: A study of fieldian nominalism.Fraser MacBride - 1999 - British Journal for the Philosophy of Science 50 (3):431-455.
    One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers.
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  • Plural quantification exposed.Øystein Linnebo - 2003 - Noûs 37 (1):71–92.
    This paper criticizes George Boolos's famous use of plural quantification to argue that monadic second-order logic is pure logic. I deny that plural quantification qualifies as pure logic and express serious misgivings about its alleged ontological innocence. My argument is based on an examination of what is involved in our understanding of the impredicative plural comprehension schema.
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  • Plurals and complexes.Keith Hossack - 2000 - British Journal for the Philosophy of Science 51 (3):411-443.
    Atomism denies that complexes exist. Common-sense metaphysics may posit masses, composite individuals and sets, but atomism says there are only simples. In a singularist logic, it is difficult to make a plausible case for atomism. But we should accept plural logic, and then atomism can paraphrase away apparent reference to complexes. The paraphrases require unfamiliar plural universals, but these are of independent interest; for example, we can identify numbers and sets with plural universals. The atomist paraphrases would fail if plurals (...)
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  • Fiction, indifference, and ontology.Matti Eklund - 2005 - Philosophy and Phenomenological Research 71 (3):557–579.
    In this paper I outline an alternative to hermeneutic fictionalism, an alternative I call indifferentism, with the same advantages as hermeneutic fictionalism with respect to ontological issues but avoiding some of the problems that face fictionalism. The difference between indifferentism and fictionalism is this. The fictionalist about ordinary utterances of a sentence S holds, with more orthodox views, that the speaker in some sense commits herself to the truth of S. It is only that for the fictionalist this is truth (...)
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  • Empty names, fictional names, mythical names.David Braun - 2005 - Noûs 39 (4):596–631.
    John Stuart Mill (1843) thought that proper names denote individuals and do not connote attributes. Contemporary Millians agree, in spirit. We hold that the semantic content of a proper name is simply its referent. We also think that the semantic content of a declarative sentence is a Russellian structured proposition whose constituents are the semantic contents of the sentence’s constituents. This proposition is what the sentence semantically expresses. Therefore, we think that sentences containing proper names semantically express singular propositions, which (...)
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  • Go figure: A path through fictionalism.Stephen Yablo - 2001 - Midwest Studies in Philosophy 25 (1):72–102.
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  • Hermeneutic fictionalism.Jason Stanley - 2001 - Midwest Studies in Philosophy 25 (1):36–71.
    Fictionalist approaches to ontology have been an accepted part of philosophical methodology for some time now. On a fictionalist view, engaging in discourse that involves apparent reference to a realm of problematic entities is best viewed as engaging in a pretense. Although in reality, the problematic entities do not exist, according to the pretense we engage in when using the discourse, they do exist. In the vocabulary of Burgess and Rosen (1997, p. 6), a nominalist construal of a given discourse (...)
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  • Success by default?Augustín Rayo - 2003 - Philosophia Mathematica 11 (3):305-322.
    I argue that Neo-Fregean accounts of arithmetical language and arithmetical knowledge tacitly rely on a thesis I call [Success by Default]—the thesis that, in the absence of reasons to the contrary, we are justified in thinking that certain stipulations are successful. Since Neo-Fregeans have yet to supply an adequate defense of [Success by Default], I conclude that there is an important gap in Neo-Fregean accounts of arithmetical language and knowledge. I end the paper by offering a naturalistic remedy.
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  • How to apply mathematics.Ulrich Meyer - 2004 - Erkenntnis 61 (1):17-28.
    This paper presents a novel account of applied mathematics. It shows how we can distinguish the physical content from the mathematical form of a scientific theory even in cases where the mathematics applied is indispensable and cannot be eliminated by paraphrase.
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  • From Sherlock and buffy to klingon and norrathian platinum pieces: Pretense, contextalism, and the myth of fiction.Peter Ludlow - 2006 - Philosophical Issues 16 (1):162–183.
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  • Is Cantor's continuum problem inherently vague?Kai Hauser - 2002 - Philosophia Mathematica 10 (3):257-285.
    I examine various claims to the effect that Cantor's Continuum Hypothesis and other problems of higher set theory are ill-posed questions. The analysis takes into account the viability of the underlying philosophical views and recent mathematical developments.
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  • On specifying truth-conditions.Jason M. Byron - manuscript
    I develop a technique for specifying truth-conditions.
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