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  1. Pragmatic accounts of justification, epistemic analyticity, and other routes to easy knowledge of abstracta.Brett Topey - forthcoming - In Xavier de Donato-Rodríguez, José Falguera & Concha Martínez-Vidal (eds.), Deflationist Conceptions of Abstract Objects. Springer.
    One common attitude toward abstract objects is a kind of platonism: a view on which those objects are mind-independent and causally inert. But there's an epistemological problem here: given any naturalistically respectable understanding of how our minds work, we can't be in any sort of contact with mind-independent, causally inert objects. So platonists, in order to avoid skepticism, tend to endorse epistemological theories on which knowledge is easy, in the sense that it requires no such contact—appeals to Boghossian’s notion of (...)
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  • A fictionalist theory of universals.Tim Button & Robert Trueman - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press.
    Universals are putative objects like wisdom, morality, redness, etc. Although we believe in properties (which, we argue, are not a kind of object), we do not believe in universals. However, a number of ordinary, natural language constructions seem to commit us to their existence. In this paper, we provide a fictionalist theory of universals, which allows us to speak as if universals existed, whilst denying that any really do.
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  • Nominalism and Immutability.Daniel Berntson - manuscript
    Can we do science without numbers? How much contingency is there? These seemingly unrelated questions--one in the philosophy of math and science and the other in metaphysics--share an unexpectedly close connection. For as it turns out, a radical answer to the second leads to a breakthrough on the first. The radical answer is new view about modality called compossible immutabilism. The breakthrough is a new strategy for doing science without numbers. One of the chief benefits of the new strategy is (...)
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  • Rigour, Proof and Soundness.Oliver M. W. Tatton-Brown - 2020 - Dissertation, University of Bristol
    The initial motivating question for this thesis is what the standard of rigour in modern mathematics amounts to: what makes a proof rigorous, or fail to be rigorous? How is this judged? A new account of rigour is put forward, aiming to go some way to answering these questions. Some benefits of the norm of rigour on this account are discussed. The account is contrasted with other remarks that have been made about mathematical proof and its workings, and is tested (...)
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  • To Shape a New World, Tommie Shelby and Brandon Terry.Myisha Cherry - 2020 - Mind 129 (514):656-664.
    To Shape a New World, ShelbyTommie and TerryBrandon. Cambridge, MA: Harvard University Press, 2018. Pp. x + 449.
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  • Relativity and the Causal Efficacy of Abstract Objects.Tim Juvshik - 2020 - American Philosophical Quarterly 57 (3):269-282.
    Abstract objects are standardly taken to be causally inert, however principled arguments for this claim are rarely given. As a result, a number of recent authors have claimed that abstract objects are causally efficacious. These authors take abstracta to be temporally located in order to enter into causal relations but lack a spatial location. In this paper, I argue that such a position is untenable by showing first that causation requires its relata to have a temporal location, but second, that (...)
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  • Mathematical Abstraction, Conceptual Variation and Identity.Jean-Pierre Marquis - 2014 - In Peter Schroeder-Heister, Gerhard Heinzmann, Wilfred Hodges & Pierre Edouard Bour (eds.), Logic, Methodology and Philosophy of Science, Proceedings of the 14th International Congress. London, UK: pp. 299-322.
    One of the key features of modern mathematics is the adoption of the abstract method. Our goal in this paper is to propose an explication of that method that is rooted in the history of the subject.
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  • Mathematics, Morality, and Self‐Effacement.Jack Woods - 2016 - Noûs 52 (1):47-68.
    I argue that certain species of belief, such as mathematical, logical, and normative beliefs, are insulated from a form of Harman-style debunking argument whereas moral beliefs, the primary target of such arguments, are not. Harman-style arguments have been misunderstood as attempts to directly undermine our moral beliefs. They are rather best given as burden-shifting arguments, concluding that we need additional reasons to maintain our moral beliefs. If we understand them this way, then we can see why moral beliefs are vulnerable (...)
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  • Explanatory Indispensability Arguments in Metaethics and Philosophy of Mathematics.Debbie Roberts - 2016 - In Uri D. Leibowitz & Neil Sinclair (eds.), Explanation in Ethics and Mathematics: Debunking and Dispensability. Oxford, England: Oxford University Press UK.
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  • Individuals: an essay in revisionary metaphysics.Shamik Dasgupta - 2009 - Philosophical Studies 145 (1):35-67.
    We naturally think of the material world as being populated by a large number of individuals . These are things, such as my laptop and the particles that compose it, that we describe as being propertied and related in various ways when we describe the material world around us. In this paper I argue that, fundamentally speaking at least, there are no such things as material individuals. I then propose and defend an individual-less view of the material world I call (...)
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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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  • A Novel Category of Vague Abstracta.Jeffrey Goodman - 2007 - Metaphysica 8 (1):79-96.
    Much attention has been given to the question of ontic vagueness, and the issues usually center around whether certain paradigmatically concrete entities – cats, clouds, mountains, etc. – are vague in the sense of having indeterminate spatial boundaries. In this paper, however, I wish to focus on a way in which some abstracta seem to be locationally vague. To begin, I will briefly cover some territory already covered regarding certain types of “traditional” abstracta and the ways they are currently alleged (...)
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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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  • From nihilism to monism.Jonathan Schaffer - 2007 - Australasian Journal of Philosophy 85 (2):175 – 191.
    Mereological nihilism is the view that all concrete objects are simple. Existence monism is the view that the only concrete object is one big simple: the world. I will argue that nihilism culminates in monism. The nihilist demands the simplest sufficient ontology, and the monist delivers it.
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  • The Return of Moral Fictionalism.Nadeem J. Z. Hussain - 2004 - Philosophical Perspectives 18 (1):149–188.
    Fictionalism has recently returned as a standard response to ontologically problematic domains. This article assesses moral fictionalism. It argues (i) that a correct understanding of the dialectical situation in contemporary metaethics shows that fictionalism is only an interesting new alternative if it can provide a new account of normative content: what is it that I am thinking or saying when I think or say that I ought to do something; and (ii) that fictionalism, qua fictionalism, does not provide us with (...)
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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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  • Something is true.Jamin Asay - 2021 - Philosophy and Phenomenological Research 105 (3):687-705.
    The thesis that nothing is true has long been thought to be a self-refuting position not worthy of serious philosophical consideration. Recently, however, the thesis of alethic nihilism—that nothing is true—has been explicitly defended (notably by David Liggins). Nihilism is also, I argue, a consequence of other views about truth that have recently been advocated, such as fictionalism about truth and the inconsistency account. After offering an account of alethic nihilism, and how it purports to avoid the self-refutation problem, I (...)
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  • Why Aboutness Matters: Meta-Fictionalism as a Case Study.Matteo Plebani - 2020 - Philosophia 49 (3):1177-1186.
    Recent work in the philosophy of language attempts to elucidate the elusive notion of aboutness. A natural question concerning such a project has to do with its motivation: why is the notion of aboutness important? Stephen Yablo offers an interesting answer: taking into consideration not only the conditions under which a sentence is true, but also what a sentence is about opens the door to a new style of criticism of certain philosophical analyses. We might criticize the analysis of a (...)
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  • Deflationary Nominalism and Puzzle Avoidance.David Mark Kovacs - 2019 - Philosophia Mathematica 27 (1):88-104.
    In a series of works, Jody Azzouni has defended deflationary nominalism, the view that certain sentences quantifying over mathematical objects are literally true, although such objects do not exist. One alleged attraction of this view is that it avoids various philosophical puzzles about mathematical objects. I argue that this thought is misguided. I first develop an ontologically neutral counterpart of Field’s reliability challenge and argue that deflationary nominalism offers no distinctive answer to it. I then show how this reasoning generalizes (...)
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  • Labyrinth of Continua.Patrick Reeder - 2018 - Philosophia Mathematica 26 (1):1-39.
    This is a survey of the concept of continuity. Efforts to explicate continuity have produced a plurality of philosophical conceptions of continuity that have provably distinct expressions within contemporary mathematics. I claim that there is a divide between the conceptions that treat the whole continuum as prior to its parts, and those conceptions that treat the parts of the continuum as prior to the whole. Along this divide, a tension emerges between those conceptions that favor philosophical idealizations of continuity and (...)
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  • Abstract Objects, Causal Efficacy, and Causal Exclusion.Tim Juvshik - 2018 - Erkenntnis 83 (4):805-827.
    objects are standardly taken to be causally inert, but this claim is rarely explicitly argued for. In the context of his platonism about musical works, in order for musical works to be audible, Julian Dodd argues that abstracta are causally efficacious in virtue of their concrete tokens participating in events. I attempt to provide a principled argument for the causal inertness of abstracta by first rejecting Dodd’s arguments from events, and then extending and generalizing the causal exclusion argument to the (...)
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  • There is No Easy Road to Nominalism.M. Colyvan - 2010 - Mind 119 (474):285-306.
    Hartry Field has shown us a way to be nominalists: we must purge our scientific theories of quantification over abstracta and we must prove the appropriate conservativeness results. This is not a path for the faint hearted. Indeed, the substantial technical difficulties facing Field's project have led some to explore other, easier options. Recently, Jody Azzouni, Joseph Melia, and Stephen Yablo have argued that it is a mistake to read our ontological commitments simply from what the quantifiers of our best (...)
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  • Giving Up on “the Rest of the Language".Adam C. Podlaskowski - 2015 - Acta Analytica 30 (3):293-304.
    In this essay, the tension that Benacerraf identifies for theories of mathematical truth is used as the vehicle for arguing against a particular desideratum for semantic theories. More specifically, I place in question the desideratum that a semantic theory, provided for some area of discourse, should run in parallel with the semantic theory holding for the rest of the language. The importance of this desideratum is also made clear by means of tracing out the subtle implications of its rejection.
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  • Moral Epistemology: The Mathematics Analogy.Justin Clarke-Doane - 2012 - Noûs 48 (2):238-255.
    There is a long tradition comparing moral knowledge to mathematical knowledge. In this paper, I discuss apparent similarities and differences between knowledge in the two areas, realistically conceived. I argue that many of these are only apparent, while others are less philosophically significant than might be thought. The picture that emerges is surprising. There are definitely differences between epistemological arguments in the two areas. However, these differences, if anything, increase the plausibility of moral realism as compared to mathematical realism. It (...)
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  • (2 other versions)Philosophy of mathematics.Jeremy Avigad - manuscript
    The philosophy of mathematics plays an important role in analytic philosophy, both as a subject of inquiry in its own right, and as an important landmark in the broader philosophical landscape. Mathematical knowledge has long been regarded as a paradigm of human knowledge with truths that are both necessary and certain, so giving an account of mathematical knowledge is an important part of epistemology. Mathematical objects like numbers and sets are archetypical examples of abstracta, since we treat such objects in (...)
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  • Syntactic reductionism.Richard Heck - 2000 - Philosophia Mathematica 8 (2):124-149.
    Syntactic Reductionism, as understood here, is the view that the ‘logical forms’ of sentences in which reference to abstract objects appears to be made are misleading so that, on analysis, we can see that no expressions which even purport to refer to abstract objects are present in such sentences. After exploring the motivation for such a view, and arguing that no previous argument against it succeeds, sentences involving generalized quantifiers, such as ‘most’, are examined. It is then argued, on this (...)
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  • Ontology, Commitment, and Quine's Criterion.Yvonne Raley - 2007 - Philosophia Mathematica 15 (3):271-290.
    For Quine, the ontological commitments of a discourse are what fall under its (objectual) quantifiers. The recent literature, however, is beginning to move away from this picture. There are direct challenges to Quine's criterion, and there are also attempts to provide alternatives. Azzouni suggests that the ontological commitments of a discourse should be determined by an existence predicate instead. The availability of this alternative forces an adjudication between Qune's criterion and the predicate approach to ontological commitment. I argue that to (...)
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  • Abstracta Are Causal.David Friedell - 2020 - Philosophia 48 (1):133-142.
    Many philosophers think all abstract objects are causally inert. Here, focusing on novels, I argue that some abstracta are causally efficacious. First, I defend a straightforward argument for this view. Second, I outline an account of object causation—an account of how objects cause effects. This account further supports the view that some abstracta are causally efficacious.
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  • (1 other version)On representationalism, common-factorism, and whether consciousness is here and now.Pär Sundström - 2018 - Philosophical Studies:1-12.
    A strong form of representationalism says that every conscious property of every mental state can be identified with some part of the state’s representational properties. A weaker representationalism says that some conscious property of some mental state can be identified with some part of the state’s representational properties. David Papineau has recently argued that all such theories are incorrect since they construe consciousness as consisting in “relations to propositions or other abstract objects outside space and time”, whereas consciousness is “concrete” (...)
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  • Generality, Extensibility, and Paradox.J. P. Studd - 2017 - Proceedings of the Aristotelian Society 117 (1):81-101.
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  • On the imaginative constructivist nature of design: a theoretical approach.Akin Osman Kazakci - unknown
    Most empirical accounts of design suggest that designing is an activity where objects and representations are progressively constructed. Despite this fact, whether design is a constructive process or not is not a question directly addressed in the current design research. By contrast, in other fields such as Mathematics or Psychology, the notion of constructivism is seen as a foundational issue. The present paper defends the point of view that forms of constructivism in design need to be identified and integrated as (...)
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  • A Theory of Sentience.Austen Clark (ed.) - 2000 - New York: Oxford University Press.
    Drawing on the findings of neuroscience, this text proposes and defends the hypothesis that the various modalities of sensation share a generic form that the author, Austen Clark, calls feature-placing.
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  • Deflating existence away? A critique of Azzouni's nominalism.Yvonne Raley - 2009 - Philosophia Mathematica 17 (1):73-83.
    Yet, he also says that it is philosophically indeterminate which criterion for what exists is correct. Nominalism is the view that certain objects ( i.e ., abstract objects) do not exist, and not the view that it is philosophically indeterminate whether or not they do. I resolve the dilemma that Azzouni's claims pose: Azzouni is a non-factualist about what exists, but he is a factualist about which criterion for what exists our community of speakers has adopted. It is in the (...)
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  • Beyond the axioms: The question of objectivity in mathematics.W. TaitW - 2001 - Philosophia Mathematica 9 (1):21-36.
    This paper contains a defense against anti-realism in mathematics in the light both of incompleteness and of the fact that mathematics is a ‘cultural artifact.’. Anti-realism (here) is the view that theorems, say, of aritltmetic cannot be taken at face value to express true propositions about the system of numbers but must be reconstrued to be about somctliiiig else or about nothing at all. A ‘bite-the-bullet’ aspect of the defease is that, adopting new axioms, liitherto independent, is not. a matter (...)
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  • Hartry Field. Science Without Numbers: A Defense of Nominalism 2nd ed. [REVIEW]Geoffrey Hellman & Mary Leng - 2019 - Philosophia Mathematica 27 (1):139-148.
    FieldHartry. Science Without Numbers: A Defense of Nominalism 2nd ed.Oxford University Press, 2016. ISBN 978-0-19-877792-2. Pp. vi + 56 + vi + 111.
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  • The Magic of Holes.Achille C. Varzi - 2019 - In Pina Marsico & Luca Tateo (eds.), (eds.), Ordinary Things and Their Extraordinary Meanings, Charlotte (NC),. Information Age Publishing. pp. 21-33.
    There is no doughnut without a hole, the saying goes. And that’s true. If you think you can come up with an exception, it simply wouldn’t be a doughnut. Holeless doughnuts are like extensionless color, or durationless sound—nonsense. Does it follow, then, that when we buy a doughnut we really purchase two sorts of thing—the edible stuff plus the little chunk of void in the middle? Surely we cannot just take the doughnut and leave the hole at the grocery store, (...)
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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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  • Indexing and Mathematical Explanation.Alan Baker & Mark Colyvan - 2011 - Philosophia Mathematica 19 (3):323-334.
    We discuss a recent attempt by Chris Daly and Simon Langford to do away with mathematical explanations of physical phenomena. Daly and Langford suggest that mathematics merely indexes parts of the physical world, and on this understanding of the role of mathematics in science, there is no need to countenance mathematical explanation of physical facts. We argue that their strategy is at best a sketch and only looks plausible in simple cases. We also draw attention to how frequently Daly and (...)
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  • Of Numbers and Electrons.Cian Dorr - 2010 - Proceedings of the Aristotelian Society 110 (2pt2):133-181.
    According to a tradition stemming from Quine and Putnam, we have the same broadly inductive reason for believing in numbers as we have for believing in electrons: certain theories that entail that there are numbers are better, qua explanations of our evidence, than any theories that do not. This paper investigates how modal theories of the form ‘Possibly, the concrete world is just as it in fact is and T’ and ‘Necessarily, if standard mathematics is true and the concrete world (...)
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  • The nature of semantics: On Jackendoff's arguments.Steven Gross - 2005 - Linguistic Review 22:249-270.
    Jackendoff defends a mentalist approach to semantics that investigates conceptual structures in the mind/brain and their interfaces with other structures, including specifically linguistic structures responsible for syntactic and phonological competence. He contrasts this approach with one that seeks to characterize the intentional relations between expressions and objects in the world. The latter, he argues, cannot be reconciled with mentalism. He objects in particular that intentionality cannot be naturalized and that the relevant notion of object is suspect. I critically discuss these (...)
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  • Logic and time.John P. Burgess - 1979 - Journal of Symbolic Logic 44 (4):566-582.
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  • Thin Objects: An Abstractionist Account, by Øystein Linnebo. [REVIEW]J. P. Studd - 2020 - Mind 129 (514):646-656.
    Thin Objects: Anionist Account, by LinneboØystein. Oxford: Oxford University Press, 2018. Pp. xviii + 238.
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  • Book Reviews. [REVIEW][author unknown] - 2006 - History and Philosophy of Logic 27 (4):339-343.
    S. Shapiro, The Oxford handbook of philosophy of mathematics and logic Oxford and New York: Oxford University Press, 2005. xv + 833 pp. £52.00. ISBN 0-19-514...
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  • Logical Consequence for Nominalists.Marcus Rossberg & Daniel Cohnitz - 2009 - Theoria 24 (2):147-168.
    It is often claimed that nominalistic programmes to reconstruct mathematics fail, since they will at some point involve the notion of logical consequence which is unavailable to the nominalist. In this paper we use an idea of Goodman and Quine to develop a nominalistically acceptable explication of logical consequence.
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  • Recovering What Is Said With Empty Names.Gualtiero Piccinini & Sam Scott - 2010 - Canadian Journal of Philosophy 40 (2):239-273.
    As our data will show, negative existential sentences containing socalled empty names evoke the same strong semantic intuitions in ordinary speakers and philosophers alike.Santa Claus does not exist.Superman does not exist.Clark Kent does not exist.Uttering the sentences in (1) seems to say something truth-evaluable, to say something true, and to say something different for each sentence. A semantic theory ought to explain these semantic intuitions.The intuitions elicited by (1) are in apparent conflict with the Millian view of proper names. According (...)
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  • On Putnam’s Proof of the Impossibility of a Nominalistic Physics.Thomas William Barrett - 2020 - Erkenntnis 88 (1):1-28.
    In his book Philosophy of Logic, Putnam (1971) presents a short argument which reads like—and indeed, can be reconstructed as—a formal proof that a nominalistic physics is impossible. The aim of this paper is to examine Putnam’s proof and show that it is not compelling. The precise way in which the proof fails yields insight into the relation that a nominalistic physics should bear to standard physics and into Putnam’s indispensability argument.
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  • Ontological commitment and reconstructivism.Massimiliano Carrara & Achille C. Varzi - 2001 - Erkenntnis 55 (1):33-50.
    Some forms of analytic reconstructivism take natural language (and common sense at large) to be ontologically opaque: ordinary sentences must be suitably rewritten or paraphrased before questions of ontological commitment may be raised. Other forms of reconstructivism take the commitment of ordinary language at face value, but regard it as metaphysically misleading: common-sense objects exist, but they are not what we normally think they are. This paper is an attempt to clarify and critically assess some common limits of these two (...)
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  • Multistable Figures: On the Critical Potentials of Ir/Reversible Aspect-Seeing.Christoph Holzhey (ed.) - 2014 - Vienna: Turia + Kant.
    Multistable figures offer an intriguing model for arbitrating conflicting positions. Moving back and forth between the different aspects under which something can be seen, one recognizes that mutually contradictory descriptions can be equally valid and that disputes over the correct account can be resolved without dissolving differences or establishing a higher synthesis. Yet, the experience of a gestalt switch also offers a model for radical conversions and revolutions – that is, for irreversible leaps to incommensurable alternatives foiling ideals of rational (...)
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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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  • (1 other version)Truth and reduction.Volker Halbach - 2000 - Erkenntnis 53 (1-2):97-126.
    The proof-theoretic results on axiomatic theories oftruth obtained by different authors in recent years are surveyed.In particular, the theories of truth are related to subsystems ofsecond-order analysis. On the basis of these results, thesuitability of axiomatic theories of truth for ontologicalreduction is evaluated.
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