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The reality of numbers: a physicalist's philosophy of mathematics

New York: Oxford University Press (1988)

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  1. Two Concepts of Truthmaking: a Compatibilist Solution to the Controversy Between Substantive and Deflationary Approach.Błażej Mzyk - 2023 - Acta Analytica:1-20.
    For many years there has been a debate in truthmaking theory between proponents of the substantive and deflationary approaches. Substantivists about truthmaking maintain that we need entities called truthmakers, while deflationists of truthmaking argue that the asymmetric form of the T-schema is sufficient. In contrast to incompatibilists, who argue that one should adopt only one of these approaches, I propose a compatibilist theory of truthmaking in which the two approaches complement each other through the distribution of different functions of truthmaking. (...)
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  • Corrupting the youth: a history of philosophy in Australia.James Franklin - 2003 - Sydney, Australia: Macleay Press.
    A polemical account of Australian philosophy up to 2003, emphasising its unique aspects (such as commitment to realism) and the connections between philosophers' views and their lives. Topics include early idealism, the dominance of John Anderson in Sydney, the Orr case, Catholic scholasticism, Melbourne Wittgensteinianism, philosophy of science, the Sydney disturbances of the 1970s, Francofeminism, environmental philosophy, the philosophy of law and Mabo, ethics and Peter Singer. Realist theories especially praised are David Armstrong's on universals, David Stove's on logical probability (...)
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  • Why truthmaker theory cannot save divine simplicity.Dean Da Vee - 2021 - International Journal for Philosophy of Religion 90 (1):43-60.
    Although the doctrine of divine simplicity has faced substantial criticism in recent years, Jeffrey Brower has recently offered a novel defense of the view by appealing to contemporary truthmaker theory. In this paper, I will argue that Brower’s defense of divine simplicity requires an implausible account of how truthmaking works for essential intrinsic predications. I will first argue that, unless Brower is willing to make an ad hoc exception for how truthmaking works in God’s case, he is committed to saying (...)
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  • Presentism and the grounding objection.Thomas M. Crisp - 2007 - Noûs 41 (1):90–109.
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  • The Multi-location Trilemma.Damiano Costa & Claudio Calosi - 2022 - Erkenntnis 87 (3):1063-1079.
    The possibility of multi-location—of one entity having more than one exact location—is required by several metaphysical theories such as the immanentist theory of universals and three-dimensionalism about persistence. One of the most pressing challenges for multi-location theorists is that of making sense of exact location—in that extant definitions of exact location entail a principle called ‘functionality’, according to which nothing can have more than one exact location. Recently in a number of promising papers, Antony Eagle has proposed and defended a (...)
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  • Presentism, Truthmakers and Distributional Properties.Phil Corkum - 2014 - Synthese 191 (14):3427-46.
    Presentists face a challenge from truthmaker theory: if you hold both that the only existing objects are presently existing and that truth supervenes on being, then you will be hard pressed to identify some existent on which a given true but traceless claim about the past supervenes. One reconciliation strategy, advocated by Cameron (2011), is to appeal to distributional properties so to serve as presently existing truthmakers for past truths. I argue that a presentist ought to deny that distributional properties (...)
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  • The miracle of applied mathematics.Mark Colyvan - 2001 - Synthese 127 (3):265-277.
    Mathematics has a great variety ofapplications in the physical sciences.This simple, undeniable fact, however,gives rise to an interestingphilosophical problem:why should physical scientistsfind that they are unable to evenstate their theories without theresources of abstract mathematicaltheories? Moreover, theformulation of physical theories inthe language of mathematicsoften leads to new physical predictionswhich were quite unexpected onpurely physical grounds. It is thought by somethat the puzzles the applications of mathematicspresent are artefacts of out-dated philosophical theories about thenature of mathematics. In this paper I argue (...)
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  • Multiple reductions revisited.Justin Clarke-Doane - 2008 - Philosophia Mathematica 16 (2):244-255.
    Paul Benacerraf's argument from multiple reductions consists of a general argument against realism about the natural numbers (the view that numbers are objects), and a limited argument against reductionism about them (the view that numbers are identical with prima facie distinct entities). There is a widely recognized and severe difficulty with the former argument, but no comparably recognized such difficulty with the latter. Even so, reductionism in mathematics continues to thrive. In this paper I develop a difficulty for Benacerraf's argument (...)
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  • Existence claims and causality.Colin Cheyne - 1998 - Australasian Journal of Philosophy 76 (1):34 – 47.
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  • Algumas observações introdutórias sobre o princípio de veritação.César Schirmer dos Santos - 2016 - Principia: An International Journal of Epistemology 20 (2):201-214.
    The truth-making principle is one of the main subjects in contemporary meta- physics, and this paper is an elementar exposition of the main issues of the on-going debate. I will proceed as follows. First, I will expose the basics, including the principle’s range, the main kinds of truth-making, the main interpretations of the principle, and some applications. Second, I will expose some technical issues about ontological commitment, reification, necessity, reality, and truth.
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  • Truth-making : What it is not and What it Could be.Stefano Caputo - 2007 - In Jean-Maurice Monnoyer (ed.), Metaphysics and Truthmakers. Ontos Verlag. pp. 275-311.
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  • The Way Things Were.Ben Caplan & David Sanson - 2010 - Philosophy and Phenomenological Research 81 (1):24-39.
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  • Presentism and Truthmaking.Ben Caplan & David Sanson - 2011 - Philosophy Compass 6 (3):196-208.
    Three plausible views—Presentism, Truthmaking, and Independence—form an inconsistent triad. By Presentism, all being is present being. By Truthmaking, all truth supervenes on, and is explained in terms of, being. By Independence, some past truths do not supervene on, or are not explained in terms of, present being. We survey and assess some responses to this.
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  • Truthmakers, Realism and Ontology.Ross P. Cameron - 2008 - Royal Institute of Philosophy Supplement 62:107-128.
    Together, these entail that for every true proposition p, there exists some thing which could not exist and p be false.
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  • The contingency of composition.Ross P. Cameron - 2007 - Philosophical Studies 136 (1):99-121.
    There is widespread disagreement as to what the facts are concerning just when a collection of objects composes some further object; but there is widespread agreement that, whatever those facts are, they are necessary. I am unhappy to simply assume this, and in this paper I ask whether there is reason to think that the facts concerning composition hold necessarily. I consider various reasons to think so, but find fault with each of them. I examine the theory of composition as (...)
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  • Truthmakers and ontological commitment: or how to deal with complex objects and mathematical ontology without getting into trouble.Ross P. Cameron - 2008 - Philosophical Studies 140 (1):1 - 18.
    What are the ontological commitments of a sentence? In this paper I offer an answer from the perspective of the truthmaker theorist that contrasts with the familiar Quinean criterion. I detail some of the benefits of thinking of things this way: they include making the composition debate tractable without appealing to a neo-Carnapian metaontology, making sense of neo-Fregeanism, and dispensing with some otherwise recalcitrant necessary connections.
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  • Simplicity and aseity.Jeffrey E. Brower - 2008 - In Thomas P. Flint & Michael Rea (eds.), The Oxford handbook of philosophical theology. New York: Oxford University Press. pp. 105-28.
    There is a traditional theistic doctrine, known as the doctrine of divine simplicity, according to which God is an absolutely simple being, completely devoid of any metaphysical complexity. On the standard understanding of this doctrine—as epitomized in the work of philosophers such as Augustine, Anselm, and Aquinas—there are no distinctions to be drawn between God and his nature, goodness, power, or wisdom. On the contrary, God is identical with each of these things, along with anything else that can be predicated (...)
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  • Making Sense of Divine Simplicity.Jeffrey E. Brower - 2008 - Faith and Philosophy 25 (1):3-30.
    According to the doctrine of divine simplicity, God is an absolutely simple being lacking any distinct metaphysical parts, properties, or constituents. Although this doctrine was once an essential part of traditional philosophical theology, it is now widely rejected as incoherent. In this paper, I develop an interpretation of the doctrine designed to resolve contemporary concerns about its coherence, as well as to show precisely what is required to make sense of divine simplicity.
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  • Truthmaking without necessitation.Rachael Briggs - 2012 - Synthese 189 (1):11-28.
    I propose an account truthmaking that provides truthmakers for negative truths. The account replaces Truthmaker Necessitarianism with a "Duplication Principle", according to which a suitable entity T is a truthmaker for a proposition P just in case the existence of an appropriate counterpart of T entails the truth of P, where the counterpart relation is cashed out in terms of qualitative duplication. My account captures an intuitive notion of truthmakers as "things the way they are", validates two appealing principles about (...)
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  • Truth and Truthmakers in Early Modern Scholasticism.Brian Embry - 2015 - Journal of the American Philosophical Association 1 (2):196-216.
    17th-century Iberian and Italian scholastics had a concept of a truthmaker [verificativum] similar to that found in contemporary metaphysical debates. I argue that the 17th-century notion of a truthmaker can be illuminated by a prevalent 17th-century theory of truth according to which the truth of a proposition is the mereological sum of that proposition and its intentional object. I explain this theory of truth and then spell out the account of truthmaking it entails.
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  • Explaining Why There is Something Rather than Nothing.Andrew Brenner - 2022 - Erkenntnis 87 (4):1831-1847.
    It is sometimes supposed that, in principle, we cannot offer an explanation for why there is something rather than nothing. I argue that this supposition is a mistake, and stems from a needlessly myopic conception of the form explanations can legitimately take. After making this more general point, I proceed to offer a speculative suggestion regarding one sort of explanation which can in principle serve as an answer to the question “why is there something rather than nothing?” The suggestion is (...)
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  • The necessity of universalism versus the possibility of junky worlds: A rejoinder.Einar Duenger Bohn - 2010 - Analysis 70 (2):296-298.
    (No abstract is available for this citation).
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  • Resemblance nominalism and counterparts.Alexander Bird - 2003 - Analysis 63 (3):221–228.
    In his (2002) Gonzalo Rodriguez-Pereyra provides a powerful articulation of the claim that Resemblance Nominalism provides the best answer to the so-called Problem of Universals. Resemblance Nominalism has not been popular for some time, and one influential reason for this is the widespread belief that Resemblance Nominalism cannot dispense with all universals. The realist critics appeal to what is known as Russell’s Regress (cf. Russell 1997). If properties are to be explained in terms of one object’s resembling another, then this (...)
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  • God and the new math.John Bigelow - 1996 - Philosophical Studies 84 (2-3):127 - 154.
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  • Truthmaking and Case-Making. [REVIEW]Karen Bennett - 2011 - Philosophy and Phenomenological Research 83 (1):187-195.
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  • Brower and Saenz on Divine Truthmaker Simplicity.James R. Beebe - 2018 - Faith and Philosophy 35 (4):473-484.
    Jeffrey Brower has recently articulated a way to make sense of the doctrine of divine simplicity using resources from contemporary truthmaker theory. Noël Saenz has advanced two objections to Brower’s account, arguing that it violates constraints on adequate metaphysical explanations at various points. I argue that Saenz’s objections fail to show that Brower’s account is explanatorily inadequate.
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  • Tensed Truthmaker Theory.Sam Baron - 2015 - Erkenntnis 80 (5):923-944.
    Presentism faces a serious challenge from truthmaker theory. Standard solutions to the truthmaker objection against presentism proceed in one of two ways. Easy road presentists invoke new entities to satisfy the requirements of truthmaker theory. Hard road presentists, by contrast, flatly refuse to give in to truthmaker demands. Recently, a third way has been proposed. This response seeks to address the truthmaking problem by tensing our truthmaker principles. These views, though intuitive, are under-developed. In this paper, I get serious about (...)
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  • Tensed Supervenience: A No‐Go for Presentism.Sam Baron - 2013 - Southern Journal of Philosophy 51 (3):383-401.
    Recent attempts to resolve the truthmaker objection to presentism employ a fundamentally tensed account of the relationship between truth and being. On this view, the truth of a proposition concerning the past supervenes on how things are, in the present, along with how things were, in the past. This tensed approach to truthmaking arises in response to pressure placed on presentists to abandon the standard response to the truthmaker objection, whereby one invokes presently existing entities as the supervenience base for (...)
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  • Talking About the Past.Sam Baron - 2013 - Erkenntnis 78 (3):547-560.
    In this paper I consider the aboutness objection against standard truth-preserving presentism (STP). According to STP: (1) past-directed propositions (propositions that seem to be about the past) like , are sometimes true (2) truth supervenes on being and (3) the truth of past-directed propositions does not supervene on how things were, in the past. According to the aboutness objection (3) is implausible, given (1) and (2): for any proposition, P, P ought to be true in virtue of what P is (...)
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  • Much ado about aboutness.Sam Baron, Reginald Mary Chua, Kristie Miller & James Norton - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy (3).
    Strong non-maximalism holds that some truths require no ontological ground of any sort. Strong non-maximalism allows one to accept that some propositions are true without being forced to endorse any corresponding ontological commitments. We show that there is a version of truthmaker theory available—anti-aboutness truthmaking—that enjoys the dialectical benefits of the strong non-maximalist’s position. According to anti-aboutness truthmaking, all truths require grounds, but a proposition need not be grounded in the very thing(s) that the proposition is about. We argue that (...)
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  • Groundless Truth.Sam Baron, Kristie Miller & James Norton - 2014 - Inquiry: An Interdisciplinary Journal of Philosophy 57 (2):175-195.
    We defend two claims: (1) if one is attracted to a strong non-maximalist view about truthmaking, then it is natural to construe this as the view that there exist fundamental truths; (2) despite considerable aversion to fundamental truths, there is as yet no viable independent argument against them. That is, there is no argument against the existence of fundamental truths that is independent of any more specific arguments against the ontology accepted by the strong non-maximalist. Thus there is no argument (...)
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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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  • Presentism and the grounding of truth.Alex Baia - 2012 - Philosophical Studies 159 (3):341-356.
    Many philosophers believe that truth is grounded: True propositions depend for their truth on the world. Some philosophers believe that truth’s grounding has implications for our ontology of time. If truth is grounded, then truth supervenes on being. But if truth supervenes on being, then presentism is false since, on presentism, e.g., that there were dinosaurs fails to supervene on the whole of being plus the instantiation pattern of properties and relations. Call this the grounding argument against presentism. Many presentists (...)
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  • Unstable Truthmaking.Jamin Asay & Sam Baron - 2012 - Thought: A Journal of Philosophy 1 (3):230-238.
    Recent discussion of the problem of negative existentials for truthmaker theory suggests a modest solution to the problem: fully general negative truths like do not require truthmakers, whereas partially general negative truths like do. This modest solution provides a third alternative to the two standard solutions to the problem of negative existentials: the endorsement of truthmaker gaps, and the appeal to contentious ontological posits. We argue that this modest, middle-ground position is inconsistent with certain plausible general principles for truthmaking. The (...)
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  • We don’t need no explanation.Jamin Asay - 2018 - Philosophical Studies 175 (4):903-921.
    Explanation has played myriad roles in truthmaker theory. The notion of explanation is sometimes thought to give content to the very idea of truthmaking, and is sometimes used as a weapon to undermine the entire point of truthmaker theory. I argue that the notion of explanation is dialectically useless in truthmaker theory: while it’s true that truthmaking offers a form of explanation, this claim is theoretically unilluminating, and leaves truthmaker theorists vulnerable to various kinds of attack. I advocate an alternative (...)
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  • The best thing about the deflationary theory of truth.Jamin Asay - 2021 - Philosophical Studies 179 (1):109-131.
    I argue that deflationary theories of truth reveal an important lesson for the broader theory of truth: although the notion of truthmaking has played an essential role in many traditional theories of truth, it can be separated from and survive the rejection of substantive theories of truth. I argue that many of the traditional substantive theories of truth are unified in defining truth in terms of the ontological grounds that are needed to account for truth. Deflationists reject the idea that (...)
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  • The Facts about Truthmaking: An Argument for Truthmaker Necessitarianism.Jamin Asay - 2016 - Ergo: An Open Access Journal of Philosophy 3:493-500.
    Truthmaker necessitarianism is the view that an object is a truthmaker for a truth-bearer only if it is impossible for the object to exist and the truth-bearer be false. While this thesis is widely regarded as truthmaking "orthodoxy", it is rarely explicitly defended. In this paper I offer an argument in favor of necessitarianism that raises the question of what the truthmakers are for the truths about truthmaking. The supposed advantages of non-necessitarianism dissolve once we take these truths into account.
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  • The Hard Road to Presentism.Jamin Asay & Sam Baron - 2014 - Pacific Philosophical Quarterly 95 (3):314-335.
    It is a common criticism of presentism – the view according to which only the present exists – that it errs against truthmaker theory. Recent attempts to resolve the truthmaker objection against presentism proceed by restricting truthmaker maximalism (the view that all truths have truthmakers), maintaining that propositions concerning the past are not made true by anything, but are true nonetheless. Support for this view is typically garnered from the case for negative existential propositions, which some philosophers contend are exceptions (...)
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  • A Truthmaking Account of Realism and Anti-Realism.Jamin Asay - 2012 - Pacific Philosophical Quarterly 93 (3):373-394.
    Realism and anti-realism about a domain of thought are metaphysical theses that involve the natures of the truthmakers in that domain and the truthmaking relation that is operant in the domain. Truthmaker theory is not exclusive territory for realists: anti-realist views are also best understood in terms of how they understand truthmakers and truthmaking. In particular, I explore the possibility of projectivist truthmaking, and show how it makes sense of quasi-realism. In addition to critically examining some extant accounts of the (...)
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  • Against Truth.Jamin Asay - 2014 - Erkenntnis 79 (1):147-164.
    I argue that there is no metaphysically substantive property of truth. Although many take this thesis to be central to deflationism about truth, it is sometimes left unclear what a metaphysically substantive property of truth is supposed to be. I offer a precise account by relying on the distinction between the property and concept of truth. Metaphysical substantivism is the view that the property of truth is a sparse property, regardless of how one understands the nature of sparse properties. I (...)
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  • Nothing but Gold: Complexities in terms of Non-difference and Identity. Part 2. Contrasting Equivalence, Equality, Identity, and Non-difference.Alberto Anrò - 2021 - Journal of Indian Philosophy 49 (3):387-420.
    The present paper is a continuation of a previous one by the same title, the content of which faced the issue concerning the relations of coreference and qualification in compliance with the Navya-Nyāya theoretical framework, although prompted by the Advaita-Vedānta enquiry regarding non-difference. In a complementary manner, by means of a formal analysis of equivalence, equality, and identity, this section closes the loop by assessing the extent to which non-difference, the main issue here, cannot be reduced to any of the (...)
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  • The Logical Structure of Truthmaking.Staffan Angere - 2015 - Journal of Philosophical Logic 44 (4):351-374.
    This paper is an investigation in the use of truthmaker theory for exploring the relation of logic to world, and as a tool for metaphysics. A variant of truthmaker theory, which we call the simple theory, is defined and defended against objections. It is characterized formally, and its central features are derived. As part of this project, we give a formal metaphysics based on nondeterministic necessitation relations among possible entities. In what is called the fundamental theorem of truthmaking, it is (...)
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  • A Theistic Argument Against Platonism (and in Support of Truthmakers and Divine Simplicity).Michael Bergmann & Jeffrey E. Brower - 2006 - Oxford Studies in Metaphysics 2:357-386.
    Predication is an indisputable part of our linguistic behavior. By contrast, the metaphysics of predication has been a matter of dispute ever since antiquity. According to Plato—or at least Platonism, the view that goes by Plato’s name in contemporary philosophy—the truths expressed by predications such as “Socrates is wise” are true because there is a subject of predication (e.g., Socrates), there is an abstract property or universal (e.g., wisdom), and the subject exemplifies the property.1 This view is supposed to be (...)
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  • Can Truthmaker Theorists Claim Ontological Free Lunches?Peter Schulte - 2011 - European Journal of Philosophy 22 (2):249-268.
    Truthmaker theorists hold that propositions about higher-level entities (e.g. the proposition that there is a heap of sand) are often made true by lower-level entities (e.g. by facts about the configuration of fundamental particles). This generates a problem: what should we say about these higher-level entities? On the one hand, they must exist (since there are true propositions about them), on the other hand, it seems that they are completely superfluous and should be banished for reasons of ontological parsimony. Some (...)
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  • Quantity and number.James Franklin - 2013 - In Daniel Novotný & Lukáš Novák (eds.), Neo-Aristotelian Perspectives in Metaphysics. London: Routledge. pp. 221-244.
    Quantity is the first category that Aristotle lists after substance. It has extraordinary epistemological clarity: "2+2=4" is the model of a self-evident and universally known truth. Continuous quantities such as the ratio of circumference to diameter of a circle are as clearly known as discrete ones. The theory that mathematics was "the science of quantity" was once the leading philosophy of mathematics. The article looks at puzzles in the classification and epistemology of quantity.
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  • Naturalness.Cian Dorr & John Hawthorne - 2013 - In Karen Bennett & Dean W. Zimmerman (eds.), Oxford Studies in Metaphysics, Volume 8. Oxford, GB: Oxford University Press. pp. 1.
    Lewis's notion of a "natural" property has proved divisive: some have taken to the notion with enthusiasm, while others have been sceptical. However, it is far from obvious what the enthusiasts and the sceptics are disagreeing about. This paper attempts to articulate what is at stake in this debate.
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  • Absence Causation and a Liberal Theory of Causal Explanation.Zhiheng Tang - 2015 - Australasian Journal of Philosophy 93 (4):688-705.
    For the framework of event causation—i.e. the framework according to which causation is a relation between events—absences or omissions pose a problem. Absences, it is generally agreed, are not events; so, under the framework of event causation, they cannot be causally related. But, as a matter of fact, absences are often taken to be causes or effects. The problem of absence causation is thus how to make sense of causation that apparently involves absences as causes or effects. In an influential (...)
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  • Indeterminate truth.Patrick Greenough - 2008 - Midwest Studies in Philosophy 32 (1):213-241.
    In §2-4, I survey three extant ways of making sense of indeterminate truth and find each of them wanting. All the later sections of the paper are concerned with showing that the most promising way of making sense of indeterminate truth is via either a theory of truthmaker gaps or via a theory of truthmaking gaps. The first intimations of a truthmaker–truthmaking gap theory of indeterminacy are to be found in Quine (1981). In §5, we see how Quine proposes to (...)
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  • Space, Supervenence and Entailment.Sophie C. Gibb - 2006 - Philosophical Papers 35 (2):171-184.
    Le Poidevin has recently presented an argument that gives rise to a serious problem for relationist theories of space. It appeals to the simple geometrical fact that if A, B and C are three points lying in a straight line, then AB and BC together entail AC. He suggests that an ontological relationship of supervenience must be appealed to to explain this entailment. Given this thesis of supervenience, relationism is implausible. I argue that the problem that Le Poidevin raises for (...)
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  • A Defense of Hume's Dictum.Cameron Gibbs - 2019 - Dissertation, University of Massachusetts Amherst
    Is the world internally connected by a web of necessary connections or is everything loose and independent? Followers of David Hume accept the latter by upholding Hume’s Dictum, according to which there are no necessary connections between distinct existences. Roughly put, anything can coexist with anything else, and anything can fail to coexist with anything else. Hume put it like this: “There is no object which implies the existence of any other if we consider these objects in themselves.” Since Hume’s (...)
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