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Hilary Putnam (1971). Philosophy of Logic.

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  1.  87
    Parsimony and Inference to the Best Mathematical Explanation.Alan Baker - 2016 - Synthese 193 (2).
    Indispensability-based arguments for mathematical platonism are typically motivated by drawing an analogy between abstract mathematical objects and concrete scientific posits. In this paper, I argue that mathematics can sometimes help to reduce our concrete ontological, ideological, and structural commitments. My focus is on optimization explanations, and in particular the case study involving periodical cicadas. I argue that in this case, stronger mathematical apparatus yields explanations that have fewer concrete commitments. The nominalist cannot accept these more parsimonious explanations without embracing the (...)
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  2. Grounding and the Indispensability Argument.David Liggins - 2016 - Synthese 193 (2):531-548.
    There has been much discussion of the indispensability argument for the existence of mathematical objects. In this paper I reconsider the debate by using the notion of grounding, or non-causal dependence. First of all, I investigate what proponents of the indispensability argument should say about the grounding of relations between physical objects and mathematical ones. This reveals some resources which nominalists are entitled to use. Making use of these resources, I present a neglected but promising response to the indispensability argument—a (...)
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  3.  45
    Evidence, Explanation and Enhanced Indispensability.Daniele Molinini - 2016 - Synthese 193 (2):403-422.
    In this paper I shall adopt a possible reading of the notions of ‘explanatory indispensability’ and ‘genuine mathematical explanation in science’ on which the Enhanced Indispensability Argument proposed by Alan Baker is based. Furthermore, I shall propose two examples of mathematical explanation in science and I shall show that, whether the EIA-partisans accept the reading I suggest, they are easily caught in a dilemma. To escape this dilemma they need to adopt some account of explanation and offer a plausible answer (...)
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  4.  43
    The Varieties of Indispensability Arguments.Marco Panza & Andrea Sereni - 2016 - Synthese 193 (2):469-516.
    The indispensability argument comes in many different versions that all reduce to a general valid schema. Providing a sound IA amounts to providing a full interpretation of the schema according to which all its premises are true. Hence, arguing whether IA is sound results in wondering whether the schema admits such an interpretation. We discuss in full details all the parameters on which the specification of the general schema may depend. In doing this, we consider how different versions of IA (...)
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  5. Against Mathematical Convenientism.Seungbae Park - 2016 - Axiomathes 26 (2):115-122.
    Indispensablists argue that when our belief system conflicts with our experiences, we can negate a mathematical belief but we do not because if we do, we would have to make an excessive revision of our belief system. Thus, we retain a mathematical belief not because we have good evidence for it but because it is convenient to do so. I call this view ‘ mathematical convenientism.’ I argue that mathematical convenientism commits the consequential fallacy and that it demolishes the Quine-Putnam (...)
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  6. A Deflationist Error Theory of Properties.Arvid Båve - 2015 - Dialectica 69 (1):23-59.
    I here defend a theory consisting of four claims about ‘property’ and properties, and argue that they form a coherent whole that can solve various serious problems. The claims are (1): ‘property’ is defined by the principles (PR): ‘F-ness/Being F/etc. is a property of x iff F’ and (PA): ‘F-ness/Being F/etc. is a property’; (2) the function of ‘property’ is to increase the expressive power of English, roughly by mimicking quantification into predicate position; (3) property talk should be understood at (...)
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  7.  48
    Bait and Switch Philosophy.Chris Daly - 2015 - Analysis 75 (3):372-379.
    Many philosophers employ an intellectual division of labour. Philosophy tells us what the truth conditions of various philosophically interesting sentences are. For example, atomic sentences containing numerals are sentences containing singular terms putatively referring to numbers; sentences about what could be are sentences quantifying over possible worlds and so on. Some discipline outside of philosophy tells us that certain of these sentences are true. The purported result is that such philosophically controversial entities as numbers and possible worlds have been shown (...)
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  8.  76
    Two Cornell Realisms: Moral and Scientific.Elliott Sober - 2015 - Philosophical Studies 172 (4):905-924.
    Richard Boyd and Nicholas Sturgeon develop distinctive naturalistic arguments for scientific realism and moral realism. Each defends a realist position by an inference to the best explanation. In this paper, I suggest that these arguments for realism should be reformulated, with the law of likelihood replacing inference to the best explanation. The resulting arguments for realism do not work.
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  9.  88
    Optimisation and Mathematical Explanation: Doing the Lévy Walk.Sam Baron - 2014 - Synthese 191 (3).
    The indispensability argument seeks to establish the existence of mathematical objects. The success of the indispensability argument turns on finding cases of genuine extra- mathematical explanation. In this paper, I identify a new case of extra- mathematical explanation, involving the search patterns of fully-aquatic marine predators. I go on to use this case to predict the prevalence of extra- mathematical explanation in science.
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  10.  51
    The Holistic Presumptions of the Indispensability Argument.Russell Marcus - 2014 - Synthese 191 (15):3575-3594.
    The indispensability argument is sometimes seen as weakened by its reliance on a controversial premise of confirmation holism. Recently, some philosophers working on the indispensability argument have developed versions of the argument which, they claim, do not rely on holism. Some of these writers even claim to have strengthened the argument by eliminating the controversial premise. I argue that the apparent removal of holism leaves a lacuna in the argument. Without the holistic premise, or some other premise which facilitates the (...)
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  11. Truths and Processes: A Critical Approach to Truthmaker Theory.Gustavo Picazo - 2014 - Philosophia 42 (3):713-739.
    The starting point of this paper is the idea that linguistic representation is the result of a global process: a process of interaction of a community of cognitive-linguistic agents, with one another and with the environment. I maintain that the study of truth, meaning and related notions should be addressed without losing perspective of this process, and I oppose the ‘static’ or ‘analytic’ approach, which is fundamentally based on our own knowledge of the conventional meaning of words and sentences, and (...)
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  12.  29
    The Logical Structure of Evolutionary Explanation and Prediction: Darwinism's Fundamental Schema.Neil Tennant - 2014 - Biology and Philosophy 29 (5):611-655.
    We present a logically detailed case-study of Darwinian evolutionary explanation. Special features of Darwin’s explanatory schema made it an unusual theoretical breakthrough, from the point of view of the philosophy of science. The schema employs no theoretical terms, and puts forward no theoretical hypotheses. Instead, it uses three observational generalizations—Variability, Heritability and Differential Reproduction—along with an innocuous assumption of Causal Efficacy, to derive Adaptive Evolution as a necessary consequence. Adaptive Evolution in turn, with one assumption of scale (‘Deep Time’), implies (...)
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  13. 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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  14. Can Indispensability‐Driven Platonists Be (Serious) Presentists?Sam Baron - 2013 - Theoria 79 (3):153-173.
    In this article I consider what it would take to combine a certain kind of mathematical Platonism with serious presentism. I argue that a Platonist moved to accept the existence of mathematical objects on the basis of an indispensability argument faces a significant challenge if she wishes to accept presentism. This is because, on the one hand, the indispensability argument can be reformulated as a new argument for the existence of past entities and, on the other hand, if one accepts (...)
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  15.  43
    Modal Property Comprehension.Ulrich Meyer - 2013 - Synthese 190 (4):693-707.
    To define new property terms, we combine already familiar ones by means of certain logical operations. Given suitable constraints, these operations may presumably include the resources of first-order logic: truth-functional sentence connectives and quantification over objects. What is far less clear is whether we can also use modal operators for this purpose. This paper clarifies what is involved in this question, and argues in favor of modal property definitions.
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  16.  9
    Inscriptionalism and Intensionality.David Parsons - 2013 - Philosophia 41 (2):567-585.
    Intensional contexts are typically characterised by an apparent failure of either (A) the principle of the inter-substitution of co-referring terms salva veritate, or (B) existential generalisation. The difficulties which are seen to occur do so in contexts involving either modality or the propositional attitudes. In this paper attempts are made to determine whether or not Scheffler’s inscriptional analysis can provide a viable means of accounting for the problems which are thought to occur in intensional contexts. Somewhat unexpectedly, little effort has (...)
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  17.  64
    Can the New Indispensability Argument Be Saved From Euclidean Rescues?Jacob Busch - 2012 - Synthese 187 (2):489-508.
    The traditional formulation of the indispensability argument for the existence of mathematical entities (IA) has been criticised due to its reliance on confirmational holism. Recently a formulation of IA that works without appeal to confirmational holism has been defended. This recent formulation is meant to be superior to the traditional formulation in virtue of it not being subject to the kind of criticism that pertains to confirmational holism. I shall argue that a proponent of the version of IA that works (...)
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  18.  85
    In Defense of Quinean Ontological Naturalism.Patrick Dieveney - 2012 - Erkenntnis 76 (2):225-242.
    Quinean Ontological Naturalism addresses the question “What is there?” Advocates of the view maintain that we can answer this question by applying Quine’s criterion of ontological commitment to our best scientific theories. In this paper, I discuss two major objections that are commonly offered to this view, what I call the “Paraphrase Objection” and “First Philosophy Objection”. I argue that these objections arise from a common uncharitable characterization of the Quinean Ontological Naturalist’s project that fails to distinguish two distinct roles (...)
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  19.  98
    Evidential Holism and Indispensability Arguments.Joe Morrison - 2012 - Erkenntnis 76 (2):263-278.
    The indispensability argument is a method for showing that abstract mathematical objects exist. Various versions of this argument have been proposed. Lately, commentators seem to have agreed that a holistic indispensability argument will not work, and that an explanatory indispensability argument is the best candidate. In this paper I argue that the dominant reasons for rejecting the holistic indispensability argument are mistaken. This is largely due to an overestimation of the consequences that follow from evidential holism. Nevertheless, the holistic indispensability (...)
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  20. Neo-Positivist Metaphysics.Alyssa Ney - 2012 - Philosophical Studies 160 (1):53-78.
    Some philosophers argue that many contemporary debates in metaphysics are “illegitimate,” “shallow,” or “trivial,” and that “contemporary analytic metaphysics, a professional activity engaged in by some extremely intelligent and morally serious people, fails to qualify as part of the enlightened pursuit of objective truth, and should be discontinued” (Ladyman and Ross, Every thing must go: Metaphysics naturalized , 2007 ). Many of these critics are explicit about their sympathies with Rudolf Carnap and his circle, calling themselves ‘neo-positivists’ or ‘neo-Carnapians.’ Yet (...)
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  21. Getting Rid of Interventions.Alexander Reutlinger - 2012 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 43 (4):787-795.
    According to James Woodward’s influential interventionist account of causation, X is a cause of Y iff, roughly, there is a possible intervention on X that changes Y. Woodward requires that interventions be merely logically possible. I will argue for two claims against this modal character of interventions: First, merely logically possible interventions are dispensable for the semantic project of providing an account of the meaning of causal statements. If interventions are indeed dispensable, the interventionist theory collapses into a counterfactual theory (...)
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  22. Is the Indispensability Argument Dispensable?Jacob Busch - 2011 - Theoria 77 (2):139-158.
    When the indispensability argument for mathematical entities (IA) is spelled out, it would appear confirmational holism is needed for the argument to work. It has been argued that confirmational holism is a dispensable premise in the argument if a construal of naturalism, according to which it is denied that we can take different epistemic attitudes towards different parts of our scientific theories, is adopted. I argue that the suggested variety of naturalism will only appeal to a limited number of philosophers. (...)
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  23. 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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  24.  41
    Nominalistic Adequacy.Jeffrey Ketland - 2011 - Proceedings of the Aristotelian Society 111 (2pt2):201-217.
    Instrumentalist nominalism responds to the indispensability arguments by rejecting the demand that successful mathematicized scientific theories be nominalized, and instead claiming merely that such theories are nominalistically adequate: the concreta behave ‘as if’ the theory is true. This article examines some definitions of the concept of nominalistic adequacy and concludes with some considerations against instrumentalist nominalism.
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  25. Magicicada, Mathematical Explanation and Mathematical Realism.Davide Rizza - 2011 - Erkenntnis 74 (1):101-114.
    Baker claims to provide an example of mathematical explanation of an empirical phenomenon which leads to ontological commitment to mathematical objects. This is meant to show that the positing of mathematical entities is necessary for satisfactory scientific explanations and thus that the application of mathematics to science can be used, at least in some cases, to support mathematical realism. In this paper I show that the example of explanation Baker considers can actually be given without postulating mathematical objects and thus (...)
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  26. Thermoscopes, Thermometers, and the Foundations of Measurement.David Sherry - 2011 - Studies in History and Philosophy of Science Part A 42 (4):509-524.
    Psychologists debate whether mental attributes can be quantified or whether they admit only qualitative comparisons of more and less. Their disagreement is not merely terminological, for it bears upon the permissibility of various statistical techniques. This article contributes to the discussion in two stages. First it explains how temperature, which was originally a qualitative concept, came to occupy its position as an unquestionably quantitative concept (§§1–4). Specifically, it lays out the circumstances in which thermometers, which register quantitative (or cardinal) differences, (...)
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  27. 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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  28. Inference to the Best Explanation and Mathematical Realism.Sorin Ioan Bangu - 2008 - Synthese 160 (1):13-20.
    Arguing for mathematical realism on the basis of Field’s explanationist version of the Quine–Putnam Indispensability argument, Alan Baker has recently claimed to have found an instance of a genuine mathematical explanation of a physical phenomenon. While I agree that Baker presents a very interesting example in which mathematics plays an essential explanatory role, I show that this example, and the argument built upon it, begs the question against the mathematical nominalist.
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  29. The Ontological Commitments of Inconsistent Theories.Mark Colyvan - 2008 - Philosophical Studies 141 (1):115 - 123.
    In this paper I present an argument for belief in inconsistent objects. The argument relies on a particular, plausible version of scientific realism, and the fact that often our best scientific theories are inconsistent. It is not clear what to make of this argument. Is it a reductio of the version of scientific realism under consideration? If it is, what are the alternatives? Should we just accept the conclusion? I will argue (rather tentatively and suitably qualified) for a positive answer (...)
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  30.  92
    Ontological Infidelity.Patrick Dieveney - 2008 - Synthese 165 (1):1 - 12.
    In ethical discourse, it is common practice to distinguish between normative commitments and descriptive commitments. Normative commitments reflect what a person ought to be committed to, whereas descriptive commitments reflect what a person actually is committed to. While the normative/descriptive distinction is widely accepted as a way of talking about ethical commitments, philosophers have missed this distinction in discussing ontological commitments. In this paper, I distinguish between descriptive ontological commitments and normative ontological commitments and discuss several significant benefits of recognizing (...)
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  31.  70
    Kant's Theory of Arithmetic: A Constructive Approach? [REVIEW]Kristina Engelhard & Peter Mittelstaedt - 2008 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 39 (2):245 - 271.
    Kant’s theory of arithmetic is not only a central element in his theoretical philosophy but also an important contribution to the philosophy of arithmetic as such. However, modern mathematics, especially non-Euclidean geometry, has placed much pressure on Kant’s theory of mathematics. But objections against his theory of geometry do not necessarily correspond to arguments against his theory of arithmetic and algebra. The goal of this article is to show that at least some important details in Kant’s theory of arithmetic can (...)
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  32.  10
    Kant’s Theory of Arithmetic: A Constructive Approach?Kristina Engelhard & Peter Mittelstaedt - 2008 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 39 (2):245-271.
    Kant's theory of arithmetic is not only a central element in his theoretical philosophy but also an important contribution to the philosophy of arithmetic as such. However, modern mathematics, especially non-Euclidean geometry, has placed much pressure on Kant's theory of mathematics. But objections against his theory of geometry do not necessarily correspond to arguments against his theory of arithmetic and algebra. The goal of this article is to show that at least some important details in Kant's theory of arithmetic can (...)
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  33. 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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  34.  38
    Confirmational Holism and its Mathematical (W)Holes.Anthony F. Peressini - 2008 - Studies in History and Philosophy of Science Part A 39 (1):102-111.
    I critically examine confirmational holism as it pertains to the indispensability arguments for mathematical Platonism. I employ a distinction between pure and applied mathematics that grows out of the often overlooked symbiotic relationship between mathematics and science. I argue that this distinction undercuts the notion that mathematical theories fall under the holistic scope of the confirmation of our scientific theories.Keywords: Confirmational holism; Indispensability argument; Mathematics; Application; Science.
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  35.  44
    From Numerical Concepts to Concepts of Number.Lance J. Rips, Amber Bloomfield & Jennifer Asmuth - 2008 - Behavioral and Brain Sciences 31 (6):623-642.
    Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept (...)
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  36. Dispensability in the Indispensability Argument.Patrick S. Dieveney - 2007 - Synthese 157 (1):105-128.
    One of the most influential arguments for realism about mathematical objects is the indispensability argument. Simply put, this is the argument that insofar as we are committed to the existence of the physical objects existentially quantified over in our best scientific theories, we are also committed to the mathematical objects existentially quantified over in these theories. Following the Quine–Putnam formulation of the indispensability argument, some proponents of the indispensability argument have made the mistake of taking confirmational holism to be an (...)
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  37. Metaontology.Matti Eklund - 2006 - Philosophy Compass 1 (3):317-334.
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  38.  70
    Conjoining Mathematical Empiricism with Mathematical Realism: Maddy’s Account of Set Perception Revisited.Alex Levine - 2005 - Synthese 145 (3):425-448.
    Penelope Maddy's original solution to the dilemma posed by Benacerraf in his 'Mathematical Truth' was to reconcile mathematical empiricism with mathematical realism by arguing that we can perceive realistically construed sets. Though her hypothesis has attracted considerable critical attention, much of it, in my view, misses the point. In this paper I vigorously defend Maddy's account against published criticisms, not because I think it is true, but because these criticisms have functioned to obscure a more fundamental issue that is well (...)
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  39.  25
    Is Platonism a Bad Bet?Mark Colyvan - 1998 - Australasian Journal of Philosophy 76 (1):115 – 119.
    Recently Colin Cheyne and Charles Pigden have challenged supporters of mathematical indispensability arguments to give an account of how causally inert mathematical entities could be indispensable to science. Failing to meet this challenge, claim Cheyne and Pigden, would place Platonism in a no win situation: either there is no good reason to believe in mathematical entities or mathematical entities are not causally inert. The present paper argues that Platonism is well equipped to meet this challenge.
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  40. Pythagorean Powers or a Challenge to Platonism.Colin Cheyne & Charles R. Pigden - 1996 - Australasian Journal of Philosophy 74 (4):639 – 645.
    The Quine/Putnam indispensability argument is regarded by many as the chief argument for the existence of platonic objects. We argue that this argument cannot establish what its proponents intend. The form of our argument is simple. Suppose indispensability to science is the only good reason for believing in the existence of platonic objects. Either the dispensability of mathematical objects to science can be demonstrated and, hence, there is no good reason for believing in the existence of platonic objects, or their (...)
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  41.  33
    Constructive Mathematics and Quantum Mechanics: Unbounded Operators and the Spectral Theorem. [REVIEW]Geoffrey Hellman - 1993 - Journal of Philosophical Logic 22 (3):221 - 248.
  42.  10
    Putnam, G Del and Mathematical Realism.Alan Weir - 1993 - International Journal of Philosophical Studies 1 (2):255 – 285.
  43.  50
    Philosophy of Mathematics: Prospects for the 1990s.Penelope Maddy - 1991 - Synthese 88 (2):155 - 164.
    For some time now, academic philosophers of mathematics have concentrated on intramural debates, the most conspicuous of which has centered on Benacerraf's epistemological challenge. By the late 1980s, something of a consensus had developed on how best to respond to this challenge. But answering Benacerraf leaves untouched the more advanced epistemological question of how the axioms are justified, a question that bears on actual practice in the foundations of set theory. I suggest that the time is ripe for philosophers of (...)
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  44.  30
    Mathematical Fictionalism.David Papineau - 1988 - International Studies in the Philosophy of Science 2 (2):151 – 174.
  45.  3
    Normative Theory and the Human Mind.Rachel Joffe Falmagne - 1985 - Behavioral and Brain Sciences 8 (4):750-751.
  46.  3
    Probability Intervals and Rational Norms.Henry E. Kyburg - 1985 - Behavioral and Brain Sciences 8 (4):753-754.
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  47.  2
    Three Decision Rules for Generalized Probability Representations.Nils-Eric Sahlin - 1985 - Behavioral and Brain Sciences 8 (4):751.
  48.  27
    Evolutionary Theory and the Ontological Status of Properties.Elliott Sober - 1981 - Philosophical Studies 40 (2):147 - 176.
  49.  18
    Validity and Quantification in Intuitionism.H. C. M. Swart & C. J. Posy - 1981 - Journal of Philosophical Logic 10 (1):117 - 126.
    We distinguish three different readings of the intuitionistic notions of validity, soundness, and completeness with respect to the quantification occurring in the notion of validity, and we establish certain relations between the different readings. For each of the meta-logicalnotions considered we suggest that the "most natural" reading (which is not the same for all cases) is precisely the one which is required by the recent intuitionistic completeness theorems for IPC.
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  50.  11
    Artificial Intelligence as a Possible Tool for Discovering Laws of Logic.David Isles - 1978 - Cognitive Science 2 (4):329-360.
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