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Collected Papers on Mathematics, Logic, and Philosophy

Wiley-Blackwell. Edited by Brian McGuinness (1991)

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  1. Mental Files.François Recanati - 2012 - Oxford, GB: Oxford University Press.
    Over the past fifty years the philosophy of language and mind has been dominated by a nondescriptivist approach to content and reference. This book attempts to recast and systematize that approach by offering an indexical model in terms of mental files. According to Recanati, we refer through mental files, the function of which is to store information derived through certain types of contextual relation the subject bears to objects in his or her environment. The reference of a file is determined (...)
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  • Materialism and qualia: The explanatory gap.Joseph Levine - 1983 - Pacific Philosophical Quarterly 64 (October):354-61.
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  • How (Not) to Think of Emotions as Evaluative Attitudes.Jean Moritz Müller - 2017 - Dialectica 71 (2):281-308.
    It is popular to hold that emotions are evaluative. On the standard account, the evaluative character of emotion is understood in epistemic terms: emotions apprehend or make us aware of value properties. As this account is commonly elaborated, emotions are experiences with evaluative intentional content. In this paper, I am concerned with a recent alternative proposal on how emotions afford awareness of value. This proposal does not ascribe evaluative content to emotions, but instead conceives of them as evaluative at the (...)
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  • Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method.Carlo Cellucci - 2013 - Dordrecht, Netherland: Springer.
    This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without (...)
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  • Hyperintensional semantics: a Fregean approach.Mattias Skipper & Jens Christian Bjerring - 2020 - Synthese 197 (8):3535-3558.
    In this paper, we present a new semantic framework designed to capture a distinctly cognitive or epistemic notion of meaning akin to Fregean senses. Traditional Carnapian intensions are too coarse-grained for this purpose: they fail to draw semantic distinctions between sentences that, from a Fregean perspective, differ in meaning. This has led some philosophers to introduce more fine-grained hyperintensions that allow us to draw semantic distinctions among co-intensional sentences. But the hyperintensional strategy has a flip-side: it risks drawing semantic distinctions (...)
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  • The A-Theory of Time, The B-Theory of Time, and ‘Taking Tense Seriously’.Dean W. Zimmerman - 2005 - Dialectica 59 (4):401-457.
    The paper has two parts: First, I describe a relatively popular thesis in the philosophy of propositional attitudes, worthy of the name ‘taking tense seriously’; and I distinguish it from a family of views in the metaphysics of time, namely, the A-theories (or what are sometimes called ‘tensed theories of time’). Once the distinction is in focus, a skeptical worry arises. Some A-theorists maintain that the difference between past, present, and future, is to be drawn in terms of what exists: (...)
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  • The Non-Conceptuality of the Content of Intuitions: A New Approach.Clinton Tolley - 2013 - Kantian Review 18 (1):107-36.
    There has been considerable recent debate about whether Kant's account of intuitions implies that their content is conceptual. This debate, however, has failed to make significant progress because of the absence of discussion, let alone consensus, as to the meaning of ‘content’ in this context. Here I try to move things forward by focusing on the kind of content associated with Frege's notion of ‘sense ’, understood as a mode of presentation of some object or property. I argue, first, that (...)
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  • Logical constants.John MacFarlane - 2008 - Mind.
    Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...)
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  • A Millian Heir Rejects the Wages of Sinn.Nathan Salmon - 1990 - In C. Anthony Anderson & Joseph Owens (eds.), Propositional Attitudes: The Role of Content in Language, Logic, and Mind. CSLI Publications. pp. 215-247.
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  • Semantics and Truth.Jan Woleński - 2019 - Cham, Switzerland: Springer Verlag.
    The book provides a historical and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s. This theory became famous very soon and inspired logicians and philosophers. It has two different, but interconnected aspects: formal-logical and philosophical. The book deals with both, but it is intended mostly as a philosophical monograph. It explains Tarski’s motivation and presents discussions about his ideas as well as points out various applications of the semantic theory of truth to philosophical (...)
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  • How (not) to construct worlds with responsibility.Fabio Lampert & Pedro Merlussi - 2021 - Synthese 199 (3-4):10389-10413.
    In a recent article, P. Roger Turner and Justin Capes argue that no one is, or ever was, even partly morally responsible for certain world-indexed truths. Here we present our reasons for thinking that their argument is unsound: It depends on the premise that possible worlds are maximally consistent states of affairs, which is, under plausible assumptions concerning states of affairs, demonstrably false. Our argument to show this is based on Bertrand Russell’s original ‘paradox of propositions’. We should then opt (...)
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  • Linguistic understanding and knowledge.Guy Longworth - 2008 - Noûs 42 (1):50–79.
    Is linguistic understanding a form of knowledge? I clarify the question and then consider two natural forms a positive answer might take. I argue that, although some recent arguments fail to decide the issue, neither positive answer should be accepted. The aim is not yet to foreclose on the view that linguistic understanding is a form of knowledge, but to develop desiderata on a satisfactory successor to the two natural views rejected here.
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  • The Composition of Thoughts.Richard Heck & Robert May - 2010 - Noûs 45 (1):126-166.
    Are Fregean thoughts compositionally complex and composed of senses? We argue that, in Begriffsschrift, Frege took 'conceptual contents' to be unstructured, but that he quickly moved away from this position, holding just two years later that conceptual contents divide of themselves into 'function' and 'argument'. This second position is shown to be unstable, however, by Frege's famous substitution puzzle. For Frege, the crucial question the puzzle raises is why "The Morning Star is a planet" and "The Evening Star is a (...)
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  • The Unity of Wittgenstein's Philosophy: Necessity, Intelligibility, and Normativity.Jose Medina - 2002 - State University of New York Press.
    Explores the stable core of Wittgenstein's philosophy as developed from the Tractatus to the Philosophical Investigations.
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  • (1 other version)Kant on the Content of Cognition.Clinton Tolley - 2014 - European Journal of Philosophy 22 (2):200-228.
    I present an argument for an interpretation ofKant's views on the nature of the ‘content [Inhalt]’ of ‘cognition [Erkenntnis]’. In contrast to one of the longest standing interpretations ofKant's views on cognitive content, which ascribes toKant a straightforwardly psychologistic understanding of content, and in contrast as well to the more recently influential reading ofKant put forward byMcDowell and others, according to whichKant embraces a version ofRussellianism, I argue thatKant's views on this topic are of a much moreFregean bent than has (...)
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  • Άδύνατον and material exclusion 1.Francesco Berto - 2008 - Australasian Journal of Philosophy 86 (2):165 – 190.
    Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and it is rational to accept and assert them. Such a position is naturally portrayed as a challenge to the Law of Non-Contradiction (LNC). But all the classic formulations of the LNC are, in a sense, not questioned by a typical dialetheist, since she is (cheerfully) required to accept them by her own theory. The goal of this paper is to develop a formulation of the (...)
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  • Composition and Relative Counting.Massimiliano Carrara & Giorgio Lando - 2017 - Dialectica 71 (4):489-529.
    According to the so-called strong variant of Composition as Identity (CAI), the Principle of Indiscernibility of Identicals can be extended to composition, by resorting to broadly Fregean relativizations of cardinality ascriptions. In this paper we analyze various ways in which this relativization could be achieved. According to one broad variety of relativization, cardinality ascriptions are about objects, while concepts occupy an additional argument place. It should be possible to paraphrase the cardinality ascriptions in plural logic and, as a consequence, relative (...)
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  • First-Person Perspective in Experience: Perspectival De Se Representation as an Explanation of the Delimitation Problem.Miguel Ángel Sebastián - 2024 - Erkenntnis 89 (3):947-969.
    In developing a theory of consciousness, one of the main problems has to do with determining what distinguishes conscious states from non-conscious ones—the delimitation problem. This paper explores the possibility of solving this problem in terms of self-awareness. That self-awareness is essential to understanding the nature of our conscious experience is perhaps the most widely discussed hypothesis in the study of consciousness throughout the history of philosophy. Its plausibility hinges on how the notion of self-awareness is unpacked. The idea that (...)
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  • Ontological superpluralism.Ben Caplan - 2011 - Philosophical Perspectives 25 (1):79-114.
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  • Second-order logic: properties, semantics, and existential commitments.Bob Hale - 2019 - Synthese 196 (7):2643-2669.
    Quine’s most important charge against second-, and more generally, higher-order logic is that it carries massive existential commitments. The force of this charge does not depend upon Quine’s questionable assimilation of second-order logic to set theory. Even if we take second-order variables to range over properties, rather than sets, the charge remains in force, as long as properties are individuated purely extensionally. I argue that if we interpret them as ranging over properties more reasonably construed, in accordance with an abundant (...)
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  • (1 other version)Kant on the Content of Cognition.Clinton Tolley - 2012 - European Journal of Philosophy 20 (4):200-228.
    I present an argument for an interpretation of Kant's views on the nature of the ‘content [Inhalt]’ of ‘cognition [Erkenntnis]’. In contrast to one of the longest standing interpretations of Kant's views on cognitive content, which ascribes to Kant a straightforwardly psychologistic understanding of content, and in contrast as well to the more recently influential reading of Kant put forward by McDowell and others, according to which Kant embraces a version of Russellianism, I argue that Kant's views on this topic (...)
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  • Simplex sigillum veri: Peano, Frege, and Peirce on the Primitives of Logic.Francesco Bellucci, Amirouche Moktefi & Ahti-Veikko Pietarinen - 2018 - History and Philosophy of Logic 39 (1):80-95.
    We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. (...)
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  • Content, Mood, and Force.Francois Recanati - 2013 - Philosophy Compass 8 (7):622-632.
    In this survey paper, I start from two classical theses of speech act theory: that speech act content is uniformly propositional and that sentence mood encodes illocutionary force. These theses have been questioned in recent work, both in philosophy and linguistics. The force/content distinction itself – a cornerstone of 20‐century philosophy of language – has come to be rejected by some theorists, unmoved by the famous ‘Frege–Geach’ argument. The paper reviews some of these debates.
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  • Frege's Judgement Stroke and the Conception of Logic as the Study of Inference not Consequence.Nicholas J. J. Smith - 2009 - Philosophy Compass 4 (4):639-665.
    One of the most striking differences between Frege's Begriffsschrift (logical system) and standard contemporary systems of logic is the inclusion in the former of the judgement stroke: a symbol which marks those propositions which are being asserted , that is, which are being used to express judgements . There has been considerable controversy regarding both the exact purpose of the judgement stroke, and whether a system of logic should include such a symbol. This paper explains the intended role of the (...)
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  • The Ways of Hilbert's Axiomatics: Structural and Formal.Wilfried Sieg - 2014 - Perspectives on Science 22 (1):133-157.
    It is a remarkable fact that Hilbert's programmatic papers from the 1920s still shape, almost exclusively, the standard contemporary perspective of his views concerning (the foundations of) mathematics; even his own, quite different work on the foundations of geometry and arithmetic from the late 1890s is often understood from that vantage point. My essay pursues one main goal, namely, to contrast Hilbert's formal axiomatic method from the early 1920s with his existential axiomatic approach from the 1890s. Such a contrast illuminates (...)
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  • Intuition and the Substitution Argument.Richard G. Heck - 2014 - Analytic Philosophy 55 (1):1-30.
    The 'substitution argument' purports to demonstrate the falsity of Russellian accounts of belief-ascription by observing that, e.g., these two sentences: (LC) Lois believes that Clark can fly. (LS) Lois believes that Superman can fly. could have different truth-values. But what is the basis for that claim? It seems widely to be supposed, especially by Russellians, that it is simply an 'intuition', one that could then be 'explained away'. And this supposition plays an especially important role in Jennifer Saul's defense of (...)
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  • Frege, hilbert, and the conceptual structure of model theory.William Demopoulos - 1994 - History and Philosophy of Logic 15 (2):211-225.
    This paper attempts to confine the preconceptions that prevented Frege from appreciating Hilbert?s Grundlagen der Geometrie to two: (i) Frege?s reliance on what, following Wilfrid Hodges, I call a Frege?Peano language, and (ii) Frege?s view that the sense of an expression wholly determines its reference.I argue that these two preconceptions prevented Frege from achieving the conceptual structure of model theory, whereas Hilbert, at least in his practice, was quite close to the model?theoretic point of view.Moreover, the issues that divided Frege (...)
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  • Wittgenstein, Carnap and the new american Wittgensteinians.P. M. S. Hacker - 2003 - Philosophical Quarterly 53 (210):01–23.
    James Conant, a proponent of the ‘New American Wittgenstein’, has argued that the standard inter- pretation of Wittgenstein is wholly mistaken in respect of Wittgenstein’s critique of metaphysics and the attendant conception of nonsense. The standard interpretation, Conant holds, misascribes to Wittgenstein Carnapian views on the illegitimacy of metaphysical utterances, on logical syntax and grammar, and on the nature of nonsense. Against this account, I argue that (i) Carnap is misrepresented; (ii) the so-called standard interpretation (in so far as I (...)
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  • Analysis and decomposition in Frege and Russell.James Levine - 2002 - Philosophical Quarterly 52 (207):195-216.
    Michael Dummett has long argued that Frege is committed to recognizing a distinction between two sorts of analysis of propositional contents: 'analysis', which reveals the entities that one must grasp in order to apprehend a given propositional content; and 'decomposition', which is used in recognizing the validity of certain inferences. Whereas any propositional content admits of a unique ultimate 'analysis' into simple constituents, it also admits of distinct 'decompositions', no one of which is ultimately privileged over the others. I argue (...)
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  • (1 other version)Singular Thought: In Defense of Acquaintance.François Recanati - 2010 - In Robin Jeshion (ed.), New Essays on Singular Thought. Oxford, GB: Oxford University Press. pp. 141.
    This paper is about the Descriptivism/Singularism debate, which has loomed large in 20-century philosophy of language and mind. My aim is to defend Singularism by showing, first, that it is a better and more promising view than even the most sophisticated versions of Descriptivism, and second, that the recent objections to Singularism (based on a dismissal of the acquaintance constraint on singular thought) miss their target.
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  • Propositional Attitudes in Modern Philosophy.Walter Ott - 2002 - Dialogue 41 (3):551-568.
    Philosophers of the modern period are often presented as having made an elementary error: that of confounding the attitude one adopts toward a proposition with its content. By examining the works of Locke and the Port-Royalians, I show that this accusation is ill-founded and that Locke, in particular, has the resources to construct a theory of propositional attitudes.
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  • The Functional Composition of Sense.Bryan Pickel - 2021 - Synthese 199 (3-4):6917-6942.
    A central dispute in understanding Frege’s philosophy concerns how the sense of a complex expression relates to the senses of its component expressions. According to one reading, the sense of a complex expression is a whole built from the senses of the component expressions. On this interpretation, Frege is an early proponent of structured propositions. A rival reading says that senses compose by functional application: the sense of a complex expression is the value of the function denoted by its functional (...)
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  • The functions of Russell’s no class theory.Kevin C. Klement - 2010 - Review of Symbolic Logic 3 (4):633-664.
    Certain commentators on Russell's “no class” theory, in which apparent reference to classes or sets is eliminated using higher-order quantification, including W. V. Quine and (recently) Scott Soames, have doubted its success, noting the obscurity of Russell’s understanding of so-called “propositional functions”. These critics allege that realist readings of propositional functions fail to avoid commitment to classes or sets (or something equally problematic), and that nominalist readings fail to meet the demands placed on classes by mathematics. I show that Russell (...)
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  • Identity theories of truth and the tractatus.Peter M. Sullivan - 2005 - Philosophical Investigations 28 (1):43–62.
    The paper is concerned with the idea that the world is the totality of facts, not of things – with what is involved in thinking of the world in that way, and why one might do so. It approaches this issue through a comparison between Wittgenstein’s Tractatus and the identity theory of truth proposed by Hornsby and McDowell.The paper’s positive conclusion is that there is a genuine affinity between these two. A negative contention is that the modern identity theory is (...)
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  • The Priority Principle from Kant to Frege.Jeremy Heis - 2013 - Noûs 48 (2):268-297.
    In a famous passage (A68/B93), Kant writes that “the understanding can make no other use of […] concepts than that of judging by means of them.” Kant's thought is often called the thesis of the priority of judgments over concepts. We find a similar sounding priority thesis in Frege: “it is one of the most important differences between my mode of interpretation and the Boolean mode […] that I do not proceed from concepts, but from judgments.” Many interpreters have thought (...)
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  • What is special about indexical attitudes?Matheus Valente - 2018 - Inquiry: An Interdisciplinary Journal of Philosophy 61 (7):692-712.
    In this paper, I assess whether indexical attitudes, e.g. beliefs and desires, have any special properties or present any special challenge to theories of propositional attitudes. I being by investigating the claim that allegedly problematic indexical cases are just instances of the familiar phenomenon of referential opacity. Regardless of endorsing that claim, I provide an argument to the effect that indexical attitudes do have a special property. My argument relies on the fact that one cannot account for what is it (...)
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  • In Defence of the Shareability of Fregean Self-Thought.Víctor M. Verdejo - 2019 - Acta Analytica 34 (3):281-299.
    Consider the Unshareability View, namely, the view that first person thought or self-thought—thought as typically expressed via the first person pronoun—is not shareable from subject to subject. In this article, I show that a significant number of Fregean and non-Fregean commentators of Frege have taken the Unshareability View to be the default Fregean position, rehearse Frege’s chief claims about self-thought and suggest that their combination entails the Unshareability View only on the assumption that there is a one-to-one correspondence between way (...)
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  • Frege, Dedekind, and the Origins of Logicism.Erich H. Reck - 2013 - History and Philosophy of Logic 34 (3):242-265.
    This paper has a two-fold objective: to provide a balanced, multi-faceted account of the origins of logicism; to rehabilitate Richard Dedekind as a main logicist. Logicism should be seen as more deeply rooted in the development of modern mathematics than typically assumed, and this becomes evident by reconsidering Dedekind's writings in relation to Frege's. Especially in its Dedekindian and Fregean versions, logicism constitutes the culmination of the rise of ?pure mathematics? in the nineteenth century; and this rise brought with it (...)
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  • The Reference Principle.Alex Oliver - 2005 - Analysis 65 (3):177-187.
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  • The concept horse with no name.Robert Trueman - 2015 - Philosophical Studies 172 (7):1889-1906.
    In this paper I argue that Frege’s concept horse paradox is not easily avoided. I do so without appealing to Wright’s Reference Principle. I then use this result to show that Hale and Wright’s recent attempts to avoid this paradox by rejecting or otherwise defanging the Reference Principle are unsuccessful.
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  • Belief and the Error Theory.Andrew T. Forcehimes & Robert B. Talisse - 2016 - Ethical Theory and Moral Practice 19 (4):849-856.
    A new kind of debate about the normative error theory has emerged. Whereas longstanding debates have fixed on the error theory’s plausibility, this new debate concerns the theory’s believability. Bart Streumer is the chief proponent of the error theory’s unbelievability. In this brief essay, we argue that Streumer’s argument prevails against extant critiques, and then press a criticism of our own.
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  • Russell's Paradox in Appendix B of the Principles of Mathematics : Was Frege's response adequate?Kevin C. Klement - 2001 - History and Philosophy of Logic 22 (1):13-28.
    In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy (...)
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  • Knowledge, Truth and Plausibility.Carlo Cellucci - 2014 - Axiomathes 24 (4):517-532.
    From antiquity several philosophers have claimed that the goal of natural science is truth. In particular, this is a basic tenet of contemporary scientific realism. However, all concepts of truth that have been put forward are inadequate to modern science because they do not provide a criterion of truth. This means that we will generally be unable to recognize a scientific truth when we reach it. As an alternative, this paper argues that the goal of natural science is plausibility and (...)
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  • Maddy On The Multiverse.Claudio Ternullo - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 43-78.
    Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...)
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  • Philosophy of mathematics: Making a fresh start.Carlo Cellucci - 2013 - Studies in History and Philosophy of Science Part A 44 (1):32-42.
    The paper distinguishes between two kinds of mathematics, natural mathematics which is a result of biological evolution and artificial mathematics which is a result of cultural evolution. On this basis, it outlines an approach to the philosophy of mathematics which involves a new treatment of the method of mathematics, the notion of demonstration, the questions of discovery and justification, the nature of mathematical objects, the character of mathematical definition, the role of intuition, the role of diagrams in mathematics, and the (...)
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  • Learning, prediction and causal Bayes nets.Clark Glymour - 2003 - Trends in Cognitive Sciences 7 (1):43-48.
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  • A Strengthening of the Caesar Problem.Joongol Kim - 2011 - Erkenntnis 75 (1):123-136.
    The neo-Fregeans have argued that definition by abstraction allows us to introduce abstract concepts such as direction and number in terms of equivalence relations such as parallelism between lines and one-one correspondence between concepts. This paper argues that definition by abstraction suffers from the fact that an equivalence relation may not be sufficient to determine a unique concept. Frege’s original verdict against definition by abstraction is thus reinstated.
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  • Grundlagen, Section 64: Frege's Discussion of Definitions by Abstraction in Historical Context.Paolo Mancosu - 2015 - History and Philosophy of Logic 36 (1):62-89.
    I offer in this paper a contextual analysis of Frege's Grundlagen, section 64. It is surprising that with so much ink spilled on that section, the sources of Frege's discussion of definitions by abstraction have remained elusive. I hope to have filled this gap by providing textual evidence coming from, among other sources, Grassmann, Schlömilch, and the tradition of textbooks in geometry for secondary schools . In addition, I put Frege's considerations in the context of a widespread debate in Germany (...)
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  • Frege on definitions.Sanford Shieh - 2008 - Philosophy Compass 3 (5):992-1012.
    This article treats three aspects of Frege's discussions of definitions. First, I survey Frege's main criticisms of definitions in mathematics. Second, I consider Frege's apparent change of mind on the legitimacy of contextual definitions and its significance for recent neo-Fregean logicism. In the remainder of the article I discuss a critical question about the definitions on which Frege's proofs of the laws of arithmetic depend: do the logical structures of the definientia reflect the understanding of arithmetical terms prevailing prior to (...)
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  • Russell's 1903 - 1905 Anticipation of the Lambda Calculus.Kevin C. Klement - 2003 - History and Philosophy of Logic 24 (1):15-37.
    It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church's “lambda calculus” for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts written by Russell between 1903–1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the lambda calculus. Russell also anticipated Schönfinkel's combinatory logic approach of treating multiargument functions as functions having other functions as value. (...)
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