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The Principles of Mathematics

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  1. Roy Weintraub's Studies in Appraisal: Lakatosian Consolations or Something Else?: Andrea Salanti.Andrea Salanti - 1991 - Economics and Philosophy 7 (2):221-234.
    As made manifest by Clower's comments on their “science fiction” nature, general equilibrium theories present such peculiar and puzzling features that the methodologist must perforce seek some specific methodological accommodation for this part of economic theory. The role played by such theories in contemporary economics is so fundamental that the impossibility of appraising them by means of any version of falsificationism, and their patent lack of empirical content if approached with the conceptual devices of the methodology of scientific research programs, (...)
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  • Bolzano and the Analytical Tradition.Sandra Lapointe - 2014 - Philosophy Compass 9 (2):96-111.
    In the course of the last few decades, Bolzano has emerged as an important player in accounts of the history of philosophy. This should be no surprise. Few authors stand at a more central junction in the development of modern thought. Bolzano's contributions to logic and the theory of knowledge alone straddle three of the most important philosophical traditions of the 19th and 20th centuries: the Kantian school, the early phenomenological movement and what has come to be known as analytical (...)
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  • The Metaphysics of Quantity.Brent Mundy - 1987 - Philosophical Studies 51 (1):29 - 54.
    A formal theory of quantity T Q is presented which is realist, Platonist, and syntactically second-order (while logically elementary), in contrast with the existing formal theories of quantity developed within the theory of measurement, which are empiricist, nominalist, and syntactically first-order (while logically non-elementary). T Q is shown to be formally and empirically adequate as a theory of quantity, and is argued to be scientifically superior to the existing first-order theories of quantity in that it does not depend upon empirically (...)
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  • On the Relationship Between Plane and Solid Geometry.Andrew Arana & Paolo Mancosu - 2012 - Review of Symbolic Logic 5 (2):294-353.
    Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned areas.
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  • The Metaphysics of Words.Roy Sorensen - 1996 - Philosophical Studies 81 (2-3):193 - 214.
    Semantic indeterminacy is the ether of philosophy of language. It fills the interstices of our intentions and pervades accounts of presupposition, tense, fiction, translation, and especially, vagueness. Yet semantic indeterminacy is as impossible as ectoplasm. Indeed, more so! The demonstration need only borrow a few assumptions used elsewhere in widely accepted impossibility results. Since an impossibility is never a necessary condition for anything actual, semantic indeterminacy must be superfluous. Language is no more explained by semantic indeterminacy than calculus is explained (...)
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  • On Language and the Passage of Time.Ned Markosian - 1992 - Philosophical Studies 66 (1):1 - 26.
    Since the early part of this century there has been a considerable amount of discussion of the question 'Does time pass?'. A useful way of approaching the debate over the passage of time is to consider the following thesis: The space-time thesis (SPT): Time is similar to the dimensions of space in at least this one respect: there is no set of properties such that (i) these properties are possessed by time, (ii) these properties are not possessed by any dimension (...)
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  • Cartwright on Laws and Composition.David Spurrett - 2000 - International Studies in the Philosophy of Science 15 (3):253 – 268.
    Cartwright attempts to argue from an analysis of the composition of forces, and more generally the composition of laws, to the conclusion that laws must be regarded as false. A response to Cartwright is developed which contends that properly understood composition poses no threat to the truth of laws, even though agreeing with Cartwright that laws do not satisfy the "facticity" requirement. My analysis draws especially on the work of Creary, Bhaskar, Mill, and points towards a general rejection of Cartwright's (...)
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  • An Overview of Type Theories.Nino Guallart - 2015 - Axiomathes 25 (1):61-77.
    Pure type systems arise as a generalisation of simply typed lambda calculus. The contemporary development of mathematics has renewed the interest in type theories, as they are not just the object of mere historical research, but have an active role in the development of computational science and core mathematics. It is worth exploring some of them in depth, particularly predicative Martin-Löf’s intuitionistic type theory and impredicative Coquand’s calculus of constructions. The logical and philosophical differences and similarities between them will be (...)
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  • A New Interpretation of the Representational Theory of Measurement.Conrad Heilmann - 2015 - Philosophy of Science 82 (5):787-797.
    On the received view, the Representational Theory of Measurement reduces measurement to the numerical representation of empirical relations. This account of measurement has been widely criticized. In this article, I provide a new interpretation of the Representational Theory of Measurement that sidesteps these debates. I propose to view the Representational Theory of Measurement as a library of theorems that investigate the numerical representability of qualitative relations. Such theorems are useful tools for concept formation that, in turn, is one crucial aspect (...)
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  • Relations and Truthmaking.Fraser MacBride - 2011 - Proceedings of the Aristotelian Society 111 (1pt1):161-179.
    Can Bradley's Regress be solved by positing relational tropes as truth-makers? No, no more than Russell's paradox can be solved by positing Fregean extensions. To call a trope relational is to pack into its essence the relating function it is supposed to perform but without explaining what Bradley's Regress calls into question, viz. the capacity of relations to relate. This problem has been masked from view by the (questionable) assumption that the only genuine ontological problems that can be intelligibly raised (...)
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  • How Wittgenstein Defeated Russell’s Multiple Relation Theory of Judgment.Peter W. Hanks - 2007 - Synthese 154 (1):121 - 146.
    In 1913 Wittgenstein raised an objection to Russell’s multiple relation theory of judgment that eventually led Russell to abandon his theory. As he put it in the Tractatus, the objection was that “the correct explanation of the form of the proposition, ‘A makes the judgement p’, must show that it is impossible for a judgement to be a piece of nonsense. (Russell’s theory does not satisfy this requirement,” (5.5422). This objection has been widely interpreted to concern type restrictions on the (...)
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  • The Content–Force Distinction.Peter W. Hanks - 2007 - Philosophical Studies 134 (2):141-164.
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  • The Causal Argument Against Component Forces.Jessica Wilson - 2009 - Dialectica 63 (4):525-554.
    Do component forces exist in conjoined circumstances? Cartwright (1980) says no; Creary (1981) says yes. I'm inclined towards Cartwright's side in this matter, but find several problems with her argumentation. My primary aim here is to present a better, distinctly causal, argument against component forces: very roughly, I argue that the joint posit of component and resultant forces in conjoined circumstances gives rise to a threat of causal overdetermination, avoidance of which best proceeds via eliminativism about component forces. A secondary (...)
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  • Universals.Chad Carmichael - 2010 - Philosophical Studies 150 (3):373-389.
    In this paper, I argue that there are universals. I begin (Sect. 1) by proposing a sufficient condition for a thing’s being a universal. I then argue (Sect. 2) that some truths exist necessarily. Finally, I argue (Sects. 3 and 4) that these truths are structured entities having constituents that meet the proposed sufficient condition for being universals.
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  • To Be is to Be the Object of a Possible Act of Choice.Massimiliano Carrara & Enrico Martino - 2010 - Studia Logica 96 (2):289-313.
    Aim of the paper is to revise Boolos’ reinterpretation of second-order monadic logic in terms of plural quantification ([4], [5]) and expand it to full second order logic. Introducing the idealization of plural acts of choice, performed by a suitable team of agents, we will develop a notion of plural reference . Plural quantification will be then explained in terms of plural reference. As an application, we will sketch a structuralist reconstruction of second-order arithmetic based on the axiom of infinite (...)
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  • Specifying Desires.Delia Graff Fara - 2013 - Noûs 47 (2):250-272.
    A report of a person's desire can be true even if its embedded clause underspecifies the content of the desire that makes the report true. It is true that Fiona wants to catch a fish even if she has no desire that is satisfied if she catches a poisoned minnow. Her desire is satisfied only if she catches an edible, meal-sized fish. The content of her desire is more specific than the propositional content of the embedded clause in our true (...)
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  • Higher‐Level Plurals Versus Articulated Reference, and an Elaboration of Salva Veritate.Hanoch Ben-Yami - 2013 - Dialectica 67 (1):81-102.
    In recent literature on plurals the claim has often been made that the move from singular to plural expressions can be iterated, generating what are occasionally called higher-level plurals or superplurals, often correlated with superplural predicates. I argue that the idea that the singular-to-plural move can be iterated is questionable. I then show that the examples and arguments intended to establish that some expressions of natural language are in some sense higher-level plurals fail. Next, I argue that these and some (...)
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  • What is a Situation?Tom Burke - 2000 - History and Philosophy of Logic 21 (2):95-113.
    This paper examines the role of ?situations? in John Dewey's philosophy of logic. To do this properly it is necessary to contrast Dewey's conception of experience and mentality with views characteristic of modern epistemology. The primary difference is that, rather than treat experience as peripheral and or external to mental functions (reason, etc.), we should treat experience as a field in and as a part of which thinking takes place. Experience in this broad sense subsumes theory and fact, hypothesis and (...)
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  • What is the Problem of Non-Existence?Tim Crane - 2012 - Philosophia 40 (3):417-434.
    It is widely held that there is a problem of talking about or otherwise representing things that not exist. But what exactly is this problem? This paper presents a formulation of the problem in terms of the conflict between the fact that there are truths about non-existent things and the fact that truths must be answerable to reality, how things are. Given this, the problem of singular negative existential statements is no longer the central or most difficult aspect of the (...)
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  • How May the Propositional Calculus Represent?Tristan Haze - 2017 - South American Journal of Logic 3 (1):173-184.
    This paper is a conceptual study in the philosophy of logic. The question considered is 'How may formulae of the propositional calculus be brought into a representational relation to the world?'. Four approaches are distinguished: (1) the denotational approach, (2) the abbreviational approach, (3) the truth-conditional approach, and (4) the modelling approach. (2) and (3) are very familiar, so I do not discuss them. (1), which is now largely obsolete, led to some interesting twists and turns in early analytic philosophy (...)
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  • Response to Westerstahl.Hanoch Ben-Yami - 2012 - Logique Et Analyse 55 (217):47-55.
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  • Quantification and Contributing Objects to Thoughts.Michael Glanzberg - 2008 - Noûs 42 (1):207 - 231.
    In this paper, I shall explore a determiner in natural language which is ambivalent as to whether it should be classified as quantificational or objectdenoting: the determiner both. Both in many ways appears to be a paradigmatic quantifier; and yet, I shall argue, it can be interpreted as having an individual—an object—as semantic value. To show the significance of this, I shall discuss two ways of thinking about quantifiers. We often think about quantifiers via intuitions about kinds of thoughts. Certain (...)
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  • Abstraction in Computer Science.Timothy Colburn & Gary Shute - 2007 - Minds and Machines 17 (2):169-184.
    We characterize abstraction in computer science by first comparing the fundamental nature of computer science with that of its cousin mathematics. We consider their primary products, use of formalism, and abstraction objectives, and find that the two disciplines are sharply distinguished. Mathematics, being primarily concerned with developing inference structures, has information neglect as its abstraction objective. Computer science, being primarily concerned with developing interaction patterns, has information hiding as its abstraction objective. We show that abstraction through information hiding is a (...)
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  • Grandeurs, vecteurs et relations chez Russell (1897-1903).Sébastien Gandon - 2006 - Philosophiques 33 (2):333-361.
    La théorie russellienne des relations est ordinairement conçue comme le résultat d'une réflexion logique et ontologique sur l'ordre et l'asymétrie. Le présent article vise à présenter une autre généalogie, centrée sur les concepts de grandeur et de vecteur. Nous montrons en premier lieu que la thèse de l'irréductibilité des relations est avancée pour la première fois en 1897, à l'occasion d'une reformulation de la dialectique hégélienne de la quantité. Nous soulignons, en second lieu, que la notion de grandeur fait, autour (...)
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  • Old and New Problems in Philosophy of Measurement.Eran Tal - 2013 - Philosophy Compass 8 (12):1159-1173.
    The philosophy of measurement studies the conceptual, ontological, epistemic, and technological conditions that make measurement possible and reliable. A new wave of philosophical scholarship has emerged in the last decade that emphasizes the material and historical dimensions of measurement and the relationships between measurement and theoretical modeling. This essay surveys these developments and contrasts them with earlier work on the semantics of quantity terms and the representational character of measurement. The conclusions highlight four characteristics of the emerging research program in (...)
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  • No Lacuna and No Vicious Regress: A Reply to le Poidevin.Christina Conroy - 2008 - Acta Analytica 23 (4):367-372.
    In his “Space, supervenience and substantivalism”, Le Poidevin proposes a substantivalism in which space is discrete, implying that there are unmediated spatial relations between neighboring primitive points. This proposition is motivated by his concern that relationism suffers from an explanatory lacuna and that substantivalism gives rise to a vicious regress. Le Poidevin implicitly requires that the relationist be committed to the “only x and y ” principle regarding spatial relations. It is not obvious that the relationist is committed to this (...)
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  • The Metaphysics of Forces.Olivier Massin - 2009 - Dialectica 63 (4):555-589.
    This paper defends the view that Newtonian forces are real, symmetrical and non-causal relations. First, I argue that Newtonian forces are real; second, that they are relations; third, that they are symmetrical relations; fourth, that they are not species of causation. The overall picture is anti-Humean to the extent that it defends the existence of forces as external relations irreducible to spatio-temporal ones, but is still compatible with Humean approaches to causation (and others) since it denies that forces are a (...)
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  • The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper.John Corcoran & José Miguel Sagüillo - 2011 - History and Philosophy of Logic 32 (4):359 - 374.
    This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple (...)
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  • Panpsychism and Structural Realism.Godehard Brüntrup - 2011 - In Michael Blamauer (ed.), The Mental as Fundamental. New Perspectives on Panpsychism. pp. 15-35.
    Paper on structural realism and how its problems lend support to some kind of panpsychism.
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  • Institutional Objects, Reductionism and Theories of Persistence.Tobias Hansson Wahlberg - 2014 - Dialectica 68 (4):525-562.
    Can institutional objects be identified with physical objects that have been ascribed status functions, as advocated by John Searle in The Construction of Social Reality (1995)? The paper argues that the prospects of this identification hinge on how objects persist – i.e., whether they endure, perdure or exdure through time. This important connection between reductive identification and mode of persistence has been largely ignored in the literature on social ontology thus far.
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  • A Note on Binary Inductive Logic.C. J. Nix & J. B. Paris - 2007 - Journal of Philosophical Logic 36 (6):735-771.
    We consider the problem of induction over languages containing binary relations and outline a way of interpreting and constructing a class of probability functions on the sentences of such a language. Some principles of inductive reasoning satisfied by these probability functions are discussed, leading in turn to a representation theorem for a more general class of probability functions satisfying these principles.
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  • Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics.Vladimir Kanovei, Mikhail G. Katz & Thomas Mormann - 2013 - Foundations of Science 18 (2):259-296.
    We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...)
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  • Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes From Berkeley toRussell to Beyond. [REVIEW]Mikhail G. Katz & David Sherry - 2013 - Erkenntnis 78 (3):571-625.
    Many historians of the calculus deny significant continuity between infinitesimal calculus of the seventeenth century and twentieth century developments such as Robinson’s theory. Robinson’s hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, (...)
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  • Ten Misconceptions From the History of Analysis and Their Debunking.Piotr Błaszczyk, Mikhail G. Katz & David Sherry - 2013 - Foundations of Science 18 (1):43-74.
    The widespread idea that infinitesimals were “eliminated” by the “great triumvirate” of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum (...)
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  • The Concept of Relevance and the Logic Diagram Tradition.Jan Dejnožka - 2010 - Logica Universalis 4 (1):67-135.
    What is logical relevance? Anderson and Belnap say that the “modern classical tradition [,] stemming from Frege and Whitehead-Russell, gave no consideration whatsoever to the classical notion of relevance.” But just what is this classical notion? I argue that the relevance tradition is implicitly most deeply concerned with the containment of truth-grounds, less deeply with the containment of classes, and least of all with variable sharing in the Anderson–Belnap manner. Thus modern classical logicians such as Peirce, Frege, Russell, Wittgenstein, and (...)
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  • Kant on Intentionality, Magnitude, and the Unity of Perception.Sacha Golob - 2014 - European Journal of Philosophy 22 (4):505-528.
    This paper addresses a number of closely related questions concerning Kant's model of intentionality, and his conceptions of unity and of magnitude [Gröβe]. These questions are important because they shed light on three issues which are central to the Critical system, and which connect directly to the recent analytic literature on perception: the issues are conceptualism, the status of the imagination, and perceptual atomism. In Section 1, I provide a sketch of the exegetical and philosophical problems raised by Kant's views (...)
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  • Who Gave You the Cauchy–Weierstrass Tale? The Dual History of Rigorous Calculus.Alexandre Borovik & Mikhail G. Katz - 2012 - Foundations of Science 17 (3):245-276.
    Cauchy’s contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the basis of the epsilon-delta doctrine in the context of an Archimedean continuum. What does one see if one refrains from viewing Cauchy as if he had read Weierstrass already? One sees, with Felix Klein, a parallel thread for the development of analysis, in the context of an infinitesimal-enriched continuum. One sees, with Emile Borel, (...)
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  • Deep Platonism.Chad Carmichael - 2016 - Philosophy and Phenomenological Research 92 (2):307-328.
    According to the traditional bundle theory, particulars are bundles of compresent universals. I think we should reject the bundle theory for a variety of reasons. But I will argue for the thesis at the core of the bundle theory: that all the facts about particulars are grounded in facts about universals. I begin by showing how to meet the main objection to this thesis (which is also the main objection to the bundle theory): that it is inconsistent with the possibility (...)
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  • Judgment and the Identity Theory of Truth.Colin Johnston - 2013 - Philosophical Studies 166 (2):381-397.
    The identity theory of truth takes on different forms depending on whether it is combined with a dual relation or a multiple relation theory of judgment. This paper argues that there are two significant problems for the dual relation identity theorist regarding thought’s answerability to reality, neither of which takes a grip on the multiple relation identity theory.
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  • Seeing the Anger in Someone's Face.Rowland Stout - 2010 - Aristotelian Society Supplementary Volume 84 (1):29-43.
    Starting from the assumption that one can literally perceive someone's anger in their face, I argue that this would not be possible if what is perceived is a static facial signature of their anger. There is a product–process distinction in talk of facial expression, and I argue that one can see anger in someone's facial expression only if this is understood to be a process rather than a product.
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  • Reply to Gregory Landini’s Review of Formal Ontology and Conceptual Realism.Nino B. Cocchiarella - 2009 - Axiomathes 19 (2):143-153.
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  • Hilbert, Logicism, and Mathematical Existence.José Ferreirós - 2009 - Synthese 170 (1):33 - 70.
    David Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here. I consider strong evidence for the fact that Hilbert was a logicist at that time, following upon Dedekind’s footsteps in his understanding of pure mathematics. This insight makes it possible to throw new light on the evolution of Hilbert’s foundational ideas, including his early contributions to the foundations of geometry and the real number system. The context of Dedekind-style logicism makes it possible to offer a new (...)
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  • A Remark on Collective Quantification.Juha Kontinen & Jakub Szymanik - 2008 - Journal of Logic, Language and Information 17 (2):131-140.
    We consider collective quantification in natural language. For many years the common strategy in formalizing collective quantification has been to define the meanings of collective determiners, quantifying over collections, using certain type-shifting operations. These type-shifting operations, i.e., lifts, define the collective interpretations of determiners systematically from the standard meanings of quantifiers. All the lifts considered in the literature turn out to be definable in second-order logic. We argue that second-order definable quantifiers are probably not expressive enough to formalize all collective (...)
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  • A Closer Look at Manifest Consequence.Max Weiss - 2014 - Journal of Philosophical Logic 43 (2-3):471-498.
    Fine (2007) argues that Frege’s puzzle and its relatives demonstrate a need for a basic reorientation of the field of semantics. According to this reorientation, the domain of semantic facts would be closed not under the classical consequence relation but only under a stronger relation Fine calls “manifest consequence.” I examine Fine’s informally sketched analyses of manifest consequence, showing that each can be amended to determine a class of strong consequence relations. A best candidate relation emerges from each of the (...)
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  • Philosophy, Thought and Language.Hans-Johann Glock - 1997 - Royal Institute of Philosophy Supplement 42:151-.
    One of the most striking features of twentieth-century philosophy has been its obsession with language. For the most part, this phenomenon is greeted with hostile incredulity by external observers. Surely, they say, if philosophy is the profound and fundamental discipline which it has purported to be for more than two millennia, it must deal with something more serious than mere words, namely the things they stand for, and ultimately the essence of reality or of the human mind.
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  • Zeno's Arrow and the Significance of the Present.Robin LePoidevin - 2002 - Royal Institute of Philosophy Supplement 50:57-.
    Perhaps the real paradox of Zeno's Arrow is that, although entirely stationary, it has, against all odds, successfully traversed over two millennia of human thought to trouble successive generations of philosophers. The prospects were not good: few original Zenonian fragments survive, and our access to the paradoxes has been for the most part through unsympathetic commentaries. Moreover, like its sister paradoxes of motion, the Arrow has repeatedly been dismissed as specious and easily dissolved. Even those commentators who have taken it (...)
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  • Conceptual Realism Versus Quine on Classes and Higher-Order Logic.Nino B. Cocchiarella - 1992 - Synthese 90 (3):379 - 436.
    The problematic features of Quine's set theories NF and ML are a result of his replacing the higher-order predicate logic of type theory by a first-order logic of membership, and can be resolved by returning to a second-order logic of predication with nominalized predicates as abstract singular terms. We adopt a modified Fregean position called conceptual realism in which the concepts (unsaturated cognitive structures) that predicates stand for are distinguished from the extensions (or intensions) that their nominalizations denote as singular (...)
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  • Mathematical, Philosophical and Semantic Considerations on Infinity : General Concepts.José-Luis Usó-Doménech, Josué Antonio Nescolarde Selva & Mónica Belmonte Requena - 2016 - Foundations of Science 21 (4):615-630.
    In the Reality we know, we cannot say if something is infinite whether we are doing Physics, Biology, Sociology or Economics. This means we have to be careful using this concept. Infinite structures do not exist in the physical world as far as we know. So what do mathematicians mean when they assert the existence of ω? There is no universally accepted philosophy of mathematics but the most common belief is that mathematics touches on another worldly absolute truth. Many mathematicians (...)
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  • Predicativity, the Russell-Myhill Paradox, and Church’s Intensional Logic.Sean Walsh - 2016 - Journal of Philosophical Logic 45 (3):277-326.
    This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model other axioms (...)
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  • Wittgenstein’s Philosophy of Arithmetic.Marc A. Joseph - 1998 - Dialogue 37 (1):83-.
    It is argued that the finitist interpretation of wittgenstein fails to take seriously his claim that philosophy is a descriptive activity. Wittgenstein's concentration on relatively simple mathematical examples is not to be explained in terms of finitism, But rather in terms of the fact that with them the central philosophical task of a clear 'ubersicht' of its subject matter is more tractable than with more complex mathematics. Other aspects of wittgenstein's philosophy of mathematics are touched on: his view that mathematical (...)
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