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Bemerkungen über die Grundlagen der Mathematik

Frankfurt am Main,: Suhrkamp (1974)

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  1. Feng Ye. Strict Finitism and the Logic of Mathematical Applications.Nigel Vinckier & Jean Paul Van Bendegem - 2016 - Philosophia Mathematica 24 (2):247-256.
  • Mathematical Intuition and Natural Numbers: A Critical Discussion.Felix Mühlhölzer - 2010 - Erkenntnis 73 (2):265-292.
    Charles Parsons’ book “Mathematical Thought and Its Objects” of 2008 (Cambridge University Press, New York) is critically discussed by concentrating on one of Parsons’ main themes: the role of intuition in our understanding of arithmetic (“intuition” in the specific sense of Kant and Hilbert). Parsons argues for a version of structuralism which is restricted by the condition that some paradigmatic structure should be presented that makes clear the actual existence of structures of the necessary sort. Parsons’ paradigmatic structure is the (...)
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  • Prediction and Novel Facts in the Methodology of Scientific Research Programs.Wenceslao J. Gonzalez - 2015 - In Philosophico-Methodological Analysis of Prediction and its Role in Economics. Cham: Imprint: Springer. pp. 103-124.
    In the methodology of scientific research programs (MSRP) there are important features on the problem of prediction, especially regarding novel facts. In his approach, Imre Lakatos proposed three different levels on prediction: aim, process, and assessment. Chapter 5 pays attention to the characterization of prediction in the methodology of research programs. Thus, it takes into account several features: (1) its pragmatic characterization, (2) the logical perspective as a proposition, (3) the epistemological component, (4) its role in the appraisal of research (...)
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  • Enciclopédia de Termos Lógico-Filosóficos.João Miguel Biscaia Branquinho, Desidério Murcho & Nelson Gonçalves Gomes (eds.) - 2006 - São Paulo, SP, Brasil: Martins Fontes.
    Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...)
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  • Hinter das Bewusstsein zurück: Implizites Wissen als Ansatzpunkt der Sozialontologie.Stephan Zimmermann - 2020 - Deutsche Zeitschrift für Philosophie 68 (6):848-866.
    The state of recent as well as older research on social ontology suggests a paradigmatic approach, according to which it is our consciousness that must provide the framework for conceptualising the social. I, however, argue that Wittgenstein’s treatment of rule-following opens up a new horizon for the ontology of the social. The fact that the rules of our language are social in nature and that we need not be aware of them in order to follow them shifts the problem to (...)
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  • Intuitionistic mathematics and wittgenstein.Wenceslao J. Gonzalez - 1991 - History and Philosophy of Logic 12 (2):167-183.
    The relation between Wittgenstein's philosophy of mathematics and mathematical Intuitionism has raised a considerable debate. My attempt is to analyse if there is a commitment in Wittgenstein to themes characteristic of the intuitionist movement in Mathematics and if that commitment is one important strain that runs through his Remarks on the foundations of mathematics. The intuitionistic themes to analyse in his philosophy of mathematics are: firstly, his attacks on the unrestricted use of the Law of Excluded Middle; secondly, his distrust (...)
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  • Selbsterkenntnis und Lebensform: Kritische Subjektivität nach Wittgenstein Und Foucault.Jörg Volbers - 2009 - Transcript Verlag. Edited by Jörg Volbers.
    Die sprachliche und soziale Natur der Erkenntnis ist eine Grundeinsicht der Moderne. Doch welchen Spielraum lässt sie noch der Kritik, der distanzierten Prüfung der eigenen Sprache und Lebensform? Vor dem Hintergrund des Werkes Stanley Cavells fragt dieses Buch nach dem Verhältnis von Lebensform und Selbsterkenntnis. In ungewohnter Weise liest es Wittgenstein und Foucault als komplementäre Antwortstrategien auf dieses Grundproblem: Philosophie muss als eine »Arbeit an sich« (Wittgenstein), als körperliche »Selbsttechnik« (Foucault) verstanden werden. Nicht ethische Programmatik, so kann gezeigt werden, sondern (...)
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  • Wittgenstein et l’«arrière-plan» de l’intentionnalité.Denis Sauvé - 2009 - Dialogue 48 (2):313.
    RÉSUMÉ : John Searle, Hubert Dreyfus et Charles Taylor défendent la thèse voulant qu’il y ait des formes de «compréhension» ou de «savoir» qui, contrairement aux formes courantes, ne sont pas de nature représentationnelle ou conceptuelle mais sont plutôt du type des «savoir-faire». Cet article examine l’argument avancé en faveur de cette thèse ainsi que l’affirmation de ces auteurs suivant laquelle les Recherches philosophiques de Wittgenstein démontrent que celui-ci, au moins implicitement, l’acceptait. Les conclusions qui découlent de cet examen sont, (...)
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  • The "natural" and the "formal".Jaroslav Peregrin - 2000 - Journal of Philosophical Logic 29 (1):75-101.
    The paper presents an argument against a "metaphysical" conception of logic according to which logic spells out a specific kind of mathematical structure that is somehow inherently related to our factual reasoning. In contrast, it is argued that it is always an empirical question as to whether a given mathematical structure really does captures a principle of reasoning. (More generally, it is argued that it is not meaningful to replace an empirical investigation of a thing by an investigation of its (...)
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  • Meaning as an inferential role.Jaroslav Peregrin - 2006 - Erkenntnis 64 (1):1-35.
    While according to the inferentialists, meaning is always a kind of inferential role, proponents of other approaches to semantics often doubt that actual meanings, as they see them, can be generally reduced to inferential roles. In this paper we propose a formal framework for considering the hypothesis of the.
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  • Logic and Natural Selection.Jaroslav Peregrin - 2010 - Logica Universalis 4 (2):207-223.
    Is logic, feasibly, a product of natural selection? In this paper we treat this question as dependent upon the prior question of where logic is founded. After excluding other possibilities, we conclude that logic resides in our language, in the shape of inferential rules governing the logical vocabulary of the language. This means that knowledge of (the laws of) logic is inseparable from the possession of the logical constants they govern. In this sense, logic may be seen as a product (...)
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  • Interpreting formal logic.Jaroslav Peregrin - 1994 - Erkenntnis 40 (1):5 - 20.
    The concept ofsemantic interpretation is a source of chronic confusion: the introduction of a notion ofinterpretation can be the result of several quite different kinds of considerations.Interpretation can be understood in at least three ways: as a process of dis-abstraction of formulas, as technical tool for the sake of characterizing truth, or as a reconstruction of meaning-assignment. However essentially different these motifs are and however properly they must be kept apart, these can all be brought to one and the same (...)
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  • Doing Worlds with Words: Formal Semantics Without Formal Metaphysics.Jaroslav Peregrin - 1995 - Dordrecht, Netherland: Springer.
    Doing Worlds with Words throws light on the problem of meaning as the meeting point of linguistics, logic and philosophy, and critically assesses the possibilities and limitations of elucidating the nature of meaning by means of formal logic, model theory and model-theoretical semantics. The main thrust of the book is to show that it is misguided to understand model theory metaphysically and so to try to base formal semantics on something like formal metaphysics; rather, the book states that model theory (...)
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  • Brandom’s Incompatibility Semantics.Jaroslav Peregrin - 2008 - Philosophical Topics 36 (2):99-121.
    Formal semantics is an enterprise which accounts for meaning in formal, mathematical terms, in the expectation of providing a helpful explication1 of the concept of the meaning of specific word kinds (such as logical ones), or of words and expressions generally. Its roots go back to Frege, who proposed exempting concepts, meanings of predicative expressions, from the legislation of psychology and relocating them under that of mathematics. This started a spectacular enterprise, fostered at first within formal logic and later moving (...)
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  • Beim sternenlicht der nichtexistierenden.J. C. Nyíri - 1974 - Inquiry: An Interdisciplinary Journal of Philosophy 17 (1-4):399-443.
    Der Aufsatz schildert den platonisierenden Antipsychologismus welchen Bolzano, der junge Brentano, Twardowski, Meinong, der Husserl der Logischen Untersuchungen, Frege, der Russell der Jahrhundertwende und der junge Wittgenstein philosophisch vertraten, und versucht eine soziologische und ideologiekritische Interpretation sowohl dieser Einstellung als auch derjenigen des traditionellen Psychologismus des achtzehnten Jahrhunderts. Der Platonismus des neunzehnten und zwanzigsten Jahrhunderts wird als ein Ausdruck fiir ? oder vielmehr als eine Reaktion gegen ? den Verfall der klassischen burgerlichen Werte aufgefaBt. In Wittgensteins Tractatus spielen Elemente sowohl (...)
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  • Continuum, name and paradox.Vojtěch Kolman - 2010 - Synthese 175 (3):351 - 367.
    The article deals with Cantor's argument for the non-denumerability of reals somewhat in the spirit of Lakatos' logic of mathematical discovery. At the outset Cantor's proof is compared with some other famous proofs such as Dedekind's recursion theorem, showing that rather than usual proofs they are resolutions to do things differently. Based on this I argue that there are "ontologically" safer ways of developing the diagonal argument into a full-fledged theory of continuum, concluding eventually that famous semantic paradoxes based on (...)
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  • Boole and mill: differing perspectives on logical psychologism.John Richards - 1980 - History and Philosophy of Logic 1 (1-2):19-36.
    Logical psychologism is the position that logic is a special branch of psychology, that logical laws are descriptíons of experience to be arrived at through observation, and are a posteriori.The accepted arguments against logical psychologism are effective only when directed against this extreme version. However, the clauses in the above characterization are independent and ambiguous, and may be considered separately. This separation permits a reconsideration of less extreme attempts to tie logic to psychology, such as those defended by Mill and (...)
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  • Epistemic logicism & Russell's regressive method.A. D. Irvine - 1989 - Philosophical Studies 55 (3):303 - 327.
  • Frege on the psychological significance of definitions.John F. Horty - 1993 - Philosophical Studies 72 (2-3):223 - 263.
  • From Intelligence to Rationality of Minds and Machines in Contemporary Society: The Sciences of Design and the Role of Information.Wenceslao J. Gonzalez - 2017 - Minds and Machines 27 (3):397-424.
    The presence of intelligence and rationality in Artificial Intelligence and the Internet requires a new context of analysis in which Herbert Simon’s approach to the sciences of the artificial is surpassed in order to grasp the role of information in our contemporary setting. This new framework requires taking into account some relevant aspects. In the historical endeavor of building up AI and the Internet, minds and machines have interacted over the years and in many ways through the interrelation between scientific (...)
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  • Wittgenstein et le logicisme de Russell : Remarques critiques sur « A Mathematical Proof Must be Surveyable » de F. Mühlhölzer.Sébastien Gandon - 2012 - Philosophiques 39 (1):163-187.
    Ce texte discute certaines conclusions d’un article récent de F. Mülhölzer et vise à montrer que le logicisme russellien a les moyens de résister à la critique que Wittgenstein lui adresse dans la partie III des Remarques sur les fondements desmathématiques.This paper discusses some conclusions of a recent article from F.Mülhölzer. It aims at showing that Russell’s logicism has the means to overcome the criticisms Wittgenstein expounded in Remarks on the Foundations of Mathematics, part III.
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  • On the copernican turn in semantics.Cesare Cozzo - 2008 - Theoria 74 (4):295-317.
    Alberto Coffa used the phrase "the Copernican turn in semantics" to denote a revolutionary transformation of philosophical views about the connection between the meanings of words and the acceptability of sentences and arguments containing those words. According to the new conception resulting from the Copernican turn, here called "the Copernican view", rules of use are constitutive of the meanings of words. This view has been linked with two doctrines: (A) the instances of meaning-constitutive rules are analytically and a priori true (...)
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  • Cogency and Context.Cesare Cozzo - 2019 - Topoi 38 (3):505-516.
    The problem I address is: how are cogent inferences possible? In § 1 I distinguish three senses in which we say that one is “compelled” by an inference: automatic, seductive-rhetorical and epistemic compulsion. Cogency is epistemic compulsion: a cogent inference compels us to accept its conclusion, if we accept its premises and we aim at truth. In §§ 2–3 I argue that cogency is intelligible if we consider an inference as a compound linguistic act in which several component acts are (...)
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  • Causation.Lorenzo Casini - 2012 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 27 (2):203-219.
    How many notions of cause are there? The causality literature is witnessing a flourishing of pluralist positions. Here I focus on a recent debate on whether interpreting causality in terms of inferential relations commits one to semantic pluralism (Reiss 2011) or not (Williamson 2006). I argue that inferentialism is compatible with a ‘weak’ form of monism, where causality is envisaged as one, vague cluster concept. I offer two arguments for this, one for vagueness, one for uniqueness. Finally, I qualify in (...)
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  • John W. Dawson, Jr. Why Prove it Again: Alternative Proofs in Mathematical Practice.Jessica Carter - 2016 - Philosophia Mathematica 24 (2):256-263.
  • The transzendenz of mathematical 'experience'.William Boos - 1998 - Synthese 114 (1):49-98.
  • Consistency and konsistenz.William Boos - 1987 - Erkenntnis 26 (1):1 - 43.
    A ground-motive for this study of some historical and metaphysical implications of the diagonal lemmas of Cantor and Gödel is Cantor's insightful remark to Dedekind in 1899 that the Inbegriff alles Denkbaren (aggregate of everything thinkable) might, like some class-theoretic entities, be inkonsistent. In the essay's opening sections, I trace some recent antecedents of Cantor's observation in logical writings of Bolzano and Dedekind (more remote counterparts of his language appear in the First Critique), then attempt to relativize the notion of (...)
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  • Wittgenstein on Incompleteness Makes Paraconsistent Sense.Francesco Berto - 2008 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 257--276.
    I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...)
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  • Analytic feminism.Ann Garry - 2008 - Stanford Encyclopedia of Philosophy.
    Analytic feminists are philosophers who believe that both philosophy and feminism are well served by using some of the concepts, theories and methods of analytic philosophy modified by feminist values and insights. By using ‘ analytic feminist’ to characterize their style of feminist philosophizing, these philosophers acknowledge their dual feminist and analytic roots and their intention to participate in the ongoing conversations within both traditions. In addition, the use of ‘ analytic feminist’ attempts to rebut two frequently made presumptions: that (...)
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  • Freges Pragmatismus im Streit um den Begriff der Wahrheit.V. Kolman - 2005 - Philosophisches Jahrbuch 112 (2):292-310.
    Since the appearance of Dummett’s monumental monograph in the early seventies of the last century there have been two interpretative traditions of reading Frege, one contradicting the other: the platonistic (or realistic) interpretation and the holistic (rationalistic) one. In this article, as a kind of intermediation, I firstly point out some pragmatic aspects of Frege’s work. Secondly, and more ambitiously, I outline the controversy between the most influential theories of truth (the correspondence, coherence, redundancy and pragmatic theory) in the light (...)
     
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  • Observaciones críticas sobre cierta noción dizque hermenéutica de lo que es traducir.Miguel Ángel Quintana Paz - 2008 - Daimon: Revista Internacional de Filosofía:283-294.
    El artículo analiza hasta que punto puede equipararse la labor del traductor con la de realizar una interpretación de los textos sobre los que trabaja. Utilizaremos para ello instrumental tanto de la tradición de la filosofía hermenéutica (especialmente Hans-Georg Gadamer) como de la inspirada en la obra de Ludwig Wittgenstein. La conclusión intenta mostrar las fuertes diferencias que existen entre traducir e interpretar, y con ello entender mejor qué quiere decir realmente la idea de "universalidad hermenéutica" que funda la citada (...)
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  • Juicio no-racionalizado dentro del pensamiento racional.Mª Dolores García-Arnaldos - 2018 - Rivista Italiana di Filosofia del Linguaggio 12 (2):70-82.
    In this article, we consider Wittgenstein’s approach to non-inferential knowledge, its relation to special propositions, and the nature of the justification of these propositions. According to Wittgenstein, there is a kind of non-inferential knowledge whose rational status is not the result of basic beliefs (in a foundational sense) that justify it. In Wittgenstein’s rule-following analysis, Frege’s theory is criticized. This theory is based on the idea that having a conceptual repertoire prior to the understanding of any rule, requires having grasped (...)
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  • Cavell's Challenge. Cynicism and Moral Realism in Light of the Later Wittgenstein.Cecilie Eriksen - 2018 - Res Cogitans 13 (2).
    Legitimacy challenges are part of human societies. Whenever we recognise a person, law, ideal or institution as authoritative, questions can be raised about their legitimacy. Why follow this law? Why strive to honour this moral ideal? If such questions are repeatedly raised, they pose an undermining threat to the authorities in question. This is good if the challenged law or ideal is harmful, but problematic, if it is beneficial. Where the first kind of legitimacy challenges are raised by ethical pioneers (...)
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  • Jaroslav Peregrin.Jaroslav Peregrin - unknown
    The paper presents an argument against a "metaphysical'* conception of logic according to which logic spells out a specific kind of mathematical structure that is somehow inherently related to our factual reasoning. In contrast, it is argued that it is always an empirical question as to whether a given mathematical structure really does captures a principle of reasoning. lMore generally, it is argued that it is not meaningful to replace an empirical investigation of a thing by an investigation of its (...)
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  • Metaphysics as an attempt to have one's cake and eat it.Jaroslav Peregrin - manuscript
    Metaphysics is usually understood as the investigation of being qua being and of its ultimate categories. Given this characterization, it may be hard to grasp why anyone might wish to oppose metaphysics, why anyone might claim that metaphysics ”leads the philosopher into complete darkness” (Wittgenstein, 1958, p.18)? What could be so misleading about the investigation of the most abstract vestiges of being? One source of disparagement towards metaphysics, of course, stems from the relativist conviction that there is no absolute being, (...)
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  • Co je to (fregovská) logika?Jaroslav Peregrin - manuscript
    Filosofové odedávna snili o jazyce, který by byl z hlediska řešení těch problémů, se kterými se potýkají (případně všech lidských problémů vůbec), vhodnější než jazyk, jímž nás obdařila příroda. Mnozí z nich si představovali, že filosofické problémy vznikají zčásti nebo zcela v důsledku toho, že přirozený jazyk není dostatečně přesným prostředkem vyjádření našich idejí a myšlenek - a že by se tedy vše spravilo, kdyby byl k dispozici jazyk, jehož výrazivo by bylo s našim myšlením - případně s naším světem (...)
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  • Wittgenstein a pravidla našich jazykových her.Jaroslav Peregrin - unknown
    Abstrakt. Když se řekne Ludwig Wittgenstein, vybaví se člověku, který to jméno už někdy slyšel, nejspíše termín jazyková hra. Tento termín si Wittgenstein vybral, aby se v rámci své pozdní filosofie distancoval od určitého druhu názorů na jazyk (druhu, kterého byly i jeho vlastní ranější filosofické názory). Chtěl jeho pomocí zdůraznit různorodost lidských aktivit, které se opírají o jazyk. Avšak ač to Wittgenstein úplně explicitně neříká, zdá se mi že je tu něco podstatného, co je podle něj pro jazykové hry (...)
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  • Logical Rules and the a priori: Good and Bad Questions.Jaroslav Peregrin - 2007 - In Jean-Yves Béziau & Alexandre Costa-Leite (eds.), Perspectives on Universal Logic. pp. 111--122.