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  1. Die Verteidigung des Logizismus: Carnaps Versuch von 1930.Adrian Frey - 2012 - History of Philosophy & Logical Analysis 15 (1):417-438.
    According to Carnap an account of the nature of mathematics, both pure and applied, must include the thesis that mathematical truths are devoid of factual content. He first formulated this thesis around 1930 and in its defence attempted to combine the reduction of mathematics to logic undertaken in the Principia with Wittgenstein’s insights into the nature of logic. In this paper I will show that this synthesis faces serious difficulties. Thus, it plays, with good reason, no longer a role in (...)
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  • The Road to Modern Logic—An Interpretation.José Ferreirós - 2001 - Bulletin of Symbolic Logic 7 (4):441-484.
    This paper aims to outline an analysis and interpretation of the process that led to First-Order Logic and its consolidation as a core system of modern logic. We begin with an historical overview of landmarks along the road to modern logic, and proceed to a philosophical discussion casting doubt on the possibility of a purely rational justification of the actual delimitation of First-Order-Logic. On this basis, we advance the thesis that a certain historical tradition was essential to the emergence of (...)
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  • The Road to Modern Logic—An Interpretation.Jos\'E. Ferreir\'os - 2001 - Bulletin of Symbolic Logic 7 (4):441-484.
    This paper aims to outline an analysis and interpretation of the process that led to First-Order Logic and its consolidation as a core system of modern logic. We begin with an historical overview of landmarks along the road to modern logic, and proceed to a philosophical discussion casting doubt on the possibility of a purely rational justification of the actual delimitation of First-Order Logic. On this basis, we advance the thesis that a certain historical tradition was essential to the emergence (...)
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  • Learning Logical Tolerance: Hans Hahn on the Foundations of Mathematics.Thomas E. Uebel - 2005 - History and Philosophy of Logic 26 (3):175-209.
    Hans Hahn's long-neglected philosophy of mathematics is reconstructed here with an eye to his anticipation of the doctrine of logical pluralism. After establishing that Hahn pioneered a post-Tractarian conception of tautologies and attempted to overcome the traditional foundational dispute in mathematics, Hahn's and Carnap's work is briefly compared with Karl Menger's, and several significant agreements or differences between Hahn's and Carnap's work are specified and discussed.
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  • Logicism and Principle of Tolerance: Carnap’s Philosophy of Logic and Mathematics.Stefano Domingues Stival - 2023 - History and Philosophy of Logic 44 (4):491-504.
    In this paper, the connection between logicism and the principle of tolerance in Carnap’s philosophy of logic and mathematics is to be presented in terms of the history of its development. Such development is conditioned by two lines of criticism to Carnap’s attempt to combine Logicism and Conventionalism, the first of which comes from Gödel, the second from Alfred Tarski. The presentation will take place in three steps. First, the Logicism of Carnap before the publication of The Logical Syntax of (...)
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  • The Calculus of Higher-Level Rules, Propositional Quantification, and the Foundational Approach to Proof-Theoretic Harmony.Peter Schroeder-Heister - 2014 - Studia Logica 102 (6):1185-1216.
    We present our calculus of higher-level rules, extended with propositional quantification within rules. This makes it possible to present general schemas for introduction and elimination rules for arbitrary propositional operators and to define what it means that introductions and eliminations are in harmony with each other. This definition does not presuppose any logical system, but is formulated in terms of rules themselves. We therefore speak of a foundational account of proof-theoretic harmony. With every set of introduction rules a canonical elimination (...)
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  • Carnap's Untersuchungen: Logicism, Formal Axiomatics, and Metatheory.Georg Schiemer - 2012 - In R. Creath (ed.), Vienna Circle Institute Yearbook. Springer Verlag. pp. 13--36.
    This paper discusses Carnap’s attempts in the late 1920s to provide a formal reconstruction of modern axiomatics.1 One interpretive theme addressed in recent scholarly literature concerns Carnap’s underlying logicism in his philosophy of mathematics from that time, more specifically, his attempt to “reconcile” the logicist approach of reducing mathematics to logic with the formal axiomatic method. For instance, Awodey & Carus characterize Carnap’s manuscript Untersuchungen zur allgemeinen Axiomatik from 1928 as a “large-scale project to reconcile axiomatic definitions with logicism, and (...)
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  • Carnap’s Early Semantics.Georg Schiemer - 2013 - Erkenntnis 78 (3):487-522.
    This paper concerns Carnap’s early contributions to formal semantics in his work on general axiomatics between 1928 and 1936. Its main focus is on whether he held a variable domain conception of models. I argue that interpreting Carnap’s account in terms of a fixed domain approach fails to describe his premodern understanding of formal models. By drawing attention to the second part of Carnap’s unpublished manuscript Untersuchungen zur allgemeinen Axiomatik, an alternative interpretation of the notions ‘model’, ‘model extension’ and ‘submodel’ (...)
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  • “The boundless ocean of unlimited possibilities”: Logic in carnap'slogical syntax of language. [REVIEW]Sahotra Sarkar - 1992 - Synthese 93 (1-2):191 - 237.
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  • Carnap and the compulsions of interpretation: Reining in the liberalization of empiricism. [REVIEW]Sahotra Sarkar - 2013 - European Journal for Philosophy of Science 3 (3):353-372.
    Carnap’s work was instrumental to the liberalization of empiricism in the 1930s that transformed the logical positivism of the Vienna Circle to what came to be known as logical empiricism. A central feature of this liberalization was the deployment of the Principle of Tolerance, originally introduced in logic, but now invoked in an epistemological context in “Testability and Meaning”. Immediately afterwards, starting with Foundations of Logic and Mathematics, Carnap embraced semantics and turned to interpretation to guide the choice of a (...)
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  • Logic and science: science and logic.Marcus Rossberg & Stewart Shapiro - 2021 - Synthese 199 (3-4):6429-6454.
    According to Ole Hjortland, Timothy Williamson, Graham Priest, and others, anti-exceptionalism about logic is the view that logic “isn’t special”, but is continuous with the sciences. Logic is revisable, and its truths are neither analytic nor a priori. And logical theories are revised on the same grounds as scientific theories are. What isn’t special, we argue, is anti-exceptionalism about logic. Anti-exceptionalists disagree with one another regarding what logic and, indeed, anti-exceptionalism are, and they are at odds with naturalist philosophers of (...)
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  • Intensional Harmony as Isomorphism.Paolo Pistone & Luca Tranchini - 2024 - In Thomas Piecha & Kai F. Wehmeier (eds.), Peter Schroeder-Heister on Proof-Theoretic Semantics. Springer. pp. 315-337.
    In the present paper we discuss a recent suggestion of Schroeder-Heister concerning the possibility of defining an intensional notion of harmony using isomorphism in second-order propositional logic. The latter is not an absolute notion, but its definition is relative to the choice of criteria for identity of proofs. In the paper, it is argued that in order to attain a satisfactory account of harmony, one has to consider a notion of identity stronger than the usual one (based on β- and (...)
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  • Peter Schroeder-Heister on Proof-Theoretic Semantics.Thomas Piecha & Kai F. Wehmeier (eds.) - 2024 - Springer.
    This open access book is a superb collection of some fifteen chapters inspired by Schroeder-Heister's groundbreaking work, written by leading experts in the field, plus an extensive autobiography and comments on the various contributions by Schroeder-Heister himself. For several decades, Peter Schroeder-Heister has been a central figure in proof-theoretic semantics, a field of study situated at the interface of logic, theoretical computer science, natural-language semantics, and the philosophy of language. -/- The chapters of which this book is composed discuss the (...)
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  • A Note on Dummett and Frege on Sense‐Identity.Eva Picard - 1993 - European Journal of Philosophy 1 (1):69-80.
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  • Toward a Theory of the Pragmatic A Priori. From Carnap to Lewis and Beyond.Thomas Mormann - 2012 - Rudolf Carnap and the Legacy of Logical Empiricism 16:113 - 132.
    The aim of this paper is make a contribution to the ongoing search for an adequate concept of the a priori element in scientific knowledge. The point of departure is C.I. Lewis’s account of a pragmatic a priori put forward in his "Mind and the World Order" (1929). Recently, Hasok Chang in "Contingent Transcendental Arguments for Metaphysical Principles" (2008) reconsidered Lewis’s pragmatic a priori and proposed to conceive it as the basic ingredient of the dynamics of an embodied scientific reason. (...)
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  • El Tractatus al rescate de Principia Mathematica: Ramsey y los fundamentos logicistas de las matemáticas.Emilio Méndez Pinto - 2022 - Critica 54 (161):43-69.
    Mi objetivo es discutir las principales dificultades que Frank P. Ramsey encontró en Principia Mathematica y la solución que, vía el Tractatus Logico-Philosophicus, propuso al respecto. Sostengo que las principales dificultades que Ramsey encontró en Principia Mathematica están, todas, relacionadas con que Russell y Whitehead desatendieron la forma lógica de las proposiciones matemáticas, las cuales, según Ramsey, deben ser tautológicas.
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  • Vorurteile und Wahn im logisch-mathematischen Grundlagenstreit und Probleme empirischer Begründung.Werner Loh - 1984 - Zeitschrift Für Allgemeine Wissenschaftstheorie 15 (2):211-231.
    Der Titel dieses Aufsatzes mag zunächst befremden, gar als unsachliche Bösartigkeit aufgefaßt werden, doch „Vorurteil“ und „Wahn“ sind im Rahmen von Psychologie bzw. Sozialpsychologie und Psychopathologie definierte Begriffe. Untersucht man unter diesem Aspekt den mathematischen Grundlagenstreit in diesem Jahrhundert, der richtiger „logisch-mathematischer Grundlagenstreit“ zu nennen wäre, dann wird ein Argumentationsklima deutlich, das von Vorurteils- und Wahnstrukturen geprägt ist, das sich zu Ungungsten der empirisch orientierten Begründungsposition auswirkte. Sollte sich angesichts erneuter Stimmen für die empirische Position wieder eine Grundlagendiskussion entwickeln, wäre (...)
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  • Reasons and Causes in Psychiatry: Ideas from Donald Davidson’s Work.Elisabetta Lalumera - 2018 - In Annalisa Coliva, Paolo Leonardi & Sebastiano Moruzzi (eds.), Eva Picardi on Language, Analysis and History. Londra, Regno Unito: Palgrave. pp. 281-296.
    Though the divide between reason-based and causal-explanatory approaches in psychiatry and psychopathology is old and deeply rooted, current trends involving multi-factorial explanatory models and evidence-based approaches to interpersonal psychotherapy, show that it has already been implicitly bridged. These trends require a philosophical reconsideration of how reasons can be causes. This paper contributes to that trajectory by arguing that Donald Davidson’s classic paradigm of 1963 is still a valid option.
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  • A renaissance of empiricism in the recent philosophy of mathematics.Imre Lakatos - 1976 - British Journal for the Philosophy of Science 27 (3):201-223.
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  • Moderne Wissenschaft und moderne Dichtung Hermann Brochs Beitrag zur Beilegung der „Grundlagenkrise“ der Mathematik.Carsten Konnexer - 1999 - Deutsche Vierteljahrsschrift für Literaturwissenschaft Und Geistesgeschichte 73 (2):319-351.
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  • Dedekind's Logicism.Ansten Mørch Klev - 2015 - Philosophia Mathematica:nkv027.
    A detailed argument is provided for the thesis that Dedekind was a logicist about arithmetic. The rules of inference employed in Dedekind's construction of arithmetic are, by his lights, all purely logical in character, and the definitions are all explicit; even the definition of the natural numbers as the abstract type of simply infinite systems can be seen to be explicit. The primitive concepts of the construction are logical in their being intrinsically tied to the functioning of the understanding.
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  • Dedekind's Logicism†.Ansten Mørch Klev - 2015 - Philosophia Mathematica 25 (3):341-368.
    A detailed argument is provided for the thesis that Dedekind was a logicist about arithmetic. The rules of inference employed in Dedekind's construction of arithmetic are, by his lights, all purely logical in character, and the definitions are all explicit; even the definition of the natural numbers as the abstract type of simply infinite systems can be seen to be explicit. The primitive concepts of the construction are logical in their being intrinsically tied to the functioning of the understanding.
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  • Discussion on the foundation of mathematics.John W. Dawson - 1984 - History and Philosophy of Logic 5 (1):111-129.
    This article provides an English translation of a historic discussion on the foundations of mathematics, during which Kurt GÖdel first announced his incompleteness theorem to the mathematical world. The text of the discussion is preceded by brief background remarks and commentary.
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  • Epistemic logicism & Russell's regressive method.A. D. Irvine - 1989 - Philosophical Studies 55 (3):303 - 327.
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  • Benjamin Peirce's Linear Associative Algebra (1870): New light on its preparation and ‘publication’: In fond memory of Max H. Fisch.I. Grattan-Guinness - 1997 - Annals of Science 54 (6):597-606.
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  • Shaping the Enemy: Foundational Labelling by L.E.J. Brouwer and A. Heyting.Miriam Franchella - 2018 - History and Philosophy of Logic 40 (2):152-181.
    The use of the three labels to denote the three foundational schools of the early twentieth century are now part of literature. Yet, neither their number nor the...
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  • Carnap’s Defense of Impredicative Definitions.Vera Flocke - 2019 - Review of Symbolic Logic 12 (2):372-404.
    A definition of a property P is impredicative if it quantifies over a domain to which P belongs. Due to influential arguments by Ramsey and Gödel, impredicative mathematics is often thought to possess special metaphysical commitments. It seems that an impredicative definition of a property P does not have the intended meaning unless P already exists, suggesting that the existence of P cannot depend on its explicit definition. Carnap (1937 [1934], p. 164) argues, however, that accepting impredicative definitions amounts to (...)
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  • Predicativity and Feferman.Laura Crosilla - 2017 - In Gerhard Jäger & Wilfried Sieg (eds.), Feferman on Foundations: Logic, Mathematics, Philosophy. Cham: Springer. pp. 423-447.
    Predicativity is a notable example of fruitful interaction between philosophy and mathematical logic. It originated at the beginning of the 20th century from methodological and philosophical reflections on a changing concept of set. A clarification of this notion has prompted the development of fundamental new technical instruments, from Russell's type theory to an important chapter in proof theory, which saw the decisive involvement of Kreisel, Feferman and Schütte. The technical outcomes of predica-tivity have since taken a life of their own, (...)
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  • When Logic Meets Engineering: Introduction to Logical Issues in the History and Philosophy of Computer Science.Liesbeth De Mol & Giuseppe Primiero - 2015 - History and Philosophy of Logic 36 (3):195-204.
    The birth, growth, stabilization and subsequent understanding of a new field of practical and theoretical enquiry is always a conceptual process including several typologies of events, phenomena an...
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  • Popper’s Theory of World 3 and the Evolution of the Internet.Peter Backes - 2016 - Philosophy of the Social Sciences 46 (3):265-287.
    While developing his theory of world 3, Popper rejects two claims made by Plato: first, that the inhabitants of world 3, ideas, are a source of ultimate explanation, a divine revelation of truth, and second, that these ideas are unchanging. I will rehabilitate the second claim. Man does not construct world 3 by creating his theories, nor is it a source of ultimate truth. Instead, world 3 is discovered by man, and it destroys some of his theories: destructive Platonism. I (...)
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  • Carnap, completeness, and categoricity:The gabelbarkeitssatz OF 1928. [REVIEW]S. Awodey & A. W. Carus - 2001 - Erkenntnis 54 (2):145-172.
    In 1929 Carnap gave a paper in Prague on Investigations in General Axiomatics; a briefsummary was published soon after. Its subject lookssomething like early model theory, and the mainresult, called the Gabelbarkeitssatz, appears toclaim that a consistent set of axioms is complete justif it is categorical. This of course casts doubt onthe entire project. Though there is no furthermention of this theorem in Carnap''s publishedwritings, his Nachlass includes a largetypescript on the subject, Investigations inGeneral Axiomatics. We examine this work here,showing (...)
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  • Inquiries into Cognition: Wittgenstein’s Language-Games and Peirce’s Semeiosis for the Philosophy of Cognition.Andrey Pukhaev - 2013 - Dissertation, Gregorian University
    SUMMARY Major theories of philosophical psychology and philosophy of mind are examined on the basis of the fundamental questions of ontology, metaphysics, epistemology, semantics and logic. The result is the choice between language of eliminative reductionism and dualism, neither of which answers properly the relation between mind and body. In the search for a non–dualistic and non–reductive language, Wittgenstein’s notion of language–games as the representative links between language and the world is considered together with Peirce’s semeiosis of cognition. The result (...)
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  • Frank Plumpton Ramsey.Brad Armendt - 2005 - In Sahotra Sarkar & Jessica Pfeifer (eds.), The Philosophy of Science: An Encyclopedia. New York: Routledge. pp. 671-681.
    On the work of Frank Ramsey, emphasizing topics most relevant to philosophy of science.
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  • Plato's Problem: An Introduction to Mathematical Platonism.Marco Panza & Andrea Sereni - 2013 - New York: Palgrave-Macmillan. Edited by Andrea Sereni & Marco Panza.
    What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on (...)
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  • Der junge Carnap in historischem Kontext: 1918-1935 / Young Carnap in an Historical Context: 1918–1935.Christian Damböck & Gereon Wolters (eds.) - forthcoming - Springer.
    Im Zentrum dieses Bandes stehen die Beiträge einer Tagung, die im Oktober 2017 an der Universität Konstanz stattgefunden hat. Thema der Tagung war ein den historischen Kontext einbeziehender Blick auf den frühen Rudolf Carnap, vom Ende des Ersten Weltkriegs bis zur Emigration Ende 1935. Der 1891 in Ronsdorf bei Wuppertal geborene Rudolf Carnap entschloss sich erst relativ spät zu einer Karriere als akademischer Philosoph, nämlich 1920, nachdem er sein durch den Krieg unterbrochenes Studium der Physik und Philosophie in Jena und (...)
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  • Pasch's empiricism as methodological structuralism.Dirk Schlimm - 2020 - In Erich H. Reck & Georg Schiemer (eds.), The Pre-History of Mathematical Structuralism. Oxford: Oxford University Press. pp. 80-105.
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  • History and Philosophy of Constructive Type Theory.Giovanni Sommaruga - 2000 - Dordrecht, Netherland: Springer.
    A comprehensive survey of Martin-Löf's constructive type theory, considerable parts of which have only been presented by Martin-Löf in lecture form or as part of conference talks. Sommaruga surveys the prehistory of type theory and its highly complex development through eight different stages from 1970 to 1995. He also provides a systematic presentation of the latest version of the theory, as offered by Martin-Löf at Leiden University in Fall 1993. This presentation gives a fuller and updated account of the system. (...)
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  • Logicism and Neologicism.Neil Tennant - 2013 - Stanford Encyclopedia of Philosophy.
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  • El simposio de Königsberg sobre fundamentos de la matemática en perspectiva.Oscar M. Esquisabel & Javier Legris - 2020 - Metatheoria – Revista de Filosofía E Historia de la Ciencia 10 (2):7--15.
    This volume of Metatheoria includes translations into Spanish of the three famous papers on the schools in foundations of mathematics, logicism, intuitionism and formalism, presented at the Königsberg’s Symposium on Foundations of Mathematics in September 1930 and finally published in the journal Erkenntnis in 1931. The three papers constituted a milestone in the Philosophy of Mathematics of the last century. In this introduction to the translations, the editors of the volume outline the historical context in which the original papers were (...)
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