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  1. It's Not Given Us to Foretell How Our Words Will Echo Through the Ages: The Reception of Novel Ideas by Scientific Community.Valentin Bazhanov - 2009 - Principia: An International Journal of Epistemology 13 (2):129-136.
    The paper reveals some mostly unnoticed and unexpected trends in reception of novel ideas in science. The author formulates certain principles of the reception of these ideas by scientific communities and justifies them by examples from modern mathematics and non-classical logic.
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  • The Development of Mathematical Logic From Russell to Tarski, 1900-1935.Paolo Mancosu, Richard Zach & Calixto Badesa - 2009 - In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press.
    The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim (...)
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  • Gödel's Incompleteness Theorems.Panu Raatikainen - 2013 - The Stanford Encyclopedia of Philosophy (Winter 2013 Edition), Edward N. Zalta (Ed.).
    Gödel's two incompleteness theorems are among the most important results in modern logic, and have deep implications for various issues. They concern the limits of provability in formal axiomatic theories. The first incompleteness theorem states that in any consistent formal system F within which a certain amount of arithmetic can be carried out, there are statements of the language of F which can neither be proved nor disproved in F. According to the second incompleteness theorem, such a formal system cannot (...)
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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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  • Undefinability of Truth. The Problem of Priority:Tarski Vs Gödel.Roman Murawski - 1998 - History and Philosophy of Logic 19 (3):153-160.
    The paper is devoted to the discussion of some philosophical and historical problems connected with the theorem on the undefinability of the notion of truth. In particular the problem of the priority of proving this theorem will be considered. It is claimed that Tarski obtained this theorem independently though he made clear his indebtedness to Gödel?s methods. On the other hand, Gödel was aware of the formal undefinability of truth in 1931, but he did not publish this result. Reasons for (...)
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  • Limited Ink : Interpreting and Misinterpreting GÜdel's Incompleteness Theorem in Legal Theory.Karen Crawley - unknown
    This thesis explores the significance of Godel's Theorem for an understanding of law as rules, and of legal adjudication as rule-following. It argues that Godel's Theorem, read through Wittgenstein's understanding of rules and language as a contextual activity, and through Derrida's account of 'undecidability,' offers an alternative account of the relationship of judging to justice. Instead of providing support for the 'indeterminacy' claim, Godel's Theorem illuminates the predicament of undecidability that structures any interpretation and every legal decision, and which constitutes (...)
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  • Hilbert's Finitism: Historical, Philosophical, and Metamathematical Perspectives.Richard Zach - 2001 - Dissertation, University of California, Berkeley
    In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...)
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  • Distortions and Discontinuities of Mathematical Progress: A Matter of Style, A Matter of Luck, A Matter of Time A Matter of Fact.Irving H. Anellis - 1989 - Philosophica 43.
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  • Seventh Quadrennial Fellows Conference of the Center for Philosophy of Science.-Preprint Volume- - unknown
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  • The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program.Richard Zach - 2003 - Synthese 137 (1-2):211 - 259.
    After a brief flirtation with logicism around 1917, David Hilbertproposed his own program in the foundations of mathematics in 1920 and developed it, in concert with collaborators such as Paul Bernays andWilhelm Ackermann, throughout the 1920s. The two technical pillars of the project were the development of axiomatic systems for everstronger and more comprehensive areas of mathematics, and finitisticproofs of consistency of these systems. Early advances in these areaswere made by Hilbert (and Bernays) in a series of lecture courses atthe (...)
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  • Gödel on Truth and Proof.Dan Nesher - unknown
  • Wittgenstein and Gödel: An Attempt to Make ‘Wittgenstein’s Objection’ Reasonable†.Timm Lampert - 2018 - Philosophia Mathematica 26 (3):324-345.
    According to some scholars, such as Rodych and Steiner, Wittgenstein objects to Gödel’s undecidability proof of his formula $$G$$, arguing that given a proof of $$G$$, one could relinquish the meta-mathematical interpretation of $$G$$ instead of relinquishing the assumption that Principia Mathematica is correct. Most scholars agree that such an objection, be it Wittgenstein’s or not, rests on an inadequate understanding of Gödel’s proof. In this paper, I argue that there is a possible reading of such an objection that is, (...)
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  • On How Logic Became First-Order.Matti Eklund - 1996 - Nordic Journal of Philosophical Logic 1 (2):147-67.
    Added by a category editor--not an official abstract. -/- Discusses the history (and reasons for the history) implicit in the title, as well as the author's view on same.
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  • Husserl and Gödel’s Incompleteness Theorems.Mirja Hartimo - 2017 - Review of Symbolic Logic 10 (4):638-650.
    The paper examines Husserl’s interactions with logicians in the 1930s in order to assess Husserl’s awareness of Gödel’s incompleteness theorems. While there is no mention about the results in Husserl’s known exchanges with Hilbert, Weyl, or Zermelo, the most likely source about them for Husserl is Felix Kaufmann (1895–1949). Husserl’s interactions with Kaufmann show that Husserl may have learned about the results from him, but not necessarily so. Ultimately Husserl’s reading marks on Friedrich Waismann’s Einführung in das mathematische Denken: die (...)
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