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105L.E.J. Brouwer's ‘Unreliability of the Logical Principles’: A New Translation, with an IntroductionHistory and Philosophy of Logic 38 (1): 24-47. 2017.We present a new English translation of L.E.J. Brouwer's paper ‘De onbetrouwbaarheid der logische principes’ of 1908, together with a philosophical and historical introduction. In this paper Brouwer for the first time objected to the idea that the Principle of the Excluded Middle is valid. We discuss the circumstances under which the manuscript was submitted and accepted, Brouwer's ideas on the principle of the excluded middle, its consistency and partial validity, and his argument against the p…Read more
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6The Completeness Theorem? So What!In Antonio Piccolomini D'Aragona (ed.), Perspectives on Deduction: Contemporary Studies in the Philosophy, History and Formal Theories of Deduction, Springer Verlag. pp. 39-50. 2024.Bolzano reduced inferential validity of the inference (from premise judgements to conclusion judgment) to the holding of logical consequence between the propositions (in themselves) that serve as contents of the respective judgements. This explicit reduction of inferential validity among judgements to logical consequence among propositions (or, alternatively, to logical truth of certain implicational propositions) has been largely taken over by current logical theory, say, by Wittgenstein’s Trac…Read more
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11Grundlagen der Arithmetik, §17: Part 1. Frege’s Anticipation of the Deduction TheoremIn Thomas Piecha & Kai F. Wehmeier (eds.), Peter Schroeder-Heister on Proof-Theoretic Semantics, Springer. pp. 53-84. 2024.A running commentary is offered on the first half of Frege’s Grundlagen der Arithmetik, §17, and suggests that Frege anticipated the method of demonstration used by Paul Bernays for the Deduction Theorem.
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11A Logical FrameworkRevista de Humanidades de Valparaíso 1 35-40. 2013.The paper presents a framework of distinctions for the philosophy of logic in which the interrelations between some central logical notions, such as statement, judgement, judgement, proposition, consequence, and inference are spelled out.
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56The General Form of the Operation in Wittgenstein's TractatusGrazer Philosophische Studien 42 (1): 57-76. 1992.The paper offers an interpretation of thesis 6.01. The treatment touches upon variables, identity, elementary propositions, internal relations. Klammerausdrücke, and operations. Wittenstein's notations are found not to cover the particular form of definition by induction that is used at 6 and 6.01. It is concluded that Wittgenstein's ability to design of a formal system of logic does not match his outstanding logico-philosophical insight.
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18Criss-crossing a Philosophical LandscapeGrazer Philosophische Studien 42 (1): 57-76. 1992.The paper offers an interpretation of thesis 6.01. The treatment touches upon variables, identity, elementary propositions, internal relations. Klammerausdrücke, and operations. Wittenstein's notations are found not to cover the particular form of definition by induction that is used at 6 and 6.01. It is concluded that Wittgenstein's ability to design of a formal system of logic does not match his outstanding logico-philosophical insight.
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232“Inference versus consequence” revisited: inference, consequence, conditional, implicationSynthese 187 (3): 943-956. 2012.Inference versus consequence , an invited lecture at the LOGICA 1997 conference at Castle Liblice, was part of a series of articles for which I did research during a Stockholm sabbatical in the autumn of 1995. The article seems to have been fairly effective in getting its point across and addresses a topic highly germane to the Uppsala workshop. Owing to its appearance in the LOGICA Yearbook 1997 , Filosofia Publishers, Prague, 1998, it has been rather inaccessible. Accordingly it is republished…Read more
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62Proof-Theoretical Semantics and Fregean Identity Criteria for PropositionsThe Monist 77 (3): 294-314. 1994.In his Grundgesetze, §32, Frege launched the idea that the meaning of a sentence is given by its truth condition, or, in his particular version, the condition under which it will be a name of the True. This, indeed, was only one of the many roles in which truth has to serve within the Fregean system. In particular, truth is an absolute notion in the sense that bivalence holds: every Gedanke is either true or false, in complete independence of any conative activity, whether by God or man. Thus va…Read more
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93Frege, August Bebel and the Return of Alsace-Lorraine: The dating of the distinction between Sinn and BedeutungHistory and Philosophy of Logic 22 (2): 57-73. 2001.A detailed chronology is offered for the writing of Frege's central philosophical essays from the early 1890s. Particular attention is given to (the distinction between) Sinn and Bedeutung. Suggestions are made as to the origin of the examples concerning the Morning Star/Evening Star and August Bebel's views on the return of Alsace-Lorraine. Likely sources are offered for Frege's use of the terms Bestimmungsweise, Art des Gegebenseins and Sinn und Bedeutung
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33The proof-explanation of logical constants is logically neutralRevue Internationale de Philosophie 4 401-410. 2004.
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9A Completeness Proof For An Infinitary Tense LogicBulletin of the Section of Logic 6 (2): 70-72. 1977.
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70Proofs as Acts and Proofs as Objects: Some questions for Dag PrawitzTheoria 64 (2-3): 187-216. 1998.