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84Semantic Values for Natural Deduction DerivationsSynthese 148 (3): 623-638. 2006.Drawing upon Martin-Löf’s semantic framework for his constructive type theory, semantic values are assigned also to natural-deduction derivations, while observing the crucial distinction between consequence among propositions and inference among judgements. Derivations in Gentzen’s format with derivable formulae dependent upon open assumptions, stand, it is suggested, for proof-objects, whereas derivations in Gentzen’s sequential format are proof-acts
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30The General Form of the Operation in Wittgenstein's TractatusGrazer Philosophische Studien 42 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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15Intuitionism and Logical ToleranceVienna Circle Institute Yearbook 6 135-148. 1999.Tradition is classical. Surely, nothing could be more pleonastic than that? The logical tradition, certainly, was squarely classical from Bolzano to Carnap, with, say, Frege, Moore, Russell and the Wittgenstein of the Tractatus as intermediaries. Propositions are construed as being in themselves true-or-false. Indeed, in this tradition, a declarative sentence S expresses a proposition by being true-or-false. So the meaningfulness of a sentence consists in its being true-or-false. But S is true-o…Read more
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115Constructions, proofs and the meaning of logical constantsJournal of Philosophical Logic 12 (2). 1983.
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26A century of judgement and inference, 1837-1936: Some strands in the development of logicIn Leila Haaparanta (ed.), The development of modern logic, Oxford University Press. pp. 263. 2011.
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85Inference, Consequence, Implication: A Constructivist's PerspectivePhilosophia Mathematica 6 (2): 178-194. 1998.An implication is a proposition, a consequence is a relation between propositions, and an inference is act of passage from certain premise-judgements to another conclusion-judgement: a proposition is true, a consequence holds, whereas an inference is valid. The paper examines interrelations, differences, refinements and linguistic renderings of these notions, as well as their history. The truth of propositions, respectively the holding of consequences, are treated constructively in terms of veri…Read more
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27Brouwer's Anticipation of the Principle of CharityProceedings of the Aristotelian Society 85 263-276. 1985.Göran Sundholm; Brouwer's Anticipation of the Principle of Charity*, Proceedings of the Aristotelian Society, Volume 85, Issue 1, 1 June 1985, Pages 263–276, ht.
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25Inference, consequence, implication: a constructivist's perspectivePhilosophia Mathematica 6 (2): 178-194. 1998.An implication is a proposition, a consequence is a relation between propositions, and an inference is act of passage from certain premise-judgements to another conclusion-judgement: a proposition is true, a consequence holds, whereas an inference is valid. The paper examines interrelations, differences, refinements and linguistic renderings of these notions, as well as their history. The truth of propositions, respectively the holding of consequences, are treated constructively in terms of veri…Read more
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74ErrorTopoi 31 (1): 87-92. 2012.The possibility of error is related to the existence a norm. Connections are spelled out to the notion of infallibility and to that of a modifying predicate, to traditional truth theories in connection with “truth of things”, as well as the primacy of the negative cases, for instance “ false friend”
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48Brouwer's Anticipation of the Principle of CharityProceedings of the Aristotelian Society 85. 1985.
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18Heinrich Scholz between Frege and HilbertIn Kai Wehmeier & H.-C. Schmidt am Busch (eds.), Heinrich Scholz. Logiker, Philosoph, Theologe, . pp. 103-117. 2004.
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78Implicit epistemic aspects of constructive logicJournal of Logic, Language and Information 6 (2): 191-212. 1997.In the present paper I wish to regard constructivelogic as a self-contained system for the treatment ofepistemological issues; the explanations of theconstructivist logical notions are cast in anepistemological mold already from the outset. Thediscussion offered here intends to make explicit thisimplicit epistemic character of constructivism.Particular attention will be given to the intendedinterpretation laid down by Heyting. This interpretation, especially as refined in the type-theoretical wo…Read more
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155Existence, proof and truth-making: A perspective on the intuitionistic conception of truthTopoi 13 (2): 117-126. 1994.Truth-maker analyses construe truth as existence of proof, a well-known example being that offered by Wittgenstein in theTractatus. The paper subsumes the intuitionistic view of truth as existence of proof under the general truth-maker scheme. Two generic constraints on truth-maker analysis are noted and positioned with respect to the writings of Michael Dummett and theTractatus. Examination of the writings of Brouwer, Heyting and Weyl indicates the specific notions of truth-maker and existence …Read more
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25Brouwer's Anticipation of the Principle of CharityProceedings of the Aristotelian Society 84 145. 1984.
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43A century of judgement and inference,1837-1936 : Some strands in the development of logicIn Leila Haaparanta (ed.), The development of modern logic, Oxford University Press. 2011.This chapter tells how, within a century, the notions of judgment and inference were driven out of logical theory and replaced by propositions and consequence. Systematic considerations guide the treatment. The history is unashamedly Whiggish: the current position is shown as the outcome, or even culmination, of a historical development.
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27Antirealism and the roles of truthIn M. Sintonen, J. Wolenski & I. Niiniluoto (eds.), Handbook of Epistemology, Kluwer Academic Publishers. pp. 437--466. 2004.
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41Criss-crossing a Philosophical Landscape: Essays on Wittgensteinian Themes Dedicated to Brian McGuinness (edited book)Rodopi. 1992.Essays on Wittgensteinian Themes Dedicated to Brian McGuinness Joachim Schulte, Göran Sundholm. PREFACE For thirty-five years the international community of philosophers have known Brian McGuinness as a major authority on the...
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