-
5The 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
-
10Grundlagen 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.
-
7History of Logic: MedievalIn Dale Jacquette (ed.), A Companion to Philosophical Logic, Blackwell. 2006.This chapter contains sections titled: A Timeline of Medieval Logicians A Guide to the Literature.
-
14Un marco lógicoRevista 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.
-
1This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, ho…Read more
-
45The Neglect of Epistemic Considerations in Logic: The Case of Epistemic AssumptionsTopoi 38 (3): 551-559. 2019.The two different layers of logical theory—epistemological and ontological—are considered and explained. Special attention is given to epistemic assumptions of the kind that a judgement is granted as known, and their role in validating rules of inference, namely to aid the inferential preservation of epistemic matters from premise judgements to conclusion judgement, while ordinary Natural Deduction assumptions serve to establish the holding of consequence from antecedent propositions to succeden…Read more
-
22Vestiges of realismIn Brian F. McGuinness & Gianluigi Oliveri (eds.), The Philosophy of Michael Dummett, Kluwer Academic Publishers. pp. 137--165. 1994.
-
57Brouwer's demonstration of his Bar Theorem gives rise to provocative questions regarding the proper explanation of the logical connectives within intuitionistic and constructivist frameworks, respectively, and, more generally, regarding the role of logic within intuitionism. It is the purpose of the present note to discuss a number of these issues, both from an historical, as well as a systematic point of view
-
85Semantic 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
-
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
-
17Varieties of ConsequenceIn Dale Jacquette (ed.), A Companion to Philosophical Logic, Blackwell. 2006.This chapter contains sections titled: I II III IV V VI VII VIII IX X.
-
38When, and why, did Frege read Bolzano?In Timothy Childers (ed.), the logica yearbook 1999, . pp. 164-174. 2000.
-
40Summa de Veritate Hamburgensis: Truth According to Wolfgang KünneDialectica 62 (3): 359-371. 2008.No Abstract
Leiden, Zuid-Holland, Netherlands
Areas of Specialization
Metaphysics and Epistemology |
Science, Logic, and Mathematics |
Areas of Interest
Metaphysics and Epistemology |
Science, Logic, and Mathematics |