•  21
    Introduction
    Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 49 (4): 499-501. 2018.
  •  4
    Newton’s experimental proofs
    Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 36 (2): 261-283. 2021.
    Newton claims that his theorems in the Opticks are derived from experiments alone. The paper explains this dictum by relating Newton’s proof method to an iconic conception of proof as opposed to a symbolic one. Theorems are not derived from hypotheses; instead properties of light are identified by experimental properties based on rules of inductive reasoning.
  •  8
    In his Lecture on Ethics, Wittgenstein mentions the difficulty a recipient of his philosophy has in ‘seeing both the road he is led and the goal which it leads to’. Oskari Kuusela's b...
  •  32
    In his Lecture on Ethics, Wittgenstein mentions the difficulty a recipient of his philosophy has in ‘seeing both the road he is led and the goal which it leads to’. Oskari Kuusela's b...
  •  17
    Wittgenstein’s Conjecture
    In Gabriele M. Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium, De Gruyter. pp. 515-534. 2019.
  •  64
    Wittgenstein’s Elimination of Identity for Quantifier-Free Logic
    Review of Symbolic Logic 14 (1): 1-21. 2021.
    One of the central logical ideas in Wittgenstein’sTractatus logico-philosophicusis the elimination of the identity sign in favor of the so-called “exclusive interpretation” of names and quantifiers requiring different names to refer to different objects and (roughly) different variables to take different values. In this paper, we examine a recent development of these ideas in papers by Kai Wehmeier. We diagnose two main problems of Wehmeier’s account, the first concerning the treatment of indivi…Read more
  •  44
    This paper reveals two fallacies in Turing's undecidability proof of first-order logic (FOL), namely, (i) an 'extensional fallacy': from the fact that a sentence is an instance of a provable FOL formula, it is inferred that a meaningful sentence is proven, and (ii) a 'fallacy of substitution': from the fact that a sentence is an instance of a provable FOL formula, it is inferred that a true sentence is proven. The first fallacy erroneously suggests that Turing's proof of the non-existence of a c…Read more
  •  2
    Das Buch vermittelt die Grundlagen der Aussagen- und erweiterten Prädikatenlogik in 12 Lektionen. Neben Techniken zum überprüfen der Schlüssigkeit von Argumenten bilden die Kunst des Formalisierens wissenschaftlicher Argumente und metalogische Fragen den Inhalt des Buches. Das Buch eignet sich in Verbindung mit begleitenden interaktiven Übungseinheiten und Klausuren, die ber Internet zugänglich sind, sowohl zum Selbststudium als auch für Einführungskurse in die Logik. Die zweite berarbeitete Auf…Read more
  • Zur Wissenschaftstheorie der Farbenlehre
    Berne Studies in the History and Philosophy of Sciences. 2000.
    Es wird anhand von Fallbeispielen aus der Geschichte der Farbenlehre inwissenschaftstheoretische Probleme eingeführt. Das Buch dient als Grundlagefür eine anwendungsbezogene Lehre und als Einführung in folgende ThemenbereicheNewton vs. Goethe; Theorie und Experiment, Colormetrie; Empfindungsmessung;Helmholtz vs. Hering; Theorienevaluation, Psychologische Farbenlehre; Phänomenologie,Farbausschluss; Beweistheorie, Farbdefinitionen; Theorien- und Begriffsbildung.Neben Aufgaben, Texten und Lösungsvo…Read more
  •  247
    Es wird gezeigt, dass Wittgenstein in seiner Frühphilosophie ein nicht-axiomatisches Beweisverständnis entwickelt, für das sich das Problem der Begründung der Axiome nicht stellt. Nach Wittgensteins Beweisverständnis besteht der Beweis einer formalen Eigenschaft einer Formel – z.B. der logischen Wahrheit einer prädikatenlogischen Formel oder der Gleichheit zweier arithmetischer Ausdrücke – in der Transformation der Formel in eine andere Notation, an deren Eigenschaften sich entscheiden lässt, ob…Read more
  •  342
    In §8 of Remarks on the Foundations of Mathematics (RFM), Appendix 3 Wittgenstein imagines what conclusions would have to be drawn if the Gödel formula P or ¬P would be derivable in PM. In this case, he says, one has to conclude that the interpretation of P as “P is unprovable” must be given up. This “notorious paragraph” has heated up a debate on whether the point Wittgenstein has to make is one of “great philosophical interest” revealing “remarkable insight” in Gödel’s proof, as Floyd and Putn…Read more
  •  422
    Anhand der genaueren Analyse von Newtons experimentum crucis und der Argumentation, die er auf dieses Experiment stützt, sowie Goethes Kritik hieran sollen im Folgenden zwei verbreitete Vorurteile revidiert werden: 1. Newton ist kein Dogmatiker, der methodische Ansprüche vertritt, die er nicht einlösen kann, sondern gründet seinen Anspruch, experimentelle Beweise führen zu können, auf einer vorbildlichen Methodologie kausaler Erklärungen, was seine Kritiker allerdings übersehen. 2. Goethe ist ke…Read more
  • Undecidability reconsidered
    In A. Costa-Leite J. Y. Bezieau (ed.), Dimensions of Logical Concepts, . pp. 33-68. 2007.
    In vol. 2 of Grundlagen der Mathematik Hilbert and Bernays carry out their undecid- ability proof of predicate logic basing it on their undecidability proof of the arithmeti- cal systemZ00. In this paper, the latter proof is reconstructed and summarized within a formal derivation schema. Formalizing the proof makes the presumed use of a meta language explicit by employing formal predicates as propositional functions, with ex- pressions as their arguments. In the final section of the paper, the p…Read more
  • In this paper Richard’s Paradox and the Proof of Cantor’s Theorem are compared. It is argued that there is no conclusive reason to treat them differently such as to call the one a Paradox and the other a Proof.
  •  166
    The young Wittgenstein called his conception of logic “New Logic” and opposed it to the “Old Logic”, i.e. Frege’s and Russell’s systems of logic. In this paper the basic objects of Wittgenstein’s conception of a New Logic are outlined in contrast to classical logic. The detailed elaboration of Wittgenstein’s conception depends on the realization of his ab-notation for first order logic.
  •  307
    In his early philosophy as well as in his middle period, Wittgenstein holds a purely syntactic view of logic and mathematics. However, his syntactic foundation of logic and mathematics is opposed to the axiomatic approach of modern mathematical logic. The object of Wittgenstein’s approach is not the representation of mathematical properties within a logical axiomatic system, but their representation by a symbolism that identifies the properties in question by its syntactic features. It rests on …Read more
  •  49
    The Problem of Validity Proofs
    Grazer Philosophische Studien 80 (1): 79-109. 2010.
    In philosophical contexts, logical formalisms are often resorted to as a means to render the validity and invalidity of informal arguments formally transparent. Since Oliver and Massey , however, it has been recognized in the literature that identifying valid arguments is easier than identifying invalid ones. Still, any viable theory of adequate logical formalization should at least reliably identify valid arguments. This paper argues that accounts of logical formalization as developed by Blau a…Read more
  •  175
    This paper compares several models of formalization. It articulates criteria of correct formalization and identifies their problems. All of the discussed criteria are so called “semantic” criteria, which refer to the interpretation of logical formulas. However, as will be shown, different versions of an implicitly applied or explicitly stated criterion of correctness depend on different understandings of “interpretation” in this context.