•  1
    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.
  •  93
    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
  •  13
    Epistemology Versus Ontology: Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf (edited book)
    with Peter Dybjer, Sten Lindström, and Erik Palmgren
    Springer. 2012.
    This 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. This framework is, however,…Read more
  •  9
    A Logical Framework
    Revista 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.
  •  216
    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
  •  55
    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
  • Maccoll On Judgement And Inference
    Nordic Journal of Philosophical Logic 3 119-132. 1998.
  •  45
    The General Form of the Operation in Wittgenstein's Tractatus
    Grazer 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.
  •  11
    Criss-crossing a Philosophical Landscape
    Grazer 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.
  •  56
    DUMMETT, MICHAEL. The elements of intuitionism (review)
    Theoria 45 (2): 90-95. 1979.
  •  117
    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
  •  6
    A Completeness Proof For An Infinitary Tense Logic
    Bulletin of the Section of Logic 6 (2): 70-72. 1977.
  •  28
    The proof-explanation of logical constants is logically neutral
    Revue Internationale de Philosophie 4 401-410. 2004.
  •  15
    Les détectives de la raison
    with Grahame Lock
    le Cahier (Collège International de Philosophie) 2 129-136. 1986.