Questions to Danielle Macbeth on Frege's Logical Notation and Related Topics

Fabrice Pataut (1)

1 SND - Sciences, Normes, Démocratie

Danielle Macbeth's purpose in Macbeth 2005 is threefold. Her monograph proposes "to provide a logical justification for all aspects of Frege's peculiar notation, to motivate and explain the developments in Frege's views over the course of his intellectual life, and to explicate his most developed, critically reflective conception of his Begriffschrift, his formula language of pure thought" (p. vii). I shall focus here on a few selected aspects of the first and third points and leave on the side the discussion of the historical development of Frege's views on logic, semantics and mathematics. The book's underlying claim is that although Frege's logical language, "can of course be read as a language of quantificational logic, [it] can also be read very differently" (p. vii), so much so, as a matter of fact, that although Frege's logic is usually thought of as a "notational variant of standard quantificational logic", it is nevertheless "unknown to us" (p. 1). This naturally prompts three questions : "What is Frege's logic?", "What is quantificational logic?", and given the way we understand formal languages for first and higher order predicate logic, most notably the notions of argument 2 place (for a predicate symbol), of scope and of binding (of variables - either individual or predicate of first or higher order): "How come Frege's logic says nothing about such notions, or something so different from what we say?"

Mots clés: Sinn und Bedeutung

Mots clés: Philosophy of logic; Philosophy of mathematics; Philosophy of language; Frege's Begriffschrift; Quantification theory

Domaines: Histoire, Philosophie et Sociologie des sciences

Fabrice Pataut. Questions to Danielle Macbeth on Frege's Logical Notation and Related Topics. Logic Colloqium 2006, Jul 2006, Radboud, Netherlands. ⟨halshs-00791199⟩