Traces the development of the integral and the differential calculus and related theories since ancient times.

It hath been an old remark, that Geometry is an excellent Logic.

Canadian Journal of Philosophy, 37: 263–282. [preprint] This paper is a critical discussion of Mathias Frisch’s book Inconsistency, Asymmetry, and Nonlocality.

Just what forms do (or should) our cognitive attitudes towards scientific theories take? The nature of cognitive commitment becomes particularly puzzling when scientists' commitments are) inconsistent. And inconsistencies have often infected our best efforts in science and mathematics. Since there are no models of inconsistent sets of sentences, straightforward semantic accounts fail. And syntactic accounts based on classical logic also collapse, since the closure of any inconsistent set under classical logic includes every sentence. In this essay I present some evidence (...) that there really was a substantial cognitive commitment to OQT, and that some of its characteristics have a simple and straightforward explanation in terms of a model based on a form of paraconsistent logic. (shrink)

Clearly, if a man holds a self-contradictory belief, then his belief cannot be rational, for there can be no set of evidence sufficient to justify it. This is most apparent when the self contradictory belief is a belief in a conjunction, , rather than when it is a non-conjunctive self-contradictory belief, e.g. a belief that red is not a color.

In diesem Aufsatz erläutere ich Leibniz' Versuche, seinen Infinitesimalkalkül zu rechtfertigen. Die Untersuchung zielt ab auf ein klareres Verständnis, wie tief Leibniz die Begriffe, Ziele und Methoden im Hinblick auf das fragliche Problem faßte. Mein Überblick ist in zwei Teile gegliedert. Der erste stellt die Definition und den Gebrauch einiger Leibnizscher Begriffe dar, die bei der Rechtfertigung des Calculus eine wichtige Rolle spielen. Im zweiten skizziere ich, auf welche Weise Leibniz die Infinitesimalrechnung zu rechtfertigen versuchte.