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93The mechanization of reasonPhilosophia Mathematica 3 (1). 1995.Introduction to a special issue of Philosophia Mathematica on the mechanization of reasoning. Authors include: M. Detlefsen, D. Mundici, S. Shanker, S. Shapiro, W. Sieg and C. Wright.
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20Purity as an ideal of proofIn Paolo Mancosu (ed.), The Philosophy of Mathematical Practice, Oxford University Press. pp. 179-197. 2008.Various ideals of purity are surveyed and discussed. These include the classical Aristotelian ideal, as well as certain neo-classical and contemporary ideals. The focus is on a type of purity ideal I call topical purity. This is purity which emphasizes a certain symmetry between the conceptual resources used to prove a theorem and those needed for the clarification of its content. The basic idea is that the resources of proof ought ideally to be restricted to those which determine its content.
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163Löb's theorem as a limitation on mechanismMinds and Machines 12 (3): 353-381. 2002.We argue that Löb's Theorem implies a limitation on mechanism. Specifically, we argue, via an application of a generalized version of Löb's Theorem, that any particular device known by an observer to be mechanical cannot be used as an epistemic authority (of a particular type) by that observer: either the belief-set of such an authority is not mechanizable or, if it is, there is no identifiable formal system of which the observer can know (or truly believe) it to be the theorem-set. This gives, …Read more
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28Duality, Epistemic Efficiency & ConsistencyIn Godehard Link (ed.), Formalism and Beyond: On the Nature of Mathematical Discourse, De Gruyter. pp. 1-24. 2014.Duality has often been described as a means of extending our knowledge with a minimal additional outlay of investigative resources. I attempt to construct a serious argument for this view. Certain major elements of this argument are then considered at length. They’re found to be out of keeping with certain widely held views concerning the nature of axiomatic theories (both in projective geometry and elsewhere). They’re also found to require a special form of consistency requirement.
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147An Essay on Mathematical Instrumentalism M. Detlefsen. THE PHILOSOPHICAL FUNDAMENTALS OF HILBERT'S PROGRAM 1. INTRODUCTION In this chapter I shall attempt to set out Hilbert's Program in a way that is more revealing than...
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106Essay ReviewHistory and Philosophy of Logic 9 (1): 93-105. 1988.S. SHAPIRO (ed.), Intensional Mathematics (Studies in Logic and the Foundations of Mathematics, vol. 11 3). Amsterdam: North-Holland, 1985. v + 230 pp. $38.50/100Df
Michael Detlefsen
(1948 - 2019)
Notre Dame, Indiana, United States of America
Areas of Specialization
| Logic and Philosophy of Logic |
| Philosophy of Mathematics |