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RESEARCH PRODUCT

The Calm Before the Storm: Hilbert’s Early Views on Foundations

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In recent years there has been a growing interest among historians and philosophers of mathematics in the history of logic, set theory, and foundations.1 This trend has led to a major reassessment of early work undertaken in these fields, particularly when seen in the light of motivations that animated the leading actors. The present volume may thus be seen as a reflection of this renewed fascination with the work of Hilbert, Brouwer, Weyl, Bernays, and others, an interest that stems in part from the desire to understand the historical and intellectual context that inspired their investigations. With regard to Hilbert, it has been my contention for some time that his stance in the acrimonious foundations debates of the 1920s has tended to reinforce a quite misleading picture of his actual views on the nature of mathematical knowledge. In particular, I have argued that the main tenets of Hilbert’s “formalist program” of the 1920s represent only a portion of his mature “philosophy” of mathematics, as should be readily apparent from the views Hilbert set forth in his 1919-20 lectures “Natur and mathematisches Erkennen” [Hilbert 1992].2