Lost on the way from Frege to Carnap: How the philosophy of science forgot the applicability problem

Grazer Philosophische Studien 73 (1):69-82 (2006)
Torsten Wilholt
Universität Hannover
This paper offers an explanation of how philosophy of science in the second half of the 20th century came to be so conspicuously silent on the problem of how to explain the applicability of mathematics. It examines the idea of the early logicists that the analyticity of mathematics accounts for its applicability, and how this idea was transformed during Carnap's efforts to establish a consistent and substantial philosophy of mathematics within the larger framework of Logical Empiricism. I argue that at the end point of this development, philosophical discussion of the applicability problem was terminated although important aspects of the logicists' original response to the applicability problem had had to be sacrificed along the way.
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