Abstract
The debate over the truth or falsity of Kant’s statement is still going on, and is far beyond the scope of this book. However, if “nature” is replaced by “mathematics” in the first sentence of the quotation, the issue specializes to the controversy over constructive versus classical mathematics: does everything in mathematics proceed according to rules? Evidently the subject of “rules” plays a central role. In the spirit of this book, we will examine some formal theories of rules, to see if they can shed any light on the issues. At this point the reader may reasonably wish to inquire, “What exactly are the issues?” I should tentatively reply,
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(1)
What is the nature of “rules”?
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(2)
What is the precise relationship between “rules” and mathematics?
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© 1985 Springer-Verlag Berlin Heidelberg
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Beeson, M.J. (1985). Theories of Rules. In: Foundations of Constructive Mathematics. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-68952-9_6
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DOI: https://doi.org/10.1007/978-3-642-68952-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-68954-3
Online ISBN: 978-3-642-68952-9
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