How do we account for the truth of arithmetic? And if it does not
depend for its truth on the way the world is, what constrains the
world to conform to arithmetic? Reason's Nearest Kin is a critical
examination of the astonishing progress made towards answering these
questions from the late nineteenth to the mid-twentieth century. In
the space of fifty years Frege, Dedekind, Russell, Wittgenstein,
Ramsey, Hilbert, and Carnap developed accounts of the content of
arithmetic that were brilliantly original both technically and
philosophically. Michael Potter's innovative study presents them all
as finding that content in various aspects of the complex linkage
between experience, language, thought, and the world. Potter's reading
places them all in Kant's shadow since it was his attempt to ground
arithmetic in the spatio-temporal structure of reality that they were
reacting against; but it places us in Gödel's shadow since his
incompleteness theorems supply us with a measure of the richness of
the content they were trying to explain. This stimulating reassessment
of some of the classic texts in the philosophy of mathematics reveals
many unexpected connections and illuminating comparisons, and offers a
wealth of ideas for future work in the subject.
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Philosophies of Arithmetic from Kant to Carnap
Product details
ISBN
9780191520228
Published
2020
Publisher
Oxford University Press Academic UK
Language
Product language
Engelsk
Format
Product format
Digital bok
Author