Frege's Theorem collects eleven essays by Richard G Heck, Jr, one
of the world's leading authorities on Frege's philosophy. The
Theorem is the central contribution of Gottlob Frege's formal work
on arithmetic. It tells us that the axioms of arithmetic can be
derived, purely logically, from a single principle: the number of
these things is the same as the number of those things just in case
these can be matched up one-to-one with those. But that principle
seems so utterly fundamental to thought about number that it might
almost count as a definition of number. If so, Frege's Theorem
shows that arithmetic follows, purely logically, from a near
definition. As Crispin Wright was the first to make clear, that
means that Frege's logicism, long thought dead, might yet be
viable. Heck probes the philosophical significance of the Theorem,
using it to launch and then guide a wide-ranging exploration of
historical, philosophical, and technical issues in the philosophy
of mathematics and logic, and of their connections with
metaphysics, epistemology, the philosophy of language and mind, and
even developmental psychology. The book begins with an overview
that introduces the Theorem and the issues surrounding it, and
explores how the essays that follow contribute to our understanding
of those issues. There are also new postscripts to five of the
essays, which discuss changes of mind, respond to published
criticisms, and advance the discussion yet further.
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