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Dedekind's "Was sind und was sollen die Zahlen?"

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If you have a question about this talk, please contact Richard.

Dedekind’s “Was sind und was sollen die Zahlen?” is well known as presenting second order axioms for natural numbers, and proving their categoricity. This is also the work where the notion of “Dedekind finite set” is introduced.

Perhaps less well known is that Dedekind also gives a full proof of the recursion theorem to justify the iteration of functions over the naturals. (Dedekind’s iteration of functions is nearly, but not quite the same as the familiar scheme of primitive recursion. The differences are quite interesting.) Perhaps even more interesting is that Dedekind also gives a “well-ordering theorem” for Dedekind finite sets.

I will lead this discussion, attempting also to put this work into historical context as far as possible. This should be of interest to many people involved in logic, history of maths, philosophy and computer science, and all are welcome.

Richard Kaye,

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This talk is part of the Midlands Logic Seminar series.

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