nLab Edward Nelson

Writing

Edward Nelson (May 4, 1932 – September 10, 2014) was a professor in the Mathematics Department at Princeton University.

Writing

Ultrafinitism

Nelson argued for a position in the philosophy of mathematics known as ultrafinitism:

  • Edward Nelson, Warning Signs of a Possible Collapse of Contemporary Mathematics (pdf)

Nelson arithmetic

In the same paper he defined a first order theory that was weaker than Peano arithmetic, which replaces the induction schema of induction on natural numbers with a predicate and two axioms that state that induction on natural numbers for that predicate is true:

  • Edward Nelson, Warning Signs of a Possible Collapse of Contemporary Mathematics (pdf)

He did not give a name to the theory, so it has been called “Nelson arithmetic” for lack of a better name.

(In)Consistency of Peano Arithmetic

At one point Nelson claimed to have a formal proof of inconsistency of Peano arithmetic (PA). While the proof turned out to be wrong, as acknowledged by Nelson, given that the supicion that PA might be inconsistent after all is shared by others (e.g. Vladimir Voevodsky) it is still interesting to see Nelson’s proof strategy via Chaitin's incompleteness theorem:

  • Edward Nelson, Outline (of an attempt to prove inconsistency of PA) (pdf)
category: people

Last revised on May 8, 2022 at 14:19:48. See the history of this page for a list of all contributions to it.