__Article:__

** Samuel R. Buss
"Nelson's Work on Logic and Foundations and Other
Reflections on Foundations of Mathematics"
In **

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** Abstract: **This paper starts by discussing
Nelson's philosophy of mathematics, which is a blend of mathematical formalism
and a radical constructivism. As such, it makes strong assertions about the
foundations of mathematic and the reality of mathematical objects. We then
offer our own suggestions for the definition of mathematics and the nature of
mathematical reality. We suggest a second characterization of mathematical
reasoning in terms of common sense reasoning and argue its relevance for
mathematics education.

Nelson's philosophy is the foundation of his definition of
predicative arithmetic. There are close connections between predicative
arithmetic and the common theories of bounded arithmetic. We prove that
polynomial space (PSPACE) predicates and exponential time (EXPTIME) predicates
are predicative.

We discuss Nelson's formalist philosophies and his
unpublished work in automatic theorem checking.

__Talk slides:__

Slides from a presentation at **Workshop on Analysis, Probability and Logic, Pacific Institute of Mathematical Studies, UBC, Vancouver, June 2004.**

**Download slides: postscript or PDF. **