Gödel and the Metamathematical Tradition

Developments in Logic: Carnap, Gödel, and Tarski

Analytic philosophy and modern logic are intimately connected, both historically and systematically. Thinkers such as Frege, Russell, and Wittgenstein were major contributors to the early development of both; and the fruitful use of modern logic in addressing philosophical problems was, and still is, definitive for large parts of the analytic tradition. More specifically, Frege's analysis of th...

The metamathematics of ergodic theory

The metamathematical tradition, tracing back to Hilbert, employs syntactic modeling to study the methods of contemporary mathematics. A central goal has been, in particular, to explore the extent to which infinitary methods can be understood in computational or otherwise explicit terms. Ergodic theory provides rich opportunities for such analysis. Although the field has its origins in seventeen...

Kronecker in Contemporary Mathematics. General Arithmetic as a Foundational Programme

tion “General Arithmetic” (Allgemeine Arithmetik). In his view, arithmetic is the building block of the whole edifice of mathematics. The aim of this paper is to show that Kronecker’s arithmetical philosophy and mathematical practice have exerted a permanent influence on a long tradition of mathematicians from Hilbert to Weil, Grothendieck and Langlands. The conclusion hints at a constructivist...

and Metamathematical Perspectives

Hilbert’s Finitism: Historical, Philosophical, and Metamathematical Perspectives

Gödel Without (Too Many) Tears Second edition: revised draft