From the Foundational Crisis of Mathematics to Explicit Mathematics

Gerhard Jäger

Starting off from a short overview over the foundational crisis of mathematics I will sketch a few approaches that have been proposed within the last 100 years to overcome this crisis. Afterwards I will try to “judge” these proposals from a modern perspective and in the light of present day logic. In the last part I will turn the formal framework of explicit mathematics - originally proposed by Solomon Feferman - and will try to work out what the strengths and weaknesses of this operational paradigm are.