Logic

Where does crisis come from In the last chapter we talked about Russel’s paradox and the need for a formalized system of mathematics. In this section of the blog, we will discuss why mathematics needed to be formalized and what ideas were involved. A mathematician called Cantor created the set theory in the 1870s, he was confident about his theory. He did make a real leap in mathematics in terms of modernization. I mentioned naive set theory a little bit here. Well, I’m not someone who can criticize Cantor, but Bertrand Russell did. He developed a very clever paradox that created a major bottleneck in set theory. ...

Introduction In 1931 a mathematician with round glasses wrote a quite short paper with title “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme”. He was 25 years old. So young was he that, instead of tearing mathematics apart with the energy of his youth, he could have spent his time doing nothing. He was at the University of Vienna and since 1938 a permanent member of the Institute for Advanced Study at Princeton. ...