Partially examined life precognitions introduce philosophical topics for upcoming episodes

to give you a few weeks to do the reading yourself.

They also serve as quick standalone summaries of the work.

You can read more about these topics, get the words we cover, and listen to Partially

Examined Life Conversations at partiallyexaminedlife.com.

Hello again.

This is Audie, a parapetically pontificating from sunny New York, and I'll be joining the

guys this week to discuss two awesome readings by Kurt Gertl on the famous incompleteness

theorems and the philosophy of mathematics.

Since philosophy of math isn't the most mainstream philosophy, I think a quick intro to Gertl

might be helpful.

Kurt Gertl, born in Austria in 1906, was one of the most influential mathematicians slash

logicians of the last century.

His work was not only pivotal to the foundations of mathematics and philosophy of mathematics,

but his work has been influential across the sciences and humanities.

Before I get into the incompleteness theorems, I want to step back and discuss the mathematical

turmoil which Gertl was born in.

In the early part of the last century, mathematics had been struck with a series of apparent contradictions

and inconsistency.

The most famous of these was Russell's paradox, which is simple, but kind of fun.

The informal statement is something like this.

A male barber shapes all the only men who don't shave themselves.

...