When Infinity Defied the Logicians
Notes on Roger Penrose’s notes on the foundations of mathematics
Introduction
I spent many years studying philosophy, knowing this was going to be my profession. Now I am compelled to think not only about philosophy but also about my professional life, which means I need to publish articles and apply for jobs as a professor or researcher.
For this reason, I’ve been writing, researching, and revising articles like I never did before. Only to prove to others that I know what I’m talking about. It’s not an easy task.
There are many topics, many authors, many themes, and many historical contexts — so much to consider before finally proposing something relevant to my fellow researchers.
It’s competitive, stimulating, sleep-depriving, maddening. It makes you constantly think, edit, and rethink your own work and that of the many others who share the philosophical domain with you.
In this journey a question has bothered me but also never stopped me from keep reading and thinking:
Why are you discussing all these things? Paradoxes? Cardinality? Natural numbers? Infinity? Finitism? Frege? Russell? Gödel? Wittgenstein? Logicism? Intuitionism? Platonism? Dialetheism?
