At school, I was never good at maths. At the uni­ver­si­ty, I was inter­est­ed in sta­tis­tics, but only mar­gin­al­ly. Hon­est­ly, I start­ed to learn about the beau­ty of maths many years later, when work­ing with more intel­li­gent peo­ple than me who under­stand com­put­ers and data, in gen­er­al. After I start­ed work­ing on Blockchain in 2014, I began to real­ize that some aspects of maths, such as game the­o­ry or cat­e­go­ry the­o­ry, play togeth­er with other fields of inter­est of mine, phi­los­o­phy, and neu­ro­science, in par­tic­u­lar. Human beings aren’t inven­tors, but rather dis­cov­er­ers. There­fore, we should think Beyond Logic — The Case For Math­e­mat­i­cal Platonism

Last week, Jonatan shared this very inter­est­ing and inspir­ing arti­cle about math­e­mati­cian and philoso­pher Kurt Gödel with me. In com­par­i­son to Albert Ein­stein, or Bertrand Rus­sell, Kurt Gödel lacks fame. Where­as all peo­ple have heard of Einstein’s The­o­ry of Rel­a­tiv­i­ty, and most peo­ple have at least an idea of what Rus­sel described in his Prin­cip­ia Math­e­mat­i­ca, not so many peo­ple might have heard of Gödel’s Incom­plete­ness The­o­rems. One, and prob­a­bly the best rea­son for not know­ing Gödel’s work is that nobody real­ly has under­stood it, yet. If you think you do, please start by read­ing the above-mentioned arti­cle, then the orig­i­nal The­o­ry and then enlight­en us by adding your 2 cents in the com­ment sec­tion below.

Pos­i­tivism Vs. Platonism

For me the most inter­est­ing aspect of Kurt Gödel is that he did not com­ply with the pre­dom­i­nant school of thought of his time — the Log­i­cal Pos­i­tivism, or ‘Con­struc­tivism’, main­ly rep­re­sent­ed by the Vien­na Cir­cle. Some­what strange for a bril­liant sci­en­tif­ic thinker like him, Gödel believed in God and he pas­sion­ate­ly believed in math­e­mat­i­cal Pla­ton­ism. In short, where­as the Con­struc­tivists believe math­e­mat­ics to be the inven­tion of the human mind; the Pla­ton­ists believe it to be a set of truths dis­cov­ered by human rea­son. Thus, for the main­stream math­e­mati­cian, Pla­ton­ism involves some meta­physics or other, beyond-logic aspects. 

Beyond Logic — The Case For Math­e­mat­i­cal Platonism

For me, math­e­mat­i­cal Pla­ton­ism is a per­fect (math­e­mat­i­cal) descrip­tion of my per­son­al world­view that I lime to describe with ‘Con­nect­ing The Dots’: for me, human beings aren’t inven­tors, but rather dis­cov­er­ers. We don’t invent things, but we uncov­er and dis­cov­er them by con­nect­ing the dots of our uni­verse. In my opin­ion, this world­view bet­ter ful­fills the ambi­tion of human beings: it was­n’t and it isn’t us who cre­ate — we are only good at discovering.

Albert Einstein Bertrand Russel Constructivism Kurt Gödel PLatonism Vienna Circle