Gödels theorem and uncalculability
Gödels theorem
Kurt Gödel was an austrian logician. His main contribution was the incompleteness
theorem presented 1931. The theorem uses a formal system (for example arithmetic)
and proves that within this system there are theorems that are true but not provable
within the system. A formal system uses some axioms that are taken for granted and
then theorems can be proved within this system. If you have a within the system
unprovable theorem you can not get away with adding an axiom to make it provable,
then there will be another theorem that is unprovable. Gödel himself thought that
this theorem implied the existans of a platonic perfect world of ideas. I do not
quit understand how he found this implication and do not believe in it.
Uncalculability
I have heard that there are problems in logic that you can prove that there are
no general algorithm to solve them. That is, they are impossible for a computer
to solve. Yet, a human can solve them. This is an indication (to some people at
least) that something uncalculable process is going on in the brain. It is important
to stress that just because we cannot calculate this process it does not mean it
is non physical or not scientific even though a religious person probably would
say that. This also raises some interesting questions. How did this uncalculable
process appear during evolution? Maybe it can arise from calculable processes? Maybe
there is som uncalculable process involved in physics from the big bang but why
should it end up in our brain? Maybe there are more uncalculable things than we
expect in the world? This is a counterargument against those scientists that
thinks that the whole universe is a simulation in a supercomputer. Could we replicate
this uncalculable physical (I think at least) process and maybe connect it to
a computer, in fact constructing a computer capable of uncalculatable processes?
As I have believed in a purely calculable universe for a long time I am a little
sceptic about this, but I have to learn more.
Gödels God theorem
Gödel spent the last 30 years of his life trying to prove Gods existence through
logical means. If he would have succeeded it would not have proved the Christian
or Muslim Gods existance of course but merely that there have to be some supernatural
entity. If you are an atheist imagine that he would have succeeded. What would you do?
I think that you (and I) would have to change our belief. Otherwise we are no better
than fundamental religious people as they will probably not change their belief no
matter what proof materializes.