4 ms·

I'm curious to hear about those arguments. My intuition tells me that what makes it hard is that if you are part of the system trying to understand the full sy

I'm curious to hear about those arguments. My intuition tells me that what makes it hard is that if you are part of the system trying to understand the full system, you must change the system in order to observe it. In effect, you can never have a perfect model of the system because the system will always be affected by the model you build.

api 11y ago
I'd suggest googling Godel's incompleteness theorem for starters. It proves that within any given system of rules there exist valid theorems that cannot be reached by only logical 'graph traversal' of the state space represented by that system. All systems of rules have 'islands of unreachable truth' within them. (My attempt at a summary.) A lot of people maybe read too much into it, but it's a very interesting and profound theorem. Among other things it more or less proved that attempts to logically deduce all possible theorems of mathematics from axioms -- which were popular at the time -- are futile because this is impossible. It's related in some ways to the Church-Turing thesis, which also proved such efforts impossible by showing that the halting problem is not solvable... you could never enumerate all the theorems of mathematics because it's impossible to tell if you're done.
- escherplex 11y ago
  Pragmatic implications of Godel's theorem are that by extension it is possible to derive ambiguities in any formal system. And as to the possibility of formulating a 'general theory of everything' it's good to remember that the one thing a knife can't cut is itself. Attempt 'Gnothi Seauton' as the old Greeks put it. Meaning understand self before seriously attempting to employ received cognitive analytical functionalities to understand other stuff. But then Kantean musings about what it is that's doing the understanding crop up, which can go on forever.

api 11y ago

I'd suggest googling Godel's incompleteness theorem for starters. It proves that within any given system of rules there exist valid theorems that cannot be reached by only logical 'graph traversal' of the state space represented by that system. All systems of rules have 'islands of unreachable truth' within them. (My attempt at a summary.) A lot of people maybe read too much into it, but it's a very interesting and profound theorem. Among other things it more or less proved that attempts to logically deduce all possible theorems of mathematics from axioms -- which were popular at the time -- are futile because this is impossible. It's related in some ways to the Church-Turing thesis, which also proved such efforts impossible by showing that the halting problem is not solvable... you could never enumerate all the theorems of mathematics because it's impossible to tell if you're done.

escherplex 11y ago
Pragmatic implications of Godel's theorem are that by extension it is possible to derive ambiguities in any formal system. And as to the possibility of formulating a 'general theory of everything' it's good to remember that the one thing a knife can't cut is itself. Attempt 'Gnothi Seauton' as the old Greeks put it. Meaning understand self before seriously attempting to employ received cognitive analytical functionalities to understand other stuff. But then Kantean musings about what it is that's doing the understanding crop up, which can go on forever.