Inertia wrote:I realised it's a bit of a derail but since the thread was turning into science vs religion I thought this more interesting, and I was curious to understand what you were getting at.
It's called the Liar paradox, which is embedded into a formal system so you have metamathematical assumptions in a formal logical system. But it's very dry and tedious for a games forum.
And as said earlier this is a derail on the OP but I thought was worth pointing out as people tend to ignore the larger philosophical questions that science, which has a more specific methodology, has no intention of answering.
The liar paradox (introduced into logic by Russell, not Godel) isn't an example of subjectivity though. It is a contradiction in axioms of a formal system, and it was addressed by Russell (among others) anyway. And of course you have assumptions in the system! They are called axioms and rules and they are what defines the system!
When you say "logic is only as good as the information you have", I think you're confusing it with empirical sciences and experimentation, e.g. what particle physicists are doing now at CERN. Formal logic as in maths isn't based on collecting information/data like this, or having "partial evidence". Maths is based on abstract, a priori reasoning and absolutely does not require any form of information-collection or 'faith' as you say.