Yes and no. There’s a boundary where we can do math that says what might happen, but we can’t test those hypotheses. At least that’s my understanding.
What I was referring to is Goedel’s incompleteness theorem which says that in a logic system there are things that are true that cannot be proven in the system, and logic systems can become complex enough that you can’t prove they’re consistent.
So it’s not really saying logic is illogical, but it is saying in logic you sometimes have to build on foundations you can’t prove to be true, despite believing very strongly that they are.
What I was referring to is Goedel’s incompleteness theorem which says that in a logic system there are things that are true that cannot be proven in the system, and logic systems can become complex enough that you can’t prove they’re consistent.
If you get into the real guts of the theorem, the limit becomes a system attempting to describe itself.
But there’s plenty of room for logical analysis outside the artificially engineered naval gazing that Goedel uses to prove incompleteness.
in logic you sometimes have to build on foundations you can’t prove to be true, despite believing very strongly that they are.
In logic, you do have certain unprovable truths known as axioms, which you use to form the foundation of a model. And one way to evaluate a model is to try and prove statements that force one axiom to contradict another (typically referred to as a paradox).
“Time Travel is impossible” is a conclusion we can make IRL, but not one that holds in a narrative fantasy.
Yes and no. There’s a boundary where we can do math that says what might happen, but we can’t test those hypotheses. At least that’s my understanding.
What I was referring to is Goedel’s incompleteness theorem which says that in a logic system there are things that are true that cannot be proven in the system, and logic systems can become complex enough that you can’t prove they’re consistent.
So it’s not really saying logic is illogical, but it is saying in logic you sometimes have to build on foundations you can’t prove to be true, despite believing very strongly that they are.
If you get into the real guts of the theorem, the limit becomes a system attempting to describe itself.
But there’s plenty of room for logical analysis outside the artificially engineered naval gazing that Goedel uses to prove incompleteness.
In logic, you do have certain unprovable truths known as axioms, which you use to form the foundation of a model. And one way to evaluate a model is to try and prove statements that force one axiom to contradict another (typically referred to as a paradox).
“Time Travel is impossible” is a conclusion we can make IRL, but not one that holds in a narrative fantasy.