A: Sure, why not? Logic is just another language or protocol, it can be whatever you define it to be.
Q: Even if the logic directly contradicts itself?
A: Sure. People change their mind all the time. It can be encoded as a logic system.
Q: But surely nobody would *think* it's actually "true" to keep contradicting oneself, right?
A: People believe in all sorts of funny things. It's only because you are immersed in the environment that believes those things to be true and real, that you don't see how strange it can be from the outside.
Q: Yes, there are things that took me decades of contemplation to figure out, but in retrospect is very simple.
A: People are also very slow to figure things out, so to speak.
Q: But what about computation? Is the result of a computation fixed?
A: It depends on whether you had an idea what the outcome is. If you already have a concrete idea, then it is more fixed than if you didn't. Since a computational system is designed by "you", it system will behave exactly as you *think* it would behave -- in retrospect. So the computation system will *eventually* make sense (because you think things will eventually be figured out), but not necessarily at the outset.
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