This is a well thought out post and I appreciate it because, if nothing else, it gave me things to think about I haven't considered.

The halting problem is interesting to think about in relationship to this. We can't determine whether a program will halt, but given a Turing machine, we can know the next state of the program given the current state. So the machine is deterministic, knowing the current state tells you the next state.

It sounds like your assertion is more that a system cannot be deterministic because the complete state is not knowable and without the complete state of a system, there is no way for it to be deterministic because state form outside of it will influence it?

A Turing machine is decidable from outside itself if state is finite and known. The halting problem is solvable given finite state.

> You are predicting my state in advance of it having been achieved. I'm fully capable of intentionally disrupting your prediction, for example, by drugging the nerves in my arms such that they cannot send signals to my brain. Your claim of knowledge is a false claim and I deny it.

My claim is with perfect knowledge of the current state of existence, the next state will be predictable, the hand smash statement was not rigorous.

It is my belief that reality is governed by physical processes. Drugged nerves are still a physical process. The outcome is a function of the inputs.

My claim requires the assumption of perfect knowledge of state. I am open to the idea that is poor choice of assumption.

> https://www.reddit.com/r/philosophy/comments/4lbck4/computat...

This was a great read, it had satisfying premises and an interesting conclusion. I will have to think about this.

> [5][6][7][8]

I don't think I understand why game theory is relevant, particularly in light of the assumption of perfect knowledge (that very well could lead to a contradiction and therefore be definitely wrong).

I definitely think there is probably a contradiction between perfect knowledge and self reference, thus it is impossible to have perfect knowledge of a system from within the system.

> Even if you know the deterministic rules of a system it is not the case that you can predict the state of that system

This is an interesting and strong statement. The word predict seems to be the key to it. If you can model a system and run it to the next state, I would call that a predictable system, while it seems like the statement you are making is saying that if the only way to find the result of a system is to re-create it and get the next state, that means it is not predictable?

> restated: logic breaks down under self reference therefore humans struggle with thinking about free will and humans cooperate with each other therefore humans struggle with thinking about free well.

I think I will have to read the links to form coherent thoughts.

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The idea of computation reducability is quite interesting. The extension of that idea is equally interesting. "Computational expand-ability."

I would submit for consideration that a particular human brain may have a finite number of physical configurations and therefore there is a fundamental limit for any given snapshot of time of the axiomatic and consistent statements that can be captured from it.

Finite configurations means that "there will always be statements about natural numbers that are true, but that are unprovable within the system." is true, but that it is unintuitive.

If time has a start point, and the present is another point, all patterns of state (and therefore a finite set of true statements about natural numbers) can at some point be proven via "non reducible" calculations/via expansion.

Likewise "shows that the system cannot demonstrate its own consistency." is also true, but that via expansion, all previously known truths can be shown to be consistent.

This is a very intuitive explanation of math to me. With time (computational expansion) true statements can be proven. With time (computational expansion) true statements will be discovered. Because a proof requires the use of true statements, the number of true statements will always be larger than the set of proofs.