But your state is also deterministically a function of your prior experiences, per this model. If you consider the input the entire stream of events, rather than each individual event, the output stream will be deterministic even with state.

So basically it's still a 'pure' function in the end?

Per the materialist/deterministic 'there is no free will' mental model, yes: the function taking the input stream is pure.

On the per-event basis, this model boils down to a 'function' evaluating each event with multiple outputs and inputs:

Inputs: the stimuli, mental state prior to stimuli

Outputs: your actions and resultant mental state

The output mental state is then the input for the next iteration/evaluation.

Internal state makes understanding the output more difficult: your output is now a function of the input plus the internal state. However, it does not make it freer: the same input paired with the same internal state will always produce the same output.

But if your actions still could change randomly with your personality, memories and everything else that defines you how would that allow for free will?

Say the universe is perfectly deterministic. You could look into the future by simulating everything perfectly but why would that prohibit free will? Most people wouldn't argue that an all knowing god would mean free will is impossible, why is this different?

I think randomness would undermine the "will" part of "free will", whilst perfect determinism would undermine the "free" part of "free will".

> Most people wouldn't argue that an all knowing god would mean free will is impossible, why is this different?

I'd argue that an all-knowing God is something that can't really be reasoned about. It's the introduction of an infinite value into the discussion (or maybe more like a division by zero?). You end up with logically contradictory statements when describing the properties of such a being.

But isn't it essentially just taking away time as a factor which is pretty much what predicting via determinism would do?

Maybe the general definition of free will most people seem to go with just doesn't deal with weird edge cases because it basically developed to fit reality.