The phenomenon of free will actually also occurs in the chaotic and unpredictable multiverse of the natural numbers. This multiverse is replete with logic sentences that are true but not provable from their theory, i.e. Godelian facts.
These unpredictable facts represent free will in the world natural numbers.
We normally do not observe these strange facts, because we always implicitly approach the standard universe of natural numbers, i.e. the so-called "intended interpretation", through its theory. This creates the fundamentally wrong impression that:
- There is just one universe of natural numbers. Wrong. There are an endless number of nonstandard universes replete with nonstandard natural numbers.
- The universe of natural numbers is predictable. Wrong. It is full of arbitrary, random truths. It is actually incredibly chaotic.
If we were ourselves placed inside the universe of natural numbers, and we would be able to look around, we would see something as chaotic as our own physical universe.
The man who discovered this, Thoralf Skolem, actually did not like his own discovery one single bit:
Wikipedia on "The Lowenheim-Skolem theorem" wrote:
"Legend has it that Thoralf Skolem, up until the end of his life, was scandalized by the association of his name to a result of this type, which he considered an absurdity, nondenumerable sets being, for him, fictions without real existence." – Poizat (2000).
If the Lowenheim-Skolem theorem is provable from a particular theory, then this theory will generate ("be interpreted by") an unpredictable, chaotic multiverse that contains a large number of elements of "free will".