On #3, Argument from free will: God endowed Creation with free will, including our freedom to believe in Him or not. Corollary: it is a contradiction in terms for God to ever reveal Himself in a repeatable measurable manner. Doing so would limit our free will to believe.
Wrestling with the question of free will led some earnest scientists, eg Sabine Hossenfelder, to consider superdeterminism as an alternative. Paradoxically, or not, the choice between an Universe governed by free will and superdeterminism is itself subject to free will.
Most excellent.
On #3, Argument from free will: God endowed Creation with free will, including our freedom to believe in Him or not. Corollary: it is a contradiction in terms for God to ever reveal Himself in a repeatable measurable manner. Doing so would limit our free will to believe.
Wrestling with the question of free will led some earnest scientists, eg Sabine Hossenfelder, to consider superdeterminism as an alternative. Paradoxically, or not, the choice between an Universe governed by free will and superdeterminism is itself subject to free will.
The free will discussion is really interesting.
I wrote about the necessity of God's hiddenness and free will in my chapter of The Story of the Cosmos.