If you made the laws that regulate the way his brain work in a way that, given this choice, he would choose cake, then it is not a real choice. He will think about it and choose cake. Assuming the laws you created and your plan aren't conflicting with each other, of course.
Theres really no need to try and solve a paradox, because travel to the past looks impossible. Otherwise we'd be seeing time travelers around.
While I think atheistic, I see both approaches leading to the same place, with the distinction that for religious people there is a plan, suggesting an intelligence, and in my point of view there is no plan, only laws in place that guide everything. The outcome is the same, though.
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Maybe they are all around us. Brilliant minds ahead of their times. Normal folks living the moment. Crazies on the streets shouting "I'm from the future and the end is near!"...
Or maybe travaling to the past requires an arriving beacon that we haven't created yet.
Yes the future is set in stone. Determinism is true as there is no incorporeal thing which is able to act on a physical body
There's no fate but what we make for ourselves
"Would you please let me join your p-p-party?