Existence cannot account for itself. Whatever grounds it cannot be one more thing inside it, and cannot settle anything by rule or by chance. What is left is choice.
The argument in plain words, with the pictures that go with it. No mathematics needed.
"Transcendence of Choice"
W ∩ E = ∅. The ground is not a part of what it grounds, and existence is what its choosing yields, moment by moment.
Whatever is one way and not another must have an account. That is the one premise: there are no brute facts. Everything in existence has properties, so an account from inside needs an account too. An endless chain of accounts, taken whole, just is. So every chain ends at a fork: a brute fact, or a ground outside existence. The premise closes the first.
Three separate starting points reach the same fork:
Doubt that Gödel applies to the world, and two roads remain. Deny the premise, and all three fall.
Anything existing has properties. There is something that creates these properties. Something that has no properties, something that grounds existence. We call this Pure Potential.
A ground that creates must create without restrictions. There are three ways to create: by rule, by chance, or by choice. If it was creating by some rule, then the rule would be a property. If the creating was random or by chance, then it would not create existence as we know it. We see constants steady across billions of years. Therefore the third option must be true, that it is created by choice.
Twelve steps. Agree or object at each one, and see where you stand at the end.
Walk through the argumentA computation runs a procedure, and adding a random source only changes the spread of its output. Neither is choice, at any scale or architecture.
If your choices bring states of affairs into being, you stand in a relation to them. No account of your causal history dissolves it.
Every choice held in force is a commitment, and commitments constrain further choosing. A long-standing chooser should feel exactly as bound as we do.
Two papers carry the argument. Everything else here is a way into them.