What must be true for anything to be true finally answered???
This question stopped me cold two weeks ago. Screenshot above is where it started.
I went looking for an actual answer and I cannot find the hole in what I found.
The short answer to the original question, for anything to exist clearly and stably it has to satisfy exactly two conditions simultaneously. Its identity has to remain stable under every change that constitutes what it is. And the number of distinct states it passes through can never exceed the capacity of whatever supports it. Everything that persists does so because it satisfies both. Everything that cannot persist fails at least one.
That answer came from here. Christopher Lamarr Brown, a systems architect, dropped this on PhilPapers. https://philpapers.org/rec/BROOBT
Full formal papers and complete Lean 4 archive here https://zenodo.org/records/19841644
Every treatment of Leibniz’s question leaves the same gap. A lone entity in a one member domain is supposed to be indistinguishable from nothing but nobody derives this. They assert it. Brown closes it by identifying what all prior work missed, the identity predicate has to be non-vacuous. True of the thing, false of at least one other thing. That single closure condition forces exactly three primitives and no more.
The bedrock instantiates its own conditions. Any denial of it presupposes it. Brown proves that too.
Lean archive claims zero sorrys and one external axiom. If that holds the implications are not small. Not sure if it holds as I have never used lean 4.
One place I keep returning to is the Kleene application. Not saying it breaks. Saying I have not closed it in my own head yet. That’s why I need someone to look at the lean files. Does the proof depend on the external axiom? Or what’s going on with that aspect.
So has any mathematician pulled the Lean files? And if you take the survival filter as given, what does it force in your specific domain.