https://en.wikipedia.org/wiki/Critique_ ... _Existence
https://en.wikipedia.org/wiki/Critique_ ... _Existence
Coupled with showing the fallacy of the Ontological Argument, Kant completed the refutation of the rational theology (included Tommy's work) in KrV.
Want to call it an intrinsic limitation of logic? Likely. But it shows that logic cannot prove the existance of deities - much less so about their eventual qualities.