I might be wrong, but I believe this is not correct. The diagonal lemma lets you construct a sentence that is logically equivalent to something including its own godel numeral. This is different from having its own godel numeral be part of the syntactic definition.
In particular, the former isn’t recursive. It defines one sentence and then, once that sentence is defined, proves something about a second sentence which includes the godel numeral of the first. But what seed attempted (unless I misunderstood it) was to use the godel numeral ┌ψ┐ in the syntactic definition for ψ, which doesn’t make sense because ┌ψ┐ is not defined until ψ is.
I might be wrong, but I believe this is not correct. The diagonal lemma lets you construct a sentence that is logically equivalent to something including its own godel numeral. This is different from having its own godel numeral be part of the syntactic definition.
In particular, the former isn’t recursive. It defines one sentence and then, once that sentence is defined, proves something about a second sentence which includes the godel numeral of the first. But what seed attempted (unless I misunderstood it) was to use the godel numeral ┌ψ┐ in the syntactic definition for ψ, which doesn’t make sense because ┌ψ┐ is not defined until ψ is.