[Ethan Clive Osgoode]

There are no closed, self-defining systems

The real field is complete in the sense of Goedel.

“logical systems of arithmetic can never contain a valid proof of their own consistency.”

But you're not talking about peano arithmetic, are you? So why not simply leave Goedel out of this?

[Pelham]

“So why not simply leave Goedel out of this?”

Because Goedel is ultimately about epistemology.

http://theor.jinr.ru/~kuzemsky/JakiGodel.pdf