> there is another possible escape hatch that hasn't been fully explored IMO, and that's some variant of finitism. All these impossibility proofs depend on infi

> there is another possible escape hatch that hasn't been fully explored IMO, and that's some variant of finitism. All these impossibility proofs depend on infinite structures to derive incompleteness or contradiction, but if infinite structures are not expressible... Could you elaborate on what such a formalism where infinite structures are not expressible might look like? It sounds an intriguing notion, though I'm unable to quite get at it.