Machine people

I can't calculate a paradoxical Gödel number. This is a 'fact' about me - about the kind of machine that I am?. We know, I think, that this is a fact about any possible machine. But, of course, he has proved that these numbers 'exist', despite this. They do not, of course, exist in any machine world - any world of of 'facts' - however organised. And so, in no 'possible' world of facts? And what would this mean?

I suppose, at least, that we shouldn't worry about them so far as 'practical' (machine manageable) arithmetic is concerned.

This machine world doesn't render up rules. It can't define them.

But a 'describable' or 'completely narrated' machine world's rules would be contained in its narration - we could only desribe it in this abstract way. Even a single determinate fact has a hidden rule - that a description of it is always true. If we can't narrate a world without some rules being true, then these rules might as well be in the world we are narrating.

But 'might as well be' ... this is metaphysics. It is 'as if' the world contains these rules. We can talk 'as if' the world contains these rules. Even: we could not talk except to talk as if the world contained these rules, except here the 'cannot' is a product of an argument within our talk, and is perhaps circular.