Open Questions

Open question paradoxes arise from questions that have this structure:

"What intelligible account can we give of the reliability of our intelligible accounts?"

What sensible story can we tell about how to tell sensible stories?

Formal systems within which questions with this character can be raised will be incomplete or inconsistent.  Even if we try to ask the question in a very disguised way - for instance by looking for a foundation for mathematics in set theory - our trick will be found out.

It cannot be sensible, or even intelligible, to say that we cannot give sensible or intelligible accounts - because our 'serious' statements must be accompanied by a tacit claim that they are, themselves, sensible and intelligible.  The claim that we cannot give intelligible account is either unintelligible or false.

So (a) we must be able to give intelligible accounts and (b) we cannot give a 'complete' account of why they are intelligible.

We can, however, found our accounts of the intelligibility of some statements on the intelligibility of others - even down to the intelligibility of logical axia, to the extent that these can be shown to be intelligible as a consequence of the necessity of intelligibility itself.

So that's OK, then.

However intolerable our private epistemic anxieties, we cannot intelligibly aritculate them.