 the claim that the formula with such and such a code in the mathematical representation of the syntax (the code represented in the meta-meta-theory here by ‘\(\langle\sin^2\theta +\cos^2\theta = 1\rangle\)’) is provable. Likewise in the meta-theory we can prove lots of other things about proof and refutation, for instance we may be able to show that lots of sentences are neither provable nor refutable.