Here is an overview: https://plato.stanford.edu/entries/goedel-incompleteness/#ConCasUnpSta https://plato.stanford.edu/entries/goedel-incompleteness/#Co... It

Here is an overview: https://plato.stanford.edu/entries/goedel-incompleteness/#ConCasUnpSta https://plato.stanford.edu/entries/goedel-incompleteness/#Co... It ends with an interesting point about the continuum hypothesis: > Sometimes Paul Cohen’s celebrated result that the Continuum Hypothesis (CH) is independent of ZFC (Cohen 1963, 1964; see the entry on independence and large cardinals). However, this case is very different. In all the above independence results the relevant statements are still theorems of mathematics, taken as shown to be true (the last case, which requires large cardinal axioms that go beyond ZFC, is more controversial; still, at least many set-theoreticians find such axioms plausible). And with the first incompleteness theorem itself, the truth of the unprovable statement easily follows, given that the assumption of the consistency of the system is indeed correct. However, in the case of Cohen’s result, there is absolutely no indication whether CH should be considered true, false, or perhaps lacking a truth-value.