Gödel's incompleteness theorem shows that there are undecidable statements, i.e., formal logical claims which neither have proofs nor disproofs.


In doing so, Gödel famously enumerated all well-formed formulas with his so-called "Gödel numbering". Thus, the following question is well posed:



> 
> What proportion of well-formed formulas in ZFC are undecidable?
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> 
> 


I seems clear to me that this proportion should converge. Moreover, there are really only two reasonable options - 0% or 100%. My money is on 100%, since that feels in line with the sort of logical weirdness inherent in this area, though I do not have any rigorous heuristic.



Are 100% of statements undecidable, in Gödel's numbering?
This is going to depend sensitively on your exact choice of Gödel number, and the limit will often not be defined. Pick your favorite very short undecidable statement S. Then for any statement A, you have the nearly the same length statements like "A or S", "A and S", "A and True", "A or False". However, one can construct Gödel numberings where any use of an "or" is much longer than any use of an "and" or the reverse, which will change how common these statements are.


So, the answer can be, with a little work, $100\%$, $0\%$, or undefined (which will probably be the case for most natural numbering choices). It is likely that for any computable $x$ where $0 \leq x \leq 1$, there is a numbering which gives an answer of $x$ to your question.


