He was ahead of his time, definitely, and binary logic is one critical step in getting there, but we're a long way from having a formal language to represent all claims that would ever arise in human argumentation to the point that it's simply a matter of calculation to resolve them.
Check out metamath.org I can't fathom any valid argument that couldn't be formalized to mathematical statements. There would still be disagreements on axioms and physical postulates, especially where there are conflicts of interest.
The whole project kind of died with Gödel.