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.
The whole project kind of died with Gödel.
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.