I've already asked this question on philosophy.stackexchange, I'm hoping for a different answer here:
Descarte has been lauded for putting together geometry and algebra, and his achievement allowed the invention of calculus by Leibniz & Newton and allowed its efficacious and explosive development by subsequent mathematicians & physicists in contrast to the rudimentary and primitive steps taken by Archimedes in integration and the Keralan school in power series.
Now various propositional Logic can be algebraised:
classical propositional logic -> boolean algebras
intuitionistic propositional logic -> heyting algebra
modal logic -> modal algebra
The question: is there a significant geometric form of these logics? Significant, simply in not being just a translation into geometric form, as in Venn Diagrams for boolean algebras (first being represented as some system of sets), but that allows for something deeper to be said about logic itself?
There is of course the Stone representation for a Boolean Algebra, but what does this significantly say about logic?