Looking to the day we can make our ascent to logical graphs with increasing numbers of variables, I’d like to flag the following points of departure for future development.
- Most of the recent discussion is about two-variable logic forms where there is a logical relation between two logical variables. I want to bring up the subject of three-variable logic which I think is very rich but not much discussed.
- One of the biggest advantages of the systems of graphical forms derived from C.S. Peirce’s logical graphs and Spencer Brown’s calculus of indications is precisely the conceptual and computational efficiencies they afford us in dealing with propositional forms and boolean functions of many variables.
- As it happens, I did once write out all 256 boolean functions on three variables in cactus syntax several years ago — pursuant to discussions in Stephen Wolfram’s New Kind of Science (NKS) Forum regarding Elementary Cellular Automaton Rules (ECARs), which are in effect just that set of boolean functions. I’ll have to dig up a passel of ancient links from the WayBack Machine, but see the following archive page for a hint of how it went.
There is now a copy of the above content at the following location and I’ll be working to improve the formatting and graphics as time goes on.