> That could make equations mostly trivial, since our symbols wouldn't be constrained to any particular arrangement in the first place You might find this litt

> That could make equations mostly trivial, since our symbols wouldn't be constrained to any particular arrangement in the first place You might find this little tidbit[1] from C.S. Peirce by way of John Sowa interesting then. Existential Graphs (EG) are an unordered diagramatic representation of mathematical logic. And Peirce is the real deal. His more conventional notation was adopted by Peano (who substituted the familiar symbols for capital sigma and pi (which created confusion when used in the context of broader proofs, even though sigma and pi pretty much directly correspond to what existence and universality mean)) and he is credited as an independent co-discoverer of both quantifiers with Frege. For EGs, only one axiom is necessary: a blank sheet of assertion, from which all the axioms and rules of inference by Frege, Whitehead, and Russell can be proved by Peirce’s rules. As an example, Frege’s first axiom, a⊃(b⊃a), can be proved in five steps by Peirce’s rules Peirce gives us the entire predicate calculus with three rules and one axiom. And of course it's all built on NAND. And another teaser: In the Principia Mathematica, Whitehead and Russell proved the following theorem, which Leibniz called the Praeclarum Theorema (Splendid Theorem). It is one of the last and most complex theorems in propositional logic in the Principia, and the proof required a total of 43 steps ... With Peirce’s rules, this theorem can be proved in just seven steps starting with a blank sheet of paper. John Sowa himself is also no slouch, having been one of the leading lights of the earlier AI push. I expect advances in modern AI will come when we stop trying to do everything with ngrams and start building on richer models of knowledge representation. [1] https://www.jfsowa.com/pubs/egtut.pdf https://www.jfsowa.com/pubs/egtut.pdf