A Fregean Diagramatic Notation for Classical Logic
One of the main philosophical peeves of mine are philosophers confounding symbols and what they represent, and in particular mistaking features of logical notation with actual logical facts. For example, is d ouble negation an actual logical rule or is it actually a notational convention of certain logical notations? It seems to be the later, since we can have expressively equivalent logical notations where double negation is not even expressible, for example, if we consider diagrammatic systems where negation is represented by a reversible transformation of diagrammatic elements (Monroy forthcoming). For similar reasons, one might consider the c ommutativity (of disjunction or conjunction) not as an actual logical rule but a notational convention of certain logical notations, since we can have expressively equivalent logical notations where commutativity is not even expressible , for example, if we consider expressions that are not sequences but sets of symbols. . It is very