Fregean Logical Graphs

In “Gedankengefüge” Frege says that any two sentences of the form “A and B” and “B and A” have the same sense. In a 1906 letter to Husserl he says that sentences with the same sense should be represented in a perfect notation by one and the same formula. Frege’s own notation, just like any linear notation for sentential logic, is not perfect in this sense, because in it “A and B” and “B and A” are represented by distinct formulas, as is any pair of logically equivalent compound conditionals. A notation for the sentential calculus that meets Frege’s worries about conjunction, and indeed about any symmetric relation that there may be occasion to symbolize, is Peirce’s Alpha graphs