A thing I didn't appreciate the first time I read Spencer-Brown's book is that he actually cites Sheffer's 01913 paper, and proves Sheffer's postulates within his system in an appendix. This situates him significantly closer to the mathematical mainstream than I had thought previously, however flawed his proof of the four-color theorem may have been.
His first statement of the first axiom in the book is a little more general than the version I reproduced earlier and which is inscribed on his gravestone; rather than his "form of condensation"
[][] = []
his "law of calling" is general idempotence, i.e.,
AA = A
although the two statements are equipotent within the system he constructs. Similarly, before stating his "form of cancellation"
[[]] =
he phrases it as the "law of crossing", which I interpret as
Also, the axioms I cited above are written in his notation on his gravestone: https://en.wikipedia.org/wiki/G._Spencer-Brown#/media/File:G... but I have evidently reversed left and right in my rendering of the DNF rewrite rule above. It should be:
His first statement of the first axiom in the book is a little more general than the version I reproduced earlier and which is inscribed on his gravestone; rather than his "form of condensation" his "law of calling" is general idempotence, i.e., although the two statements are equipotent within the system he constructs. Similarly, before stating his "form of cancellation" he phrases it as the "law of crossing", which I interpret as