Complementary Calculi: Distinction and Differentiation
Headaches with complementary calculi
If two formal systems have a very close familiarity as a duality or even a complementarity, and are therefore to some degree nearly indistinguishable, but you nevertheless discovered in a strange situation of an insight a decisive difference between them.
That’s what happens with the discovery of the complementary calculus of indication, a calculus I call a Mersenne calculus of differentiation and separation, in contrast to the Spencer-Brown calculus of indication and distinction.
Obviously, to get rid of the headache with the CI and its ambitious and annoying celebrations, especially in German humanities, the best is to show, or even to prove, that there is a complementary calculus to the calculus of indication, too.
With that, the sectarian propaganda of the CI boils down to a strictly one-sided and utterly blind endeavour.
In-between I have written some papers dealing with the complementarity and applications of the concepts of the CI and the MC.
There might still be too much non-deliberated obfuscation involved, at least, some clear aspects of the new calculus of differentiation, CD, and its complementarity to the calculus of indication and distinction are now elaborated as far as it takes to get a primary understanding of the new situation.
S ⟶ SS|(S)| λ
is generating the proper paranthesis for formal languages.
Set the restriction of bracket rules to:
(()) () = () (())
and you get the basic foundation of the famous CI as introduced by George Spencer-Brown.
(( )) = ( ).
This decision is delivering the base system for a Mersenne calculus, interpreted as a calculus of differentiation, CD.
It will shown that, despite of its non-motivated adhocism, both calculi are well founded in graphematical systems, and are to be seen as interpretations of independent complementary graphematical calculi.
In fact, they belong, with the identity system for semiotics to the only two non-kenogrammatic graphematical systems of the general architectonics of graphematics.
The paper "Diamond Calculus of Formation of Forms. A calculus of dynamic complexions of distinctions as an interplay of worlds and distinctions” was mainly based on a deconstruction of the conditions of the calculus of indiction, i.e. the assumption of a “world” and “distinctions” in it.
Graphematics was invented in the early 1970s as an interpretation of Gotthard Gunther’s keno- and morphogrammatics, inspired by Jaques Derrida’s grammatology and graphematics.