George Spencer Browns Laws of form zwischen Mathematik und Philosophie : Gehalt - Genese - Geltung

With Laws of Form (1969), George Spencer-Brown presented a calculus of indication that can partly be viewed as axiomatization of the structure of Boolean Algebras.

The first section of the present thesis deals with the CONTENT of this calculus of indications and thus can be regarded in the paradigm of "mathematics as structure". Here, the calculus will be examined as system of propositions in relation of mathematics as product. This approach is based on common proof theory and will in turn be contrasted with an alternative approach based upon equational logic that shows to grasp the text far better.

The calculus of indications starts out with a two-valued arithmetic and opens to considerations of extension by so-called Brownian values. In the meantime, various inner and extra-mathematical applications of this calculus and its extensions have been put forward. It is not my intention to further these extensions by another contribution.

Instead, the second section of my thesis deals with the GENESIS of the calculus and thus can be related to the paradigm "mathematics as activity". In the context of mathematics as process, the calculus will be examined for the potentialities of its language. Influenced by Josef Simon’s Zeichenphilosophie I will firstly discuss the book reversely, starting in the middle, and will then in turn concretize the genesis from a linguistic perspective according to Ladislav Kvasz starting at the beginning.

The mathematical essay, Laws of Form, can especially be regarded as mathematics in a nutshell and as a proposal of mathematical foundations. The laws of forms mentioned in the title can then be interpreted as laws of sign usage, especially of indication and distinction. Both, indication and distinction, are discussed in terms of their methodical application.

The last section of this thesis deals then with the VALIDITY of the mathematics discussed by Brown and relates it to the discourse concerned with philosophy and question of meaning. Thus, I will analyze the conception of the text on the basis of Peter Reisinger’s Rationalitätstypologie, its beginning by means of the philosophy of mathematics by Pirmin Stekeler-Weithofer and subsequently Spencer-Brown’s mathematics in the light of Josef Simon’s Zeichenphilosophie.