Re-reading Laws of Form as a Language in Change

摘要

In Laws of Form, the calculus of indications is unfolded step by step. George Spencer-Brown (1969) shows 'the orderly development of mathematical conventions and formulations stage by stage' (p. xiii). I want to re-read the Laws of Form to focus on the augmentation of itssymbolic language. And I will focus on paradigmatic aspects by the use of notions stipulated by Ladislav Kvasz. In Language in Change, Kvasz (2012) characterizes symbolic languages of mathematics, as for example the common algebra, with respect to six potentialities, namely their logical,expressive, methodical, integrative, explanatory, and metaphorical powers. By this linguistic perspective, I will observe how each of these powers gradually increases the symbolic language of the primary algebra and the primary arithmetic; the latter is a linguistic innovation of Spencer-Brownstipulated and examined in chapters 2 through 4 of Laws of Form. I assume that the reader of my article is more or less familiar with Laws of Form, but not in all of its details.