division-vs-cleavage

Division results in indistinguishable divisions at the same level, whereas cleavage produces distinguishable states at different hierarchical levels.

1 chapter across 1 book

Laws of Form (1969)G. Spencer Brown

CHAPTER 5 In theorem 9 we see the difference between our use of the verb divide and our use of the verb cleave. Any division of a space results in otherwise indistinguishable divisions of a state, which are all at the same level, whereas a severance or cleavage shapes distinguishable states, which are at different levels. An idea of the relative strengths of severance and division may be gathered from the fact that the rule of number is sufficient to unify a divided space, but not to void a cloven space. Chapter 5 In eliciting rules for algebraic manipulation the text explicitly refers to the existence of systems of calculation other than the system described. This reference is both deliberate and in- essential. It marks the level at which these systems are usually fitted out with their false, or truncated, or postulated, origins. It is deliberate to inform the reader that, in the system of calculation we are building, we are not departing from the basic methods of other systems. Thus what we arrive at, in the end, will serve to elucidate them, as well as to fit them with their true origin. But, at the same time, it is important for the reader to see that the reference to other systems is inessential to the development of the argument in the text. For here it stands or falls on its own merit, dependent in no way for its validity upon agreement or disagreement with other systems. Thus rules 1 and 2, as can be seen from their justifications, say nothing that has not, in the text, already been said. They merely summarize the commands and instructions that will be relevant to the new kind of calculation we are about to undertake. The replacement referred to in rule 2 is usually confined to independent variable expressions of simple (i.e. literal) form, and is in fact so confined in the text. But the greater licence granted by the rule is not devoid of significant application, if required. Chapter 6 By the revelation and incorporation of its own origin, the primary algebra provides immediate access to the nature of the 87

Chapter 5 of Laws of Form distinguishes between the verbs 'divide' and 'cleave', explaining that division creates indistinguishable states at the same level, while cleavage produces distinguishable states at different levels. The chapter also introduces rules for algebraic manipulation within the primary algebra system, emphasizing that these rules stand independently of other calculation systems and clarify the relationship between operators and operands by revealing their partial identity.