Tag Archives: Laws of Form

Primary Arithmetic as Semiotic System (concl.) Let be the set of rooted trees and let be the 2‑element subset consisting of a rooted node and a rooted edge.  Simple intuition, or a simple inductive proof, will assure us that any … Continue reading →

Primary Arithmetic as Semiotic System (cont.) The axioms of the primary arithmetic are shown below, as they appear in both graph and string forms, along with pairs of names which come in handy for referring to the two opposing directions … Continue reading →

Quick Tour of the Neighborhood This much preparation allows us to take up the founding axioms or initial equations which determine the entire system of logical graphs. Primary Arithmetic as Semiotic System Though it may not seem too exciting, logically … Continue reading →

Computational Representation (concl.) At the next level of concreteness, a pointer‑record data structure can be represented as follows. (11) This portrays index0 as the address of a record which contains the following data. datum1, datum2, datum3, …, and so on. … Continue reading →

Computational Representation The parse graphs we’ve been looking at so far bring us one step closer to the pointer graphs it takes to make the above types of maps and trees live in computer memory but they are still a … Continue reading →

Duality : Logical and Topological (concl.) We have now treated in some detail various forms of the axiom or initial equation which is formulated in string form as “( ( ) ) =    ”.  For the sake of comparison, let’s record the planar and dual … Continue reading →

Duality : Logical and Topological (cont.) It is easy to see the relation between the parenthetical expressions of Peirce’s logical graphs, showing their contents in order of containment, and the corresponding dual graphs, forming a species of rooted trees to be … Continue reading →

Duality : Logical and Topological (cont.) Last time we took up the axiom or initial equation shown below. (3) We noted it could be written inline as “( ( ) ) =    ” or set off in the following text display. ( ( ) ) =     When we turn … Continue reading →

Duality : Logical and Topological In using logical graphs there are two types of duality to consider, logical duality and topological duality. Graphs of the order Peirce considered, those embedded in a continuous manifold like that represented by a plane sheet of … Continue reading →

Abstract Point of View The bird’s eye view in question is more formally known as the perspective of formal equivalence, from which remove one overlooks many distinctions which appear momentous in more concrete settings.  Expressions inscribed in different formalisms whose … Continue reading →