Tag Archives: Spencer Brown

Frequently Used Theorems (cont.) C2.  Generation Theorem One theorem of frequent use goes under the nickname of the weed and seed theorem (WAST).  The proof is just an exercise in mathematical induction, once a suitable basis is laid down, and … Continue reading →

Frequently Used Theorems To familiarize ourselves with equational proofs in logical graphs let’s run though the proofs of a few basic theorems in the primary algebra. C1.  Double Negation Theorem The first theorem goes under the names of Consequence 1 (C1), … Continue reading →

Equational Inference All the initials have the form of equations.  This means the inference steps they license are reversible.  The proof annotation scheme employed below makes use of double bars to mark this fact, though it will often be left … Continue reading →

Logical Interpretation One way of assigning logical meaning to the initial equations is known as the entitative interpretation (En).  Under En, the axioms read as follows. Another way of assigning logical meaning to the initial equations is known as the existential interpretation … Continue reading →

Axioms The formal system of logical graphs is defined by a foursome of formal equations, called initials when regarded purely formally, in abstraction from potential interpretations, and called axioms when interpreted as logical equivalences.  There are two arithmetic initials and … Continue reading →

Logical graphs are next presented as a formal system by going back to the initial elements and developing their consequences in a systematic manner. Formal Development Logical Graphs • First Impressions gives an informal introduction to the initial elements of … Continue reading →

Logical graphs are next presented as a formal system by going back to the initial elements and developing their consequences in a systematic manner. Formal Development Logical Graphs • First Impressions gives an informal introduction to the initial elements of … Continue reading →

Formal Development Discussion of the topic continues at Logical Graphs • Formal Development. Resources Logical Graphs Futures Of Logical Graphs Propositional Equation Reasoning Systems Charles Sanders Peirce • Bibliography Survey of Animated Logical Graphs cc: FB | Logical Graphs • … Continue reading →

Primary Algebra as Pattern Calculus (concl.) Speaking of algebra, and having just encountered one example of an algebraic law, we might as well introduce the axioms of the primary algebra, once again deriving their substance and their name from the … Continue reading →

Primary Algebra as Pattern Calculus Experience teaches that complex objects are best approached in a gradual, laminar, modular fashion, one step, one layer, one piece at a time, especially when that complexity is irreducible, when all our articulations and all … Continue reading →