Charles Sanders Peirce, George Spencer Brown, and Me • 20
Re: Laws of Form • James Bowery JB: I’m interested in those who have approached the notion of self‑duality from the meta‑perspective of switching perspectives between Directed Cyclic Graphs of NiNAND...
View ArticleCharles Sanders Peirce, George Spencer Brown, and Me • 19
Re: Laws of Form • James Bowery JB: I’m interested in those who have approached the notion of self‑duality from the meta‑perspective of switching perspectives between Directed Cyclic Graphs of NiNAND...
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Charles Sanders Peirce, George Spencer Brown, and Me • 18
Re: Laws of Form • James Bowery JB: I’m interested in those who have approached the notion of self‑duality from the meta‑perspective of switching perspectives between Directed Cyclic Graphs of NiNAND...
View ArticleCharles Sanders Peirce, George Spencer Brown, and Me • 17
Re: Laws of Form • James Bowery JB: I’m interested in those who have approached the notion of self‑duality from the meta‑perspective of switching perspectives between Directed Cyclic Graphs of NiNAND...
View ArticleSurvey of Theme One Program • 7
This is a Survey of resources relating to the Theme One Program I worked on all through the 1980s. The aim was to develop fundamental algorithms and data structures for integrating empirical learning...
View ArticleSurvey of Animated Logical Graphs • 8
This is a Survey of blog and wiki posts on Logical Graphs, encompassing several families of graph‑theoretic structures originally developed by Charles S. Peirce as graphical formal languages or visual...
View ArticleLogical Graphs • Discussion 11
Re: Logical Graphs • Formal Development Re: Laws of Form • Lyle Anderson LA: What does it mean to assign a label or name to a node of the Logical Graph? In LoF, the variables of the algebra represent...
View ArticleLogical Graphs • Discussion 10
Re: Logical Graphs • Formal Development Re: Laws of Form • Armahedi Mahzar AM: GSB took J1 : (a(a)) = as the first algebraic primitive and the second one is transposition so he only need only 2...
View ArticleLogical Graphs • Formal Development 8
Exemplary Proofs Using no more than the axioms and theorems recorded so far, it is possible to prove a multitude of much more complex theorems. A number of all‑time favorites are linked below....
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Logical Graphs • Formal Development 7
Frequently Used Theorems (concl.) C3. Dominant Form Theorem The third of the frequently used theorems of service to this survey is one Spencer Brown annotates as Consequence 3 (C3) or Integration. A...
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Logical Graphs • Formal Development 6
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...
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Logical Graphs • Formal Development 5
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...
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Logical Graphs • Formal Development 4
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...
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Logical Graphs • Formal Development 3
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...
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Logical Graphs • Formal Development 2
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...
View ArticleLogical Graphs • Formal Development 1
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...
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Theme One Program • Jets and Sharks 3
Re: Theme One Program • Jets and Sharks • (1) • (2) Example 5. Jets and Sharks (cont.) Given a representation of the Jets and Sharks universe in computer memory, we naturally want to see if the memory...
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Theme One Program • Jets and Sharks 2
Example 5. Jets and Sharks (cont.) As we saw last time, Theme One reads the text file shown below and constructs a cactus graph data structure in computer memory. The cactus graph represents a single...
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Theme One Program • Jets and Sharks 1
It is easy to spend a long time on the rudiments of learning and logic before getting down to practical applications — but I think we’ve circled square one long enough to expand our scope and see what...
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Theme One Program • Exposition 9
Transformation Rules and Equivalence Classes The abstract character of the cactus language relative to its logical interpretations makes it possible to give abstract rules of equivalence for...
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