In the midst of this strife, whereat the halls of Ilúvatar shook and a tremor ran out into the silences yet unmoved, Ilúvatar arose a third time, and his face was terrible to behold. Then he raised up both his hands, and in one chord, deeper than the Abyss, higher than the Firmament, piercing as the light of the eye of Ilúvatar, the Music ceased.
Tolkien • Ainulindalë
Continuing my review of previous discussions concerned with various proposals to extend bivalent logic to encompass sundry dimensions of alterity, change, diversity, dynamics, imagination, indefinability, indeterminacy, information, interpretation, intuitionism, likelihood, mutability, probability, quantity, relativity, time, uncertainty, and so on.
For continuity’s sake I’m recycling my replies to a comment by Helmut Raulien on the Peirce List which raised a host of questions about Peirce’s categories, logic, and semiotics in the light of Spencer Brown’s Laws of Form.
George Spencer Brown’s Laws of Form tends to be loved XOR hated by most folks, with few coming down in between. I ran across the book early in my undergrad years, shortly after encountering C.S. Peirce, so I recognized the way it revived Peirce’s logical graphs, emphasizing the entitative interpretation of the abstract formal calculus immanent in Peirce’s “Alpha” graphs. It took me a decade to gain a modicum of clarity about all that “imaginary truth value” and “re-entry” folderol. I’ll say some things about that later on.
I mulled the matter over for a fair spell of days and nights and decided it wouldn’t be good to jump into the middle of the muddle about re-entry and imaginary truth values right off the bat, that it would be better in the long run to get a solid grip on what is going on with the propositional level of Peirce’s logical graphs and how Spencer Brown’s elaborations can be seen to manifest the same spirit of reasoning, if they are read the right way. Toward that end I’ll append a list of resources to break the ice on this approach.
- Logic Syllabus
- Semeiotic, Semiotics
- Precursors Of Category Theory
- Logical Graphs • Introduction • Formal Development
- Differential Propositional Calculus • Part 1 • Part 2