All other sciences without exception depend upon the principles of mathematics; and mathematics borrows nothing from them but hints.
C.S. Peirce • “Logic of Number”
A principal intention of this essay is to separate what are known as algebras of logic from the subject of logic, and to re‑align them with mathematics.
G. Spencer Brown • Laws of Form
Re: Peirce’s 1870 “Logic of Relatives” • Overview
Re: Laws of Form • James Bowery (1) (2)
I am pleased to see you engaging the material on Peirce’s Logic of Relatives. For my part I’ll need to lay out several more Selections before the major themes of Peirce’s essay begin to emerge from the supporting but sometimes distracting details.
In the meantime two clues to the Big Picture can be gleaned from the paired epigraphs I put up in lights at the top of the post. For what we have here is a return to the thrilling days of yesteryear when the mathematics of logic was still mathematics, shortly before Frege (maybe unwittingly) and Russell (in a way less wittingly) detoured it down the linguistic U‑turn to nominalism.
cc: Conceptual Graphs • Cybernetics • Ontolog Forum
cc: Peirce (1) (2) • Structural Modeling • Systems Science
cc: FB | Peirce Matters • Laws of Form
Peirce saw mathematics as naturally incomplete, and only answering selected questions, didn’t he?
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