Recognition Science / Technical book
The δ
Foundation
Distinction, Arithmetic, and the Limits of Abstraction
Jonathan Washburn · Recognition Physics Institute
FoundationDistinction, Arithmetic,
and the Limits of AbstractionJonathan Washburn
What follows from a distinction that can be repeated? This book builds arithmetic from that starting point, then asks which conclusions follow from the construction and which require additional logical principles.
The argument moves from counting and ratios to effective descriptions, approximation and finite physical records. Definitions, proofs and worked examples keep the assumptions visible at each step.
Follow the argument
- From distinction to arithmetic
Repeated distinction, faithful tallies, signed differences and ratios.
- What a proof uses
Logical rules, the cost of additional principles and the information retained by recognition quotients.
- Construction and its limits
Effective descriptions, rational enclosures and the difference between approximation and exact decision.
- Mathematics in a physical record
Finite channels and recorders under stated preparation, control and resource assumptions, followed by limits imposed by conservation.
How to read it
Begin with the introduction and follow the four parts in order. Seven appendices supply supporting arguments and selected exercise solutions. The text is the mathematical companion to The Structure of Reality.
Each result retains its hypotheses. The physical constructions state the apparatus and resources they require. This openly available technical manuscript has not undergone independent peer review as a book.
Cite the book
Washburn, Jonathan. The δ Foundation: Distinction, Arithmetic, and the Limits of Abstraction. Recognition Physics Institute, 2026. doi:10.67347/pith.preprint.2026.000013.