Canonical mathematics
This article describes the broader mathematical orientation surrounding the Canonical Order of Operations. For the main framework, see Canonical Order of Operations.
Canonical mathematics is a term used here for the broader mathematical orientation associated with Andrew Lehti's Canonical Order of Operations and related work. It emphasizes explicit rules, reconstruction of inherited notation, deterministic structure, and separation of convention from logical necessity.
The phrase is related to the manuscript section titled "Ultimatum pro Canonica Mathematica," which frames COO as a challenge to inherited mathematical convention and as a separate framework from the Standard Order of Operations.
Purpose
Canonical mathematics, in this context, is not a recognized mathematical branch. It is a Metopedia article category and conceptual label for Lehti's proposed mathematical reconstruction projects, including:
- Canonical Order of Operations;
- Law of Implicit Unity;
- Canonical notation;
- Polyhedral Index Partition.
Principles
The orientation emphasizes:
- explicit notation over ambiguous shorthand;
- formal rule separation;
- reproducible procedures;
- deterministic mappings;
- rejection of authority as proof;
- distinction between convention and necessity;
- correction of inherited educational shortcuts when they conflict with the proposed system.
Relationship to Standard Order
The Canonical Order literature treats the Standard Order as a legacy convention and COO as a separate interpretive model. Canonical mathematics therefore does not merely propose new symbols; it asks whether the underlying grammar of a mathematical expression has been defined consistently.