Proof-Theoretic Strength Challenge
F15
foundations logic
foundations logic
External: philosophical foundational debate
τ response: further investigation
What is the proof-theoretic strength of τ or of its major fragments?
Current τ response
See the paired Proof-Theoretic Strength Challenge — Challenge Response on the Results lane for the program's current response status, registry evidence, verification route, and external-review boundary.
Current status: further investigation.
Challenge statement
What is the proof-theoretic strength of τ or of its major fragments?
Why this challenge is in the ledger
Proof theory supplies tools for comparing formal systems. τ needs comparable strength claims where possible.
τ-facing burden
Give proof-theoretic comparison points: weaker than PA, comparable to arithmetic fragments, comparable to reverse-mathematical subsystems, comparable to ZFC fragments, or outside ordinary ladders.
First reviewer questions
- How does τ position itself with respect to proof-theoretic strength challenge?
- Are τ's claims here theorem-like, programmatic, or descriptive?
- What external review would settle the open questions?
Source anchors
Source anchors are background references, not endorsements of Panta Rhei claims.