Foundations & Logic
Curated structural set drawn from socially stabilised foundational programmes: Hilbert/Gödel, reverse mathematics, set-theoretic independence, categorical foundations, type theory, linear logic, paraconsistency, model theory, proof theory, computability, and the ontology of mathematical objects.
Foundations & Logic challenge set
The Foundations & Logic Challenge Set is not an official prize-problem list. It is a curated structural set drawn from socially stabilised foundational programmes and debates. A challenge is included when it tests whether τ can provide a foundation adequate for the mathematics needed to describe reality.
| ID | Challenge | τ Response |
|---|---|---|
| F1 | Foundational Adequacy | structurally constrained |
| F2 | Minimal Expressive Power | further investigation |
| F3 | Finitism / Constructivism Boundary | structurally constrained |
| F4 | Continuum Ontic-Status | structurally constrained |
| F5 | Gödel Limitation | partially addressed |
| F6 | Consistency and Relative Consistency | structurally constrained |
| F7 | Categoricity / Non-Categoricity | structurally constrained |
| F8 | Categorical Foundations | partially addressed |
| F9 | Type-Theoretic / Univalent Foundations | structurally constrained |
| F10 | Linear / Resource-Sensitive Logic | further investigation |
| F11 | Paraconsistent / Belnap-Style Logic | further investigation |
| F12 | Internal Logic | partially addressed |
| F13 | Set-Theoretic Strength | structurally constrained |
| F14 | Independence and Large Cardinals | further investigation |
| F15 | Proof-Theoretic Strength | further investigation |
| F16 | Computability and Formalisation | partially addressed |
| F17 | Ontology of Mathematical Objects | structurally constrained |
| F18 | Pluralism versus Uniqueness | structurally constrained |
Save or share this page for inspection
Download a portable dossier, copy a reviewer note, or send this page to someone who can inspect it.