An impossibility result for theories of type-free determinateness - PhilArchive
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A new impossibility result shows that Halbach and Fujimoto's axiomatic theory of truth and determinateness hits a hard logical ceiling — revealing the hidden limits of self-referential formal systems.
Axiomatic Truth TheoryGödel's Incompleteness TheoremsType-Free SemanticsFormal Paradoxes
Theory Briefing
- Halbach and Fujimoto's theory CD combines truth and determinateness axioms, but a new result proves it cannot be consistently extended in a key direction.
- The impossibility echoes Gödelian incompleteness — type-free systems that try to capture their own determinateness inevitably run into contradiction.
- The result forces philosophers to rethink whether any single axiomatic framework can fully capture the concept of determinate truth without self-defeat.