- Constant tension between symbols and meaning.
- Different possible worlds and interpretations.
- Going back and forth between formal and informal, axioms and models.
- Deep connection and equivalence between syntax and semantics:
| Correspondence | Syntax | ↔ | Semantics |
|---|---|---|---|
| Soundness and Completeness | Provability | ↔ | Truth |
| Soundness and Completeness | Abstract proof | ↔ | Concrete model |
| Curry-Howard Isomorphism | Proofs | ↔ | Programs |