Can Intensional Logic Resolve the Temperature Paradox?

The Temperature Paradox, formulated by Barbara Partee in the 1970s, challenges traditional logic systems by illustrating a discrepancy between formal semantics and common language understanding. It presents an argument that, while seemingly valid in extensional logic, leads to an obviously incorrect conclusion when applied to a natural language scenario involving the concept of a rising temperature.

To resolve this paradox, Richard Montague proposed using intensional logic, suggesting that expressions denote not just static values but also functions of time and possibility, highlighting the dynamic and context-dependent nature of meaning in natural language.

This paradox underscores the complexity of accurately modeling natural language semantics in formal logic systems.

How do you think the nuances of natural language impact logical formalisms?
Can you think of other examples where common language expressions challenge traditional logic?