Gödel’s conjecture: every set has a defining concept

Establish whether for every set there exists a defining concept in the envisaged logic of concepts whose extension is exactly that set, thereby enabling set theory to be encompassed within a hierarchy of concepts.

Background

The paper describes Gödel’s vision that the future logic of concepts could subsume set theory by associating each set with a defining concept, effectively treating sets as extensions of concepts. This is presented as a conjectural bridge between intensional and extensional frameworks.

Confirming or refuting this conjecture would clarify the relationship between concepts and sets and the potential for the logic of concepts to provide a more complete foundation for mathematics.