Intellectica 2009/1, n° 51

The Mathematical Continuum. New Conceptions, New Challenges

Solomon Feferman

Conceptions of the Continuum

 Abstract: A number of conceptions of the continuum are examined from the perspective of conceptual structuralism, a view of the nature of mathematics according to which mathematics emerges from humanly constructed, intersubjectively established, basic structural conceptions. This puts into question the idea from current set theory that the continuum is somehow a uniquely determined concept.

 Key words: The continuum, structuralism, conceptual structuralism, basic structural conceptions, Euclidean geometry, Hilbertian geometry, the real number system, set-theoretical conceptions, phenomenological conceptions, foundational conceptions, physical conceptions.