  One of the main difficulty concerning the nature of the continuum is to do
justice, inside the set theoretical Cantorian framework, to the classical
conception (from Aristotle to Thom, via Kant, Peirce, Brentano, Husserl and
Weyl) according to which the continuum is a non-compositional, cohesive,
primitive, and intuitive datum. This paper investigates such possibilities,
from G\"{o}del to Woodin, of modelling inside a ZFC-universe the transcendence
of the intuitive continuum w.r.t. its symbolic determination.
  Keywords: constructive universe, continuum, G\"{o}del, forcing, Kant, large
cardinals, $\Omega$-logic, projective hierarchy, $V = L$, Woodin, $0^{\#}$.
