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One of the main difficulty concerning the nature of the continuum is to dojustice, inside the set theoretical Cantorian framework, to the classicalconception (from Aristotle to Thom, via Kant, Peirce, Brentano, Husserl andWeyl) 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 transcendenceof the intuitive continuum w.r.t. its symbolic determination.  Keywords: constructive universe, continuum, G\"{o}del, forcing, Kant, largecardinals, $\Omega$-logic, projective hierarchy, $V = L$, Woodin, $0^{\#}$.

A transcendental view on the continuum: Woodin's conditional platonism