The Gödel sentence is uncomputable but is commonly held to be true. A non-constructivst would probably be more inclined to say that something which is uncomputa

The Gödel sentence is uncomputable but is commonly held to be true. A non-constructivst would probably be more inclined to say that something which is uncomputable can exist. But it is not obvious (to me). Noteworthy is that Per Martin-Löf who is also credited for the accepted definition of algorithmic randomness for infinite sequences, based on Kolmogorov complexity, developed inuitionistic type theory, a framework for the foundation of mathematics in the constructivist school.