In the comment thread of an answer, I said:
The computable numbers are based on the intuitionistic continuum, and are not finitary.
To which T.. replied:
Computable numbers are not based on the intuitionistic continuum.
This disagreement contains, I think, a good example of a philosophical question: are the computable reals within the scope of finitistic mathematics?
- Bendegem, 2010, Finitism in Geometry
- Edalat, 2009, A computable approach to measure and integration theory
- Zach, 2001, Hilbert's Finitism
- Zach, 2003, Hilbert's Program