Full Idea
The question of the completeness of the full intuitionistic logic for its intended interpretation is not yet fully resolved.
Clarification
'Complete' means all its truths can be proved
Gist of Idea
It is still unsettled whether standard intuitionist logic is complete
Source
John P. Burgess (Philosophical Logic [2009], 6.9)
Book Reference
Burgess,John P.: 'Philosophical Logic' [Princeton 2009], p.141