From incompleteness to incompletability: a note on Gödel’s view of mathematical knowledge

Although G¨odel’s assumption concerning mathematical concepts as existing independently from our definitions and constructions remains the main feature of his viewpoint, certain related issues have nonetheless attracted the attention of researchers in the field. This is the case for G¨odel’s rationalistic approach as related to a discussion concerning mathematical omnisciency (Does every mathematical problem have a disclosable solution?), which takes the form of a Leibnizian, optimistic confidence in the ability of reason of solving every wellformulated mathematical problem.