Reflections on Skolem's relativity of set-theoretical concepts (Q2765249)

In 1958 Skolem viewed all mathematical notions as relative, where the main instrument he used in his argument for the set-theoretical relativity was the Löwenheim-Skolem theorem in the form that every consistent first-order countable set of sentences has a countable model. In this paper Skolem's basic points are elaborated including the status of the set-theoretical fundamental notions, where Skolem's critique of set theory is seen as part of a larger argument to the effect that no conclusive evidence has been given for the existence of uncountable sets. The paper concludes with an assessment of the assumptions on which Skolem's argument rests from a present-day perspective.