Skolem is commonly portrayed as arguing that certain otherwise well understood concepts are suspect simply because they cannot be characterized in a first-order language; in particular that, since all first-order formalizations of set theory (if consistent) have countable models, the concept of uncountability is flawed.... Skolem's position is more solid than that. I see Skolem as arguing that all the evidence that has been given for the existence of uncountable sets is inconclusive, and the reason why he insists on considering countable models is that axiomatisation was put forward at the time as the only way to secure set theory, and what sets are and which sets exist was claimed to be determined by the axioms and their models (much as what Euclidean geometry is about was claimed to be determined by Hilbert 's axioms and their models).
Skolem ay karaniwang portrayed bilang tiyak na sa kabilang banda arguing na din naiintindihan konsepto ng mga suspect dahil lamang sila ay hindi maaaring characterized sa isang first-order ng wika; sa partikular na, dahil ang lahat ng unang-order formalizations set ng mga teorya (kung pare-pareho) ay may countable mga modelo, ang konsepto ng uncountability ay flawed.... Skolem posisyon ay higit pa kaysa sa solid na. Ko makita ang Skolem bilang arguing na ang lahat ng mga katibayan na ito ay ibinigay para sa pagkakaroon ng hindi mabilang sets ay walang tiyak na hatol, at ang dahilan kung bakit siya insists isasaalang-alang sa countable modelo ay na axiomatisation ay ilagay sa harap at ang oras na ang tanging paraan upang secure set theory, at kung ano ang set at ang mga umiiral na set ay inaangkin na tinukoy sa pamamagitan ng axioms at ang kanilang mga modelo (marami ng kung ano Euclidean geometry ay tungkol sa noon ay natubos na tinutukoy sa pamamagitan ng Hilbert 's axioms at ang kanilang mga modelo).