  This brings us to steps 1 and 3 in the Skolemite argument. Step 1 is where different versions of this argument display the most variability. In some cases, step 1 is simply presupposed, so it's hard to get a feel for how the underlying argument is really supposed to go (Kneale and Kneale 1962; Goodstein 1963; Wang 1964). In other cases, it's suggested that any rejection of the algebraic conception—and, in particular, any move to simply take expressions like “all sets” or “is really uncountable” at face value—amounts to falling back on an unacceptably naive form of “Platonism” (Fine 1968; Thomas 1968, 1971; Klenk 1976). In still other cases, Skolemites follow Skolem's lead and appeal to the set-theoretic paradoxes to bolster their rejection of Platonism; they then suggest that the abandonment of Platonism leaves the algebraic conception of axiomatization as the only viable alternative (Klenk 1976).