But was Cantor a Formalist? He never presented his results in the formal context of stripped-down deductions from axioms. His mathematics isn’t about symbols that could mean this or that, but about what he saw as real ideas in the divine intellect, and corporeal objects in the world. Completed infinities were, for him, actual, not like the formless and merely potential apeiron of the Greeks. Hilbert purged mathematics of meaning; Cantor flooded his mathematics with metaphysics and theology.
