He made a clear defense of actual infinity and he proposed precise notions for treating infinite sets. In this way he even came quite close to such a central notion of set theory as cardinality. But after having been close to the *right* point of view, he departed from it in quite a *strange* direction. (Ferreiros 1999, p. 75).

The “right point of view” is the idea that cardinality is the only meaningful way to compare abstract sets with respect to the multiplicity of their elements, as Ferreiros explains in a note.

Experts on Bolzano are of a similar opinion. Paul Rusnock, who translated Bolzano’s *Theory of Science* into English, is very doubtful about Bolzano’s conception[^4]

> Bolzano did not see this point, and thus stopped on the boundary of Cantor’s set theory of cardinal numbers. …Bolzano falls short of a full and satisfactory treatment of the theory of the infinite. (Rusnock 2000, pp .194, 196).

Jan Šebestík believes that Bolzano’s interpretation is disputable as it wavers between two principles for comparing infinite sets.

> L’évidence intuitive de l’axiom \[du tout et de le part\], dérivée de la consideration des ensembles finis, interdit à Bolzano, comme à ces prédécesseurs, d’établir 