Admittedly Cantor was in his writings not very explicit about what he did take the set theoretic universe as a whole to be. One problem is that it is not in every instance clear whether he has a theological or a mathematical conception of absolute infinity in mind. Indeed, he argues that it is the task not of mathematics but of ‘speculative theology’ to investigate what can be humanly known about the absolutely infinite. The following passage, for example, leans heavily to the theological side: I have never assumed a “Genus Supremum” of the actual infinite. Quite on the contrary I have proved, that there can be no such “Genus Supremum” of the actual infinite. What lies beyond all that is finite and transfinite is not a “Genus”; it is the unique, completely individual unity, in which everything is, which comprises everything, the ‘Absolute’, for human intelligence unfathomable, also that not subject to mathematics, unmeasurable, the “ens simplicissimum”, the “Actus purissimus”. In this quotation, Cantor speaks of the necessity of ‘knowing’ the domain of variation through a ‘definition’. Surely Cantor is merely sloppy here, and we should discount the epistemological overtones. Another slip can be detected in Cantor’s use of the word ‘set’ in this quotation. Cantor means the argument to be applicable not just just to sets but also to absolute infinities. which is by many called “God”. All this is related to the fact that in an Augustinian vein, Cantor takes all the sets to exist as ideas in the mind of God.
And that last sentence rings a bell too 🙂 For Ramanujan said “An equation for me has no meaning, unless it represents a thought of God”.
We seem to be homing in on something here!