The popular stereotype about Cantor is that he invented transfinite arithmetic, but that he was also mentally deranged and theologically obsessed, in a naive autodidactic sort of way. However, Cantor was quite philosophically literate, and I find it interesting that he had a well-worked out philosophy of the infinite, and that he read Spinoza and Leibniz very closely. His discoveries led him to distinguish different « sizes » of infinity, allowing him to re-read the classical philosophers from a new point of view.
« Cantor’s inquisitive « how infinite » was an impossible question. To minds like Spinoza and Leibniz, the infinite in this absolute sense was incomprehensible, as was God, and therefore any attempt to assign a basis for determining magnitudes other than merely potential ones was predestined to fail » (GEORG CANTOR His Mathematics and Philosophy of the Infinite, Joseph Warren Dauben, 123).
Unlike Badiou, Cantor does not identify the Absolute with « V », the class of all sets. On the contrary, he distinguishes them for theological reasons, that I reject, and so subsumes the transfinite to the regime of the One.
However, I think that there is still good reason to distinguish the Absolute from V, and that Badiou does so implicitly in that he carefully distinguishes philosophical concepts as metaphorisations or poetisations of mathematics from mathematics itself.
(This is in reference to Badiou’s thesis that philosophy is a « poetisation » of mathematics).
One could argue from a Badiousian perspective that Deleuze’s concepts of infinity, as occurring for example in WHAT IS PHILOSOPHY? (where the words « infinite », « infinity », « absolute » – and their synonym, the « outside » and the composite terms « absolute horizon » and « absolute velocity » occur on nearly every page) are too qualitative, too vague and imprecise, remaining too intuitive and insufficiently theorised, too close to the « poetic » end of the spectrum.
In contrast, viewed from a Deleuzian perspective, Badiou’s concepts, which are based on the mathematical hierarchy of infinite cardinals, are insufficiently philosophical. While still being « poetic » they are much closer to the mathematical end of the spectrum, and so represent a slowing down of the plane of consistency. However, this Deleuzian critical term of « slowing down » is itself intuitive and poetical.