On Cantor's absolute infinite (1)

I have re-read Jané's famous article

• I. Jané, `The Role of the Absolute Infinite in Cantor's Conception of Set', Erkenntnis, 42, 1995, 375--402.

Last time I've read is about two and half years ago, and I recognized nothing remains with me :-( As if at the first time...

BTW, I can mainly agree with him where he argues that there is a shift of emphasis among Cantor's conception of the Absolute Infinite(AI). But I feel something strange when Jané writes this:

Between the writing of Grundlagen and the apperarance of Beiträge, Cantor conceived the absolute infinite as actually existing (although not an object of mathematics), while after Beiträge (from 1897 on) he viewed the absolute infinite as existing only potentially. (p. 383, emphasis is mine)

Shortly, `He is taking the actuality away from the absolute.'(p. 390) After Beiträge, did Cantor really take `the actuality' from AI? The putative evidences are, I think, such Cantor's comments in the letter Jané cites (from his translation, p. 393f.).

I say of a set that it can be thought as completed [...] if it is possible to think of the set together with the totality of their elements as actually existing.
[...] in this totality they are not an object of further mathematical consideration, I call them `absolutely infinite sets'.

Or from another letter (from Cantor to Jourain, 9 July 1904),

[...] it is essential to these[inconsistent multiplicities] that they can never be thought of as completed and actually existing.

For me, these passages suggest nothing different from the conception in Grundlagen. Here Cantor says that it is impossible to think AI as actually existing, and AI is not an object of mathematics. But who is it that cannot to think so? Surely, WE are (or, at least, not God). In these passages, I think, Cantor sees AI only from mathematical viewpoint. It does not mean he denied its actuality in non-mathematical viewpoint, esp. religious one.

More points to note...