Absolute infinity: Difference between revisions
Connection to reflection principles
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Absolute infinity and attempts to define numbers beyond (which is ironic, since the whole point of absolute infinity is that it could not be transcended beyond) feature prominently in fictional googology.
==As justification for reflection==
Later authors have connected Cantor's remark that absolute infinity "can not be conceived" to reflection principles. For example, Maddy states:<ref>P. Maddy, "[https://www.cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms1.pdf Believing the Axioms I]". Journal of Symbolic Logic, vol. 53, no. 2 (1988), pp.481--511.</ref><sup>p.503</sup>
> Hallet ... traces ''reflection'' to Cantor's theory that the sequence of all transfinite numbers is absolutely infinite, like God. As such, it is incomprehensible to the finite human mind, not subject to mathematical manipulation. Thus nothing we can say about it, no theory or description, could single it out; in other words, anything true of \( V \) is already true of some [\( V_\alpha \)].
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