Absolute infinity: Difference between revisions

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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 [\( V_\alpha \)].

: 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 [\( V_\alpha \)].

Revision as of 05:32, 1 September 2023 (edit) C7X (talk \| contribs) (Connection to reflection principles) ← Older edit		Revision as of 05:35, 1 September 2023 (edit) (undo) C7X (talk \| contribs) No edit summary Newer edit →
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	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>		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 [\( V_\alpha \)].		: 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 [\( V_\alpha \)].

Absolute infinity: Difference between revisions

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