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Full Idea
Axiom of Infinity: There is at least one limit level.
Gist of Idea
Infinity: There is at least one limit level
Source
Michael Potter (Set Theory and Its Philosophy [2004], 04.9)
Book Ref
Potter,Michael: 'Set Theory and Its Philosophy' [OUP 2004], p.68
A Reaction
A 'limit ordinal' is one which has successors, but no predecessors. The axiom just says there is at least one infinity.
Related Idea
Idea 15931 The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine]
| 10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
| 10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| 13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
| 10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
| 10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
| 13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| 10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
| 10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| 13044 | Infinity: There is at least one limit level [Potter] |
| 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
| 13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |