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Full Idea
In conjunction with Extensionality, Pairing entails that given a single non-set, infinitely many sets exist.
Gist of Idea
Pairing (with Extensionality) guarantees an infinity of sets, just from a single element
Source
Gideon Rosen (The Limits of Contingency [2006], 04)
Book Ref
'Identity and Modality', ed/tr. MacBride,Fraser [OUP 2006], p.18
| 18849 | Metaphysical necessity is absolute and universal; metaphysical possibility is very tolerant [Rosen] |
| 18850 | 'Metaphysical' modality is the one that makes the necessity or contingency of laws of nature interesting [Rosen] |
| 18848 | Something may be necessary because of logic, but is that therefore a special sort of necessity? [Rosen] |
| 18851 | Pairing (with Extensionality) guarantees an infinity of sets, just from a single element [Rosen] |
| 18852 | A Meinongian principle might say that there is an object for any modest class of properties [Rosen] |
| 18853 | A proposition is 'correctly' conceivable if an ominiscient being could conceive it [Rosen] |
| 18854 | The MRL view says laws are the theorems of the simplest and strongest account of the world [Rosen] |
| 18855 | Combinatorial theories of possibility assume the principles of combination don't change across worlds [Rosen] |
| 18858 | Sets, universals and aggregates may be metaphysically necessary in one sense, but not another [Rosen] |
| 18857 | Standard Metaphysical Necessity: P holds wherever the actual form of the world holds [Rosen] |
| 18856 | Non-Standard Metaphysical Necessity: when ¬P is incompatible with the nature of things [Rosen] |