Ideas from 'The Limits of Contingency' by Gideon Rosen [2006], by Theme Structure

[found in 'Identity and Modality' (ed/tr MacBride,Fraser) [OUP 2006,0-19-928674-8]].

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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II

18851

Pairing (with Extensionality) guarantees an infinity of sets, just from a single element

9. Objects / A. Existence of Objects / 4. Impossible objects

18852

A Meinongian principle might say that there is an object for any modest class of properties

10. Modality / A. Necessity / 5. Metaphysical Necessity

18850

'Metaphysical' modality is the one that makes the necessity or contingency of laws of nature interesting

18849

Metaphysical necessity is absolute and universal; metaphysical possibility is very tolerant

18857

Standard Metaphysical Necessity: P holds wherever the actual form of the world holds

18858

Sets, universals and aggregates may be metaphysically necessary in one sense, but not another

18856

Non-Standard Metaphysical Necessity: when ¬P is incompatible with the nature of things

10. Modality / A. Necessity / 6. Logical Necessity

18848

Something may be necessary because of logic, but is that therefore a special sort of necessity?

10. Modality / B. Possibility / 3. Combinatorial possibility

18855

Combinatorial theories of possibility assume the principles of combination don't change across worlds

10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible

18853

A proposition is 'correctly' conceivable if an ominiscient being could conceive it

26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory

18854

The MRL view says laws are the theorems of the simplest and strongest account of the world