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

18849

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

18850

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

18858

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

18857

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

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