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
Pairing (with Extensionality) guarantees an infinity of sets, just from a single element
                        Full Idea: In conjunction with Extensionality, Pairing entails that given a single non-set, infinitely many sets exist.
                        From: Gideon Rosen (The Limits of Contingency [2006], 04)
9. Objects / A. Existence of Objects / 4. Impossible objects
A Meinongian principle might say that there is an object for any modest class of properties
                        Full Idea: Meinongian abstraction principles say that for any (suitably restricted) class of properties, there exists an abstract entity (arbitrary object, subsistent entity) that possesses just those properties.
                        From: Gideon Rosen (The Limits of Contingency [2006], 04)
                        A reaction: This is 'Meinongian' because there will be an object which is circular and square. The nub of the idea presumably resides in what is meant by 'restricted'. An object possessing every conceivable property is, I guess, a step too far.
10. Modality / A. Necessity / 5. Metaphysical Necessity
'Metaphysical' modality is the one that makes the necessity or contingency of laws of nature interesting
                        Full Idea: 'Metaphysical' modality is the sort of modality relative to which it is an interesting question whether the laws of nature are necessary or contingent.
                        From: Gideon Rosen (The Limits of Contingency [2006], 02)
                        A reaction: Being an essentialist here, I take it that the stuff of the universe necessitates the so-called 'laws'. The metaphysically interesting question is whether the stuff might have been different. Search me! A nice test of metaphysical modality though.
Metaphysical necessity is absolute and universal; metaphysical possibility is very tolerant
                        Full Idea: If P is metaphysically necessary, then it is absolutely necessary, and necessary in every real (non-epistemic) sense; and if P is possible in any sense, then it's possible in the metaphysical sense.
                        From: Gideon Rosen (The Limits of Contingency [2006], 02)
                        A reaction: Rosen's shot at defining metaphysical necessity and possibility, and it looks pretty good to me. In my terms (drawing from Kit Fine) it is what is necessitated or permitted 'by everything'. So if it is necessitated by logic or nature, that's included.
Standard Metaphysical Necessity: P holds wherever the actual form of the world holds
                        Full Idea: According to the Standard Conception of Metaphysical Necessity, P is metaphysically necessary when it holds in every possible world in which the laws of metaphysics (about the form or structure of the actual world) hold
                        From: Gideon Rosen (The Limits of Contingency [2006], 10)
                        A reaction: Rosen has a second meaning, in Idea 18856. He thinks it is crucial to see that there are two senses, because many things come out as metaphysically necessary on one concept, but contingent on the other. Interesting....
Sets, universals and aggregates may be metaphysically necessary in one sense, but not another
                        Full Idea: It may be metaphysically necessary in one sense that sets or universals or mereological aggregates exist, while in another sense existence is always a contingent matter.
                        From: Gideon Rosen (The Limits of Contingency [2006], 10)
                        A reaction: This idea depends on Idea 18856 and 18857. Personally I only think mereological aggregates and sets exist when people decide that they exist, so I don't see how they could ever be necessary. I'm unconvinced about his two concepts.
Non-Standard Metaphysical Necessity: when P is incompatible with the nature of things
                        Full Idea: According to the Non-Standard conception of Metaphysical Necessity, P is metaphysically necessary when its negation is logically incompatible with the nature of things.
                        From: Gideon Rosen (The Limits of Contingency [2006], 10)
                        A reaction: Rosen's new second meaning of the term. My immediate problem is with it resting on being 'logically' incompatible. Are squares 'logically' incompatible with circles? I like the idea that it rests on 'the nature of things'. (Psst! natures = essences)
10. Modality / A. Necessity / 6. Logical Necessity
Something may be necessary because of logic, but is that therefore a special sort of necessity?
                        Full Idea: It is one thing to say that P is necessary in some generic sense because it is a truth of logic (true in all models of a language, perhaps). It is something else to say that P therefore enjoys a special sort of necessity.
                        From: Gideon Rosen (The Limits of Contingency [2006], 02)
                        A reaction: This encourages my thought that there is only one sort of necessity (what must be), and the variety comes from the different types of necessity makers (everything there could be, nature, duties, promises, logics, concepts...).
10. Modality / B. Possibility / 3. Combinatorial possibility
Combinatorial theories of possibility assume the principles of combination don't change across worlds
                        Full Idea: Combinatorial theories of possibility take it for granted ....that possible worlds in general share a syntax, as it were, differing only in the constituents from which they are generated, or in the particular manner of their arrangements.
                        From: Gideon Rosen (The Limits of Contingency [2006], 08)
                        A reaction: For instance, it might assume that every world has 'objects', to which 'properties' and 'relations' can be attached, or to which 'functions' can apply.
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
A proposition is 'correctly' conceivable if an ominiscient being could conceive it
                        Full Idea: To a first approximation, P is correctly conceivable iff it would be conceivable for a logically ominiscient being who was fully informed about the nature of things.
                        From: Gideon Rosen (The Limits of Contingency [2006], 05)
                        A reaction: Isn't the last bit covered by 'ominiscient'? Ah, I think the 'logically' only means they have a perfect grasp of what is consistent. This is to meet the standard problem, of ill-informed people 'conceiving' of things which are actually impossible.
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
The MRL view says laws are the theorems of the simplest and strongest account of the world
                        Full Idea: According to the Mill-Ramsey-Lewis account of the laws of nature, a generalisation is a law just in case it is a theorem of every true account of the actual world that achieves the best overall balance of simplicity and strength.
                        From: Gideon Rosen (The Limits of Contingency [2006], 08)
                        A reaction: The obvious objection is that many of the theorems will be utterly trivial, and that is one thing that the laws of nature are not. Unless you are including 'metaphysical laws' about very very fundamental things, like objects, properties, relations.