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

[possibilities are combinations of the actual]

4 ideas
Maybe possibilities are recombinations of the existing elements of reality [Mumford]
     Full Idea: It has been suggested that we could think of possibilities as recombinations of all the existing elements of reality.
     From: Stephen Mumford (Metaphysics: a very short introduction [2012], 8)
     A reaction: [Armstrong 1989 is the source] The obvious problem would be that the existence of an entirely different reality would be impossible, if this was all possibility could be. It seems to cramp the style of the possible too much. Are properties elements?
Combinatorial possibility has to allow all elements to be combinable, which seems unlikely [Mumford]
     Full Idea: The combinatorial account only works if you allow that the elements are recombinable. ...But could Lincoln really have been green? It seems possible that you could jump to the moon, unless we impose some restrictions.
     From: Stephen Mumford (Metaphysics: a very short introduction [2012], 8)
     A reaction: Mumford suggests different combination rules for logical and natural possibility. The general objection is that combinatorial possibility is too permissive - which it clearly is.
Combinatorial possibility relies on what actually exists (even over time), but there could be more [Mumford]
     Full Idea: Can combinatorial possibility deliver enough possibilities? It uses the existing elements, but there might have been one more particular or one more property. Even extended over time, the elements seem finite, yet there could have been more.
     From: Stephen Mumford (Metaphysics: a very short introduction [2012], 8)
     A reaction: [compressed] One objection is that the theory allows too much, and now the objection is that it allows too little. Both objections are correct, so that's the end of that. But I admire the attempt to base modality on actuality.
Combinatorial theories of possibility assume the principles of combination don't change across worlds [Rosen]
     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.