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Full Idea
That there is just one necessary existent is surely false, for if x is a necessary, {x} is a distinct necessary existent.
Gist of Idea
A thing can't be the only necessary existent, because its singleton set would be as well
Source
Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §1)
Book Ref
-: 'Dialectica' [-], p.257
A Reaction
You would have to believe that sets actually 'exist' to accept this, but it is a very neat point.
| 15131 | If metaphysical possibility is not a contingent matter, then S5 seems to suit it best [Williamson] |
| 15133 | A thing can't be the only necessary existent, because its singleton set would be as well [Williamson] |
| 15134 | The truthmaker principle requires some specific named thing to make the difference [Williamson] |
| 15135 | If the domain of propositional quantification is constant, the Barcan formulas hold [Williamson] |
| 15138 | Not all quantification is objectual or substitutional [Williamson] |
| 15136 | Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances [Williamson] |
| 15137 | If 'fact' is a noun, can we name the fact that dogs bark 'Mary'? [Williamson] |
| 15142 | Our ability to count objects across possibilities favours the Barcan formulas [Williamson] |
| 15139 | Converse Barcan: could something fail to meet a condition, if everything meets that condition? [Williamson] |
| 15141 | Truthmaker is incompatible with modal semantics of varying domains [Williamson] |
| 15140 | The converse Barcan formula will not allow contingent truths to have truthmakers [Williamson] |
| 18492 | Not all quantification is either objectual or substitutional [Williamson] |