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Full Idea
The converse Barcan formula does not allow any contingent truths at all to have a truthmaker. Once cannot combine the converse Barcan formula with any truthmaker principle worth having.
Clarification
See in Formal Logic|Modal logic for the Barcan formula
Gist of Idea
The converse Barcan formula will not allow contingent truths to have truthmakers
Source
Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §3)
Book Ref
-: 'Dialectica' [-], p.265
A Reaction
One might reply, so much the worse for the converse Barcan formula, but Williamson doesn't think that.
| 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] |