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Full Idea
If quantification into sentence position is substitutional, then it is metaphysically neutral. A substitutionally interpreted 'existential' quantification is semantically equivalent to the disjunction (possibly infinite) of its substitution instances.
Gist of Idea
Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances
Source
Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §2)
Book Ref
-: 'Dialectica' [-], p.262
A Reaction
Is it not committed to the disjunction, just as the objectual reading commits to objects? Something must make the disjunction true. Or is it too verbal to be about reality?
| 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] |