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5. Theory of Logic / G. Quantification / 4. Substitutional Quantification

[quantifiers range over expressions instead of objects]

23 ideas
Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
The values of variables can't determine existence, because they are just expressions [Ryle, by Quine]
If quantification is all substitutional, there is no ontology [Quine]
You can't base quantification on substituting names for variables, if the irrationals cannot all be named [Quine]
Some quantifications could be false substitutionally and true objectually, because of nameless objects [Quine]
Either reference really matters, or we don't need to replace it with substitutions [Quine]
Quine thought substitutional quantification confused use and mention, but then saw its nominalist appeal [Quine, by Marcus (Barcan)]
Maybe a substitutional semantics for quantification lends itself to nominalism [Marcus (Barcan)]
Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)]
A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)]
Substitutional quantification is just a variant of Tarski's account [Wallace, by Baldwin]
The substitutional quantifier is not in competition with the standard interpretation [Kripke, by Marcus (Barcan)]
Substitutional quantification is just standard if all objects in the domain have a name [Bostock]
Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C]
On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C]
We can quantify over fictions by quantifying for real over their names [Lewis]
Substitutional universal quantification retains truth for substitution of terms of the same type [Jacquette]
Nominalists like substitutional quantification to avoid the metaphysics of objects [Jacquette]
Substitutional quantification is referential quantification over expressions [Fine,K]
We might reduce ontology by using truth of sentences and terms, instead of using objects satisfying models [Shapiro]
Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances [Williamson]
The substitution view of quantification says a sentence is true when there is a substitution instance [Orenstein]
Quantification can't all be substitutional; some reference is obviously to objects [Hofweber]