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Single Idea 9026

[filed under theme 5. Theory of Logic / G. Quantification / 4. Substitutional Quantification ]

Full Idea

An existential quantification could turn out false when substitutionally construed and true when objectually construed, because of there being objects of the purported kind but only nameless ones.

Gist of Idea

Some quantifications could be false substitutionally and true objectually, because of nameless objects

Source

Willard Quine (Philosophy of Logic [1970], Ch.6)

Book Ref

Quine,Willard: 'Philosophy of Logic' [Prentice-Hall 1970], p.93


A Reaction

(Cf. Idea 9025) Some irrational numbers were his candidates for nameless objects, but as decimals they are infinite in length which seems unfair. I don't take even pi or root-2 to be objects in nature, so not naming irrationals doesn't bother me.

Related Idea

Idea 9025 You can't base quantification on substituting names for variables, if the irrationals cannot all be named [Quine]


The 23 ideas with the same theme [quantifiers range over expressions instead of objects]:

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]