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Single Idea 13674

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

Full Idea

The main role of substitutional semantics is to reduce ontology. As an alternative to model-theoretic semantics for formal languages, the idea is to replace the 'satisfaction' relation of formulas (by objects) with the 'truth' of sentences (using terms).

Gist of Idea

We might reduce ontology by using truth of sentences and terms, instead of using objects satisfying models

Source

Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4)

Book Ref

Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.243

A Reaction

I find this very appealing, and Ruth Barcan Marcus is the person to look at. My intuition is that logic should have no ontology at all, as it is just about how inference works, not about how things are. Shapiro offers a compromise.

Related Ideas

Idea 13675 Substitutional semantics only has countably many terms, so Upward Löwenheim-Skolem trivially fails [Shapiro]

Idea 13678 The most popular account of logical consequence is the semantic or model-theoretic one [Sider]

Idea 13679 Maybe logical consequence is more a matter of provability than of truth-preservation [Sider]

Idea 17988 Quantification can't all be substitutional; some reference is obviously to objects [Hofweber]

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

9874 Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
10800 The values of variables can't determine existence, because they are just expressions [Ryle, by Quine]
21642 If quantification is all substitutional, there is no ontology [Quine]
9025 You can't base quantification on substituting names for variables, if the irrationals cannot all be named [Quine]
9026 Some quantifications could be false substitutionally and true objectually, because of nameless objects [Quine]
10801 Either reference really matters, or we don't need to replace it with substitutions [Quine]
10793 Quine thought substitutional quantification confused use and mention, but then saw its nominalist appeal [Quine, by Marcus (Barcan)]
10785 Maybe a substitutional semantics for quantification lends itself to nominalism [Marcus (Barcan)]
10795 Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)]
10798 A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)]
10009 Substitutional quantification is just a variant of Tarski's account [Wallace, by Baldwin]
10792 The substitutional quantifier is not in competition with the standard interpretation [Kripke, by Marcus (Barcan)]
18123 Substitutional quantification is just standard if all objects in the domain have a name [Bostock]
9469 Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C]
9468 On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C]
15533 We can quantify over fictions by quantifying for real over their names [Lewis]
9465 Substitutional universal quantification retains truth for substitution of terms of the same type [Jacquette]
9466 Nominalists like substitutional quantification to avoid the metaphysics of objects [Jacquette]
12222 Substitutional quantification is referential quantification over expressions [Fine,K]
13674 We might reduce ontology by using truth of sentences and terms, instead of using objects satisfying models [Shapiro]
15136 Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances [Williamson]
8475 The substitution view of quantification says a sentence is true when there is a substitution instance [Orenstein]
17988 Quantification can't all be substitutional; some reference is obviously to objects [Hofweber]