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Substitutional Quantification: the substitutional quantification is concerned with the determination of whether linguistic expressions can be formed for a situation. E.g. "There is a true sentence that ...". In contrast, the referential quantification - the form of quantification normally used in predicate logic - tells us something about objects. E.g. "There is at least one object x with the property ..." or "For all objects x applies ...". The decisive difference between the two types of quantification is that, in the case of the possible replacement of a linguistic expression by another expression, a so-called substitution class must be assumed which cannot exist in the case of objects since the everyday subject area is not classified into classes is. E.g. you can replace a table by some box, but you cannot replace the word table by any available word. See also referential quantification, quantification, substitution, inference, implication, stronger/weaker, logic, systems, semantic rise.
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Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

 
Author Concept Summary/Quotes Sources

Saul A. Kripke on Substitutional Quantification - Dictionary of Arguments

III 325ff
Substitutional Quantification/SQ/Kripke: substitutional quantification is ontologically neutral, perhaps purely linguistic. Truth and satisfaction are defined here.
>Truth
, >Satisfaction, >Satisfiability.
On the other hand there is the referential quantification (RQ).
>Referential quantification, >Referential quantification/Kripke.
It refers to objects (world). The referential quantification has no satisfaction, only truth. Wallace/Tharp: thesis: there is no difference between substitutional quantification and referential quantification (KripkeVsWallace/VsTharp).
III 330
Substitutional quantification: formulas: sentences do not receive any semantic interpretation here, they only have an auxiliary function. Referential quantification: here such formulas define relations and are "satisfied" by sequences.
III 367
Form/Kripke: the form must include sentence. Well-formed/WFF/Kripke: problem: T(a) ↔ x is not well-formed when x is replaced by strings of symbols that are no sentences and therefore no form.
Substitutional quantification/(s): the substitutional quantification needs a substitution class, i.e. a set of true sentences from the extended language from the set of true sentences in the source language (it must be unambiguous, i.e. the only such set). The referential quantification does not need that.
III 332
Substitution Class/SC/Kripke: the substitution class does not contain any specific descriptions.
>Descriptions.
III 349
Substitutional Quantification/Kripke: the substitutional quantification does not interpret formulas at all. However, there is satisfaction if there is a denotation relation - but only for transparency.
>Meta language, >Opacity.
III 352
Substitutional quantification/Kripke: e.g. Cicero/Tullius: dramatic difference: (Sx1)((Sx2)(x1 = x2 u f(x1) u ~f(x2)) true (not interpreted), but the same with (Ex1) (Ex2) ... false (standard q) - if opacity is to be eliminated from the metalanguage, then its referential variables have to work through denotations of expressions ((s) objects), not only through expressions - then (substitutional) quantification in opaque contexts is possible.
III 352
Substitutional quantification/quantification in opaque contexts/Kripke: e.g. R(a): may then be explicitly defined when there are suitable predicates in the metalanguage: R(a) applies only if either a) a is a formula of the form P(t) (pseudo predicate "was so-called because of its size") and d(t) is named through the term t because of the size of d(t), or b) A is a formula of the form Q(t) and d(t) is bold - so that R(a) is eliminated as a primitive notation and the metalanguage only includes referential quantification without opacity. Meta language: it had to be expanded: so that the referential variables do not only work through expressions alone, but also through the denotations of these expressions.

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Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Kripke I
S.A. Kripke
Naming and Necessity, Dordrecht/Boston 1972
German Edition:
Name und Notwendigkeit Frankfurt 1981

Kripke II
Saul A. Kripke
"Speaker’s Reference and Semantic Reference", in: Midwest Studies in Philosophy 2 (1977) 255-276
In
Eigennamen, Ursula Wolf, Frankfurt/M. 1993

Kripke III
Saul A. Kripke
Is there a problem with substitutional quantification?
In
Truth and Meaning, G. Evans/J McDowell, Oxford 1976

Kripke IV
S. A. Kripke
Outline of a Theory of Truth (1975)
In
Recent Essays on Truth and the Liar Paradox, R. L. Martin (Hg), Oxford/NY 1984


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