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Referential Quantification: is an expression for the form of quantification normally used in predicate logic ("There is at least one object x with the property ..." or "For all objects x applies...."). Here, something is said about objects, with their existence being presupposed. On the other hand, substitutional quantification is about linguistic expressions ("There is a true sentence that ..."). 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 domain is not classified into classes is. E.g. you can replace a table by some box, but not the word table by any available word. See also substitutional quantification, quantification, substitution, inference, implication, stronger/weaker.
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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 Referential Quantification - Dictionary of Arguments

III 378
Referential quantification: if sentences are substitutes, it is again about referential quantification: are (s) sentences treated as objects? Kripke: in any case there is a dispute: are the variables going over sentences, propositions or truth values?
III 377
Referential quantification/interpretation/KripkeVsSubstitutionalism: the point is that an uninterpreted formal system is exactly what it is: uninterpreted! Then it is simply impossible to ask for the "right interpretation"!
>Interpretation/Kripke
, >Substitutional quantification/Kripke.
III 378
1. Kripke: surely there are certain formal systems that allow referential interpretation but not substitutional interpretation. Example Quine:
If (Ex)φ(x) is provable but ~φ(t) (negation!) is provable for any expression t that can be used for x, resulting in a meaningful sentence φ(t), it is obviously impossible to give the system a substitutional interpretation, but if the formation rules are standard, and it is formally consistent, a referential interpretation is possible.
((s) Although the referential interpretation makes "ontologically stronger assumptions"!).
If ~φ(t) is provable for each expression in a class C, while ((s) simultaneously) (Ex)φ(x) is provable, it is impossible to let all theorems be true and interpret the quantifier as replaceable with the substitution class C.
These conditions are sufficient, but demonstrably not necessary, so that a first-stage theory does not receive a substitutional interpretation that makes all theorems true.
2. What about the common problem? (Referential interpretation excluded but substitutional interpretation allowed):
The autonymous interpretation (see section 3 above, where each term denotes itself) could suggest a negative answer. And this will be one reason why many mathematical logicians did not want to treat substitutional quantification as an independent model-theoretical topic.
KripkeVs: however, there may be cases where substitutional quantification is more appropriate than referential quantification.
For example, if the substitution class insists on sentences of L0, a referential interpretation with sentences as substitutes leads to a philosophical dispute: do the variables go over propositions, over sentences or over truth values? Are the entities in the area denoted by the sentences?
Connectives/Kripke: connectives do not play a threefold role now: as
a) sentence connectives, b) function symbols and c) predicates. However, in Frege's system they play such a threefold role!
>Connective/Kripke, >Logical constant.

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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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