## Psychology Dictionary of ArgumentsHome | |||

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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._____________ 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 |
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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. _____________ 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 InEigennamen, Ursula Wolf, Frankfurt/M. 1993 Kripke III Saul A. Kripke Is there a problem with substitutional quantification? InTruth and Meaning, G. Evans/J McDowell, Oxford 1976 Kripke IV S. A. Kripke Outline of a Theory of Truth (1975) InRecent Essays on Truth and the Liar Paradox, R. L. Martin (Hg), Oxford/NY 1984 |