Philosophy Dictionary of ArgumentsHome
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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._____________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. | |||
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Nuel Belnap on Substitutional Quantification - Dictionary of Arguments
AMD II p340 Substitutional Quantification/SQ//Belnap/Dunn: did not even require ontology of expressions. KripkeVs: it does. >Substitutional Quantification/Kripke. KripkeVsBelnap: if there is no ontological commitment (OC), then why should L be metalanguage of L0? - Then T(x) is no predicate, then the metalanguage is a mere form without interpretation. - Then there is no truth theory. >Ontological commitment, >Metalanguage, >Truth theory, >Interpretation. II 341 Substitutional Quantification/Belnap: the expressions of the metalanguage designate, or they do not. >Designation, >Denotation, >Reference. II 344 KripkeVsBelnap: this cannot be answered so categorically. - The answer depends on both: on L0 and on the existence of simple chain predicates. - You can also define (and derive) many new symbol strings. - That does not mean that the new ontology has anything to do with the alleged or real "designation" of the expressions. II 342 Truth Theory/KripkeVsWallace/VsBelnap: the metalanguage may not purely formally be construed as uninterpreted. - (The object language may be). >Object language._____________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. |
Beln I N. Belnap Facing the Future: Agents and Choices in Our Indeterminist World Oxford 2001 |
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> Counter arguments against Belnap
> Counter arguments in relation to Substitutional Quantification
Ed. Martin Schulz, access date 2024-04-28