|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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|AMD II p340
Substitutional Quantification/SQ//Belnap/Dunn: did not even require ontology of expressions - KripkeVs: it does - KripkeVsBelnap: if no ontological commitment (OC), then why should L be metalanguage of L0? - Then T (x) no predicate, then the metalanguage is a mere form without interpretation - then no truth theory
SQ/Belnap: the expressions of metalanguage designate, or they do not.
KripkeVsBelnap: 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
Truth Theory/KripkeVsWallace/VsBelnap: metalanguage may not purely formally be construed as uninterpreted - (object language may be)_____________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.
Facing the Future: Agents and Choices in Our Indeterminist World Oxford 2001