|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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Substitutional quantification/Field: Solution for the formulation of infinite conjunctions.
Def Disquotational truth with substitutional quantification: (P: for all sentences, not objects) applies: S is true iff p (if S = p then p)._____________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.
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980