|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.|
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Referential Quantification/Schiffer: substituents: are not logical constants ((s) = Objects) - in 1. order logic these can only be singular terms - values that the objects are in the domain of discourse - they are examined, in order to obtain the truth value of the sentences with referential quantification - substitutional Quantification: here you can have substitutional variable substituents, but no values - but the substituent can have values - even in 1. order logic the expressions can be of every semantic category - ontological commitment: only has referential quantification.
Function/Referential quantification/Schiffer: functions require referential quantification instead of substitutional quantification - ((s) The values of these variables must be objects, such as numbers, not linguistic entities)._____________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.
Remnants of Meaning Cambridge 1987