|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/refQ/substitutional quantification/sQ/non-existent/non-existence/Boer: for all those who believe that there are non-existent things, it is possible to accept (8):
(8) (referential quantification) It is possible that some things that do not exist are nameless.
N.B.: with substitutional quantification, (8) would be reformulated to (9)
(9) (substutional quantification) It is possible that (Σy) (y does not exist & y is nameless).
Problem: (9) cannot be true because for every name a, the assertion [a is nameless] would be self-contradictory._____________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.
Steven E. Boer
Thought-Contents: On the Ontology of Belief and the Semantics of Belief Attribution (Philosophical Studies Series) New York 2010
Steven E. Boer
Knowing Who Cambridge 1986