|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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|EMD II 325ff
Substitutional Quantification/SQ/Kripke: ontologically neutral, perhaps purely linguistic - truth and satisfaction are defined here - contrast: referential quantification/RQ - refers to objects (world) - referential quantification: no satisfaction, only truth - Wallace/Tharp: thesis no difference between substitution quantification and referential quantification - KripkeVsWallace/VsTharp.
EMD II 330
Substitutional quantification: formulas: that are no sentences do not receive any semantic interpretation here, they have only an auxiliary function - referential quantification: here such formulas define relations and are "satisfied" by sequences.
Form/Kripke: must include sentence - well-formed/WFF/Kripke: Problem: T(a) ↔ x is not well-formed when x is replaced by strings of symbols that are no sentences and therefore no form.
Substitutional quantification/(s): needs substitution class: set of true sentences from the extended language from the set of true sentences in the source language (it must be unambiguous, i.e. the only such set) - referential quantification: does not need that.
EMD II 332
Substitution Class/SC/Kripke: must not contain any specific descriptions.
Substitutional Quantification/Kripke: does not interpret formulas at all - but there is satisfaction if there is a denotation relation - but only for transparency.
EMD II 352
Substitutional quantification/Kripke: E.g. Cicero/Tullius: dramatic difference: (Sx1)((Sx2)(x1 = x2 u f(x1) u ~f(x2)) true (not interpreted), but the same with (Ex1) (Ex2) ... false (standard q) - if opacity is to be eliminated from the metalanguage, then its referential variables have to work through denotations of expressions ((s) objects), not only through expressions - then (substitutional) quantification in opaque contexts possible.
EMD II 352
Substitutional Quantification/Quantification in opaque contexts/Kripke: E.g. R(a): may then be explicitly defined when there are suitable predicates in the metalanguage: R(a) applies only if either a) a is a formula of the form P(t) (pseudo predicate "was so-called because of its size") and d(t) is named through the term t because of the size of d(t), or b) A is a formula of the form Q(t) and d(t) is bold - so that R(a) is eliminated as a primitive notation and the metalanguage only includes referential quantification without opacity - meta-language: it had to be expanded: so that the referential variables do not only work through expressions alone, but also through the denotations of these expressions._____________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.
Name und Notwendigkeit Frankfurt 1981
S. A. Kripke
Outline of a Theory of Truth (1975)
Recent Essays on Truth and the Liar Paradox, R. L. Martin (Hg), Oxford/NY 1984
G. Evans/J. McDowell
Truth and Meaning Oxford 1977
The Varieties of Reference (Clarendon Paperbacks) Oxford 1989