|Quantification: is a function within the predicate logic, in which a property is attributed to an object yet to be determined. A) Existence quantification e.g. (Ex) (Fx) "At least one object x is F". It is assumed that the object denoted by x exists. B) Universal quantification (notation (x) ...) "For all x applies ...". Both forms of quantification can be negated, covering most of the everyday cases. In addition, a subject domain must be chosen, within which the statements that result from the insertion of objects are meaningful. See also existence, non-existence, existence assumption, existence predicate, universal quantification, existence quantification, domains, opacity, intensional objects._____________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. |
Arthur N. Prior on Quantification - Dictionary of Arguments
Non-nominal quantification / Prior: e.g. "whoever" from "who", "where ever" from "there", "somehow" - correspond to adverbs. - E.g. "it s something I m not" - an adjective and not a noun.
Tractatus: (Also Wittgenstein, Philosophical Investigations, § 134) "this is the way things are" -> "sentence variable".
Higher quantification/sentence variable/Wittgenstein/Prior: "Things are such" does not tell even how things are but "things are somehow" is doing it! - To the extent of the logically true "for some p, p". - so you can translate "x is coming": "for some x,x is coming".
Higher quantification: over non-nouns,"non-nominal quantification"_____________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. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Objects of thought Oxford 1971
Arthur N. Prior
Papers on Time and Tense 2nd Edition Oxford 2003