Philosophy Lexicon of Arguments

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Abstraction: Subsumption of objects by non-consideration of certain properties. See also equivalence relation, concretion, concreta, indiscernibility.

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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I 286
Intensional abstraction: "the act of being a dog", "the act of baking a cake", "the act of erring".
I 289
Class abstraction re-traced to singular descriptions: (iy)(x)(x from y iff
..x..) - instead of: x^(..x..) - is not possible for intensional abstraction.
I 295
Abstraction of relations, propositions and properties: opaque (E.g. of the planet).
I 322
Property abstraction (elimination) instead of "a = x(..x..)" - New: irreducible two-digit Operator "0": "a0x(..x..)" - variables are the only thing that remains - Primacy of the pronoun.
IX 12 ~
Class abstraction/Quine: "{x:Fx}" refers to "the class of all objects x with Fx" - in the eliminable combination that we have in mind "e" appears only in front of a class abstraction term and class abstraction terms appear only after "e" - the whole combination "y e {x: Fx}" is reduced according to a law:
Concretization law/Quine: reduces "y e {x: Fx}" to "Fy" - existence/ontology: thus no indication remains that such a thing as the class {x:Fx} exists at all.
Introduction: it would be a mistake, e.g., to write "*(Fx)" for "x = 1 and EyFy". Because it would be wrong to conclude "*(F0) *(F1)" from "F0 F1" - therefore we have to mistrust our definition 2.1 which has "Fx" in the definiendum, but does not have it in the definiens.
IX 16
Relations abstraction/relation abstraction/Quine: "{xy:Fxy}" is to represent the relationship of a certain x to a certain y such that Fxy - Relation/correctness/Quine: parallel to the element relationship there is the concept of correctness for relations - Definition concretization law for relations/Quine: is also the definition correctness/relation: "z{xy: Fxy}w stands for "Fzw".
IX 52
Function abstraction/lambda operator/Quine: before terms, generates terms (expressions) - (Frege/Church: here also of statements, thus a second time class abstraction, but both group statements under terms and classes under functions - (QuineVsFrege,QuineVsChurch) - Definition lambda operator/Quine: if "...x..." contains x as a free variable, lx (...x...) is that function whose value is ...x... for each argument x - therefore lx(x²) the function "the "square of" - general: "lx(...x...)" stands for "{ : y = ...x...}" - identity: lx x{: y = x } = l. - lx {z: Fxy} = {: y = {z: Fxz}} -. "lx a" stands for "{: y = a}" - new: equal sign now stands between variable and KAT (set abstraction).
IX 181
Abstraction/order/Quine: the order of the abstracting expression must not be less than that of the free variables.

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.

W.V.O. Quine
Wort und Gegenstand Stuttgart 1980

W.V.O. Quine
Theorien und Dinge Frankfurt 1985

W.V.O. Quine
Grundzüge der Logik Frankfurt 1978

W.V.O. Quine
Mengenlehre und ihre Logik Wiesbaden 1967

W.V.O. Quine
Die Wurzeln der Referenz Frankfurt 1989

W.V.O. Quine
Unterwegs zur Wahrheit Paderborn 1995

W.V.O. Quine
From a logical point of view Cambridge, Mass. 1953

W.V.O. Quine
Bezeichnung und Referenz
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982

W.V.O. Quine
Philosophie der Logik Bamberg 2005

W.V.O. Quine
Ontologische Relativität Frankfurt 2003

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Ed. Martin Schulz, access date 2017-10-24