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.
 
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I 286
Intensional abstraction: "the act of being a dog", "the act of baking a cake", "the act of erring".
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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.
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I 295
Abstraction of relations, propositions and properties: opaque (E.g. of the planet).
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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.
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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.
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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".
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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).
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IX 181
Abstraction/order/Quine: the order of the abstracting expression must not be less than that of the free variables.

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

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

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

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

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

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

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

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

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

Q XII
W.V.O. Quine
Ontologische Relativität Frankfurt 2003


> Counter arguments against Quine
> Counter arguments in relation to Abstraction



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Ed. Martin Schulz, access date 2017-05-28