Dictionary 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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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.

 
Author Item Summary Meta data
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 12ff
Class abstraction/Quine: "{x:Fx}" refers to "the class of all objects x with Fx" - in the eliminable combination that we have in mind "ε" appears only in front of a class abstraction term and class abstraction terms appear only after "ε" - the whole combination "y ε {x: Fx}" is reduced according to a law:
Concretization law/Quine: reduces "y ε {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, λx (...x...) is that function whose value is ...x... for each argument x - therefore λx(x²) the function "the "square of" - general: "λx(...x...)" stands for "{ : y = ...x...}" - identity: λx x{: y = x } = λ. - λx {z: Fxy} = {: y = {z: Fxz}} -. "λx a" stands for "{: y = a}" - new: equal sign now stands between variable and a class abstraction term.
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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.


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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.
The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Quine I
W.V.O. Quine
Word and Object, Cambridge/MA 1960
German Edition:
Wort und Gegenstand Stuttgart 1980

Quine II
W.V.O. Quine
Theories and Things, Cambridge/MA 1986
German Edition:
Theorien und Dinge Frankfurt 1985

Quine III
W.V.O. Quine
Methods of Logic, 4th edition Cambridge/MA 1982
German Edition:
Grundzüge der Logik Frankfurt 1978

Quine V
W.V.O. Quine
The Roots of Reference, La Salle/Illinois 1974
German Edition:
Die Wurzeln der Referenz Frankfurt 1989

Quine VI
W.V.O. Quine
Pursuit of Truth, Cambridge/MA 1992
German Edition:
Unterwegs zur Wahrheit Paderborn 1995

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

Quine VII (a)
W. V. A. Quine
On what there is
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (b)
W. V. A. Quine
Two dogmas of empiricism
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (c)
W. V. A. Quine
The problem of meaning in linguistics
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (d)
W. V. A. Quine
Identity, ostension and hypostasis
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (e)
W. V. A. Quine
New foundations for mathematical logic
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (f)
W. V. A. Quine
Logic and the reification of universals
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (g)
W. V. A. Quine
Notes on the theory of reference
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (h)
W. V. A. Quine
Reference and modality
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (i)
W. V. A. Quine
Meaning and existential inference
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VIII
W.V.O. Quine
Designation and Existence, in: The Journal of Philosophy 36 (1939)
German Edition:
Bezeichnung und Referenz
In
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982

Quine IX
W.V.O. Quine
Set Theory and its Logic, Cambridge/MA 1963
German Edition:
Mengenlehre und ihre Logik Wiesbaden 1967

Quine X
W.V.O. Quine
The Philosophy of Logic, Cambridge/MA 1970, 1986
German Edition:
Philosophie der Logik Bamberg 2005

Quine XII
W.V.O. Quine
Ontological Relativity and Other Essays, New York 1969
German Edition:
Ontologische Relativität Frankfurt 2003

Quine XIII
Willard Van Orman Quine
Quiddities Cambridge/London 1987


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Ed. Martin Schulz, access date 2018-12-12
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