Psychology Dictionary of ArgumentsHome
| |||
|
| |||
| 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. | |||
| Author | Concept | Summary/Quotes | Sources |
|---|---|---|---|
|
W.V.O. Quine on Abstraction - Dictionary of Arguments
I 286 Intensional abstraction means "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 is opaque (E.g. of the planet). I 322 Property abstraction (elimination) instead of "a = x(..x..)". New is the irreducible two-digit Operator "0": "a0x(..x..)". Variables are the only thing that remains. The pronoun has primacy. IX 12ff Class Abstraction/Quine: class abstraction "{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 then 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. 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 one must generate terms (expressions). (Frege/Church: is here also valid of statements and thus a second time class abstraction, but both group statements are 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}". The equal sign now stands between variable and a class abstraction term. 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. 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. |
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 |
||
> Counter arguments against Quine
> Counter arguments in relation to Abstraction
