Philosophy Dictionary of ArgumentsHome
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| Sets: a set is a summary of objects relating to a property. In the set theory, conditions are established for the formation of sets. In general, sets of numbers are considered. Everyday objects as elements of sets are special cases and are called primordial elements. Sets are, in contrast to e.g. sequences not ordered, i.e. no order is specified for the consideration of the elements. See also element relation, sub-sets, set theory, axioms._____________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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W.V.O. Quine on Sets - Dictionary of Arguments
IX 21 Ontology/Class/Sets/Relations/Quine: Classes and relations as values of quantifiable variables must be regarded as real objects. >Ontology/Quine. IX 219 Set/Quine: the property to be a set only means that ∃z(x ε z) ((s), there is something that x is a part of) - then ∃y x(x ε y (Ez(x ε z) u Fx)) - since Ez(x ε z) x ε Uϑ. - Even narrower: a ∩ Uϑ ε ϑ - Uϑ is then the class of all sets. The point is that ϑ ε ϑ (if there are extreme classes), so Uϑ is still the most comprehensive class that exists. The condition of being a set: ∃y(z ε y). III 318 Sets/class/von Neumann/Quine: (...) Classes are not sets. IX 228 Set/Neumann/Quine: a class is a set if it is not larger than a certain set (sets can be an element, classes cannot). IV 418 Ontology/Quine: Standards of ontological admissibility: two principles. 1. No entity without identity. 2. Ontological thriftiness. According to Quine, there are physical objects and quantities. V 149 Class/Set/Quantification/Quine: Classically, a quantification via classes is an object of quantification (referential quantification). >Quantification. Class: abstract terms for classes are singular terms. Include/Epsilon/Quine: "ε" is a two-digit predicate or relative general term. "Is an element of." (Originates from the predication scope "is one"). Now we get the theorem of comprehension: V 150 Comprehension/Quine: (1) (EZ)(x)(x ε Z . ≡ Fx) The compression set assigns a class to each element relationship. III 293 Classes/Sets/Condition/spelling/Quine: we always have the need to assign of the class of all and to only assign those objects that fulfill a certain condition. We write this as x^. III 294 Example x^~(x e a) the class of all non-elements of a. These are abstracts._____________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 |
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Ed. Martin Schulz, access date 2024-04-16