Philosophy Dictionary of ArgumentsHome
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| Element relation, element relationship: the existence of a number within a set. In the broader sense the existence of an object (urelement) within a set. The element relation is to be distinguished from the subset relation. See also sets, classes, subsets, elements, set theory, empty set, universal class, paradoxes._____________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 Element Relation - Dictionary of Arguments
IX 23 Element relation/identity/classes/individuals: "ε" before individuals have the property of "=". IX 113 ff Definition element relation/ordinal: "E" stands for "{ : y ε z}". Ru: y is a number, but not z (z must be a quantity). Pair of number and quantity, also the number is part of the quantity. If this is true, it is an e-relation - E should arrange the ordinals. IX 119 NO: class of ordinal numbers (≠ ordinal numbers) Element relation/ordinals/Quine: here, "ε" means "smaller" and it is interchangeable with "contains" with respect to ordinals. Therefore x U {x} is the next ordinal after x if there are still ordinals behind x at all - it is not sufficient to meet the element conditions to belong to a class. The existence is necessary. Proof of "NO ε ϑ ((s) the class of ordinals does not exist"). It is now obvious: if NO existed, 23.9 and 24.3 (see above) would be a contradiction to 23.7 - >Paradoxon of Burali-Forti. IX 219 Element relation/Epsilon/induction/Quine: the primitive predicate "ε" divides the determination of classes (a) behind the Epsilon into the requirement of having elements and (b) in front of the epsilon into the requirement of being an element. Problem of Induction: always one with the existence of classes that have been used only for the requirement (a) - Induction: in order to derive it from the definition of n we need a class {x:Fx} or N n {x: Fx} or {x:x <= z u ~Fx} as a value of a variable of this definition and this is a variable that stands only on the right hand side of "ε". >Set theory, >Sets._____________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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> Counter arguments against Quine
> Counter arguments in relation to Element Relation
Ed. Martin Schulz, access date 2024-04-28