Psychology Dictionary of ArgumentsHome
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| Classes: In logic, a class is a collection of objects that share a common characteristic or property. Statements about classes can be expressed using logical symbols, such as "∈" for membership and "⊆" for subset. Identity of classes is provided by same elements (extension) - or identity of properties by the same predicates (intension). See also Sets, Set theory, Subsets, Element relation. - B. Classes in political theory refer to societal groups sharing economic interests, often defined by their relationship to production and resources. See also Society, Conflicts._____________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 Classes - Dictionary of Arguments
I 289 Class abstraction is attributed to singular descriptions: (iy)(x)(x from y iff ..x..). Instead: x^(..x..). This does not work for intensional abstraction. Difference classes/properties: classes are identical with the same elements. Properties are not yet identical if they are assigned to the same things. >Properties/Quine. - - - II 29 Classes: one could reinterpret all classes in their complement: "no element of .." and you would never notice anything. At the bottom layer every relative clause, every general term determines a class. II 100 Russell (Principia Mathematica(1)) classes are things: they must not be confused with the concept of classes. However: paradoxes also apply to class terms and propositional functions are not only for classes. Incomplete symbols (explanation by use) are used to explain away classes. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. - - - VII (a) 18 Classes/Quine: simplify our access to physics but are still a myth. - - - VII (f) 114 Classes/Quine: classes are no accumulations or collections! E.g. the class of stones in a pile cannot be identified with the pile: otherwise another class could also be identified with the same pile: e.g. the class of stone molecules in the pile. The validity theory applies to classes, but not to the individual sentences - predicates are not names of classes, classes are the extension of predicates - classes are assumed to be pre-existent. - - - IX 21 Classes/Relations/Quine: classes are real objects if values of bound variables. IX 23 Class/Individuals/Quine: everything is class! If we understand individuals to be identical to their class of one (i.e. not elementless). IX 223 Classes/Quine: quantification through classes allows for terms that would otherwise be beyond our reach. - - - XIII 24 Class/Quantity/Quine: we humans are stingy and so predisposed that we never use two words for the same thing, or we demand a distinction that should underlie it. XIII 25 Example ape/monkey: we distinguish them by size, while French and Germans have only one word for them. Problem: how is the dictionary supposed to explain the difference between "beer, which is rightly called so" and "ale, which is rightly called so"? Example Sets/Classes/Quine: here this behaves similarly. Class/Mathematics: some mathematicians treat classes as something of the same kind as properties (Quine pro, see above): sets as something more robust, though still abstract. >Properties/Quine. Classes: can contain sets as elements, but not other classes. (see impredicativity). Paradox/Paradoxes/Quine: lead to some element relationships not being able to define sets. Nevertheless, they can still define classes! von Neumann: established such a system in 1925. It simplifies evidence and strengthens the system, albeit at the risk of paradoxes. >Paradoxes/Quine. Problem: it requires imaginative distinctions and doublings, e.g. for every set there must be a coextensive class. Solution/Quine. (Quine 1940): simply identify the sets with the coextensive classes. XIII 26 Def Classes/Def Sets/QuineVsNeuman: new: sets are then classes of a certain type: a class is a set if it is an element of a class. A class is a Def outermost class/Quine: if it is not an element of a class. Russell's Paradox/Quine: some authors thought that by distinguishing between classes and sets, it showed that Russell's antinomy was mere confusion. Solution/some authors: classes themselves are not such substantial objects that they would come into question as candidates for elements according to a condition of containment. But sets can be. On the other hand: Sets: had never been understood as defined by conditions of abstinence. And from the beginning they had been governed by principles that Zermelo later made explicit. QuineVs: these are very perishable assumptions! In reality, sets were classes from the beginning, no matter what they were called. Vagueness of one word was also vagueness of the other word. Sets/Cantor/Quine: sure, the first sets at Cantor were point sets, but that does not change anything. QuineVsTradition/Quine: it is a myth to claim that sets were conceived independently of classes, and were later confused with them by Russell. That again is the mistake of seeing a difference in a difference between words. Solution/Quine: we only need sets and outermost classes to enjoy the advantages of von Neumann. >Sets/Quine._____________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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