# Philosophy Dictionary of Arguments

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Classes: identity of classes provided by same elements (extension) - identity of properties by the same predicates (intension).

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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 Concept Summary/Quotes Sources

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.
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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) 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.
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VII (a) 18
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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.
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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.
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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.
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.

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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. 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:

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 Classes

Ed. Martin Schulz, access date 2022-06-30