# Philosophy Dictionary of Arguments

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Definability: is about the question whether the meanings of linguistic elements and symbols of a statement in a given frame, a theory, a model or a system can be stated in a way that these elements and symbols can be replaced by other symbols. This replacement is to aid understanding. Is this the case new symbols (words, terms, links) can be created the meaning of which can be understood from the symbols already defined. Therefore these new symbols are definable. See also definition, context definition, implicit definition, explicit definition, models, systems, theories, foundation.
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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 Definability - Dictionary of Arguments

VII (g) 131
Def Ideology/Quine: what ideas can be expressed in a theory? I.e. what is definable?
Example: the theory of real numbers has infinite ontology, but finite ideology: addition, division, multiplication, rationality, algebraicity, etc.
Two theories can have the same ontology and different ideologies. Example:

(1) The real number x is an integer

That can be expressed in one theory, but not in another!
>Ideology
, >Ontology, >Definitions.
VII (g) 132
Due to Goedel's incompleteness theorem for the integers, we know that Tarski's performance would have been impossible if (1) could have been translated into the notation of T.
Ontology/Theory/Quine: the ontology of a theory can even include objects that are indefinable in this theory.
For example it can be shown that the theory T includes the whole real numbers, although (1) cannot be expressed in its notation.
Ideas/Quine: "Ideas of ideas" we can drop them completely together with "ideology" (expressability). We are more interested in definability (in a theory).
VII (g) 132
Definition definable/Quine: a general term t can be defined, in any part of the language that includes a sentence S such that S contains the variable "x" and is met by all and only the values of "x", of which t is true. - E.g. "whole" is not definable in theory T.
XI 76
Analyticity/Synonymy/Necessity/Quine/Lauener: these terms can only be defined among themselves. We have nothing to break out of this circle with.
XI 122
Diversity/Distinguishability/Definability/Mark WilsonVsQuine/VsDifferentiality/Lauener:
LauenerVsWilson: Quine mistakenly assumes that two theories R and RT are different iff their union is logically incompatible.
Wilson: this is unsatisfactory, because T and RT can be considered formalizations of the same theory, and yet they are not logically equivalent, because their languages are interpreted differently.
Interdefinability/Theory/Wilson: two theories are interdefinable if each can be defined within the other, otherwise they are different. For example, one theory with mathematical vocabulary, the other with physical vocabulary. In addition, no superfluous properties may be introduced.
Quine: ditto. In addition, the application of a theory should not be confused with the theory itself.
>Theories.

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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

Ed. Martin Schulz, access date 2024-02-27