Philosophy Dictionary of ArgumentsHome
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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._____________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 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._____________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 Definability
Ed. Martin Schulz, access date 2024-04-20