Philosophy Dictionary of ArgumentsHome
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| Truth value gaps, philosophy, logic: is an expression for the problem that occurs when a statement cannot be attributed to either of the two truth values "true" or "false". The reason for this may be that the statement is meaningless (not negatable), it refers to a future event or has a paradoxical formulation. See also truth values, truth value agglomerations, supervaluation, dialethism, paradoxes, future._____________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 Truth Value Gaps - Dictionary of Arguments
I 307 Truth Value Gap/Non-existence/Quine: We interpreted "exists" as (Ex)(y=x) which applies to everything just like "x=x". But also with this procedure anomalies result. It seems strange that "Pegasus exists" should be wrong if "(x)(x exists)" is true and "Pegasus" takes a purely descriptive position. Something is wrong if Pegasus is granted the purely descriptive position. >Descriptive position. I 308 The sense should be that the term concerned is used exclusively to indicate an object about which the rest of the sentence can say something. We can call this "truth value gaps" (the expression comes from Strawson). With open sentences we have not been disturbed by the fact that they have no truth value, but they can already be recognized by the way they are written. Here the gaps are disturbing precisely because they are not recognizable. Perhaps best with trivalent logic ("undecidable")? QuineVs: one does not assume that the difficulties come from a pedantic distinction between what is true and what is neither true nor false. If one were to summarize both categories under the rubric of the false, nothing would be gained. For they are distinguished from one another by the fact that one category contains the negations of all their elements, while the other does not contain a single negation of their elements. I 318 Singular descriptions "the", e.g. "the setting of the sun" Iota operator "i" (inverted, without dot) (ix)(...x...) "This x, for that applies" Here no synonymy is claimed by additional information (as in § 33). The logical theory made possible by the canonical framework treats ambiguous terms and indicator words as if they had fixed objects of reference. I 319 Let us now compare the identity statement "y = (ix)(...x...)" with the quantification: (1) (x)(...x...if and only if x = y) can be read briefly as "...y...and exclusively y". If either (1) or the reformulation applies to an object y, both are probably true. Nevertheless, both may differ in their conditions of falsity with respect to truth values! Because one can understand these gaps in such a way that "y = (ix)(...x...)" in relation to each object y has no truth value, if it applies to none, while "...y....and exclusively y" is simply wrong in relation to any object, if it doesn't apply to any. So we can simply put our aversion to gaps into action and equate "y = (ix)( ...x...) with "...y... and exclusively y" and accordingly fill the truth value gaps of "y = (ix)(...x..)" with the truth value incorrectly. This step enables us to make the singular identifications disappear at all. I 327 Definition/singular terms/truth value gaps/Quine: if we interpret definitions as instructions for the transformation of singular terms, we can avoid the annoyance of truth value gaps: I 328 The definition of the singular descriptions is then simple as follows: Def Singular Description: Write "y = (ix)(...x...)" and "(ix)(...x...) exists" as notation variants of "...y...and exclusively y." And with recourse to §37: Write "(ix)(...x...) " as abbreviation of (7) (Ey)[y = (ix)(...x...) and y ], (In this representation, we have " y " as any open sentence.) If we apply the three parts of the above definition successively and repeatedly, they are sufficient to make "(ix)(...x...)" accessible again to any position where free variables may occur. I 389/90 Conditional: the indicative conditional is unproblematic. In unquantified form "if p then q" it is perhaps best expressed as containing a truth value gap (§ 37) if its antecedence is false.(See also EFQ (ex falso quodlibet): ex falso quodlibet). I 449 In the case of the indicative conditional, the initial problems are the truth value gaps and the ambiguity of the truth conditions. They are solved by being able to dispense with the indicative conditional in favor of a truth function. I 447 StrawsonVsRussell: Strawson has misnamed Russell's theory of descriptions because of their treatment of truth value gaps. III 282 Truth Value Gap/Quine: comes from everyday language, in logic we have to fill it. And be it arbitrary. Every sentence should have a truth value (true or false). >Everyday language. - - - XI 39 Canonical Notation/Quine/Lauener: closes truth value gaps._____________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 Truth Value Gaps
Ed. Martin Schulz, access date 2024-04-23