Philosophy Dictionary of ArgumentsHome | |||
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Satisfaction, logic: a formula is satisfied when their variables are interpreted in a way that the formula as a whole is a true statement. The interpretation is a substitution of the variables of the formula by appropriate constants (e.g. names). When the interpreted formula is true, we call it a model. See also satisfiability, models, model theory._____________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 |
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W.V.O. Quine on Satisfaction - Dictionary of Arguments
VI 121f Truth/Satisfaction/Recursion/Tarski/Quine: truth can actually not be defined by satisfaction (level) - Solution: satisfaction itself is not directly but recursively defined - then truth can be defined through satisfaction - because satisfaction of each sentence is delivered, not a rule like "x fulfils y" for variable y - direct definition: leads to rules - Recursion: on individual cases. VI 123 Hence truth and satisfaction clearly, but not eliminably defined. --- X 61 Satisfaction/Meta language/Object language/Quine(s): that what satisfies, is part of the meta language, that what is satisfied is part of the object language. >Object language, >Metalanguage. X 62 Satisfaction/Quine: the n-tuples can contain more elements than the satisfied sentence has variables. The surplus elements are irrelevant - E.g. x conquered y is fulfilled by the n-tuple (sequence) for every a - ((s) i.e. the surplus elements can be any objects.) If the n-tuple has fewer elements than there are variables in the sentence, then the last element is always repeated. Only closed sentences can be true - but also closed sentences can be satisfied - they are satisfied with any n-tuple (object sequence), because all surplus elements of the sequence (objects) are simply irrelevant - if the sentence contains no variables, all objects are irrelevant. Quine: this applies due to a convention. X 63 N-tuples/sequence/satisfaction/(s): the sequences or n-tuples are always sequences of objects, rather than strings. - A sentence (even a string) can never be satisfied by a string, only by objects. Satisfaction/alphabetical order/Quine: is important because of conjunction - E.g. satisfies both "x conquered y" and "z killed x". X 64 Satisfaction/Existential quantification/Quine/(s): existential quantification creates sentences where not all variables must be bound. Deviation at most at i-th point: the point that may deviate is just the point of the bound variable! - E.g. (Ey)(x conquered y) is fulfilled with Assuming satisfaction by too long n-tuples: e.g. existential quantification Ey(x conquered y) is filled with Caesar, i.e. by - as well as any extension of - open sentence: E.g. "x conquered y" is fulfilled by any extension of X 68 Satisfaction definition/Quine: must contain object language and metalanguage. X 72 Satisfaction/Sequences/Object sequences/General/Particular/Compound/Compound sentences/Quine: Problem: you could know of an n-tuple which simple sentences it fulfils and yet you cannot decide whether it satisfies a particular compound sentence. - E.g. one could know which simple sentences an n-tuple satisfies, but not if it fulfils a quantification "Ez Fxyz" - because that depends on whether at least one element w requires: fulfils "Fxyz"._____________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 |