Philosophy Lexicon of Arguments

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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.

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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.

 
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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.
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VI 123
Hence truth and satisfaction clearly, but not eliminably defined.
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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.
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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.
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X 62
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.
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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.
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X 63
Satisfaction/alphabetical order/Quine: is important because of conjunction - E.g. satisfies both "x conquered y" and "z killed x".
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X64
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 or every sequence for an arbitrary y - So: a closed sentence is satisfied by any sequence, an open one only if it becomes true by satisfaction - 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 .
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X 68
Satisfaction definition/Quine: must contain object language and meta language. - ((s) Perhaps applies always for the formulation of a conditions?).
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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".


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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.

Q I
W.V.O. Quine
Wort und Gegenstand Stuttgart 1980

Q II
W.V.O. Quine
Theorien und Dinge Frankfurt 1985

Q III
W.V.O. Quine
Grundzüge der Logik Frankfurt 1978

Q IX
W.V.O. Quine
Mengenlehre und ihre Logik Wiesbaden 1967

Q V
W.V.O. Quine
Die Wurzeln der Referenz Frankfurt 1989

Q VI
W.V.O. Quine
Unterwegs zur Wahrheit Paderborn 1995

Q VII
W.V.O. Quine
From a logical point of view Cambridge, Mass. 1953

Q VIII
W.V.O. Quine
Bezeichnung und Referenz
In
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982

Q X
W.V.O. Quine
Philosophie der Logik Bamberg 2005

Q XII
W.V.O. Quine
Ontologische Relativität Frankfurt 2003


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Ed. Martin Schulz, access date 2017-10-17