Lexicon 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.
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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.
>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 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 .
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".