Philosophy Lexicon of Arguments

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Model Theory: The model theory investigates whether an axiom system is fulfilled and thus provides one (or more) models. Model theory belongs to the semantics because it uses the concept of truth, while the proof theory belongs to the domain of syntax by asking for the existence of finite character string (of proofs). One problem is the exclusion of unintended models.
 
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I 85
Model theory: semantically: "all models in which A is true are models in which B is also true": B follows from A - proof theory: syntactically "there is a formal derivation of B from A".
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I 116
Model theory/Field: if one says that a logically true sentence is true in all models, a model exists in a set of objects plus the fixing which predicates (if any) of them are true in the model, which names (if any) denote these objects, etc. - "besides. attribution function" - then the truth conditions can be recursively defined - "Definition logically true: here: true for each model-".
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I 117
Kripke: with him a non-empty set of possible worlds is called actual. Definition possible/Kripke: a sentence of the form "MA" (diamond) will then be true in a model if and only if A is in at least one possible world in a model true - Problem/Kripke: in order that "MA" is logically true, A itself has to be logically true. Solution/FieldVsKripke: we do not accept a possible world" - our model is the -"acutal world portion" of the Kripkean model.
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I 121
Proof Theory: does not provide any results that could not be obtained otherwise.
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I 116
Model theory/modal logic/FieldVsKripke: unlike Kripke: without possible world - "which sentences with the operator "logically possible" are logical true?" "N.B.: Both model theories are platonic - (pure quantity theory).

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980


> Counter arguments against Field
> Counter arguments in relation to Model Theory



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Ed. Martin Schulz, access date 2017-05-25