@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 29 Mar 2024}, author = {Field,Hartry}, subject = {Model Theory}, note = {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". 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. Moreover it is an attribution function (for free variables). - Then the truth conditions can be recursively defined. Def logically true: here: true for each model. >Models. I 117 Kripke/Field: with Kripke a non-empty set of possible worlds is called actual. >Possible worlds, >Actual world/Lewis, >Actuality. Def 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 true in a model. Problem/Kripke: for "MA" being logically true, A itself has to be logically true. Solution/FieldVsKripke: we do not accept a possible world. - Our model is the "actual world portion" of the Kripkean model. I 121 Proof Theory: does not provide any results that could not be obtained otherwise. I 116 Model theory/modal logic/FieldVsKripke: unlike Kripke: we choose a solution without possible worlds. - "Which sentences with the operator "logically possible" are logical true?" N.B.: Both model theories are platonistic (pure set theory). >Set theory, >Platonism.}, note = { Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich, Aldershot 1994 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=248887} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=248887} }