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Full Idea
Model theory is the study of the interpretation of any language, formal or natural, by means of set-theoretic structures, with Tarski's truth definition as a paradigm.
Gist of Idea
Model theory studies formal or natural language-interpretation using set-theory
Source
Wilfrid Hodges (Model Theory [2005], Intro)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.1
A Reaction
My attention is caught by the fact that natural languages are included. Might we say that science is model theory for English? That sounds like Quine's persistent message.
| 10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
| 10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
| 10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
| 10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
| 10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
| 10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
| 10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
| 10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |