display all the ideas for this combination of philosophers
3 ideas
13343 | A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski] |
Full Idea: An arbitrary sequence of objects which satisfies every sentential function of the sentences L' will be called a 'model' or realization of the class L of sentences. There can also be a model of a single sentence is this way. | |
From: Alfred Tarski (The Concept of Logical Consequence [1936], p.417) | |
A reaction: [L' is L with the constants replaced by variables] Tarski is the originator of model theory, which is central to modern logic. The word 'realization' is a helpful indicator of what he has in mind. A model begins to look like a possible world. |
16323 | The object language/ metalanguage distinction is the basis of model theory [Tarski, by Halbach] |
Full Idea: Tarski's distinction between object and metalanguage forms the basis of model theory. | |
From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 11 |
17813 | Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP] |
Full Idea: The Löwenheim-Skolem theorem tells us that any theory with a true interpretation has a model in the natural numbers. | |
From: Nicholas P. White (What Numbers Are [1974], V) |