| 19188 | We can't use a semantically closed language, or ditch our logic, so a meta-language is needed [Tarski] |
| Full Idea: In a 'semantically closed' language all sentences which determine the adequate usage of 'true' can be asserted in the language. ...We can't change our logic, so we reject such languages. ...So must use two different languages to discuss truth. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 08-09) | |
| A reaction: This section explains why a meta-language is required. It rests entirely on the existence of the Liar paradox is a semantically closed language. |
| 19189 | The metalanguage must contain the object language, logic, and defined semantics [Tarski] |
| Full Idea: Every sentence which occurs in the object language must also occur in the metalanguage, or can be translated into the metalanguage. There must also be logical terms, ...and semantic terms can only be introduced in the metalanguage by definition. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 09) | |
| A reaction: He suggest that if the languages are 'typed', the meta-languag, to be 'richer', must contain variables of a higher logica type. Does this mean second-order logic? |
| 23297 | The language to define truth needs a finite vocabulary, to make the definition finite [Davidson] |
| Full Idea: If the definition of the truth predicate is to be finite (Tarski insisted on this), the definition must take advantage of the fact that sentences, though potentially infinite in number, are constructed from a finite vocabulary. | |
| From: Donald Davidson (The Folly of Trying to Define Truth [1999], p.23) | |
| A reaction: Not sure whether this is in the object language or the meta-language, though I guess the former. |
| 23288 | When Tarski defines truth for different languages, how do we know it is a single concept? [Davidson] |
| Full Idea: We have to wonder how we know that it is some single concept which Tarski indicates how to define for each of a number of well-behaved languages. | |
| From: Donald Davidson (Truth Rehabilitated [1997], P.11) | |
| A reaction: Davidson says that Tarski makes the assumption that it is a single concept, but fails to demonstrate the fact. This resembles Frege's Julius Caesar problem - of how you know whether your number definition has defined a number. |
| 19323 | 'Snow is white' depends on meaning; whether snow is white depends on snow [Etchemendy] |
| Full Idea: The difference between (a) snow is white, and (b) 'snow is white' true is that the first makes a claim that only depends on the colour of snow, while the second depends both on the colour of snow and the meaning of the sentence 'snow is white'. | |
| From: John Etchemendy (Tarski on Truth and Logical Consequence [1988], p.61), quoted by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.7 | |
| A reaction: This is a helpful first step for those who have reached screaming point by being continually offered this apparently vacuous equivalence. This sentence works well if that stuff is a particular colour. |
| 15345 | Semantic theories have a regress problem in describing truth in the languages for the models [Horsten] |
| Full Idea: Semantic theories give a class of models with a truth predicate, ...but Tarski taught us that this needs a more encompassing framework than its language...so how is the semantics of the framework expressed? The model route has a regress. | |
| From: Leon Horsten (The Tarskian Turn [2011], 02.3) | |
| A reaction: [compressed] So this regress problem, of endless theories of truth going up the hierarchy, is Horsten's main reason for opting for axiomatic theories, which he then tries to strengthen, so that they are not quite so deflated. |
| 16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach] |
| Full Idea: In semantic theories (e.g.Tarski's or Kripke's), a definition evades Tarski's Theorem by restricting the possible instances in the schema T[φ]↔φ to sentences of a proper sublanguage of the language formulating the equivalences. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 1) | |
| A reaction: The schema says if it's true it's affirmable, and if it's affirmable it's true. The Liar Paradox is a key reason for imposing this restriction. |
| 15649 | In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach] |
| Full Idea: In semantic theories of truth (Tarski or Kripke), a truth predicate is defined for an object-language. This definition is carried out in a metalanguage, which is typically taken to include set theory or another strong theory or expressive language. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) | |
| A reaction: Presumably the metalanguage includes set theory because that connects it with mathematics, and enables it to be formally rigorous. Tarski showed, in his undefinability theorem, that the meta-language must have increased resources. |
| 19120 | Semantic theories need a powerful metalanguage, typically including set theory [Halbach/Leigh] |
| Full Idea: Semantic approaches to truth usually necessitate the use of a metalanguage that is more powerful than the object-language for which it provides a semantics. It is usually taken to include set theory. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1) | |
| A reaction: This is a motivation for developing an axiomatic account of truth, that moves it into the object language. |