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3 ideas
19128 | If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh] |
Full Idea: If axioms are formulated for a language (such as set theory) that lacks names for all objects, then they require the use of a satisfaction relation rather than a unary truth predicate. | |
From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.3) | |
A reaction: I take it this is an important idea for understanding why Tarski developed his account of truth based on satisfaction. |
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. |
19127 | The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh] |
Full Idea: Although the theory is materially adequate, Tarski thought that the T-sentences are deductively too weak. …Also it seems that the T-sentences are not conservative, because they prove in PA that 0=0 and ¬0=0 are different, so at least two objects exist. | |
From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.2) | |
A reaction: They are weak because they can't prove completeness. This idea give two reasons for looking for a better theory of truth. |