more on this theme | more from this text
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.
Clarification
T-sentences say " 'p' is true iff p "
Gist of Idea
The T-sentences are deductively weak, and also not deductively conservative
Source
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.2)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.6
A Reaction
They are weak because they can't prove completeness. This idea give two reasons for looking for a better theory of truth.
| 19120 | Semantic theories need a powerful metalanguage, typically including set theory [Halbach/Leigh] |
| 19121 | We can reduce properties to true formulas [Halbach/Leigh] |
| 19122 | Nominalists can reduce theories of properties or sets to harmless axiomatic truth theories [Halbach/Leigh] |
| 19124 | A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh] |
| 19126 | If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh] |
| 19125 | If we define truth, we can eliminate it [Halbach/Leigh] |
| 19127 | The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh] |
| 19128 | If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh] |
| 19129 | The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh] |
| 19130 | KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh] |