more from this thinker
|
more from this text
Single Idea 16318
[filed under theme 3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
]
Full Idea
In the typed Compositional Truth theory CT, it is compositional because the truth of a sentence depends on the semantic values of the constituents of that sentence.
Gist of Idea
Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents
Source
Volker Halbach (Axiomatic Theories of Truth [2011], 8)
Book Ref
Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.66
A Reaction
[axioms on p. 65 of Halbach]
Related Idea
Idea 16314
Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach]
The
35 ideas
with the same theme
[theories of truth built from a set of axioms]:
16300
|
Ockham had an early axiomatic account of truth
[William of Ockham, by Halbach]
|
15716
|
If axioms and their implications have no contradictions, they pass my criterion of truth and existence
[Hilbert]
|
19190
|
We need an undefined term 'true' in the meta-language, specified by axioms
[Tarski]
|
15322
|
Tarski's had the first axiomatic theory of truth that was minimally adequate
[Tarski, by Horsten]
|
16306
|
Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses
[Tarski, by Halbach]
|
19141
|
Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies
[Tarski, by Davidson]
|
23296
|
We can elucidate indefinable truth, but showing its relation to other concepts
[Davidson]
|
14967
|
Certain three-valued languages can contain their own truth predicates
[Kripke, by Gupta]
|
14966
|
The Tarskian move to a metalanguage may not be essential for truth theories
[Kripke, by Gupta]
|
19137
|
We can get a substantive account of Tarski's truth by adding primitive 'true' to the object language
[Etchemendy]
|
15332
|
'Reflexive' truth theories allow iterations (it is T that it is T that p)
[Horsten]
|
15346
|
Axiomatic approaches to truth avoid the regress problem of semantic theories
[Horsten]
|
15350
|
The Naďve Theory takes the bi-conditionals as axioms, but it is inconsistent, and allows the Liar
[Horsten]
|
15351
|
Axiomatic theories take truth as primitive, and propose some laws of truth as axioms
[Horsten]
|
15361
|
A good theory of truth must be compositional (as well as deriving biconditionals)
[Horsten]
|
15367
|
By adding truth to Peano Arithmetic we increase its power, so truth has mathematical content!
[Horsten]
|
15371
|
An axiomatic theory needs to be of maximal strength, while being natural and sound
[Horsten]
|
15373
|
Axiomatic approaches avoid limiting definitions to avoid the truth predicate, and limited sizes of models
[Horsten]
|
16294
|
Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage
[Halbach]
|
16326
|
The main semantic theories of truth are Kripke's theory, and revisions semantics
[Halbach]
|
16299
|
Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory
[Halbach]
|
16340
|
Truth axioms need a base theory, because that is where truth issues arise
[Halbach]
|
16305
|
We know a complete axiomatisation of truth is not feasible
[Halbach]
|
16311
|
To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction'
[Halbach]
|
16313
|
A theory is 'conservative' if it adds no new theorems to its base theory
[Halbach, by PG]
|
16315
|
The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals
[Halbach]
|
16318
|
Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents
[Halbach]
|
16322
|
CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA
[Halbach]
|
16314
|
Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free'
[Halbach]
|
15648
|
Instead of a truth definition, add a primitive truth predicate, and axioms for how it works
[Halbach]
|
15650
|
Axiomatic theories of truth need a weak logical framework, and not a strong metatheory
[Halbach]
|
15655
|
Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms?
[Halbach]
|
15654
|
If truth is defined it can be eliminated, whereas axiomatic truth has various commitments
[Halbach]
|
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]
|