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Ideas for 'Axiomatic Theories of Truth (2005 ver)', 'Ordinary Objects' and 'Truth'

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12 ideas

3. Truth / A. Truth Problems / 2. Defining Truth
Truth definitions don't produce a good theory, because they go beyond your current language [Halbach]
     Full Idea: It is far from clear that a definition of truth can lead to a philosophically satisfactory theory of truth. Tarski's theorem on the undefinability of the truth predicate needs resources beyond those of the language for which it is being defined.
     From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1)
     A reaction: The idea is that you need a 'metalanguage' for the definition. If I say 'p' is a true sentence in language 'L', I am not making that observation from within language L. The dream is a theory confined to the object language.
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
Maybe analytic truths do not require truth-makers, as they place no demands on the world [Thomasson]
     Full Idea: It is a venerable view that analytic claims do not require truth-makers, as they place no demands on the world, but this claim has often been challenged.
     From: Amie L. Thomasson (Ordinary Objects [2007], 03.4)
     A reaction: She offers two challenges (bottom p.68), but I would have thought that the best response is that the meanings of the words themselves constitute truthmakers - perhaps via the essence of each word, as Fine suggests.
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
The fact which is stated by a true sentence is not something in the world [Strawson,P]
     Full Idea: The fact which is stated by a true sentence is not something in the world.
     From: Peter F. Strawson (Truth [1950], §2)
     A reaction: Everything is in the world. This may just be a quibble over how we should use the word 'fact'. At some point the substance of what is stated in a sentence must eventually be out there, or we would never act on what we say.
Facts aren't exactly true statements, but they are what those statements say [Strawson,P]
     Full Idea: Facts are what statements (when true) state; they are not what statements are about. ..But it would be wrong to identify 'fact' and 'true statement' for these expressions have different roles in our language.
     From: Peter F. Strawson (Truth [1950], §2)
     A reaction: Personally I like to reserve the word 'facts' for what is out there, independent of any human thought or speech. As a realist, I believe that the facts are quite independent of our attempts to understand the facts. True statements attempt to state facts.
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
The statement that it is raining perfectly fits the fact that it is raining [Strawson,P]
     Full Idea: What could fit more perfectly the fact that it is raining than the statement that it is raining?
     From: Peter F. Strawson (Truth [1950], §2)
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
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.
3. Truth / F. Semantic Truth / 2. Semantic Truth
The word 'true' always refers to a possible statement [Strawson,P]
     Full Idea: It is of prime importance to distinguish the fact that the use of 'true' always glances backwards or forwards to the actual or envisaged making of a statement by someone.
     From: Peter F. Strawson (Truth [1950], §1)
     A reaction: 'The truth of this matter will never be known'. Strawson is largely right, but it is crazy for any philosopher to use the word 'always' if they can possibly avoid it.
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach]
     Full Idea: If truth is not explanatory, truth axioms should not allow proof of new theorems not involving the truth predicate. It is hence said that axiomatic truth should be 'conservative' - not implying further sentences beyond what the axioms can prove.
     From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.3)
     A reaction: [compressed]
If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach]
     Full Idea: If truth can be explicitly defined, it can be eliminated, whereas an axiomatized notion of truth may bring all kinds of commitments.
     From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.3)
     A reaction: The general principle that anything which can be defined can be eliminated (in an abstract theory, presumably, not in nature!) raises interesting questions about how many true theories there are which are all equivalent to one another.
Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach]
     Full Idea: The axiomatic approach does not presuppose that truth can be defined. Instead, a formal language is expanded by a new primitive predicate of truth, and axioms for that predicate are then laid down.
     From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1)
     A reaction: Idea 15647 explains why Halbach thinks the definition route is no good.
Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach]
     Full Idea: Axiomatic theories of truth can be presented within very weak logical frameworks which require very few resources, and avoid the need for a strong metalanguage and metatheory.
     From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1)
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflationists say truth merely serves to express infinite conjunctions [Halbach]
     Full Idea: According to many deflationists, truth serves merely the purpose of expressing infinite conjunctions.
     From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.3)
     A reaction: That is, it asserts sentences that are too numerous to express individually. It also seems, on a deflationist view, to serve for anaphoric reference to sentences, such as 'what she just said is true'.