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Ideas for 'Axiomatic Theories of Truth (2005 ver)', 'Reply to Sixth Objections' and 'Tractatus Logico-Philosophicus'

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15 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 / 2. Truthmaker Relation
The best account of truth-making is isomorphism [Wittgenstein, by Mulligan/Simons/Smith]
     Full Idea: The most sophisticated account of truth-making to have appeared to date is the 'isomorphism' theory of the Tractatus.
     From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Mulligan/Simons/Smith - Truth-makers §5
     A reaction: Wittgenstein's theory is clearly closely related to Russell's 'congruence' theory of correspondence of around 1912.
3. Truth / B. Truthmakers / 5. What Makes Truths / c. States of affairs make truths
He says the world is the facts because it is the facts which fix all the truths [Wittgenstein, by Morris,M]
     Full Idea: Wittgenstein is thinking of the world as what makes truths true. …To get all the truths fixed we need more than the things: we need, as it were, the way things are - that is to say, the facts.
     From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 1.12) by Michael Morris - Guidebook to Wittgenstein's Tractatus 1
     A reaction: Morris says this is 'sometimes suggested'. It strikes me as plausible, and makes LW a key source for the modern truthmaker idea. Perhaps in David Lewis's version of it. The facts include the relations and processes of the things.
3. Truth / B. Truthmakers / 11. Truthmaking and Correspondence
All truths have truth-makers, but only atomic truths correspond to them [Wittgenstein, by Rami]
     Full Idea: In 1922 Wittgenstein said that every truth has a truth-maker, but only atomic truths correspond to their truth-makers.
     From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Adolph Rami - Introduction: Truth and Truth-Making note 04
     A reaction: Presumably this is what logical atomism is meant to be (cf Russell). The atomic sentences plug into the world, and the rest are constructions from them, making the latter more remote from the truth-makers.
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
Wittgenstein's picture theory is the best version of the correspondence theory of truth [Read on Wittgenstein]
     Full Idea: Wittgenstein's picture theory is without doubt the best thought-out and developed of all the versions of the correspondence theory of truth.
     From: comment on Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Stephen Read - Thinking About Logic Ch.1
Language is [propositions-elementary propositions-names]; reality is [facts-states of affairs-objects] [Wittgenstein, by Grayling]
     Full Idea: Language consists in propositions, which are made of 'elementary' propositions, which are based ultimately on names. This matches the world of facts, compounded out of 'states of affairs', which are compounded of objects.
     From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by A.C. Grayling - Wittgenstein Ch.2
     A reaction: This is Grayling's summary of the basic idea of the 'Tractatus'. The whole thing seems to be an elaborate version of Russell's 'congruence' account of the correspondence theory of truth. Later Wittgenstein is loss of faith in this theory.
The account of truth in the 'Tractatus' seems a perfect example of the correspondence theory [Wittgenstein, by O'Grady]
     Full Idea: Wittgenstein's account in the 'Tractatus' is often taken as a paradigm instance of a sophisticated correspondence theory of truth.
     From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Paul O'Grady - Relativism Ch.2
     A reaction: This might explain why I am so much more drawn to the 'Tractatus' than to the later relativistic anti-philosophical mind-eliminitavist, meaning-eliminativist Wittgenstein.
Pictures reach out to or feel reality, touching at the edges, correlating in its parts [Wittgenstein]
     Full Idea: A picture attaches to reality by reaching out to it; it is laid against reality like a measure; only the end-points actually touch the object; the pictorial relationship consists of correlations of picture's elements with things, the picture's feelers.
     From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.1511-5)
     A reaction: (somewhat compressed). This is Wittgenstein's so-called 'picture theory' of meaning (replaced later by 'meaning is use'). It is perhaps better seen as an account of the correspondence theory of truth. Compare Russell's 'congruence' view (Idea 5427).
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
Proposition elements correlate with objects, but the whole picture does not correspond to a fact [Wittgenstein, by Morris,M]
     Full Idea: Correlation need only be between elements of the picture and things in reality; it is not also required that there be a correspondence between the picture as a whole and a fact in reality - so things can be depicted falsely.
     From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 2.15121) by Michael Morris - Guidebook to Wittgenstein's Tractatus 3C
     A reaction: To turn his picture theory into a correspondence theory of truth would need a further step, of saying the proposition is true when the two structures coincide. I don't think LW says that.
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 / 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'.