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Ideas for 'fragments/reports', 'Letters' and 'Axiomatic Theories of Truth (2013 ver)'

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11 ideas

3. Truth / A. Truth Problems / 2. Defining Truth
If we define truth, we can eliminate it [Halbach/Leigh]
     Full Idea: If truth can be explicitly defined, it can be eliminated.
     From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.3)
     A reaction: That we could just say p corresponds to the facts, or p coheres with our accepted beliefs, or p is the aim of our enquiries, and never mention the word 'true'. Definition is a strategy for reduction or elimination.
3. Truth / B. Truthmakers / 10. Making Future Truths
The causes of future true events must exist now, so they will happen because of destiny [Chrysippus, by Cicero]
     Full Idea: True future events cannot be such as do not possess causes on account of which they will happen; therefore that which is true must possess causes: and so, when the [true future events] happen they will have happened as a result of destiny.
     From: report of Chrysippus (fragments/reports [c.240 BCE]) by M. Tullius Cicero - On Fate ('De fato') 9.23-8
     A reaction: [exact ref unclear] Presumably the current causes are the truthmakers for the future events, and so the past is the truthmaker of the future, if you are a determinist.
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
Graspable presentations are criteria of facts, and are molded according to their objects [Chrysippus, by Diog. Laertius]
     Full Idea: Of presentations, some are graspable, some non-graspable. The graspable presentation, which they say is the criterion of facts [pragmata], is that which comes from an existing object and is stamped and molded in accordance wth the existing object itself.
     From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.46
     A reaction: [in lost Physics Bk 2] The big modern anguish over truth-as-correspondence is how you are supposed to verify the 'accordance'. This idea seems to blur the ideas of truth and justification (the 'criterion'), and you can't have both as accordance.
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
How could you ever know that the presentation is similar to the object? [Sext.Empiricus on Chrysippus]
     Full Idea: One cannot say that the soul grasps the externally existing objects by means of the states of the senses on the basis of the similarity of these states to the externally existing objects. For on what basis will it know the similarity?
     From: comment on Chrysippus (fragments/reports [c.240 BCE]) by Sextus Empiricus - Outlines of Pyrrhonism 2.74
     A reaction: This exactly the main modern reason for rejecting the correspondence theory of truth. You are welcome to affirm a robust view of truth, but supporting it by claiming a correspondence or resemblance is dubious.
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
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.
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
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.
3. Truth / F. Semantic Truth / 2. Semantic Truth
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.
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh]
     Full Idea: If a natural theory of truth is added to Peano Arithmetic, it is not necessary to add explicity global reflection principles to assert soundness, as the truth theory proves them. Truth theories thus prove soundess, and allows its expression.
     From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.2)
     A reaction: This seems like a big attraction of axiomatic theories of truth for students of metamathematics.
If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh]
     Full Idea: If truth does not have any explanatory force, as some deflationists claim, the axioms of truth should not allow us to prove any new theorems that do not involve the truth predicate. That is, a deflationary axiomatisation of truth should be 'conservative'.
     From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.3)
     A reaction: So does truth have 'explanatory force'? These guys are interested in explaining theorems of arithmetic, but I'm more interested in real life. People do daft things because they have daft beliefs. Logic should be neutral, but truth has values?
3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms
The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh]
     Full Idea: It is a virtue of the Friedman-Sheard axiomatisation that it is thoroughly classical in its logic. Its drawback is that it is ω-inconsistent. That is, it proves &exists;x¬φ(x), but proves also φ(0), φ(1), φ(2), …
     From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.3)
     A reaction: It seems the theory is complete (and presumably sound), yet not fully consistent. FS also proves the finite levels of Tarski's hierarchy, but not the transfinite levels.
3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh]
     Full Idea: KF is formulated in classical logic, but describes a non-classical notion of truth. It allow truth-value gluts, making some sentences (such as the Liar) both true and not-true. Some authors add an axiom ruling out such gluts.
     From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.4)
     A reaction: [summary, which I hope is correct! Stanford is not wholly clear]