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All the ideas for 'Axiomatic Theories of Truth (2013 ver)', 'On Mental Entities' and 'Natural Science (lost)'

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13 ideas

3. Truth / A. Truth Problems / 2. Defining Truth
19125 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 / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
19128 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
19120 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
19127 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
19124 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.
19126 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
19129 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
19130 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]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
527 Everything exists which anyone perceives [Metrodorus of Chios]
     Full Idea: Everything exists which anyone perceives.
     From: Metrodorus (Chi) (Natural Science (lost) [c.340 BCE], B2), quoted by (who?) - where?
     A reaction: cf Berkeley and Epicurus. This misses out the problem of perceptual error, such as a square tower looking round from a distance, or one person in a group thinking they have seen something. It is still a good criterion, though!
8. Modes of Existence / B. Properties / 12. Denial of Properties
19121 We can reduce properties to true formulas [Halbach/Leigh]
     Full Idea: One might say that 'x is a poor philosopher' is true of Tom instead of saying that Tom has the property of being a poor philosopher. We quantify over formulas instead of over definable properties, and thus reduce properties to truth.
     From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.1)
     A reaction: [compressed] This stuff is difficult (because the axioms are complex and hard to compare), but I am excited (yes!) about this idea. Their point is that you need a truth predicate within the object language for this, which disquotational truth forbids.
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
19122 Nominalists can reduce theories of properties or sets to harmless axiomatic truth theories [Halbach/Leigh]
     Full Idea: The reduction of second-order theories (of properties or sets) to axiomatic theories of truth is a form of reductive nominalism, replacing existence assumptions (e.g. comprehension axioms) by innocuous assumptions about the truth predicate.
     From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.1)
     A reaction: I'm currently thinking that axiomatic theories of truth are the most exciting development in contemporary philosophy. See Halbach and Horsten.
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
21686 Sense-data are dubious abstractions, with none of the plausibility of tables [Quine]
     Full Idea: The notion of pure sense datum is a pretty tenuous abstraction, a good deal more conjectural than the notion of an external object, a table or a sheep.
     From: Willard Quine (On Mental Entities [1952], p.225)
     A reaction: This seems to sum up the view of sense-data held by the generation after Russell and Moore. Ayer still talks about them, but Russell had already given them up. The simple challenge is - what is the evidence for their existence? Cf innate ideas.
12. Knowledge Sources / D. Empiricism / 4. Pro-Empiricism
21685 Empiricism says evidence rests on the senses, but that insight is derived from science [Quine]
     Full Idea: The crucial insight of empiricism is that any evidence for science has its end points in the senses. This insight remains valid, but it is an insight which comes after physics, physiology, and psychology, not before.
     From: Willard Quine (On Mental Entities [1952], p.225)
     A reaction: Interesting. I think Hume and co. were probably outlining essential presuppositions and contraints which must be accepted by science. Quine offers empiricism as more like a description of science (with success as its authority?).