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All the ideas for 'Mahaprajnaparamitashastra', 'Axiomatic Theories of Truth (2013 ver)' and ''Ostrich Nominalism' or 'Mirage Realism'?'

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14 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]
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 / D. Universals / 1. Universals
8502 Realism doesn't explain 'a is F' any further by saying it is 'a has F-ness' [Devitt]
     Full Idea: Realists feel that the one-place predication 'a is F' leaves something unexplained, yet all that is offered is a two-place predication (a relational statement). There is an equal problem about 'a having F-ness'.
     From: Michael Devitt ('Ostrich Nominalism' or 'Mirage Realism'? [1980], p.97)
     A reaction: I think this is a key argument on the nominalist side - the denial that the theory of universals actually makes any progress at all in giving an explanation of what is going on around here. Platonist have the problem of 'partaking'.
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
8503 The particular/universal distinction is unhelpful clutter; we should accept 'a is F' as basic [Devitt]
     Full Idea: Talk of 'particulars' and 'universals' clutters the landscape without adding to our understanding. We should rest with the basic fact that a is F.
     From: Michael Devitt ('Ostrich Nominalism' or 'Mirage Realism'? [1980], p.98)
     A reaction: Ramsey was first to challenge the basic distinction. I find the approach of Quine and Devitt unsatisfactory. We abandon explanation when it is totally hopeless, but that is usually in the face of complexity. Properties are difficult but simple.
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
8501 Quineans take predication about objects as basic, not reference to properties they may have [Devitt]
     Full Idea: For 'a and b have the same property, F-ness' the Quinean Nominalist has a paraphrase to hand: 'a and b are both F'. ..In denying that this object need have properties, the Quinean is not denying that it really is F.
     From: Michael Devitt ('Ostrich Nominalism' or 'Mirage Realism'? [1980], p.95)
     A reaction: The question that remains is why 'F' is used of both a and b. We don't call a and b 'a', because they are different. Quine falls back on resemblance. I suspect Quineans of hiding behind the semantics.
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.
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
     Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
     From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
     A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').