18 ideas
| 15647 | 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. |
| 15649 | 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. |
| 15655 | 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] |
| 15654 | 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. |
| 15650 | 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) |
| 15648 | 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. |
| 15656 | 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'. |
| 15657 | To prove the consistency of set theory, we must go beyond set theory [Halbach] |
| Full Idea: The consistency of set theory cannot be established without assumptions transcending set theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 2.1) |
| 15652 | We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach] |
| Full Idea: The reduction of 2nd-order theories (of properties or sets) to axiomatic theories of truth may be conceived as a form of reductive nominalism, replacing existence assumptions (for comprehension axioms) by ontologically innocent truth assumptions. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.1) | |
| A reaction: I like this very much, as weeding properties out of logic (without weeding them out of the world). So-called properties in logic are too abundant, so there is a misfit with their role in science. |
| 15651 | Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach] |
| Full Idea: Quantification over (certain) properties can be mimicked in a language with a truth predicate by quantifying over formulas. Instead of saying that Tom has the property of being a poor philosopher, we can say 'x is a poor philosopher' is true of Tom. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.1) | |
| A reaction: I love this, and think it is very important. He talks of 'mimicking' properties, but I see it as philosophers mistakenly attributing properties, when actually what they were doing is asserting truths involving certain predicates. |
| 21642 | If quantification is all substitutional, there is no ontology [Quine] |
| Full Idea: Ontology is meaningless for a theory whose only quantification is substitutionally construed. | |
| From: Willard Quine (Ontological Relativity [1968], p.64), quoted by Thomas Hofweber - Ontology and the Ambitions of Metaphysics 03.5.1 n18 | |
| A reaction: Hofweber views it as none the worse for that, since clearly lots of quantification has no ontological commitment at all. But he says it is rightly called 'a nominalists attempt at a free lunch'. |
| 1633 | Absolute ontological questions are meaningless, because the answers are circular definitions [Quine] |
| Full Idea: What makes ontological questions meaningless when taken absolutely is not universality but circularity. A question of the form "What is an F?" can only be answered with "An F is a G", which makes sense relative to the uncritical acceptance of G. | |
| From: Willard Quine (Ontological Relativity [1968], p.53) |
| 18964 | Ontology is relative to both a background theory and a translation manual [Quine] |
| Full Idea: Ontology is doubly relative. Specifying the universe of a theory makes sense only relative to some background theory, and only relative to some choice of a manual of translation of one theory into another. | |
| From: Willard Quine (Ontological Relativity [1968], p.54) | |
| A reaction: People tend to forget about the double nature of Quine's notion of ontological commitment, and usually only talk about the commitment of the theory being employed. Why is the philosophical community not devoting itself to the study of tranlation manuals? |
| 16655 | Different genera are delimited by modes of predication, which rest on modes of being [Aquinas] |
| Full Idea: Being is delimited into different genera in accord with different modes of predicating, which depend on different modes of being. | |
| From: Thomas Aquinas (On Aristotle's 'Metaphysics' [1266], V.9.890), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 12.3 | |
| A reaction: I like this. When people say that predication is the way we divide things up, and go all linguistic-relativist about things, they forget how closely language not only describes reality, but arises out of, or is even caused by, reality. 'Grue' is silly. |
| 18965 | We know what things are by distinguishing them, so identity is part of ontology [Quine] |
| Full Idea: We cannot know what something is without knowing how it is marked off from other things. Identity is thus of a piece with ontology. | |
| From: Willard Quine (Ontological Relativity [1968], p.55) | |
| A reaction: Actually it is failure of identity which seems to raise questions of individuation. If I say 'this apple is [pause] identical to this apple', I don't see how that helps me to individuate apples. |
| 1634 | Two things are relative - the background theory, and translating the object theory into the background theory [Quine] |
| Full Idea: Relativity has two components: to the choice of a background theory, and to the choice of how to translate the object theory into the background theory. | |
| From: Willard Quine (Ontological Relativity [1968], p.67) |
| 8470 | Reference is inscrutable, because we cannot choose between theories of numbers [Quine, by Orenstein] |
| Full Idea: For Quine, we cannot sensibly ask which is the real number five, the Frege-Russell set or the Von Neumann one. There is no arithmetical or empirical way of deciding between the two. Reference is inscrutable. | |
| From: report of Willard Quine (Ontological Relativity [1968]) by Alex Orenstein - W.V. Quine Ch.3 | |
| A reaction: To generalise from a problem of reference in the highly abstract world of arithmetic, and say that all reference is inscrutable, strikes me as implausible. |
| 18963 | Indeterminacy translating 'rabbit' depends on translating individuation terms [Quine] |
| Full Idea: The indeterminacy between 'rabbit', 'rabbit stage' and the rest depended only on a correlative indeterminacy of translation of the English apparatus of individuation - pronouns, plurals, identity, numerals and so on. | |
| From: Willard Quine (Ontological Relativity [1968], p.35) | |
| A reaction: This spells out the problem a little better than in 'Word and Object'. I just don't believe these problems are intractable. Quine is like a child endlessly asking 'why?'. |