23 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. |
| 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. |
| 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) |
| 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'. |
| 4045 | Children may have three innate principles which enable them to learn to count [Goldman] |
| Full Idea: It has been proposed (on the basis of observations) that young children have three innate principles of counting - one-to-one correspondence of number to item, stable order for numbers, and cardinality (which labels the nth item counted). | |
| From: Alvin I. Goldman (Phil Applications of Cognitive Science [1993], p.60) | |
| A reaction: I like the idea of observed patterns as central (which is the one-to-one principle). But the other two principles are plausible, and show why pure empiricism won't work. |
| 4044 | Rat behaviour reveals a considerable ability to count [Goldman] |
| Full Idea: Rats can determine the number of times they have pressed a lever up to at least twenty-four presses,…and can consistently turn down the fifth tunnel on the left in a maze. | |
| From: Alvin I. Goldman (Phil Applications of Cognitive Science [1993], p.58) | |
| A reaction: This seems to encourage an empirical view of maths (pattern recognition?) rather than a Platonic one. Or numbers are innate in rat brains? |
| 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) | |
| A reaction: This is too precise. No one takes such questions wholly as 'absolutes', but we don't accept G uncritically. We keep going, and the target is not a foundation, but coherence. |
| 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? |
| 4048 | Infant brains appear to have inbuilt ontological categories [Goldman] |
| Full Idea: Infant behaviour implies inbuilt ontological categories of thing, place, event, path, action, sound, manner, amount and number. ...There is an algebra of relationships between them. | |
| From: Alvin I. Goldman (Phil Applications of Cognitive Science [1993], p.109) | |
| A reaction: Interesting. We would expect the categories in infant brains to have instrumental value, but we don't have to accept them as true. Adults (even Aristotle) are big infants. |
| 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. |
| 4043 | Elephants can be correctly identified from as few as three primitive shapes [Goldman] |
| Full Idea: An elephant may be fully represented by nine primitive shapes ('geons'), but it may require as few as three geons in appropriate relations to be correctly identified. | |
| From: Alvin I. Goldman (Phil Applications of Cognitive Science [1993], p.7) | |
| A reaction: Encouraging the idea of the mind as a maker of maps and models |
| 4049 | The way in which colour experiences are evoked is physically odd and unpredictable [Goldman] |
| Full Idea: A unique yellow experience may be evoked with monochrome light of 580nm, or a mixture of 540nm and 670nm. ..Our interpretation of colour experience is a highly idiosyncratic artefact of our visual system. | |
| From: Alvin I. Goldman (Phil Applications of Cognitive Science [1993], p.117) | |
| A reaction: This confirms what I have always thought - that colour (as qualia) is strictly a feature of minds, not of the world. |
| 4047 | Gestalt psychology proposes inbuilt proximity, similarity, smoothness and closure principles [Goldman] |
| Full Idea: Gestalt psychology claims that there are at least four unlearned factors in perceptual grouping - the principles of proximity (close things), of similarity, of good continuation (extending lines in a smooth course), and closure (which completes figures). | |
| From: Alvin I. Goldman (Phil Applications of Cognitive Science [1993], p.103) | |
| A reaction: This offers a bridge between Hume's associationism and rationalist claims of innate ideas |
| 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?'. |