15 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. |
| 10496 | Monothetic categories have fixed defining features, and polythetic categories do not [Ellen] |
| Full Idea: Many categories are 'monothetic' (the defining set of features is always unique), and others are 'polythetic' (single features being neither essential to group membership nor sufficient to allocate an item to a group). | |
| From: Roy Ellen (Anthropological Studies of Classification [1996], p.33) | |
| A reaction: This seems a rather important distinction which hasn't made its way into philosophy, where there is a horrible tendency to oversimplify, with the dream of a neat and unified picture. But see Goodman's 'Imperfect Community' problem (Idea 7957). |
| 10497 | In symbolic classification, the categories are linked to rules [Ellen] |
| Full Idea: Symbolic classification occurs when we use some things as a means of saying something about other things. ..They enhance the significance of some categories, so that categories imply rules and rules imply categories. | |
| From: Roy Ellen (Anthropological Studies of Classification [1996], p.35) | |
| A reaction: I'm afraid the anthropologists seem to have more of interest to say about categories than philosophers do. Though maybe we couldn't do anthropology if philosophers had made us more self-conscious about categories. Teamwork! |
| 10495 | Continuous experience sometimes needs imposition of boundaries to create categories [Ellen] |
| Full Idea: Because parts of our experience of the world are complexly continuous, it is occasionally necessary to impose boundaries to produce categories at all. | |
| From: Roy Ellen (Anthropological Studies of Classification [1996], p.33) | |
| A reaction: I like it. Ellen says that people tend to universally cut nature somewhere around the joints, but we can't cope with large things, so the sea tends to be labelled in sections, even though most of the world's seas are continuous. |
| 10498 | Classification is no longer held to be rooted in social institutions [Ellen] |
| Full Idea: The view that all classification finds its roots in social institutions is now generally considered untenable. | |
| From: Roy Ellen (Anthropological Studies of Classification [1996], p.36) | |
| A reaction: And about time too. Ellen (an anthropologist) inevitably emphasises the complexity of the situation, but endorses the idea that people everywhere largely cut nature at the joints. |
| 21137 | Rawls rejected cosmopolitanism because it doesn't respect the autonomy of 'peoples' [Rawls, by Shorten] |
| Full Idea: Rawls rejected the cosmopolitan extension of his theory because he thought it failed to respect the political autonomy of 'peoples', which was his term of art for societies or political communities. | |
| From: report of John Rawls (The Law of Peoples [1999], p.115-8) by Andrew Shorten - Contemporary Political Theory 09 | |
| A reaction: Interesting that you might well start with the concept of 'a people', prior to some sort of social contract, but end up with rather alarming conflicts or indifference between rival peoples. Why should my people help in the famine next door? |