14 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. |
18699 | Carnap tried to define all scientific predicates in terms of primitive relations, using type theory [Carnap, by Button] |
Full Idea: Carnap's ultimate ambition in the Aufbau is to provide a constitution-system within which any predicate of any scientific vocabulary can be explicitly defined in terms of primitive relations holding among basic elements, using type theory. | |
From: report of Rudolph Carnap (The Logical Structure of the World (Aufbau) [1928]) by Tim Button - The Limits of Reason 05.2 | |
A reaction: David Chalmers has a modern shot at the same project in 'Constructing the World'. Ramsey sentences seem to be part of the same game. |
12131 | All concepts can be derived from a few basics, making possible one science of everything [Carnap, by Brody] |
Full Idea: In the 'Aufbau', Carnap tried to show how all of our concepts can be derived from a few basic concepts. ..Consequently there can be one science which studied all that existed, the science of the objects corresponding to the basic concepts. | |
From: report of Rudolph Carnap (The Logical Structure of the World (Aufbau) [1928]) by Baruch Brody - Identity and Essence 2.2 | |
A reaction: This is Carnap's Constructionist programme. |
15150 | The properties of an electron can't be explained just as 'clustering' [Chakravartty on Boyd] |
Full Idea: Boyd's homeostatic mechanisms are not responsible for the co-instantiation of the mass, charge and spin of an electron. | |
From: comment on Richard Boyd (Homeostasis, Species and Higher Taxa [1999]) by Anjan Chakravarrty - Inessential Aristotle: Powers without Essences 3 | |
A reaction: I would have thought that no one has the foggiest idea (unless I have missed something?) about why electrons have those three properties. What is it about electrons that makes them do that? Explanations always run out somewhere. Substratum! |
15149 | Properties cluster together, either because of intrinsic relations, or because of an underlying process [Boyd, by Chakravartty] |
Full Idea: Boyd analyses 'sociability' between properties in terms of 'homeostasis', as causal relations between properties that favour clustering, or underlying processes that favour coinstantiation, or both. | |
From: report of Richard Boyd (Homeostasis, Species and Higher Taxa [1999]) by Anjan Chakravarrty - Inessential Aristotle: Powers without Essences 3 | |
A reaction: Chakravarty criticises this claim, but Boyd is clearly onto something. If, like me, you think natural kinds are overrated, you have to like his view. |