16 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. |
| 6387 | A minimum requirement for a theory of meaning is that it include an account of truth [Davidson] |
| Full Idea: Whatever else it embraces, a theory of meaning must include an account of truth - a statement of the conditions under which an arbitrary sentence of the language is true. | |
| From: Donald Davidson (Reality without Reference [1977], p.132) | |
| A reaction: It is a moot point whether we can define meaning if we assume truth, or if we can define truth by assuming meaning. Tarski seems to presuppose meaning when he defines truth (Idea 2345). I like Davidson's taking of truth as basic. |
| 6391 | A theory of truth tells us how communication by language is possible [Davidson] |
| Full Idea: A theory of truth lets us answer the underlying question how communication by language is possible. | |
| From: Donald Davidson (Reality without Reference [1977], p.137) | |
| A reaction: If, instead, you explain communication by understood intentions (á la Grice), you have to say more about what sort of intentions are meant. If you use reference, you still have more to say about the meaning of sentences. Davidson looks good. |
| 6388 | Is reference the key place where language and the world meet? [Davidson] |
| Full Idea: The essential question is whether reference is the, or at least one, place where there is direct contact between linguistic theory and events, actions, or objects described in nonlinguistic terms. | |
| From: Donald Davidson (Reality without Reference [1977], p.134) | |
| A reaction: How do you 'describe objects in nonlinguistic terms'? The causal theory of reference (e.g. Idea 4957) is designed to plug language straight into the world via reference. It simplifies things nicely, but I don't quite believe it. |
| 6390 | With a holistic approach, we can give up reference in empirical theories of language [Davidson] |
| Full Idea: I defend a version of the holistic approach, and urge that we must give up the concept of reference as basic to an empirical theory of language. | |
| From: Donald Davidson (Reality without Reference [1977], p.136) | |
| A reaction: He proposes to connect language to the world via the concept of truth, rather than of reference. It is a brilliant idea, and is the key issue in philosophy of language. I go back to animals, which seem to care about situations rather than things. |
| 6389 | To explain the reference of a name, you must explain its sentence-role, so reference can't be defined nonlinguistically [Davidson] |
| Full Idea: It is inconceivable that one should be able to explain the relationship between 'Kilimanjiro' and Kilimanjiro without first explaining the role of the word in sentences; hence there is no chance of explaining reference directly in nonlinguistic terms. | |
| From: Donald Davidson (Reality without Reference [1977], p.135) | |
| A reaction: I point at the mountain, and a local says 'Kilimanjiro'? There is a 'gavagai'-type problem with that. The prior question might be 'what is it about this word that enables it to have a role in sentences?' Unlike whimpering or belching. |
| 7667 | There are two sides to men - the pleasantly social, and the violent and creative [Diderot, by Berlin] |
| Full Idea: Diderot is among the first to preach that there are two men: the artificial man, who belongs in society and seeks to please, and the violent, bold, criminal instinct of a man who wishes to break out (and, if controlled, is responsible for works of genius. | |
| From: report of Denis Diderot (works [1769], Ch.3) by Isaiah Berlin - The Roots of Romanticism | |
| A reaction: This has an obvious ancestor in Plato's picture (esp. in 'Phaedrus') of the two conflicting sides to the psuché, which seem to be reason and emotion. In Diderot, though, the suppressed man has virtues, which Plato would deny. |