20 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. |
| 11184 | Aristotelian essentialism is about shared properties, individuating essentialism about distinctive properties [Marcus (Barcan)] |
| Full Idea: An object must have some of its natural properties in this world. Some of those it has in common with objects of some proximate kind (Aristotelian essentialism), and others individuate it from objects of the same kind (individuating essentialism). | |
| From: Ruth Barcan Marcus (Essential Attribution [1971], p.193) |
| 11181 | Aristotelian essentialism involves a 'natural' or 'causal' interpretation of modal operators [Marcus (Barcan)] |
| Full Idea: Aristotelian essentialism may best be understood on a 'natural' or 'causal' interpretation of the modal operators. | |
| From: Ruth Barcan Marcus (Essential Attribution [1971], p.189) | |
| A reaction: I record this because I very much like the sound of it, though I have yet to fully understand it. |
| 11180 | Essentialist sentences are not theorems of modal logic, and can even be false [Marcus (Barcan)] |
| Full Idea: In the range of modal systems for which Saul Kripke has provided a semantics, no essentialist sentence is a theorem. Furthermore, there are models for which such sentences are demonstrably false. | |
| From: Ruth Barcan Marcus (Essential Attribution [1971], p.188) |
| 11186 | 'Essentially' won't replace 'necessarily' for vacuous properties like snub-nosed or self-identical [Marcus (Barcan)] |
| Full Idea: We would never use 'is essentially' for 'is necessarily' where vacuous properties are concerned, as in 'Socrates is essentially snub-nosed' or 'Socrates is essentially Socrates'. | |
| From: Ruth Barcan Marcus (Essential Attribution [1971], p.193) | |
| A reaction: This simple point does us a huge service in rescuing the word 'essential' from several hundred years of misguided philosophy. |
| 11185 | 'Is essentially' has a different meaning from 'is necessarily', as they often cannot be substituted [Marcus (Barcan)] |
| Full Idea: There seems to be surface synonymy between 'is essentially' and de re occurrences of 'is necessarily', but intersubstitution often fails to preserve sense (as in 'Winston is essentially a cyclist' and 'Winston is necessarily a cyclist'). | |
| From: Ruth Barcan Marcus (Essential Attribution [1971], p.193) | |
| A reaction: Clearly the two sentences have different meanings, with 'essentially' being a comment about the nature of Winston, and 'necessarily' probably being a comment about the circumstances in which he finds himself. Very nice. See also Idea 11186. |
| 11182 | If essences are objects with only essential properties, they are elusive in possible worlds [Marcus (Barcan)] |
| Full Idea: Some philosophers make a metaphysical shift, by inventing objects (individual concepts, forms, substances) called 'essences', which have only essential properties, and then worry when they can't locate them by rummaging around in possible worlds. | |
| From: Ruth Barcan Marcus (Essential Attribution [1971], p.192) |
| 11183 | The use of possible worlds is to sort properties (not to individuate objects) [Marcus (Barcan)] |
| Full Idea: The usefulness of talk about possible worlds is not for purposes of individuating the object - that can be done in this world; such talk is a way of sorting its properties. | |
| From: Ruth Barcan Marcus (Essential Attribution [1971], p.192) | |
| A reaction: 'Possible worlds are a device for sorting properties' sounds to me like a promising slogan. Ruth Marcus originated rigid designation, before Kripke came up with the label. |
| 11187 | In possible worlds, names are just neutral unvarying pegs for truths and predicates [Marcus (Barcan)] |
| Full Idea: The strategem of talk about possible worlds is that truth assignments of sentences and extensions of predicates may vary, but individual names don't alter their reference (unless they don't refer). They are a neutral peg for descriptions. | |
| From: Ruth Barcan Marcus (Essential Attribution [1971], p.194) |
| 3447 | All theory is against free will, and all experience is in favour of it [Johnson,S] |
| Full Idea: All theory is against free will, and all experience is in favour of it. | |
| From: Samuel Johnson (works [1770]), quoted by PG - Db (ideas) |
| 11189 | Dispositional essences are special, as if an object loses them they cease to exist [Marcus (Barcan)] |
| Full Idea: Being gold or being a man is not accidental. ..Such essences are dispositional properties of a very special kind: if an object had such a property and ceased to have it, it would have ceased to exist or have changed (as if gold is transmuted to lead). | |
| From: Ruth Barcan Marcus (Essential Attribution [1971], p.202) | |
| A reaction: Ruth Marcus is an important founder of modern scientific essentialism, by not only proposing the notion we call rigid designation, but by explicitly defending the essential identities that seem to emerge from modal logic. |