19 ideas
| 21699 | Russell offered a paraphrase of definite description, to avoid the commitment to objects [Quine] |
| Full Idea: Russell's theory involved defining a term not by presenting a direct equivalent of it, but by 'paraphrasis', providing equivalents of the sentences. In this way, reference to fictitious objects can be simulated without our being committed to the objects. | |
| From: Willard Quine (Russell's Ontological Development [1966], p.75) | |
| A reaction: I hadn't quite grasped that the modern strategy of paraphrase tracks back to Russell - though it now looks obvious, thanks to Quine. Paraphrase is a beautiful way of sidestepping ontological problems. See Frege on the moons of Jupiter. |
| 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. |
| 21700 | Taking sentences as the unit of meaning makes useful paraphrasing possible [Quine] |
| Full Idea: The new freedom that Russell confers by paraphrasis (of definite descriptions) is our reward for recognising that the unit of communication is the sentence and not the word. | |
| From: Willard Quine (Russell's Ontological Development [1966], p.75) | |
| A reaction: Since many people hardly ever speak a properly formed sentence, I take propositions to be better candidates for this. However, I don't see how we can reject the compositional view (the meanings are assembled). |
| 21701 | Knowing a word is knowing the meanings of sentences which contain it [Quine] |
| Full Idea: We can say that knowing words is knowing how to work out the meanings of sentences containing them. Dictionary definitions are mere clauses in a recursive definition of the meanings of sentences. | |
| From: Willard Quine (Russell's Ontological Development [1966], p.76) | |
| A reaction: Do you have to recursively define all the sentences that might contain the word, before you can fully know the meaning of the word? He seems to credit Russell with the holistic view of sentences (though I think that starts with Frege). |
| 7602 | In the Bible God changes his mind (repenting of creating humanity, in the Flood) [Armstrong,K] |
| Full Idea: In the Bible God changes his mind, as when he repents of having made man and decides to destroy the human race in the Flood. | |
| From: Karen Armstrong (A History of God [1993], Ch.1) | |
| A reaction: It becomes apparent that the most startling feature of Christian fundamentalism is its uncritical reading of the Bible, in which passages are wilfully lifted from context, and inconvenient inconsistencies are ruthlessly ignored. |
| 7605 | Monotheism introduced intolerance into religious thinking [Armstrong,K] |
| Full Idea: We have become so used to the intolerance of monotheism that we may not appreciate that its hostility towards other gods was a new religious attitude; paganism was an essentially tolerant faith. | |
| From: Karen Armstrong (A History of God [1993], Ch.2) | |
| A reaction: The comedian Dave Allen always signed off with "may your god go with you". To me the most striking feature of monotheists is frequently their barely controlled aggression, beneath a mask of strained compassion. |
| 7599 | Around 800 BCE teachers superseded gods in India [Armstrong,K] |
| Full Idea: Around the eighth century BCE the gods ceased to be very important in India, and would be superseded by the religious teacher, who would be considered higher than the gods. | |
| From: Karen Armstrong (A History of God [1993], Ch.1) | |
| A reaction: At least there has been one culture that gave an appropriate status to teachers. It seems astonishing in that age that human beings could have higher status than gods - way before the European 'humanists'. |
| 7597 | There is virtually no sign of monotheism in the Pentateuch [Armstrong,K] |
| Full Idea: It is very difficult to find a single monotheistic statement in the whole of the Pentateuch, and even the Ten Commandments take the existence of other gods for granted ("There shall be no strange gods for you before my face"). | |
| From: Karen Armstrong (A History of God [1993], Ch.1) | |
| A reaction: The transition from polytheism to monotheism is very strange. First God is 'jealous' of other gods, then supremely above them, and eventually totally exclusive. It's like watching the rise of Stalin. |
| 7606 | The idea that Jesus was God was only settled in the fourth century [Armstrong,K] |
| Full Idea: Jesus himself certainly never claimed to be God, and the doctrine that Jesus had been God in human form was not finalised until the fourth century. | |
| From: Karen Armstrong (A History of God [1993], Ch.3) | |
| A reaction: It was this final view which seems to have provoked Muhammed into developing a religion with the slogan "there is only one God". In Christianity an initially promising set of teachings grew into a prolonged irrational hysteria. |
| 7596 | Faith is not just belief in propositions, but also putting trust in them [Armstrong,K] |
| Full Idea: There is a distinction between belief in a set of propositions and a faith which enables us to put our trust in them. | |
| From: Karen Armstrong (A History of God [1993], Intro) | |
| A reaction: This is interestingly distinct from the usual idea that faith is putting belief in propositions which are not sufficiently rationally justified. How many philosophers actually have faith in the propositions they say they believe? |