18 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. |
| 18810 | Aristotle's proofs give understanding, so it can't be otherwise, so consequence is necessary [Smiley, by Rumfitt] |
| Full Idea: The ingredient of necessity [in Aristotle's account of consequence] is required by his demand that proof should produce 'understanding' [episteme], coupled with his claim that understanding something involves seeing that it cannot be otherwise. | |
| From: report of Timothy Smiley (Conceptions of Consequence [1998], p.599) by Ian Rumfitt - The Boundary Stones of Thought 3.2 | |
| A reaction: An intriguing reverse of the normal order. Not 'necessity in logic delivers understanding', but 'reaching understanding shows the logic was necessary'. |
| 19419 | Not all of perception is accompanied by consciousness [Leibniz] |
| Full Idea: I do not think that the Cartesians have ever proved or can prove that every perception is accompanied by consciousness. | |
| From: Gottfried Leibniz (Principle of Life and Plastic Natures [1705], p.195) | |
| A reaction: This idea is very important in Leibniz, because non-conscious or barely conscious thoughts and perceptions explain a huge amount about behaviour, reality and morality. |
| 19421 | Souls act as if there were no bodies, and bodies act as if there were no souls [Leibniz] |
| Full Idea: Everything takes place in souls as if there were no body, and everything takes place in bodies as if there were no souls. | |
| From: Gottfried Leibniz (Principle of Life and Plastic Natures [1705], p.198) | |
| A reaction: I don't think I have ever encountered a modern thinker who accepts this view. Leibniz rejected Occasionalism, but his account depends entirely on the role of God, to set up the pre-established harmony. Why would God do that? |
| 19420 | Death and generation are just transformations of an animal, augmented or diminished [Leibniz] |
| Full Idea: Death, like generation, is only the transformation of the same animal, which is sometimes augmented and sometimes diminished. | |
| From: Gottfried Leibniz (Principle of Life and Plastic Natures [1705], p.195) | |
| A reaction: Leibniz has a very unusual view of death, since neither minds nor their bodies can ever be wholly destroyed. Death is a kind of shrinking. I suspect that he was wrong about that. |
| 19416 | Not all of matter is animated, any more than a pond full of living fish is animated [Leibniz] |
| Full Idea: It must not be said that each portion of matter is animated, just as we do not say that a pond full of fishes is an animated body, although a fish is. | |
| From: Gottfried Leibniz (Principle of Life and Plastic Natures [1705], p.190) | |
| A reaction: This is a particularly clear picture of the role of monads in matter. Monads are attached to bodies, which are entirely inanimate, but monads suffuse matter and give it its properties, like particularly bubbly champagne. Cf Idea 19422. |
| 19422 | Every particle of matter contains organic bodies [Leibniz] |
| Full Idea: There is no particle of matter which does not contain organic bodies. | |
| From: Gottfried Leibniz (Principle of Life and Plastic Natures [1705], p.198) | |
| A reaction: Cf Idea 19416. There seems to be an interaction problem here (solved, presumably, by pre-established harmony). The organic bodies are there to explain the active behaviour of matter, but the related matter seems intrinsically inert. |
| 19418 | Mechanics shows that all motion originates in other motion, so there is a Prime Mover [Leibniz] |
| Full Idea: The maxim that there is no motion which has not its origin in another motion, according to the laws of mechanics, leads us again to the Prime Mover. | |
| From: Gottfried Leibniz (Principle of Life and Plastic Natures [1705], p.194) | |
| A reaction: This is Leibniz's endorsement (uncredited) to Aquinas's First Way. It is hard to see how the laws of mechanics could have anything to say about the origin of movement. And doesn't the law say that the motions of God need a mover? |
| 19417 | All substances are in harmony, even though separate, so they must have one divine cause [Leibniz] |
| Full Idea: My system of Pre-established Harmony furnishes a new proof of God's existence, since it is manifest that the agreement of so many substances, of which the one has no influence upon the other, could only come from a general cause on which they all depend. | |
| From: Gottfried Leibniz (Principle of Life and Plastic Natures [1705], p.192) | |
| A reaction: Adjacent harmony seems self-explanatory, but remote harmony is interesting evidence for God. Hence modern quantum non-locality should make us all wonder whether there is a deeper explanation. |