22 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) |
| 10397 | Abelard's mereology involves privileged and natural divisions, and principal parts [Abelard, by King,P] |
| Full Idea: Abelard's theory of substantial integral wholes is not a pure mereology in the modern sense, since he holds that there are privileged divisions; ..the division of a whole must be into its principal parts. Some wholes have a natural division. | |
| From: report of Peter Abelard (works [1135]) by Peter King - Peter Abelard 2 | |
| A reaction: This is a mereology that cuts nature at the joints, rather than Lewis's 'unrestricted composition', so I find Abelard rather appealing. |
| 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. |
| 10396 | If 'animal' is wholly present in Socrates and an ass, then 'animal' is rational and irrational [Abelard, by King,P] |
| Full Idea: Abelard argued that if the universal 'animal' were completely present in both Socrates and an ass, making each wholly an animal, then the same thing, animal, will be simultaneously rational and irrational, with contraries present in the whole thing. | |
| From: report of Peter Abelard (works [1135]) by Peter King - Peter Abelard 2 | |
| A reaction: If we have universals for rationality and irrationality, they can distinguish the two. But we must also say that rationality is not an aspect of animal, which seems to mean that mind isn't either. What is the essence of an animal? Not reason? |
| 10395 | Abelard was an irrealist about virtually everything apart from concrete individuals [Abelard, by King,P] |
| Full Idea: Abelard was an irrealist about universals, but also about propositions, events, times other than the present, natural kinds, relations, wholes, absolute space, hylomorphic composites, and the like. The concrete individual is enough to populate the world. | |
| From: report of Peter Abelard (works [1135]) by Peter King - Peter Abelard 2 | |
| A reaction: If a Nominalist claims that 'only particulars exist', this makes him an extreme nominalist, and remarkably materialistic for his time (though he accepted the soul, as well as God). |
| 15384 | Only words can be 'predicated of many'; the universality is just in its mode of signifying [Abelard, by Panaccio] |
| Full Idea: Abelard concluded that only words can be 'predicated of many'. A universal is nothing but a general linguistic predicate, and its universality depends not on its mode of being, but on its mode of signifying. | |
| From: report of Peter Abelard (works [1135]) by Claude Panaccio - Medieval Problem of Universals 'Peter' | |
| A reaction: Abelard seems to be the originator of what is now called Predicate Nominalism, with Nelson Goodman as his modern representative. If it is just words, is there no fact of two things having the 'same' property? |
| 8481 | The de dicto-de re modality distinction dates back to Abelard [Abelard, by Orenstein] |
| Full Idea: The de dicto-de re modality distinction dates back to Abelard. | |
| From: report of Peter Abelard (works [1135]) by Alex Orenstein - W.V. Quine Ch.7 | |
| A reaction: Most modern philosophers couldn't (apparently) care less where a concept originated, but one of the principles of this database is that such things do matter. I'm not sure why, but if we want the whole picture, we need the historical picture. |
| 19553 | Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne] |
| Full Idea: If I utter 'I know I have a hand' then I can only be reckoned a cooperative conversant by my interlocutors on the assumption that there was a real question as to whether I have a hand. | |
| From: John Hawthorne (The Case for Closure [2005], 2) | |
| A reaction: This seems to point to the contextualist approach to global scepticism, which concerns whether we are setting the bar high or low for 'knowledge'. |
| 19551 | How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne] |
| Full Idea: Those who deny skepticism but accept closure will have to explain how we know the various 'heavyweight' skeptical hypotheses to be false. Do we then twist the concept of knowledge to fit the twin desiderata of closue and anti-skepticism? | |
| From: John Hawthorne (The Case for Closure [2005], Intro) | |
| A reaction: [He is giving Dretske's view; Dretske says we do twist knowledge] Thus if I remember yesterday, that has the heavyweight implication that the past is real. Hawthorne nicely summarises why closure produces a philosophical problem. |
| 19552 | We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne] |
| Full Idea: Maybe one cannot know the logical consequences of the proposition that one knows, on account of the fact that small risks add up to big risks. | |
| From: John Hawthorne (The Case for Closure [2005], 1) | |
| A reaction: The idea of closure is that the new knowledge has the certainty of logic, and each step is accepted. An array of receding propositions can lose reliability, but that shouldn't apply to logic implications. Assuming monotonic logic, of course. |
| 19554 | Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne] |
| Full Idea: How could we know that P and Q but not be in a position to know that P (as deniers of closure must say)? If my glass is full of wine, we know 'g is full of wine, and not full of non-wine'. How can we deny that we know it is not full of non-wine? | |
| From: John Hawthorne (The Case for Closure [2005], 2) | |
| A reaction: Hawthorne merely raises this doubt. Dretske is concerned with heavyweight implications, but how do you accept lightweight implications like this one, and then suddenly reject them when they become too heavy? [see p.49] |
| 15385 | Abelard's problem is the purely singular aspects of things won't account for abstraction [Panaccio on Abelard] |
| Full Idea: Abelard's problem is that it is not clear how singular forms could do the job they are supposed to do - to account for abstraction, namely - if they were purely singular aspects. | |
| From: comment on Peter Abelard (works [1135]) by Claude Panaccio - Medieval Problem of Universals 'Peter' | |
| A reaction: A very nice question! If we say that abstracta are just acquired by ignoring all but that feature in some objects, how do we identify 'that' feature in order to select it? The instances must share something in common to be abstracted. |
| 15383 | Nothing external can truly be predicated of an object [Abelard, by Panaccio] |
| Full Idea: Abelard argued from the commonly accepted definition of a universal as 'what can be predicated of man', that no external thing can ever be predicated of anything. | |
| From: report of Peter Abelard (works [1135]) by Claude Panaccio - Medieval Problem of Universals 'Peter' | |
| A reaction: It sounds to me as if Abelard is confusing predicates with properties! Maybe no external can be a property of anything, but I take predicates to just be part of what you can say about anything, and that had better included external facts. |
| 10398 | Natural kinds are not special; they are just well-defined resemblance collections [Abelard, by King,P] |
| Full Idea: In Abelard's view a natural kind is a well-defined collection of things that have the same features, so that natural kinds have no special status, being no more than discrete integral wholes whose principle of membership is similarity. | |
| From: report of Peter Abelard (works [1135]) by Peter King - Peter Abelard 2 | |
| A reaction: I take a natural kind to be a completely stable and invariant class of things. Presumably this invariance has an underlying explanation, but Abelard seems to take the Humean line that we cannot penetrate beyond the experienced surface. |