9 ideas
| 18487 | We want to know what makes sentences true, rather than defining 'true' [McFetridge] |
| Full Idea: The generalisation 'What makes a (any) sentence true?' is not a request for definitions of 'true' (the concept), but rather requests for (partial) explanations of why certain particular sentences are true. | |
| From: Ian McFetridge (Truth, Correspondence, Explanation and Knowledge [1977], II) | |
| A reaction: McFetridge is responding to the shortcomings of Tarski's account of truth. The mystery seems to be why some of our representations of the world are 'successful', and others are not. |
| 18902 | Correspondence theories can't tell you what truths correspond to [Davidson] |
| Full Idea: The real objection to correspondence theories is that such theories fail to provide entities to which truth vehicles (as statements, sentence, or utterances) can be said to correspond. | |
| From: Donald Davidson (The Structure and Content of Truth [1990], p.304), quoted by Fred Sommers - Intellectual Autobiography Notes 23 | |
| A reaction: This is the remark which provoked Sommers to come out with Idea 18901, which strikes me as rather profound. |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 18488 | We normally explain natural events by citing further facts [McFetridge] |
| Full Idea: If one were asked 'What makes salt soluble in water?', the most natural answer would be something of the style 'The fact that it has such-and-such structure'. | |
| From: Ian McFetridge (Truth, Correspondence, Explanation and Knowledge [1977], II) | |
| A reaction: Personally I would want to talk about its 'powers' (dispositional properties), rather than its 'structure' (categorical properties). This defends facts, but you could easily paraphrase 'fact' out of this reply (as McFetridge realised). |