11 ideas
| 19323 | 'Snow is white' depends on meaning; whether snow is white depends on snow [Etchemendy] |
| Full Idea: The difference between (a) snow is white, and (b) 'snow is white' true is that the first makes a claim that only depends on the colour of snow, while the second depends both on the colour of snow and the meaning of the sentence 'snow is white'. | |
| From: John Etchemendy (Tarski on Truth and Logical Consequence [1988], p.61), quoted by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.7 | |
| A reaction: This is a helpful first step for those who have reached screaming point by being continually offered this apparently vacuous equivalence. This sentence works well if that stuff is a particular colour. |
| 19137 | We can get a substantive account of Tarski's truth by adding primitive 'true' to the object language [Etchemendy] |
| Full Idea: Getting from a Tarskian definition of truth to a substantive account of the semantic properties of the object language may involve as little as the reintroduction of a primitive notion of truth. | |
| From: John Etchemendy (Tarski on Truth and Logical Consequence [1988], p.60), quoted by Donald Davidson - Truth and Predication 1 | |
| A reaction: This is, I think, the first stage in modern developments of axiomatic truth theories. The first problem would be to make sure you haven't reintroduced the Liar Paradox. You need axioms to give behaviour to the 'true' predicate. |
| 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) |
| 22449 | When we say 'is red' we don't mean 'seems red to most people' [Foot] |
| Full Idea: One might think that 'is red' means the same as 'seems red to most people', forgetting that when asked if an object is red we look at it to see if it is red, and not in order to estimate the reaction that others will have to it. | |
| From: Philippa Foot (Moral Relativism [1979], p.23) | |
| A reaction: True, but we are conscious of our own reliability as observers (e.g. if colourblind, or with poor hearing or eyesight). I don't take my glasses off, have a look, and pronounce that the object is blurred. Ordinary language philosophy in action. |
| 22451 | All people need affection, cooperation, community and help in trouble [Foot] |
| Full Idea: There is a great deal that all men have in common; all need affection, the cooperation of others, a place in a community, and help in trouble. | |
| From: Philippa Foot (Moral Relativism [1979], p.33) | |
| A reaction: There seem to be some people who don't need affection or a place in a community, though it is hard to imagine them being happy. These kind of facts are the basis for any sensible cognitivist view of ethics. They are basic to Foot's view. |
| 22452 | Do we have a concept of value, other than wanting something, or making an effort to get it? [Foot] |
| Full Idea: Do we know what we mean by saying that anything has value, or even that we value it, as opposed to wanting it or being prepared to go to trouble to get it? | |
| From: Philippa Foot (Moral Relativism [1979], p.35) | |
| A reaction: Well, I value Rembrandt paintings, but have no aspiration to own one (and would refuse it if offered, because I couldn't look after it properly). And 'we' don't want to move the Taj Mahal to London. She has not expressed this good point very well. |