11 ideas
| 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) |
| 7855 | Some suggest that materialism is empty, because 'physical' cannot be properly characterized [Mellor/Crane, by Papineau] |
| Full Idea: It is sometimes contended that the whole idea of materialism is somehow empty, on the grounds that there is no proper way to characterize the 'physical' realm. | |
| From: report of DH Mellor / T Crane (There is no question of physicalism [1990]) by David Papineau - Thinking about Consciousness 1.1 | |
| A reaction: [Papineau also cites Gabriel Segal] I agree with Papineau in rejecting this. Uncertainties about quantum states do not pose a problem, and the position tends to have an implicit dualism buried in it somewhere. |
| 6120 | Causation depends on intrinsic properties [Mellor/Crane] |
| Full Idea: The problem thoughts pose for causation is that causation depends directly only on intrinsic properties, whereas the causal powers of token thoughts depend on their contents, which are not intrinsic. | |
| From: DH Mellor / T Crane (There is no question of physicalism [1990], p.194) | |
| A reaction: This, as we find later in the paper, depends on an externalist account of thoughts. Could a relational property not be causal? Edinburgh's being wetter than London is caused by its being further north? |
| 6121 | There are many psychophysicals laws - about the effects of sweets, colours and soft cushions [Mellor/Crane] |
| Full Idea: There are many psychophysical laws, linking sensations to non-mental features of those who have them; the industries of anaesthetics, scents, narcotics, sweeteners, coloured paints, loudspeakers and soft cushions depend on them. | |
| From: DH Mellor / T Crane (There is no question of physicalism [1990], p.198) | |
| A reaction: It may be expressing it a little strongly to call these 'laws', but they are certainly reliable regularities, and they are probably enough to undermine Davidson's claim that such laws don't exist. |
| 6122 | No defences of physicalism can deprive psychology of the ontological authority of other sciences [Mellor/Crane] |
| Full Idea: Neither laws nor causation nor claims of supervenience (the last refuge of the physicalist) deprive psychology of the ontological authority of non-mental science. | |
| From: DH Mellor / T Crane (There is no question of physicalism [1990], p.203) | |
| A reaction: There is no need to defend the practice of psychologists (or garden designers) from the depradations of bandit physicalists. But what is the ontology of psychology if it isn't dualist or physicalist? |
| 23898 | Those who say immorality is not an aesthetic criterion must show that all criteria are aesthetic [Weil] |
| Full Idea: Writers and readers who cry out that immorality is not an aesthetic criterion need to prove, which they have never done, that one should apply only aesthetic criteria to literature. | |
| From: Simone Weil (Literature and Morals [1941], p.146) | |
| A reaction: I take the first criterion of literature that it not be boring, and I don't think that is an aesthetic matter. A lot must be achieved before a work can even be considered for aesthetic judgment. Being deeply offensive might rule it out. |