19 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) |
| 2181 | It is an absurd Kantian idea that at the limit rationality and freedom coincide [Williams,B] |
| Full Idea: There is a deluded Kantian idea that at the limit rationality and freedom will totally coincide. | |
| From: Bernard Williams (Shame and Necessity [1993], VI - p.158) |
| 2176 | There is only a problem of free will if you think the notion of 'voluntary' can be metaphysically deepened [Williams,B] |
| Full Idea: There is a problem of free will only for those who think that the notion of voluntary can be metaphysically deepened. | |
| From: Bernard Williams (Shame and Necessity [1993], III - p.68) | |
| A reaction: Years later, I now see that his refers to a pet hate of mine in discussions of free will, which is the idea that a person can have something called 'ultimate' responsibility for an action (which is the 'deep' version of 'you did it'). |
| 4317 | We judge weakness of will by an assessment after the event is concluded [Williams,B, by Cottingham] |
| Full Idea: Williams has shown that whether an action was weakness of will depends on an evaluation after the event, as in the question of whether Gauguin was right to abandon his family to pursue his art. | |
| From: report of Bernard Williams (Shame and Necessity [1993]) by John Cottingham - Reason, Emotions and Good Life p.1 | |
| A reaction: The 'Gauguin Problem' is that Gauguin's actions only become weakness of will if the pictures are no good, and he can't know that till he's painted them. Good point. |
| 2174 | Responsibility involves cause, intention, state of mind, and response after the event [Williams,B] |
| Full Idea: The four elements of any conception of responsibility are cause, intention, state of mind, and response after the event. | |
| From: Bernard Williams (Shame and Necessity [1993], III - p.53) |
| 2178 | In bad actions, guilt points towards victims, and shame to the agent [Williams,B] |
| Full Idea: In what I have done, the guilt points in one direction towards what has happened to others, and the shame in another direction to what I am. | |
| From: Bernard Williams (Shame and Necessity [1993], IV - p.92) | |
| A reaction: Not convinced. I think shame has the fear of being observed as an inescapable component. Even when alone shame involves imagining what others might think. |
| 2169 | Greek moral progress came when 'virtue' was freed from social status [Williams,B] |
| Full Idea: There was moral progress in the ancient Greek world, notably to the extent that the idea of areté, human excellence, was freed to some extent from determination by social position. | |
| From: Bernard Williams (Shame and Necessity [1993], I - p.7) |
| 2172 | The modern idea of duty is unknown in archaic Greece [Williams,B] |
| Full Idea: Duty in some abstract modern sense is largely unknown to the Greeks, in particular to archaic Greeks. | |
| From: Bernard Williams (Shame and Necessity [1993], II - p.41) |
| 2179 | If the moral self is seen as characterless, then other people have a very limited role in our moral lives [Williams,B] |
| Full Idea: The conception of the moral self as characterless leaves only a limited positive role to other people in one's moral life. | |
| From: Bernard Williams (Shame and Necessity [1993], IV - p.95) |
| 2180 | If reason cannot lead people to good, we must hope they have an internal voice [Williams,B] |
| Full Idea: If we think the power of reason is not enough by itself to distinguish good and bad, then we would hope that people have limited autonomy, that there is an internalised other in them that carries some social weight. | |
| From: Bernard Williams (Shame and Necessity [1993], IV - p.100) |
| 21004 | Hart (against Bentham) says human rights are what motivate legal rights [Hart,HLA, by Sen] |
| Full Idea: Whereas Bentham saw rights as a 'child of law', Herbert Hart's view takes the form of seeing human rights as, in effect, 'parents of law'; they motivate specific legislations. | |
| From: report of H.L.A. Hart (The Concept of Law [1961]) by Amartya Sen - The Idea of Justice 17 'Ethics' | |
| A reaction: [He cites Hart 1955 'Are there any natural rights?'] I agree with Hart. It is clearer if the parents of law are not referred to as 'rights'. You can demand a right, but it is only a right when it is awarded to you. |
| 20932 | Positive law needs secondary 'rules of recognition' for their correct application [Hart,HLA, by Zimmermann,J] |
| Full Idea: Hart says we have secondary legal 'rules of recognition', by which primary positive law is recognised and applied in a regulated manner. | |
| From: report of H.L.A. Hart (The Concept of Law [1961]) by Jens Zimmermann - Hermeneutics: a very short introduction 6 'Rules' | |
| A reaction: The example of the authority of a particular court is given. |
| 20931 | Hart replaced positivism with the democratic requirement of the people's acceptance [Hart,HLA, by Zimmermann,J] |
| Full Idea: Hart replaced Austin's concept of positive law as sovereign command with a more democratic ideal. In modern law-based societies the authority of law depends on the people's acceptance of a law's enduring validity. | |
| From: report of H.L.A. Hart (The Concept of Law [1961]) by Jens Zimmermann - Hermeneutics: a very short introduction 6 'Hart' | |
| A reaction: Presumably the ancestor of this view is the social contract of Hobbes and Locke. |
| 2175 | There is a problem of evil only if you expect the world to be good [Williams,B] |
| Full Idea: There is a "problem of evil" only for those who expect the world to be good. | |
| From: Bernard Williams (Shame and Necessity [1993], III - p.68) |