9 ideas
19695 | The devil was wise as an angel, and lost no knowledge when he rebelled [Whitcomb] |
Full Idea: The devil is evil but nonetheless wise; he was a wise angel, and through no loss of knowledge, but, rather, through some sort of affective restructuring tried and failed to take over the throne. | |
From: Dennis Whitcomb (Wisdom [2011], 'Argument') | |
A reaction: ['affective restructuring' indeed! philosophers- don't you love 'em?] To fail at something you try to do suggests a flaw in the wisdom. And the new regime the devil wished to introduce doesn't look like a wise regime. Not convinced. |
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) |
3271 | We can't control our own beliefs [Nagel] |
Full Idea: Our beliefs are always due to factors outside of our control. | |
From: Thomas Nagel (Moral Luck [1976], p.27) |
3272 | Moral luck can arise in character, preconditions, actual circumstances, and outcome [Nagel] |
Full Idea: Moral luck involves one's character, the antecedent circumstances of the act, the actual circumstances of the act, and the outcome of the act. | |
From: Thomas Nagel (Moral Luck [1976], p.28) | |
A reaction: Meaning, I take it, that there can be luck in any one of those four. A neat slicing up that doesn't quite fit the real world, where things flow. Helpful, though. |