9 ideas
| 19396 | Wisdom is knowing all of the sciences, and their application [Leibniz] |
| Full Idea: Wisdom is a perfect knowledge of the principles of all the sciences and of the art of applying them. | |
| From: Gottfried Leibniz (On Wisdom [1693], 0) | |
| A reaction: 'Sciences' should be understood fairly broadly here (e.g. of architecture, agriculture, grammar). This is a scholar's vision of wisdom, very different from the notion of the wisest person in a village full of illiterate people. |
| 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) |
| 19397 | Perfect knowledge implies complete explanations and perfect prediction [Leibniz] |
| Full Idea: The mark of perfect knowledge is that nothing appears in the thing under consideration which cannot be accounted for, and that nothing is encountered whose occurrence cannot be predicted in advance. | |
| From: Gottfried Leibniz (On Wisdom [1693], 1) | |
| A reaction: I would track both of these back to the concept of perfect understanding, which is admittedly a bit vague. Does a finite mind need to predict every speck of dust to have perfect knowledge? Do we have perfect knowledge of triangles? |
| 6316 | We translate in a way that makes the largest possible number of statements true [Wilson,NL] |
| Full Idea: We select as designatum that individual which will make the largest possible number of statements true. | |
| From: N.L. Wilson (Substances without Substrata [1959]), quoted by Willard Quine - Word and Object II.§13 n | |
| A reaction: From the Quine's reference, it sounds as if Wilson was the originator of the well-known principle of charity, later taken up by Davidson. If so, he should be famous, because it strikes me as a piece of fundamental and important wisdom. |