14 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) |
| 16066 | Additional or removal of any part changes a thing, so people are never the same person [Epicharmus] |
| Full Idea: If you add or take away a pebble, the same number does not remain. If you add to a length or cut off from it, the former measure does not remain. So human beings grow or waste away. Both you and I were, and shall be, other men. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B02), quoted by Diogenes Laertius - Lives of Eminent Philosophers 03.12 | |
| A reaction: [The original is in dialogue form from a play. The context is a joke about not paying a debt.] Note the early date for this metaphysical puzzle. My new favourite reply is Chrysippus's Idea 16059; identity actually requires change. |
| 436 | A dog seems handsome to another a dog, and even a pig to another pig [Epicharmus] |
| Full Idea: Dog seems very handsome to dog, and ox to ox, and donkey very handsome to donkey, and even pig to pig. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B05), quoted by (who?) - where? |
| 5997 | Dicaearchus said soul does not exist, but is just a configuration of the body [Dicaearchus, by Fortenbaugh] |
| Full Idea: Dicaearchus advanced the view that mind and soul do not exist; there is only body configured in a certain way. | |
| From: report of Dicaearchus (On the Soul (frags) [c.320 BCE]) by William W. Fortenbaugh - Dicaearchus | |
| A reaction: Pure eliminativism! It is hard to find even ruthless modern physicalists taking such a bold view. Note that he is a pupil of Aristotle, and this does not sound like a major disagreement with his teacher's views. |
| 442 | Pleasures are like pirates - if you are caught they drown you in a sea of pleasures [Epicharmus] |
| Full Idea: Pleasures for mortals are like impious pirates, for the man who is caught by pleasures is immediately drowned in a sea of them. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B44), quoted by (who?) - where? | |
| A reaction: Not all slopes are slippery. Plenty of people hold themselves to strict rules about alcohol or gambling. People have occasional treats. |
| 440 | Hands wash hands; give that you may get [Epicharmus] |
| Full Idea: The hand washes the hand; give something and you may get something. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B30), quoted by (who?) - where? |
| 441 | Against a villain, villainy is not a useless weapon [Epicharmus] |
| Full Idea: Against a villain, villainy is not a useless weapon. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B32), quoted by (who?) - where? |
| 439 | God knows everything, and nothing is impossible for him [Epicharmus] |
| Full Idea: Nothing escapes the divine, this you must realise. God himself is our overseer, and nothing is impossible for him. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B23), quoted by (who?) - where? |
| 443 | Human logos is an aspect of divine logos, and is sufficient for successful living [Epicharmus] |
| Full Idea: Man has calculation, but there is also the divine logos. But human logos is sprung from the divine logos, and it brings to each man his means of life, and his maintenance. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B57), quoted by (who?) - where? |