9 ideas
| 9288 | The magic of Asclepius enters Renaissance thought mixed into Ficino's neo-platonism [Yates] |
| Full Idea: The magic of Asclepius, reinterpreted through Plotinus, enters with Ficino's De Vita into the neo-platonic philosophy of the Renaissance, and, moreover, into Ficino's Christian Platonism. | |
| From: Frances A. Yates (Giordano Bruno and Hermetic Tradition [1964], Ch.4) | |
| A reaction: Asclepius is the source of 'Hermetic' philosophy. This move seems to be what gives the Renaissance period its rather quirky and distinctive character. Montaigne was not a typical figure. Most of them wanted to become gods and control the stars! |
| 9291 | The dating, in 1614, of the Hermetic writings as post-Christian is the end of the Renaissance [Yates] |
| Full Idea: The dating by Isaac Casaubon in 1614 of the Hermetic writings as not the work of a very ancient Egyptian priest but written in post-Christian times, is a watershed separating the Renaissance world from the modern world. | |
| From: Frances A. Yates (Giordano Bruno and Hermetic Tradition [1964], Ch.21) | |
| A reaction: I tend to place the end of the Renaissance with the arrival of the telescope in 1610, so the two dates coincide. Simply, magic was replaced by science. Religion ran alongside, gasping for breath. Mathematics was freed from numerology. |
| 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) |
| 7294 | No crime and no punishment without a law [Roman law] |
| Full Idea: An ancient principle of Roman law states, nullum crimen et nulla poene sine lege, - there is no crime and no punishment without a law. | |
| From: [Roman law] (Roman Law [c.100]), quoted by A.C. Grayling - Among the Dead Cities Ch.6 | |
| A reaction: That there is no 'punishment' without law seems the basis of civilization. Suppose a strong person imposed firm punishment in order to forestall more brutal revenge by others? What motivates the creation of criminal laws? |