9 ideas
| 6601 | Science rules the globe because of colonising power, not inherent rationality [Feyerabend] |
| Full Idea: Science now reigns supreme all over the globe; but the reason was not insight in its 'inherent rationality' but power play (the colonising nations imposed their way of living) and the need for weapons. | |
| From: Paul Feyerabend (Against Method [1975], 3), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.5 | |
| A reaction: A nice clear statement of ridiculous relativism about science. What gave the colonisers their power if it was not more accurate knowledge of how to manipulate nature? |
| 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) |
| 22668 | Apprehension is a complex intellect grasping the essence of a complex object [Holt,L] |
| Full Idea: The paradigm case of apprehension is of a complex intellect confronted with a complex object, in which the intellect understands in a particular context what is 'essential' about the object. | |
| From: Lynn Holt (Apprehension: reason in absence of Rules [2002], 3 'Expertise') | |
| A reaction: My line is that this apprehension cashes out as an immediate ability to explain the object. This is an enhanced version of the rational understanding of things found in most larger animals. Holt says her account is Aristotelian. |
| 2561 | For Feyerabend the meaning of a term depends on a whole theory [Feyerabend, by Rorty] |
| Full Idea: For Feyerabend the meaning of a term depends on a whole theory containing the term. | |
| From: report of Paul Feyerabend (Against Method [1975]) by Richard Rorty - Philosophy and the Mirror of Nature 6.3 |