10 ideas
| 21852 | Nomads are the basis of history, and yet almost unknowable [Deleuze] |
| Full Idea: There is no history from the viewpoint of nomads, although everything passes through them, to the point that they are like the noumena or the unknowable of history. | |
| From: Gilles Deleuze (Many Politics [1977], p.107) | |
| A reaction: Nomads have the same place in society that indeterminate 'stuff' has in an object-orientated metaphysics. Deleuze seems to be romanticising nomads the way the late Victorians romanticised gypsies. |
| 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) |
| 1212 | Replacing timbers on Theseus' ship was the classic illustration of the problem of growth and change [Plutarch] |
| Full Idea: At intervals they removed old timbers from the preserved ship and replaced them with sound ones, so the ship became a classic illustration for the philosophers of the disputed question of growth and change, some saying it was the same, others different. | |
| From: Plutarch (Life of Theseus [c.85], 23) |
| 21853 | We are currently extending capitalism to the whole of society [Deleuze] |
| Full Idea: What characterises our situation is ….the extension of capitalism to the whole social body. | |
| From: Gilles Deleuze (Many Politics [1977], p.110) | |
| A reaction: This is driven by the naďve people who think all problems can be solved by market forces, and that to everything that goes bankrupt we should just say 'good riddance'. |
| 21851 | The State requires self-preservation, but the war-machine desires destruction [Deleuze] |
| Full Idea: There will always be a tension between the State apparatus with its requirement for self-preservation, and the war-machine in its undertaking to destroy the State, to destroy the subjects of the State, and even to destroy itself. | |
| From: Gilles Deleuze (Many Politics [1977], p.106) | |
| A reaction: This seems to fit WWI quite well, but the desire of the war-machine to destroy the State which pays for it sounds unlikely. Nevertheless war is appalling for the state, but it is the whole point of the war-machine, which gets restless. |