11 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) |
| 20582 | World government needs a shared global identity [Oksala] |
| Full Idea: Critics have argued that a global 'demos' would require a shared global identity. | |
| From: Johanna Oksala (Political Philosophy: all that matters [2013], Ch.9 'Epi') | |
| A reaction: The great divisions are religion and language. The great unifiers are sport, arts and entertainment, plus basic human needs like food, health and housing. The reply is that there cannot be identity without differences, so global democracy is out. |
| 20568 | The principles Rawls arrives at do not just conform to benevolence, but also result from choices [Oksala] |
| Full Idea: The advantage of Rawls's method is that the principles the individual chooses are not only fair according to some abstract principle of benevolence, but also the result of rational choice. | |
| From: Johanna Oksala (Political Philosophy: all that matters [2013], Ch.5) | |
| A reaction: That is a very nice way of putting the beauty of Rawls's idea. In modern political philosophy you hear far more criticisms of Rawls than praise. If a philosopher is criticised a lot, it is probably because they have stated their views clearly. |
| 20578 | Anarchists prefer local and communal government [Oksala] |
| Full Idea: Anarchists advocate forms of governance such as communes and associations that are as local and close to the direct control of the people as possible. | |
| From: Johanna Oksala (Political Philosophy: all that matters [2013], Ch.8) | |
| A reaction: Which might explain why recent conservative governments have steadily eliminated local government in Britain. |
| 20574 | Utilitarianism neglects responsibility, duties and rights [Oksala] |
| Full Idea: A focus solely on utility excludes considerations of personal responsibility and duty, as well as considerations of the basic rights of individuals. | |
| From: Johanna Oksala (Political Philosophy: all that matters [2013], Ch.7) | |
| A reaction: [He cites these as the common modern criticisms] The defence is to explain the value of each of these in utilitarian terms. There is a general problem (conceded by Mill) of motivation in utilitarianism. There's not much in it for me! |
| 1515 | Pythagoreans believe it is absurd to seek for goodness anywhere except with the gods [Iamblichus] |
| Full Idea: The thinking behind Pythagorean philosophy is that people behave in an absurd fashion if they try to find any source for the good other than the gods. | |
| From: Iamblichus (Life of Pythagoras [c.290], 137) |