24 ideas
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
14240 | The empty set is something, not nothing! [Oliver/Smiley] |
14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
3282 | The general form of moral reasoning is putting yourself in other people's shoes [Nagel] |
3278 | An egalitarian system must give priority to those with the worst prospects in life [Nagel] |
3275 | Equality was once opposed to aristocracy, but now it opposes public utility and individual rights [Nagel] |
3281 | The ideal of acceptability to each individual underlies the appeal to equality [Nagel] |
3277 | In judging disputes, should we use one standard, or those of each individual? [Nagel] |
3274 | Equality can either be defended as good for society, or as good for individual rights [Nagel] |
3273 | Equality nowadays is seen as political, social, legal and economic [Nagel] |
3276 | A morality of rights is very minimal, leaving a lot of human life without restrictions or duties [Nagel] |