17 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] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
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] |
10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
10626 | Objects just are what singular terms refer to [Hale/Wright] |
10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |
4054 | I may exist before I become a person, just as I exist before I become an adult [Lockwood] |
4056 | If the soul is held to leave the body at brain-death, it should arrive at the time of brain-creation [Lockwood] |
4055 | It isn't obviously wicked to destroy a potential human being (e.g. an ununited egg and sperm) [Lockwood] |