30 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] |
| 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] |
| 8780 | Attributes are functions, not objects; this distinguishes 'square of 2' from 'double of 2' [Geach] |
| 16235 | Persistence conditions cannot contradict, so there must be a 'dominant sortal' [Burke,M, by Hawley] |
| 14753 | The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider] |
| 16072 | 'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman] |
| 14751 | Tib goes out of existence when the tail is lost, because Tib was never the 'cat' [Burke,M, by Sider] |
| 16071 | Sculpting a lump of clay destroys one object, and replaces it with another one [Burke,M, by Wasserman] |
| 16234 | Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley] |
| 13278 | Maybe the clay becomes a different lump when it becomes a statue [Burke,M, by Koslicki] |
| 14750 | Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider] |
| 11910 | Being 'the same' is meaningless, unless we specify 'the same X' [Geach] |
| 8775 | A big flea is a small animal, so 'big' and 'small' cannot be acquired by abstraction [Geach] |
| 8776 | We cannot learn relations by abstraction, because their converse must be learned too [Geach] |
| 2567 | You can't define real mental states in terms of behaviour that never happens [Geach] |
| 2568 | Beliefs aren't tied to particular behaviours [Geach] |
| 8781 | The mind does not lift concepts from experience; it creates them, and then applies them [Geach] |
| 8769 | If someone has aphasia but can still play chess, they clearly have concepts [Geach] |
| 8770 | 'Abstractionism' is acquiring a concept by picking out one experience amongst a group [Geach] |
| 8771 | 'Or' and 'not' are not to be found in the sensible world, or even in the world of inner experience [Geach] |
| 8772 | We can't acquire number-concepts by extracting the number from the things being counted [Geach] |
| 8773 | Abstractionists can't explain counting, because it must precede experience of objects [Geach] |
| 8774 | The numbers don't exist in nature, so they cannot have been abstracted from there into our languages [Geach] |
| 8778 | Blind people can use colour words like 'red' perfectly intelligently [Geach] |
| 8777 | If 'black' and 'cat' can be used in the absence of such objects, how can such usage be abstracted? [Geach] |
| 8779 | We can form two different abstract concepts that apply to a single unified experience [Geach] |