52 ideas
| 9572 | Realists about sets say there exists a null set in the real world, with no members [Chihara] |
| 9550 | We only know relational facts about the empty set, but nothing intrinsic [Chihara] |
| 9562 | In simple type theory there is a hierarchy of null sets [Chihara] |
| 9573 | The null set is a structural position which has no other position in membership relation [Chihara] |
| 9551 | What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara] |
| 9549 | The set theorist cannot tell us what 'membership' is [Chihara] |
| 9571 | ZFU refers to the physical world, when it talks of 'urelements' [Chihara] |
| 18151 | Could we replace sets by the open sentences that define them? [Chihara, by Bostock] |
| 9563 | A pack of wolves doesn't cease when one member dies [Chihara] |
| 8758 | We could talk of open sentences, instead of sets [Chihara, by Shapiro] |
| 9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
| 9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara] |
| 6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| 6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
| 12154 | Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry] |
| 9553 | Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara] |
| 10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
| 10735 | Abstraction from objects won't reveal an operation's being performed 'so many times' [Geach] |
| 10265 | Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro] |
| 8759 | We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro] |
| 10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro] |
| 9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara] |
| 9566 | No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara] |
| 8780 | Attributes are functions, not objects; this distinguishes 'square of 2' from 'double of 2' [Geach] |
| 8969 | We should abandon absolute identity, confining it to within some category [Geach, by Hawthorne] |
| 16075 | Denial of absolute identity has drastic implications for logic, semantics and set theory [Wasserman on Geach] |
| 12152 | Identity is relative. One must not say things are 'the same', but 'the same A as' [Geach] |
| 16073 | Leibniz's Law is incomplete, since it includes a non-relativized identity predicate [Geach, by Wasserman] |
| 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] |
| 10732 | If concepts are just recognitional, then general judgements would be impossible [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] |
| 10731 | For abstractionists, concepts are capacities to recognise recurrent features of the world [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] |
| 9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
| 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] |
| 10733 | The abstractionist cannot explain 'some' and 'not' [Geach] |
| 10734 | Only a judgement can distinguish 'striking' from 'being struck' [Geach] |
| 9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
| 22489 | 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot] |
| 9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |