58 ideas
9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
9912 | There are no such things as numbers [Benacerraf] |
9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
9151 | Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K] |
13891 | To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C] |
17904 | A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf] |
17906 | To explain numbers you must also explain cardinality, the counting of things [Benacerraf] |
9898 | We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf] |
17903 | Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf] |
9897 | The application of a system of numbers is counting and measurement [Benacerraf] |
9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf] |
9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
8697 | Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend] |
8304 | No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe] |
9906 | If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf] |
13415 | An adequate account of a number must relate it to its series [Benacerraf] |
9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf] |
9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
9909 | The number 3 defines the role of being third in a progression [Benacerraf] |
9911 | Number words no more have referents than do the parts of a ruler [Benacerraf] |
8925 | Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf] |
9938 | How can numbers be objects if order is their only property? [Benacerraf, by Putnam] |
9910 | Number-as-objects works wholesale, but fails utterly object by object [Benacerraf] |
17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
9936 | The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf] |
9903 | Number words are not predicates, as they function very differently from adjectives [Benacerraf] |
9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
6504 | For physicalists, the only relations are spatial, temporal and causal [Robinson,H] |
6520 | If reality just has relational properties, what are its substantial ontological features? [Robinson,H] |
12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
6485 | When a red object is viewed, the air in between does not become red [Robinson,H] |
6521 | Representative realists believe that laws of phenomena will apply to the physical world [Robinson,H] |
6509 | Representative realists believe some properties of sense-data are shared by the objects themselves [Robinson,H] |
6522 | Phenomenalism can be theistic (Berkeley), or sceptical (Hume), or analytic (20th century) [Robinson,H] |
6502 | Can we reduce perception to acquisition of information, which is reduced to causation or disposition? [Robinson,H] |
6513 | Would someone who recovered their sight recognise felt shapes just by looking? [Robinson,H] |
6512 | Secondary qualities have one sensory mode, but primary qualities can have more [Robinson,H] |
6497 | We say objects possess no intrinsic secondary qualities because physicists don't need them [Robinson,H] |
6494 | If objects are not coloured, and neither are sense-contents, we are left saying that nothing is coloured [Robinson,H] |
6499 | Shape can be experienced in different ways, but colour and sound only one way [Robinson,H] |
6500 | If secondary qualities match senses, would new senses create new qualities? [Robinson,H] |
6484 | Most moderate empiricists adopt Locke's representative theory of perception [Robinson,H] |
6508 | Sense-data leads to either representative realism or phenomenalism or idealism [Robinson,H] |
6480 | Sense-data do not have any intrinsic intentionality [Robinson,H] |
6482 | For idealists and phenomenalists sense-data are in objects; representative realists say they resemble objects [Robinson,H] |
6505 | Sense-data are rejected because they are a veil between us and reality, leading to scepticism [Robinson,H] |
6506 | 'Sense redly' sounds peculiar, but 'senses redly-squarely tablely' sounds far worse [Robinson,H] |
6507 | Adverbialism sees the contents of sense-experience as modes, not objects [Robinson,H] |
6511 | If there are only 'modes' of sensing, then an object can no more be red or square than it can be proud or lazy. [Robinson,H] |
6515 | An explanation presupposes something that is improbable unless it is explained [Robinson,H] |
6517 | If all possibilities are equal, order seems (a priori) to need an explanation - or does it? [Robinson,H] |
6481 | If intentional states are intrinsically about other things, what are their own properties? [Robinson,H] |
6503 | Physicalism cannot allow internal intentional objects, as brain states can't be 'about' anything [Robinson,H] |
6519 | Locke's solidity is not matter, because that is impenetrability and hardness combined [Robinson,H] |