38 ideas
| 7740 | There exists a realm, beyond objects and ideas, of non-spatio-temporal thoughts [Frege, by Weiner] |
| 19466 | The word 'true' seems to be unique and indefinable [Frege] |
| 19465 | There cannot be complete correspondence, because ideas and reality are quite different [Frege] |
| 19468 | The property of truth in 'It is true that I smell violets' adds nothing to 'I smell violets' [Frege] |
| 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] |
| 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] |
| 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] |
| 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] |
| 19470 | Thoughts in the 'third realm' cannot be sensed, and do not need an owner to exist [Frege] |
| 19471 | A fact is a thought that is true [Frege] |
| 9877 | Late Frege saw his non-actual objective objects as exclusively thoughts and senses [Frege, by Dummett] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 19469 | We grasp thoughts (thinking), decide they are true (judgement), and manifest the judgement (assertion) [Frege] |
| 8162 | Thoughts have their own realm of reality - 'sense' (as opposed to the realm of 'reference') [Frege, by Dummett] |
| 9818 | A thought is distinguished from other things by a capacity to be true or false [Frege, by Dummett] |
| 16379 | Thoughts about myself are understood one way to me, and another when communicated [Frege] |
| 19467 | A 'thought' is something for which the question of truth can arise; thoughts are senses of sentences [Frege] |
| 19472 | A sentence is only a thought if it is complete, and has a time-specification [Frege] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |