63 ideas
| 9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
| 9912 | There are no such things as numbers [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] |
| 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] |
| 9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
| 9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [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] |
| 9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
| 9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [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] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 2730 | Because 'gold is malleable' is necessary does not mean that it is analytic [Audi,R] |
| 2715 | Beliefs are based on perception, memory, introspection or reason [Audi,R] |
| 2735 | Could you have a single belief on its own? [Audi,R] |
| 2736 | We can make certain of what we know, so knowing does not entail certainty [Audi,R] |
| 2722 | Sense-data theory is indirect realism, but phenomenalism is direct irrealism [Audi,R] |
| 2721 | If you gradually remove a book's sensory properties, what is left at the end? [Audi,R] |
| 2728 | The concepts needed for a priori thought may come from experience [Audi,R] |
| 2727 | Red and green being exclusive colours seems to be rationally graspable but not analytic [Audi,R] |
| 2716 | To see something as a field, I obviously need the concept of a field [Audi,R] |
| 2717 | How could I see a field and believe nothing regarding it? [Audi,R] |
| 2719 | Sense data imply representative realism, possibly only representing primary qualities [Audi,R] |
| 2720 | Sense-data (and the rival 'adverbial' theory) are to explain illusions and hallucinations [Audi,R] |
| 2718 | Perception is first simple, then objectual (with concepts) and then propositional [Audi,R] |
| 2741 | The principles of justification have to be a priori [Audi,R] |
| 2729 | Virtually all rationalists assert that we can have knowledge of synthetic a priori truths [Audi,R] |
| 2725 | To remember something is to know it [Audi,R] |
| 2724 | I might remember someone I can't recall or image, by recognising them on meeting [Audi,R] |
| 2731 | Justification is either unanchored (infinite or circular), or anchored (in knowledge or non-knowledge) [Audi,R] |
| 2739 | Internalism about justification implies that there is a right to believe something [Audi,R] |
| 2732 | Maths may be consistent with observations, but not coherent [Audi,R] |
| 2733 | It is very hard to show how much coherence is needed for justification [Audi,R] |
| 2734 | A consistent madman could have a very coherent belief system [Audi,R] |
| 2738 | Consistent accurate prediction looks like knowledge without justified belief [Audi,R] |
| 2740 | A reliability theory of knowledge seems to involve truth as correspondence [Audi,R] |
| 2737 | 'Reliable' is a very imprecise term, and may even mean 'justified' [Audi,R] |
| 2726 | We can be ignorant about ourselves, for example, our desires and motives [Audi,R] |
| 2170 | Homer does not distinguish between soul and body [Homer, by Williams,B] |
| 2171 | The 'will' doesn't exist; there is just conclusion, then action [Homer, by Williams,B] |
| 20064 | Actions are not mere effects of reasons, but are under their control [Audi,R] |
| 21819 | Plato says the Good produces the Intellectual-Principle, which in turn produces the Soul [Homer, by Plotinus] |
| 11388 | Let there be one ruler [Homer] |
| 14829 | Homer so enjoys the company of the gods that he must have been deeply irreligious [Homer, by Nietzsche] |