50 ideas
15053 | If metaphysics can't be settled, it hardly matters whether it makes sense [Fine,K] |
15054 | 'Quietist' says abandon metaphysics because answers are unattainable (as in Kant's noumenon) [Fine,K] |
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] |
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] |
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] |
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] |
15007 | If you make 'grounding' fundamental, you have to mention some non-fundamental notions [Sider on Fine,K] |
15006 | Something is grounded when it holds, and is explained, and necessitated by something else [Fine,K, by Sider] |
15055 | Grounding relations are best expressed as relations between sentences [Fine,K] |
15050 | Reduction might be producing a sentence which gets closer to the logical form [Fine,K] |
15051 | Reduction might be semantic, where a reduced sentence is understood through its reduction [Fine,K] |
15052 | Reduction is modal, if the reductions necessarily entail the truth of the target sentence [Fine,K] |
15056 | The notion of reduction (unlike that of 'ground') implies the unreality of what is reduced [Fine,K] |
15046 | Reality is a primitive metaphysical concept, which cannot be understood in other terms [Fine,K] |
15047 | What is real can only be settled in terms of 'ground' [Fine,K] |
15048 | In metaphysics, reality is regarded as either 'factual', or as 'fundamental' [Fine,K] |
15060 | Why should what is explanatorily basic be therefore more real? [Fine,K] |
9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
15061 | Although colour depends on us, we can describe the world that way if it picks out fundamentals [Fine,K] |
15059 | Grounding is an explanation of truth, and needs all the virtues of good explanations [Fine,K] |
15057 | Ultimate explanations are in 'grounds', which account for other truths, which hold in virtue of the grounding [Fine,K] |
15058 | A proposition ingredient is 'essential' if changing it would change the truth-value [Fine,K] |
5901 | Is 'productive of happiness' the definition of 'right', or the cause of it? [Ross on Bentham] |
5934 | Of Bentham's 'dimensions' of pleasure, only intensity and duration matter [Ross on Bentham] |
3777 | Pleasure and pain control all human desires and duties [Bentham] |
3781 | The value of pleasures and pains is their force [Bentham] |
3554 | Bentham thinks happiness is feeling good, but why use morality to achieve that? [Annas on Bentham] |
3778 | The community's interest is a sum of individual interests [Bentham] |
20280 | Large mature animals are more rational than babies. But all that really matters is - can they suffer? [Bentham] |
3779 | Unnatural, when it means anything, means infrequent [Bentham] |
3780 | We must judge a thing morally to know if it conforms to God's will [Bentham] |