48 ideas
| 7910 | Pursue truth with the urgency of someone whose clothes are on fire [Ashvaghosha] |
| 11159 | My account shows how the concept works, rather than giving an analysis [Fine,K] |
| 11157 | Modern philosophy has largely abandoned real definitions, apart from sortals [Fine,K] |
| 11171 | Defining a term and giving the essence of an object don't just resemble - they are the same [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] |
| 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] |
| 11151 | An object is dependent if its essence prevents it from existing without some other object [Fine,K] |
| 11152 | Essences are either taken as real definitions, or as necessary properties [Fine,K] |
| 11161 | Essentially having a property is naturally expressed as 'the property it must have to be what it is' [Fine,K] |
| 11160 | Simple modal essentialism refers to necessary properties of an object [Fine,K] |
| 11158 | Essentialist claims can be formulated more clearly with quantified modal logic [Fine,K] |
| 11167 | Metaphysical necessity is a special case of essence, not vice versa [Fine,K] |
| 16537 | Essence as necessary properties produces a profusion of essential properties [Fine,K, by Lowe] |
| 11163 | The nature of singleton Socrates has him as a member, but not vice versa [Fine,K] |
| 11164 | It is not part of the essence of Socrates that a huge array of necessary truths should hold [Fine,K] |
| 10935 | An essential property of something must be bound up with what it is to be that thing [Fine,K, by Rami] |
| 10936 | Essential properties are part of an object's 'definition' [Fine,K, by Rami] |
| 11165 | If Socrates lacks necessary existence, then his nature cannot require his parents' existence [Fine,K] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 11166 | The subject of a proposition need not be the source of its necessity [Fine,K] |
| 11169 | Conceptual necessities rest on the nature of all concepts [Fine,K] |
| 11162 | Socrates is necessarily distinct from the Eiffel Tower, but that is not part of his essence [Fine,K] |
| 11168 | Metaphysical necessities are true in virtue of the nature of all objects [Fine,K] |
| 11170 | Analytic truth may only be true in virtue of the meanings of certain terms [Fine,K] |
| 11172 | The meaning of 'bachelor' is irrelevant to the meaning of 'unmarried man' [Fine,K] |
| 7909 | The Eightfold Path concerns morality, wisdom, and tranquillity [Ashvaghosha] |
| 7908 | At the end of a saint, he is not located in space, but just ceases to be disturbed [Ashvaghosha] |