42 ideas
| 15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
| 15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
| 15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
| 15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| 13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
| 13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
| 13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
| 13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
| 13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
| 13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
| 11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
| 11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
| 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] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |