44 ideas
| 7548 | Classes, grouped by a convenient property, are logical constructions [Russell] |
| 8195 | Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett] |
| 8194 | Surely there is no exact single grain that brings a heap into existence [Dummett] |
| 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] |
| 8190 | Intuitionists rely on the proof of mathematical statements, not their truth [Dummett] |
| 8198 | A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett] |
| 7545 | Visible things are physical and external, but only exist when viewed [Russell] |
| 8192 | I no longer think what a statement about the past says is just what can justify it [Dummett] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 8199 | The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett] |
| 7549 | If my body literally lost its mind, the object seen when I see a flash would still exist [Russell] |
| 7553 | Sense-data are purely physical [Russell] |
| 7546 | A man is a succession of momentary men, bound by continuity and causation [Russell] |
| 7550 | We could probably, in principle, infer minds from brains, and brains from minds [Russell] |
| 8193 | Verification is not an individual but a collective activity [Dummett] |
| 8189 | Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett] |
| 8191 | The truth-conditions theory must get agreement on a conception of truth [Dummett] |
| 7551 | Matter is a logical construction [Russell] |
| 7547 | Matter requires a division into time-corpuscles as well as space-corpuscles [Russell] |
| 7552 | Six dimensions are needed for a particular, three within its own space, and three to locate that space [Russell] |
| 8197 | Maybe past (which affects us) and future (which we can affect) are both real [Dummett] |
| 8196 | The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett] |