51 ideas
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| 10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
| 22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
| 10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
| 10794 | The nominalist is tied by standard semantics to first-order, denying higher-order abstracta [Marcus (Barcan)] |
| 10786 | Anything which refers tends to be called a 'name', even if it isn't a noun [Marcus (Barcan)] |
| 10788 | Nominalists see proper names as a main vehicle of reference [Marcus (Barcan)] |
| 10799 | Nominalists should quantify existentially at first-order, and substitutionally when higher [Marcus (Barcan)] |
| 10790 | Quantifiers are needed to refer to infinitely many objects [Marcus (Barcan)] |
| 10791 | Substitutional semantics has no domain of objects, but place-markers for substitutions [Marcus (Barcan)] |
| 10785 | Maybe a substitutional semantics for quantification lends itself to nominalism [Marcus (Barcan)] |
| 10795 | Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)] |
| 10798 | A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)] |
| 9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
| 10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
| 17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
| 7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
| 14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
| 17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
| 10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
| 14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
| 18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
| 18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
| 9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
| 17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
| 9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
| 18087 | If x changes by less and less, it must approach a limit [Dedekind] |
| 13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
| 18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
| 18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
| 14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
| 8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
| 9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
| 8628 | I hold that algebra and number are developments of logic [Jevons] |
| 10787 | Is being just referent of the verb 'to be'? [Marcus (Barcan)] |
| 10789 | Nominalists say predication is relations between individuals, or deny that it refers [Marcus (Barcan)] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 10796 | If objects are thoughts, aren't we back to psychologism? [Marcus (Barcan)] |
| 11181 | Aristotelian essentialism involves a 'natural' or 'causal' interpretation of modal operators [Marcus (Barcan)] |
| 11184 | Aristotelian essentialism is about shared properties, individuating essentialism about distinctive properties [Marcus (Barcan)] |
| 11180 | Essentialist sentences are not theorems of modal logic, and can even be false [Marcus (Barcan)] |
| 11186 | 'Essentially' won't replace 'necessarily' for vacuous properties like snub-nosed or self-identical [Marcus (Barcan)] |
| 11185 | 'Is essentially' has a different meaning from 'is necessarily', as they often cannot be substituted [Marcus (Barcan)] |
| 11182 | If essences are objects with only essential properties, they are elusive in possible worlds [Marcus (Barcan)] |
| 10797 | Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all [Marcus (Barcan)] |
| 11183 | The use of possible worlds is to sort properties (not to individuate objects) [Marcus (Barcan)] |
| 11187 | In possible worlds, names are just neutral unvarying pegs for truths and predicates [Marcus (Barcan)] |
| 9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
| 9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
| 9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
| 11189 | Dispositional essences are special, as if an object loses them they cease to exist [Marcus (Barcan)] |