52 ideas
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| 3750 | "It is true that x" means no more than x [Ramsey] |
| 10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
| 13430 | Infinity: there is an infinity of distinguishable individuals [Ramsey] |
| 22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
| 13428 | Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey] |
| 10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
| 13427 | Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey] |
| 13334 | Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey] |
| 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] |
| 6409 | The 'simple theory of types' distinguishes levels among properties [Ramsey, by Grayling] |
| 13426 | Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey] |
| 13425 | Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey] |
| 8495 | The distinction between particulars and universals is a mistake made because of language [Ramsey] |
| 8493 | We could make universals collections of particulars, or particulars collections of their qualities [Ramsey] |
| 8494 | Obviously 'Socrates is wise' and 'Socrates has wisdom' express the same fact [Ramsey] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 13766 | 'If' is the same as 'given that', so the degrees of belief should conform to probability theory [Ramsey, by Ramsey] |
| 10993 | Ramsey's Test: believe the consequent if you believe the antecedent [Ramsey, by Read] |
| 14279 | Asking 'If p, will q?' when p is uncertain, then first add p hypothetically to your knowledge [Ramsey] |
| 3212 | Beliefs are maps by which we steer [Ramsey] |
| 22328 | I just confront the evidence, and let it act on me [Ramsey] |
| 22325 | A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey] |
| 19724 | Belief is knowledge if it is true, certain, and obtained by a reliable process [Ramsey] |
| 6894 | Mental terms can be replaced in a sentence by a variable and an existential quantifier [Ramsey] |
| 19143 | Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson] |
| 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] |
| 18818 | Sentence meaning is given by the actions to which it would lead [Ramsey] |
| 5954 | All inventions of the mind aim at pleasure, and those that don't are worthless [Metrodorus of Lamp., by Plutarch] |
| 9418 | All knowledge needs systematizing, and the axioms would be the laws of nature [Ramsey] |
| 9420 | Causal laws result from the simplest axioms of a complete deductive system [Ramsey] |