42 ideas
| 17729 | Examining concepts can recover information obtained through the senses [Jenkins] |
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| 17740 | Instead of correspondence of proposition to fact, look at correspondence of its parts [Jenkins] |
| 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] |
| 19043 | Bivalence applies not just to sentences, but that general terms are true or false of each object [Quine] |
| 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] |
| 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] |
| 9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
| 17730 | Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins] |
| 9826 | A system S is said to be infinite when it is similar to a proper part of itself [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] |
| 17719 | Arithmetic concepts are indispensable because they accurately map the world [Jenkins] |
| 17717 | Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins] |
| 17724 | It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins] |
| 17727 | We can learn about the world by studying the grounding of our concepts [Jenkins] |
| 17720 | There's essential, modal, explanatory, conceptual, metaphysical and constitutive dependence [Jenkins, by PG] |
| 19042 | Terms learned by ostension tend to be vague, because that must be quick and unrefined [Quine] |
| 17728 | The concepts we have to use for categorising are ones which map the real world well [Jenkins] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 17726 | Examining accurate, justified or grounded concepts brings understanding of the world [Jenkins] |
| 17734 | It is not enough that intuition be reliable - we need to know why it is reliable [Jenkins] |
| 17723 | Knowledge is true belief which can be explained just by citing the proposition believed [Jenkins] |
| 17739 | The physical effect of world on brain explains the concepts we possess [Jenkins] |
| 17718 | Grounded concepts are trustworthy maps of the world [Jenkins] |
| 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] |
| 17731 | Verificationism is better if it says meaningfulness needs concepts grounded in the senses [Jenkins] |
| 17732 | Success semantics explains representation in terms of success in action [Jenkins] |
| 17725 | 'Analytic' can be conceptual, or by meaning, or predicate inclusion, or definition... [Jenkins] |