40 ideas
| 1606 | You have to be a Platonist to debate about reality, so every philosopher is a Platonist [Roochnik] |
| 1595 | Philosophy aims to satisfy the chief human desire - the articulation of beauty itself [Roochnik] |
| 1571 | 'Logos' ranges from thought/reasoning, to words, to rational structures outside thought [Roochnik] |
| 1572 | In the seventeenth century the only acceptable form of logos was technical knowledge [Roochnik] |
| 1573 | The hallmark of a person with logos is that they give reasons why one opinion is superior to another [Roochnik] |
| 1592 | Logos cannot refute the relativist, and so must admit that it too is a matter of desire (for truth and agreement) [Roochnik] |
| 1593 | Human desire has an ordered structure, with logos at the pinnacle [Roochnik] |
| 1603 | Logos is not unconditionally good, but good if there is another person willing to engage with it [Roochnik] |
| 1598 | We prefer reason or poetry according to whether basics are intelligible or not [Roochnik] |
| 1584 | Modern science, by aiming for clarity about the external world, has abandoned rationality in the human world [Roochnik] |
| 1591 | Unfortunately for reason, argument can't be used to establish the value of argument [Roochnik] |
| 1599 | Attempts to suspend all presuppositions are hopeless, because a common ground must be agreed for the process [Roochnik] |
| 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] |
| 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] |
| 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] |
| 1605 | Reality can be viewed neutrally, or as an object of desire [Roochnik] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 1577 | Relativism is a disease which destroys the possibility of rational debate [Roochnik] |
| 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] |
| 1578 | If relativism is the correct account of human values, then rhetoric is more important than reasoning [Roochnik] |
| 1596 | Reasoning aims not at the understanding of objects, but at the desire to give beautiful speeches [Roochnik] |
| 21788 | The moral will is self-determining, but the ethical will is met in society [Houlgate] |