54 ideas
| 19635 | Hegel produced modern optimism; he failed to grasp that consciousness never progresses [Hegel, by Cioran] |
| 8215 | Hegel was the last philosopher of the Book [Hegel, by Derrida] |
| 16011 | Hegel doesn't storm the heavens like the giants, but works his way up by syllogisms [Kierkegaard on Hegel] |
| 5433 | For Hegel, things are incomplete, and contain external references in their own nature [Hegel, by Russell] |
| 3301 | On the continent it is generally believed that metaphysics died with Hegel [Benardete,JA on Hegel] |
| 19661 | Making sufficient reason an absolute devalues the principle of non-contradiction [Hegel, by Meillassoux] |
| 20952 | Rather than in three stages, Hegel presented his dialectic as 'negation of the negation' [Hegel, by Bowie] |
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| 9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
| 9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
| 9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
| 9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
| 9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
| 9605 | If a proposition is false, then its negation is true [Brown,JR] |
| 21777 | Negation of negation doubles back into a self-relationship [Hegel, by Houlgate] |
| 9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
| 9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
| 9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
| 9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
| 9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
| 9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
| 9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
| 9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
| 9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
| 9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
| 9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
| 9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
| 9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
| 9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
| 9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
| 9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
| 9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
| 9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
| 9630 | The most brilliant formalist was Hilbert [Brown,JR] |
| 9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
| 9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
| 5645 | The dialectical opposition of being and nothing is resolved in passing to the concept of becoming [Hegel, by Scruton] |
| 5646 | Hegel gives an ontological proof of the existence of everything [Hegel, by Scruton] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 21755 | For Hegel, categories shift their form in the course of history [Hegel, by Houlgate] |
| 21754 | Our concepts and categories disclose the world, because we are part of the world [Hegel, by Houlgate] |
| 22079 | Hegel said Kant's fixed categories actually vary with culture and era [Hegel, by Houlgate] |
| 6019 | If someone squashed a horse to make a dog, something new would now exist [Mnesarchus] |
| 9225 | Hegel reputedly claimed to know a priori that there are five planets [Hegel, by Field,H] |
| 9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
| 9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
| 9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
| 21758 | Humans have no fixed identity, but produce and reveal their shifting identity in history [Hegel, by Houlgate] |
| 20414 | Hegel's Absolute Spirit is the union of human rational activity at a moment, and whatever that sustains [Hegel, by Eldridge] |
| 3909 | Society isn’t founded on a contract, since contracts presuppose a society [Hegel, by Scruton] |
| 4347 | When man wills the natural, it is no longer natural [Hegel] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
| 4188 | Hegel's entire philosophy is nothing but a monstrous amplification of the ontological proof [Schopenhauer on Hegel] |
| 6686 | Hegel said he was offering an encyclopaedic rationalisation of Christianity [Hegel, by Graham] |