46 ideas
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] |
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] |
22076 | Being is only perceptible to itself as becoming [Schelling] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
16643 | Accidents always remain suited to a subject [Bonaventura] |
16696 | Successive things reduce to permanent things [Bonaventura] |
22072 | Schelling always affirmed the absolute status of freedom [Schelling, by Courtine] |
21925 | For Schelling the Absolute spirit manifests as nature in which self-consciousness evolves [Schelling, by Lewis,PB] |
22045 | Metaphysics aims at the Absolute, which goes beyond subjective and objective viewpoints [Schelling, by Pinkard] |
22074 | We must show that the whole of nature, because it is effective, is grounded in freedom [Schelling] |
22073 | The basis of philosophy is the Self prior to experience, where it is the essence of freedom [Schelling] |
22075 | Only idealism has given us the genuine concept of freedom [Schelling] |
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] |
20956 | Ultimately, all being is willing. The nature of primal being is the same as the nature of willing [Schelling] |
20957 | We don't choose our characters, yet we still claim credit for the actions our characters perform [Schelling] |
22057 | Schelling sought a union between the productivities of nature and of the mind [Schelling, by Bowie] |
22031 | Schelling made organisms central to nature, because mere mechanism could never produce them [Schelling, by Pinkard] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |