68 ideas
| 20121 | Grammar only reveals popular metaphysics [Nietzsche] |
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| 24082 | Is the will to truth the desire to avoid deception? [Nietzsche] |
| 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] |
| 20360 | We Germans value becoming and development more highly than mere being of what 'is' [Nietzsche] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 24077 | Necessity is thought to require an event, but is only an after-effect of the event [Nietzsche] |
| 20126 | The strength of knowledge is not its truth, but its entrenchment in our culture [Nietzsche] |
| 20119 | We became increasingly conscious of our sense impressions in order to communicate them [Nietzsche] |
| 20122 | We have no organ for knowledge or truth; we only 'know' what is useful to the human herd [Nietzsche] |
| 4423 | We assume causes, geometry, motion, bodies etc to live, but they haven't been proved [Nietzsche] |
| 6579 | Nietzsche's perspectivism says our worldview depends on our personality [Nietzsche, by Fogelin] |
| 24083 | It would be absurd to say we are only permitted our own single perspective [Nietzsche] |
| 20115 | All of our normal mental life could be conducted without consciousness [Nietzsche] |
| 20117 | Only the need for communication has led to consciousness developing [Nietzsche] |
| 20118 | Only our conscious thought is verbal, and this shows the origin of consciousness [Nietzsche] |
| 20116 | Most of our lives, even the important parts, take place outside of consciousness [Nietzsche] |
| 20120 | Whatever moves into consciousness becomes thereby much more superficial [Nietzsche] |
| 2932 | 'Know thyself' is impossible and ridiculous [Nietzsche] |
| 24078 | Thoughts cannot be fully reproduced in words [Nietzsche] |
| 24081 | Most of our intellectual activity is unconscious [Nietzsche] |
| 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] |
| 2933 | Why do you listen to the voice of your conscience? [Nietzsche] |
| 20141 | Higher human beings see and hear far more than others, and do it more thoughtfully [Nietzsche] |
| 24076 | A morality ranks human drives and actions, for the sake of the herd, and subordinating individuals [Nietzsche] |
| 22471 | Nietzsche thought it 'childish' to say morality isn't binding because it varies between cultures [Nietzsche, by Foot] |
| 2935 | No two actions are the same [Nietzsche] |
| 20198 | Many virtues are harmful traps, but that is why other people praise them [Nietzsche] |
| 4275 | You cannot advocate joyful wisdom while rejecting pity, because the two are complementary [Scruton on Nietzsche] |
| 2934 | To see one's own judgement as a universal law is selfish [Nietzsche] |
| 24080 | We should give style to our character - by applying an artistic plan to its strengths and weaknesses [Nietzsche] |
| 20125 | The ethical teacher exists to give purpose to what happens necessarily and without purpose [Nietzsche] |
| 9306 | To ward off boredom at any cost is vulgar [Nietzsche] |
| 24079 | The best life is the dangerous life [Nietzsche] |
| 2936 | Imagine if before each of your actions you had to accept repeating the action over and over again [Nietzsche] |
| 6842 | Nietzsche says facing up to the eternal return of meaninglessness is the response to nihilism [Nietzsche, by Critchley] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| 2931 | God is dead, and we have killed him [Nietzsche] |