62 ideas
| 291 | Don't assume that wisdom is the automatic consequence of old age [Plato] |
| 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] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 20146 | 'Luck' is the unpredictable and inexplicable intersection of causal chains [Kekes] |
| 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] |
| 20169 | An action may be intended under one description, but not under another [Kekes] |
| 20149 | To control our actions better, make them result from our attitudes, not from circumstances [Kekes] |
| 19738 | Values are an attempt to achieve well-being by bringing contingencies under control [Kekes] |
| 20145 | Values help us to control life, by connecting it to what is stable and manageable [Kekes] |
| 20170 | Responsibility is unprovoked foreseeable harm, against society, arising from vicious character [Kekes] |
| 20165 | Reason and morality do not coincide; immorality can be reasonable, with an ideology [Kekes] |
| 20171 | Practical reason is not universal and impersonal, because it depends on what success is [Kekes] |
| 20175 | If morality has to be rational, then moral conflicts need us to be irrational and immoral [Kekes] |
| 20174 | Relativists say all values are relative; pluralists concede much of that, but not 'human' values [Kekes] |
| 20159 | Cultural values are interpretations of humanity, conduct, institutions, and evaluations [Kekes] |
| 20161 | The big value problems are evil (humanity), disenchantment (cultures), and boredom (individuals) [Kekes] |
| 20156 | We are bound to regret some values we never aspired to [Kekes] |
| 20150 | There are far more values than we can pursue, so they are optional possibilities [Kekes] |
| 20158 | Innumerable values arise for us, from our humanity, our culture, and our individuality [Kekes] |
| 20151 | Our attitudes include what possibilities we value, and also what is allowable, and unthinkable [Kekes] |
| 20152 | Unconditional commitments are our most basic convictions, saying what must never be done [Kekes] |
| 20153 | Doing the unthinkable damages ourselves, so it is more basic than any value [Kekes] |
| 20162 | Evil isn't explained by nature, by monsters, by uncharacteristic actions, or by society [Kekes] |
| 20154 | Control is the key to well-being [Kekes] |
| 20157 | Well-being needs correct attitudes and well-ordered commitments to local values [Kekes] |
| 293 | Being unafraid (perhaps through ignorance) and being brave are two different things [Plato] |
| 20172 | Boredom destroys our ability to evaluate [Kekes] |
| 20173 | Boredom is apathy and restlessness, yearning for something interesting [Kekes] |
| 20155 | Society is alienating if it lacks our values, and its values repel us [Kekes] |
| 20164 | The ideal of an ideology is embodied in a text, a role model, a law of history, a dream of the past... [Kekes] |
| 20163 | Ideologies have beliefs about reality, ideals, a gap with actuality, and a program [Kekes] |
| 20148 | Equal distribution is no good in a shortage, because there might be no one satisfied [Kekes] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |