68 ideas
| 19917 | Without reason and human help, human life is misery [Spinoza] |
| 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] |
| 19922 | People are only free if they are guided entirely by reason [Spinoza] |
| 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] |
| 19935 | Peoples are created by individuals, not by nature, and only distinguished by language and law [Spinoza] |
| 19914 | In nature everything has an absolute right to do anything it is capable of doing [Spinoza] |
| 19915 | Natural rights are determined by desire and power, not by reason [Spinoza] |
| 7487 | Society exists to extend human awareness [Spinoza, by Watson] |
| 19943 | The state aims to allow personal development, so its main purpose is freedom [Spinoza] |
| 19930 | Sovereignty must include the power to make people submit to it [Spinoza] |
| 19936 | Kings tend to fight wars for glory, rather than for peace and liberty [Spinoza] |
| 19937 | Monarchs are always proud, and can't back down [Spinoza] |
| 19940 | Deposing a monarch is dangerous, because the people are used to royal authority [Spinoza] |
| 19931 | Every state is more frightened of its own citizens than of external enemies [Spinoza] |
| 19920 | Democracy is a legitimate gathering of people who do whatever they can do [Spinoza] |
| 19933 | If religion is law, then piety is justice, impiety is crime, and non-believers must leave [Spinoza] |
| 19938 | Allowing religious ministers any control of the state is bad for both parties [Spinoza] |
| 19923 | Slavery is not just obedience, but acting only in the interests of the master [Spinoza] |
| 19939 | Government is oppressive if opinions can be crimes, because people can't give them up [Spinoza] |
| 19944 | Without liberty of thought there is no trust in the state, and corruption follows [Spinoza] |
| 19942 | Treason may be committed as much by words as by deeds [Spinoza] |
| 19924 | The freest state is a rational one, where people can submit themselves to reason [Spinoza] |
| 7827 | Spinoza wanted democracy based on individual rights, and is thus the first modern political philosopher [Stewart,M on Spinoza] |
| 19926 | The sovereignty has absolute power over citizens [Spinoza] |
| 19918 | Forming a society meant following reason, and giving up dangerous appetites and mutual harm [Spinoza] |
| 19919 | People only give up their rights, and keep promises, if they hope for some greater good [Spinoza] |
| 19921 | Once you have given up your rights, there is no going back [Spinoza] |
| 19925 | In democracy we don't abandon our rights, but transfer them to the majority of us [Spinoza] |
| 19928 | No one, in giving up their power and right, ceases to be a human being [Spinoza] |
| 19929 | Everyone who gives up their rights must fear the recipients of them [Spinoza] |
| 19932 | The early Hebrews, following Moses, gave up their rights to God alone [Spinoza] |
| 19916 | The order of nature does not prohibit anything, and allows whatever appetite produces [Spinoza] |
| 19927 | State and religious law can clash, so the state must make decisions about religion [Spinoza] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
| 19934 | Hebrews were very hostile to other states, who had not given up their rights to God [Spinoza] |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| 4300 | The Bible has nothing in common with reasoning and philosophy [Spinoza] |
| 6610 | I believe because it is absurd [Tertullian] |