48 ideas
19917 | Without reason and human help, human life is misery [Spinoza] |
10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
13044 | Infinity: There is at least one limit level [Potter] |
10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
10709 | Priority is a modality, arising from collections and members [Potter] |
19922 | People are only free if they are guided entirely by reason [Spinoza] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
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] |
19934 | Hebrews were very hostile to other states, who had not given up their rights to God [Spinoza] |
4300 | The Bible has nothing in common with reasoning and philosophy [Spinoza] |