41 ideas
6814 | Instead of prayer and charity, sinners pursue vain disputes and want their own personal scripture [Mohammed] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
12893 | Contextualism says sceptical arguments are true, relative to their strict context [Cohen,S] |
12896 | Knowledge is context-sensitive, because justification is [Cohen,S] |
12894 | There aren't invariant high standards for knowledge, because even those can be raised [Cohen,S] |
6828 | You may break off a treaty if you fear treachery from your ally [Mohammed] |
6823 | Repay evil with good and your enemies will become friends (though this is hard) [Mohammed] |
6826 | Allah rewards those who are devout, sincere, patient, humble, charitable, chaste, and who fast [Mohammed] |
6822 | Those who avenge themselves when wronged incur no guilt [Mohammed] |
6833 | Punish theft in men or women by cutting off their hands [Mohammed] |
6832 | Killing a human, except as just punishment, is like killing all mankind [Mohammed] |
6825 | Do not kill except for a just cause [Mohammed] |
6811 | Allah is lord of creation, compassionate, merciful, king of judgement-day [Mohammed] |
6819 | True believers see that Allah made the night for rest and the day to give light [Mohammed] |
6818 | Allah cannot have begotten a son, as He is self-sufficient [Mohammed] |
6821 | I created mankind that it might worship Me [Mohammed] |
6815 | Be patient with unbelievers, and leave them to the judgement of Allah [Mohammed] |
6834 | Unbelievers try to interpret the ambiguous parts of the Koran, simply to create dissension [Mohammed] |
6817 | The Koran is certainly composed by Allah; no one could compose a chapter like it [Mohammed] |
6831 | He that kills a believer by design shall burn in Hell for ever [Mohammed] |
6827 | Make war on the unbelievers until Allah's religion reigns supreme [Mohammed] |
6829 | There shall be no compulsion in religion [Mohammed] |
6824 | Do not split into sects, exulting in separate beliefs [Mohammed] |
6820 | The righteous shall dwell on couches in gardens, wedded to dark-eyed houris [Mohammed] |
6812 | Heaven will be reclining on couches, eating fruit, attended by virgins [Mohammed] |
6816 | The unbelievers shall drink boiling water [Mohammed] |
6830 | Unbelievers will have their skin repeatedly burned off in hell [Mohammed] |