50 ideas
| 6814 | Instead of prayer and charity, sinners pursue vain disputes and want their own personal scripture [Mohammed] |
| 18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
| 18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| 18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| 18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
| 18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
| 18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
| 18182 | The extension of concepts is not important to me [Maddy] |
| 18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
| 18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
| 18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
| 18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
| 18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 14470 | Explanatory exclusion: there cannot be two separate complete explanations of a single event [Kim] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 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] |
| 6834 | Unbelievers try to interpret the ambiguous parts of the Koran, simply to create dissension [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] |
| 6824 | Do not split into sects, exulting in separate beliefs [Mohammed] |
| 6821 | I created mankind that it might worship Me [Mohammed] |
| 6817 | The Koran is certainly composed by Allah; no one could compose a chapter like it [Mohammed] |
| 6829 | There shall be no compulsion in religion [Mohammed] |
| 6815 | Be patient with unbelievers, and leave them to the judgement of Allah [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] |