54 ideas
6814 | Instead of prayer and charity, sinners pursue vain disputes and want their own personal scripture [Mohammed] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
19125 | If we define truth, we can eliminate it [Halbach/Leigh] |
19128 | If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh] |
19120 | Semantic theories need a powerful metalanguage, typically including set theory [Halbach/Leigh] |
19127 | The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh] |
19124 | A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh] |
19126 | If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh] |
19129 | The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh] |
19130 | KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
19121 | We can reduce properties to true formulas [Halbach/Leigh] |
19122 | Nominalists can reduce theories of properties or sets to harmless axiomatic truth theories [Halbach/Leigh] |
17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
6823 | Repay evil with good and your enemies will become friends (though this is hard) [Mohammed] |
6828 | You may break off a treaty if you fear treachery from your ally [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] |
6825 | Do not kill except for a just cause [Mohammed] |
6832 | Killing a human, except as just punishment, is like killing all mankind [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] |
6827 | Make war on the unbelievers until Allah's religion reigns supreme [Mohammed] |
6829 | There shall be no compulsion in religion [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] |
6824 | Do not split into sects, exulting in separate beliefs [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] |
6831 | He that kills a believer by design shall burn in Hell for ever [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] |
6830 | Unbelievers will have their skin repeatedly burned off in hell [Mohammed] |
6816 | The unbelievers shall drink boiling water [Mohammed] |