56 ideas
| 6814 | Instead of prayer and charity, sinners pursue vain disputes and want their own personal scripture [Mohammed] |
| 10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
| 10779 | A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo] |
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| 10781 | A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo] |
| 10638 | A pure logic is wholly general, purely formal, and directly known [Linnebo] |
| 10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo] |
| 10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
| 10635 | Second-order quantification and plural quantification are different [Linnebo] |
| 10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
| 10641 | Traditionally we eliminate plurals by quantifying over sets [Linnebo] |
| 10636 | Plural plurals are unnatural and need a first-level ontology [Linnebo] |
| 10639 | Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo] |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| 14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
| 14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
| 14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
| 14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
| 14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
| 14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
| 14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| 14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
| 10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo] |
| 10637 | Ordinary speakers posit objects without concern for ontology [Linnebo] |
| 14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
| 10782 | The modern concept of an object is rooted in quantificational logic [Linnebo] |
| 2975 | That honey is sweet I do not affirm, but I agree that it appears so [Timon] |
| 10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
| 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] |