75 ideas
| 13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C] |
| 6814 | Instead of prayer and charity, sinners pursue vain disputes and want their own personal scripture [Mohammed] |
| 13883 | The best way to understand a philosophical idea is to defend it [Wright,C] |
| 10142 | The attempt to define numbers by contextual definition has been revived [Wright,C, by Fine,K] |
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| 9868 | An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett] |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| 13861 | Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C] |
| 13892 | One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C] |
| 13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C] |
| 17441 | Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Wright,C, by Heck] |
| 13862 | There are five Peano axioms, which can be expressed informally [Wright,C] |
| 17853 | Number truths are said to be the consequence of PA - but it needs semantic consequence [Wright,C] |
| 17854 | What facts underpin the truths of the Peano axioms? [Wright,C] |
| 13894 | Sameness of number is fundamental, not counting, despite children learning that first [Wright,C] |
| 10140 | We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K] |
| 8692 | Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend] |
| 17440 | Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck] |
| 13893 | It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C] |
| 13888 | If numbers are extensions, Frege must first solve the Caesar problem for extensions [Wright,C] |
| 13869 | Number platonism says that natural number is a sortal concept [Wright,C] |
| 13870 | We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism [Wright,C] |
| 13873 | Treating numbers adjectivally is treating them as quantifiers [Wright,C] |
| 7804 | Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA] |
| 13899 | The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C] |
| 13896 | The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C] |
| 13863 | Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms [Wright,C] |
| 13895 | The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C] |
| 13884 | The idea that 'exist' has multiple senses is not coherent [Wright,C] |
| 13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C] |
| 9878 | Contextually defined abstract terms genuinely refer to objects [Wright,C, by Dummett] |
| 13868 | Sortal concepts cannot require that things don't survive their loss, because of phase sortals [Wright,C] |
| 13865 | 'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [Wright,C] |
| 13866 | A concept is only a sortal if it gives genuine identity [Wright,C] |
| 13890 | Entities fall under a sortal concept if they can be used to explain identity statements concerning them [Wright,C] |
| 13898 | If we can establish directions from lines and parallelism, we were already committed to directions [Wright,C] |
| 13882 | A milder claim is that understanding requires some evidence of that understanding [Wright,C] |
| 13885 | If apparent reference can mislead, then so can apparent lack of reference [Wright,C] |
| 17857 | We can accept Frege's idea of object without assuming that predicates have a reference [Wright,C] |
| 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] |
| 6829 | There shall be no compulsion in religion [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] |
| 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] |
| 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] |