34 ideas
| 6118 | Philosophy is logical analysis, followed by synthesis [Russell] |
| 6116 | A logical language would show up the fallacy of inferring reality from ordinary language [Russell] |
| 6117 | Philosophy should be built on science, to reduce error [Russell] |
| 21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
| 17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
| 6110 | Subject-predicate logic (and substance-attribute metaphysics) arise from Aryan languages [Russell] |
| 6107 | It is logic, not metaphysics, that is fundamental to philosophy [Russell] |
| 6115 | Vagueness, and simples being beyond experience, are obstacles to a logical language [Russell] |
| 6109 | Some axioms may only become accepted when they lead to obvious conclusions [Russell] |
| 17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
| 10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
| 19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
| 10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
| 17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
| 10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
| 3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
| 10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
| 9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
| 11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
| 10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
| 10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
| 10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
| 10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
| 6108 | Maths can be deduced from logical axioms and the logic of relations [Russell] |
| 8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
| 10968 | Russell gave up logical atomism because of negative, general and belief propositions [Russell, by Read] |
| 6113 | To mean facts we assert them; to mean simples we name them [Russell] |
| 6114 | 'Simples' are not experienced, but are inferred at the limits of analysis [Russell] |
| 21722 | Better to construct from what is known, than to infer what is unknown [Russell] |
| 6111 | As propositions can be put in subject-predicate form, we wrongly infer that facts have substance-quality form [Russell] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 6112 | Meaning takes many different forms, depending on different logical types [Russell] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |