47 ideas
| 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] |
| 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] |
| 8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
| 17405 | If a theory can be fudged, so can observations [Scerri] |
| 17397 | The periodic system is the big counterexample to Kuhn's theory of revolutionary science [Scerri] |
| 17393 | Scientists eventually seek underlying explanations for every pattern [Scerri] |
| 17403 | The periodic table suggests accommodation to facts rates above prediction [Scerri] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 6017 | Nomos is king [Pindar] |
| 17394 | Natural kinds are what are differentiated by nature, and not just by us [Scerri] |
| 17421 | If elements are natural kinds, might the groups of the periodic table also be natural kinds? [Scerri] |
| 17396 | The colour of gold is best explained by relativistic effects due to fast-moving inner-shell electrons [Scerri] |
| 17420 | The stability of nuclei can be estimated through their binding energy [Scerri] |
| 17411 | If all elements are multiples of one (of hydrogen), that suggests once again that matter is unified [Scerri] |
| 17407 | The electron is the main source of chemical properties [Scerri] |
| 17415 | A big chemistry idea is that covalent bonds are shared electrons, not transfer of electrons [Scerri] |
| 17392 | How can poisonous elements survive in the nutritious compound they compose? [Scerri] |
| 17391 | Periodicity and bonding are the two big ideas in chemistry [Scerri] |
| 17404 | Chemistry does not work from general principles, but by careful induction from large amounts of data [Scerri] |
| 17409 | Does radioactivity show that only physics can explain chemistry? [Scerri] |
| 17418 | It is now thought that all the elements have literally evolved from hydrogen [Scerri] |
| 17398 | 19th C views said elements survived abstractly in compounds, but also as 'material ingredients' [Scerri] |
| 17406 | Moseley, using X-rays, showed that atomic number ordered better than atomic weight [Scerri] |
| 17408 | Some suggested basing the new periodic table on isotopes, not elements [Scerri] |
| 17412 | Elements are placed in the table by the number of positive charges - the atomic number [Scerri] |
| 17413 | Elements in the table are grouped by having the same number of outer-shell electrons [Scerri] |
| 17416 | Orthodoxy says the periodic table is explained by quantum mechanics [Scerri] |
| 17414 | Pauli explained the electron shells, but not the lengths of the periods in the table [Scerri] |
| 17410 | Moseley showed the elements progress in units, and thereby clearly identified the gaps [Scerri] |
| 17395 | Elements were ordered by equivalent weight; later by atomic weight; finally by atomic number [Scerri] |
| 17422 | The best classification needs the deepest and most general principles of the atoms [Scerri] |
| 17417 | To explain the table, quantum mechanics still needs to explain order of shell filling [Scerri] |
| 17419 | Since 99.96% of the universe is hydrogen and helium, the periodic table hardly matters [Scerri] |