41 ideas
| 10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
| 10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
| 10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
| 10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
| 10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
| 10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
| 10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
| 10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
| 10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
| 10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
| 10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
| 10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| 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] |
| 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] |