46 ideas
17641 | Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell] |
17638 | If one proposition is deduced from another, they are more certain together than alone [Russell] |
17632 | Non-contradiction was learned from instances, and then found to be indubitable [Russell] |
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
17629 | Which premises are ultimate varies with context [Russell] |
17630 | The sources of a proof are the reasons why we believe its conclusion [Russell] |
17640 | Finding the axioms may be the only route to some new results [Russell] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
17639 | Believing a whole science is more than believing each of its propositions [Russell] |
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] |
17631 | Induction is inferring premises from consequences [Russell] |
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] |
17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |
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] |