61 ideas
9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
9912 | There are no such things as numbers [Benacerraf] |
9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
9151 | Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K] |
13891 | To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C] |
17904 | A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf] |
17906 | To explain numbers you must also explain cardinality, the counting of things [Benacerraf] |
9898 | We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf] |
17903 | Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf] |
9897 | The application of a system of numbers is counting and measurement [Benacerraf] |
9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf] |
9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
8697 | Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend] |
8304 | No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe] |
9906 | If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf] |
13415 | An adequate account of a number must relate it to its series [Benacerraf] |
9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf] |
9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
9909 | The number 3 defines the role of being third in a progression [Benacerraf] |
9911 | Number words no more have referents than do the parts of a ruler [Benacerraf] |
8925 | Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf] |
9938 | How can numbers be objects if order is their only property? [Benacerraf, by Putnam] |
9910 | Number-as-objects works wholesale, but fails utterly object by object [Benacerraf] |
17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
9936 | The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf] |
9903 | Number words are not predicates, as they function very differently from adjectives [Benacerraf] |
9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
16756 | Substantial forms must exist, to explain the stability of metals like silver and tin [Albertus Magnus] |
9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
16718 | Primary qualities are the cause of all the other sensible qualities [Albertus Magnus] |
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] |