56 ideas
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
15879 | The Square of Opposition has two contradictory pairs, one contrary pair, and one sub-contrary pair [Harré] |
10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
15891 | Traditional quantifiers combine ordinary language generality and ontology assumptions [Harré] |
15878 | Some quantifiers, such as 'any', rule out any notion of order within their range [Harré] |
9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
18087 | If x changes by less and less, it must approach a limit [Dedekind] |
13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
15874 | Scientific properties are not observed qualities, but the dispositions which create them [Harré] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
15884 | Laws of nature remain the same through any conditions, if the underlying mechanisms are unchanged [Harré] |
15880 | In physical sciences particular observations are ordered, but in biology only the classes are ordered [Harré] |
15869 | Reports of experiments eliminate the experimenter, and present results as the behaviour of nature [Harré] |
15881 | We can save laws from counter-instances by treating the latter as analytic definitions [Harré] |
15882 | Since there are three different dimensions for generalising laws, no one system of logic can cover them [Harré] |
15888 | The grue problem shows that natural kinds are central to science [Harré] |
15887 | 'Grue' introduces a new causal hypothesis - that emeralds can change colour [Harré] |
15889 | It is because ravens are birds that their species and their colour might be connected [Harré] |
15890 | Non-black non-ravens just aren't part of the presuppositions of 'all ravens are black' [Harré] |
15885 | The necessity of Newton's First Law derives from the nature of material things, not from a mechanism [Harré] |
20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
15868 | Idealisation idealises all of a thing's properties, but abstraction leaves some of them out [Harré] |
9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
15886 | Science rests on the principle that nature is a hierarchy of natural kinds [Harré] |
15864 | Classification is just as important as laws in natural science [Harré] |
15865 | Newton's First Law cannot be demonstrated experimentally, as that needs absence of external forces [Harré] |
15862 | Laws can come from data, from theory, from imagination and concepts, or from procedures [Harré] |
15870 | Are laws of nature about events, or types and universals, or dispositions, or all three? [Harré] |
15871 | Are laws about what has or might happen, or do they also cover all the possibilities? [Harré] |
15876 | Maybe laws of nature are just relations between properties? [Harré] |
15872 | Must laws of nature be universal, or could they be local? [Harré] |
15867 | Laws describe abstract idealisations, not the actual mess of nature [Harré] |
15860 | We take it that only necessary happenings could be laws [Harré] |
15892 | Laws of nature state necessary connections of things, events and properties, based on models of mechanisms [Harré] |
15875 | In counterfactuals we keep substances constant, and imagine new situations for them [Harré] |