47 ideas
10528 | Definitions concern how we should speak, not how things are [Fine,K] |
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
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] |
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] |
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] |
9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
9826 | A system S is said to be infinite when it is similar to a proper part of itself [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] |
10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |
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] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
13047 | It is knowing 'why' that gives scientific understanding, not knowing 'that' [Salmon] |
13065 | Understanding is an extremely vague concept [Salmon] |
13054 | Correlations can provide predictions, but only causes can give explanations [Salmon] |
13067 | For the instrumentalists there are no scientific explanations [Salmon] |
13055 | Good induction needs 'total evidence' - the absence at the time of any undermining evidence [Salmon] |
13046 | Scientific explanation is not reducing the unfamiliar to the familiar [Salmon] |
13058 | Why-questions can seek evidence as well as explanation [Salmon] |
13050 | The 'inferential' conception is that all scientific explanations are arguments [Salmon] |
13059 | Ontic explanations can be facts, or reports of facts [Salmon] |
13064 | The three basic conceptions of scientific explanation are modal, epistemic, and ontic [Salmon] |
13049 | We must distinguish true laws because they (unlike accidental generalizations) explain things [Salmon] |
13051 | Deductive-nomological explanations will predict, and their predictions will explain [Salmon] |
13053 | A law is not enough for explanation - we need information about what makes a difference [Salmon] |
13061 | Flagpoles explain shadows, and not vice versa, because of temporal ordering [Salmon] |
13045 | Explanation at the quantum level will probably be by entirely new mechanisms [Salmon] |
13062 | Does an item have a function the first time it occurs? [Salmon] |
13063 | Explanations reveal the mechanisms which produce the facts [Salmon] |
13060 | Can events whose probabilities are low be explained? [Salmon] |
13056 | Statistical explanation needs relevance, not high probability [Salmon] |
13057 | Think of probabilities in terms of propensities rather than frequencies [Salmon] |
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] |
10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |
9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |