40 ideas
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
18365 | If truths are just identical with facts, then truths will make themselves true [David] |
18362 | Examples show that truth-making is just non-symmetric, not asymmetric [David] |
18360 | It is assumed that a proposition is necessarily true if its truth-maker exists [David] |
18358 | Two different propositions can have the same fact as truth-maker [David] |
18355 | What matters is truth-making (not truth-makers) [David] |
18354 | Correspondence is symmetric, while truth-making is taken to be asymmetric [David] |
18356 | Correspondence is an over-ambitious attempt to explain truth-making [David] |
18363 | Correspondence theorists see facts as the only truth-makers [David] |
18364 | Correspondence theory likes ideal languages, that reveal the structure of propositions [David] |
18359 | One proposition can be made true by many different facts [David] |
18357 | What makes a disjunction true is simpler than the disjunctive fact it names [David] |
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] |
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] |
18361 | A reflexive relation entails that the relation can't be asymmetric [David] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
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] |
8430 | Causal statements are used to explain, to predict, to control, to attribute responsibility, and in theories [Kim] |
8396 | Many counterfactuals have nothing to do with causation [Kim, by Tooley] |
8429 | Counterfactuals can express four other relations between events, apart from causation [Kim] |
8428 | Causation is not the only dependency relation expressed by counterfactuals [Kim] |
4781 | Many counterfactual truths do not imply causation ('if yesterday wasn't Monday, it isn't Tuesday') [Kim, by Psillos] |