52 ideas
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
9331 | How do we determine which of the sentences containing a term comprise its definition? [Horwich] |
6334 | The function of the truth predicate? Understanding 'true'? Meaning of 'true'? The concept of truth? A theory of truth? [Horwich] |
6342 | Some correspondence theories concern facts; others are built up through reference and satisfaction [Horwich] |
6332 | The common-sense theory of correspondence has never been worked out satisfactorily [Horwich] |
6335 | The redundancy theory cannot explain inferences from 'what x said is true' and 'x said p', to p [Horwich] |
6344 | Truth is a useful concept for unarticulated propositions and generalisations about them [Horwich] |
6336 | No deflationary conception of truth does justice to the fact that we aim for truth [Horwich] |
23299 | Horwich's deflationary view is novel, because it relies on propositions rather than sentences [Horwich, by Davidson] |
6337 | The deflationary picture says believing a theory true is a trivial step after believing the theory [Horwich] |
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] |
6339 | Logical form is the aspects of meaning that determine logical entailments [Horwich] |
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] |
17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
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] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
8431 | Problems with Goodman's view of counterfactuals led to a radical approach from Stalnaker and Lewis [Horwich] |
9333 | A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich] |
9342 | Understanding needs a priori commitment [Horwich] |
9332 | Meaning is generated by a priori commitment to truth, not the other way around [Horwich] |
9341 | Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich] |
9334 | If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich] |
9339 | A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich] |
2799 | Bayes' theorem explains why very surprising predictions have a higher value as evidence [Horwich] |
2798 | Probability of H, given evidence E, is prob(H) x prob(E given H) / prob(E) [Horwich] |
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] |
6338 | We could know the truth-conditions of a foreign sentence without knowing its meaning [Horwich] |
6340 | There are Fregean de dicto propositions, and Russellian de re propositions, or a mixture [Horwich] |
6341 | Right translation is a mapping of languages which preserves basic patterns of usage [Horwich] |
1460 | Religious experience deserves the same respect as our other key experiences, and is best called 'holy' [Taylor,AE, by PG] |
8432 | Analyse counterfactuals using causation, not the other way around [Horwich] |