61 ideas
6979 | Serious metaphysics cares about entailment between sentences [Jackson] |
6983 | Intuitions about possibilities are basic to conceptual analysis [Jackson] |
6980 | Conceptual analysis studies whether one story is made true by another story [Jackson] |
14707 | Conceptual analysis is needed to establish that metaphysical reductions respect original meanings [Jackson, by Schroeter] |
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
7005 | Something can only have a place in a preferred account of things if it is entailed by the account [Jackson] |
6994 | Truth supervenes on being [Jackson] |
10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
13030 | Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen] |
13032 | Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen] |
13033 | Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen] |
22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
13037 | Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen] |
13038 | Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen] |
13034 | Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen] |
13039 | Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen] |
13036 | Choice: ∀A ∃R (R well-orders A) [Kunen] |
13029 | Set Existence: ∃x (x = x) [Kunen] |
13031 | Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen] |
13040 | Constructibility: V = L (all sets are constructible) [Kunen] |
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] |
6984 | Smooth reductions preserve high-level laws in the lower level [Jackson] |
6978 | Baldness is just hair distribution, but the former is indeterminate, unlike the latter [Jackson] |
6993 | Redness is a property, but only as a presentation to normal humans [Jackson] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
6987 | We should not multiply senses of necessity beyond necessity [Jackson] |
6988 | Mathematical sentences are a problem in a possible-worlds framework [Jackson] |
6975 | Possible worlds could be concrete, abstract, universals, sentences, or properties [Jackson] |
6982 | Long arithmetic calculations show the a priori can be fallible [Jackson] |
6991 | We examine objects to determine colour; we do not introspect [Jackson] |
6976 | In physicalism, the psychological depends on the physical, not the other way around [Jackson] |
6986 | Is the dependence of the psychological on the physical a priori or a posteriori? [Jackson] |
6992 | If different states can fulfil the same role, the converse must also be possible [Jackson] |
6996 | Folk psychology covers input, internal role, and output [Jackson] |
6977 | Egocentric or de se content seems to be irreducibly so [Jackson] |
6990 | Keep distinct the essential properties of water, and application conditions for the word 'water' [Jackson] |
6985 | Analysis is finding necessary and sufficient conditions by studying possible cases [Jackson] |
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] |
6995 | Successful predication supervenes on nature [Jackson] |
6989 | I can understand "He has a beard", without identifying 'he', and hence the truth conditions [Jackson] |
6998 | Folk morality does not clearly distinguish between doing and allowing [Jackson] |
6997 | Moral functionalism says moral terms get their meaning from their role in folk morality [Jackson] |
7000 | Which are prior - thin concepts like right, good, ought; or thick concepts like kindness, equity etc.? [Jackson] |
6999 | It is hard to justify the huge difference in our judgements of abortion and infanticide [Jackson] |