56 ideas
7950 | Philosophy tries to explain how the actual is possible, given that it seems impossible [Macdonald,C] |
7923 | 'Did it for the sake of x' doesn't involve a sake, so how can ontological commitments be inferred? [Macdonald,C] |
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
7933 | Don't assume that a thing has all the properties of its parts [Macdonald,C] |
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] |
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] |
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] |
7944 | Reduce by bridge laws (plus property identities?), by elimination, or by reducing talk [Macdonald,C] |
7938 | Relational properties are clearly not essential to substances [Macdonald,C] |
7967 | Being taller is an external relation, but properties and substances have internal relations [Macdonald,C] |
7965 | Does the knowledge of each property require an infinity of accompanying knowledge? [Macdonald,C] |
7934 | Tropes are abstract (two can occupy the same place), but not universals (they have locations) [Macdonald,C] |
7958 | Properties are sets of exactly resembling property-particulars [Macdonald,C] |
7972 | Tropes are abstract particulars, not concrete particulars, so the theory is not nominalist [Macdonald,C] |
7959 | How do a group of resembling tropes all resemble one another in the same way? [Macdonald,C] |
7960 | Trope Nominalism is the only nominalism to introduce new entities, inviting Ockham's Razor [Macdonald,C] |
7951 | Numerical sameness is explained by theories of identity, but what explains qualitative identity? [Macdonald,C] |
7964 | How can universals connect instances, if they are nothing like them? [Macdonald,C] |
7971 | Real Nominalism is only committed to concrete particulars, word-tokens, and (possibly) sets [Macdonald,C] |
7955 | Resemblance Nominalism cannot explain either new resemblances, or absence of resemblances [Macdonald,C] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
7961 | A 'thing' cannot be in two places at once, and two things cannot be in the same place at once [Macdonald,C] |
7926 | We 'individuate' kinds of object, and 'identify' particular specimens [Macdonald,C] |
7936 | Unlike bundles of properties, substances have an intrinsic unity [Macdonald,C] |
7930 | The bundle theory of substance implies the identity of indiscernibles [Macdonald,C] |
7932 | A phenomenalist cannot distinguish substance from attribute, so must accept the bundle view [Macdonald,C] |
7937 | When we ascribe a property to a substance, the bundle theory will make that a tautology [Macdonald,C] |
7939 | Substances persist through change, but the bundle theory says they can't [Macdonald,C] |
7940 | A substance might be a sequence of bundles, rather than a single bundle [Macdonald,C] |
7948 | A statue and its matter have different persistence conditions, so they are not identical [Macdonald,C] |
7929 | A substance is either a bundle of properties, or a bare substratum, or an essence [Macdonald,C] |
7941 | Each substance contains a non-property, which is its substratum or bare particular [Macdonald,C] |
7942 | The substratum theory explains the unity of substances, and their survival through change [Macdonald,C] |
7943 | A substratum has the quality of being bare, and they are useless because indiscernible [Macdonald,C] |
7927 | At different times Leibniz articulated three different versions of his so-called Law [Macdonald,C] |
7928 | The Identity of Indiscernibles is false, because it is not necessarily true [Macdonald,C] |
7947 | In continuity, what matters is not just the beginning and end states, but the process itself [Macdonald,C] |
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] |
7907 | Human killing is worse if the victim is virtuous [Buddhaghosa] |