9855 | Frege's logical abstaction identifies a common feature as the maximal set of equivalent objects [Frege, by Dummett] |
10525 | Frege put the idea of abstraction on a rigorous footing [Frege, by Fine,K] |
10526 | Fregean abstraction creates concepts which are equivalences between initial items [Frege, by Fine,K] |
10556 | We create new abstract concepts by carving up the content in a different way [Frege] |
9882 | You can't simultaneously fix the truth-conditions of a sentence and the domain of its variables [Dummett on Frege] |
9881 | From basing 'parallel' on identity of direction, Frege got all abstractions from identity statements [Frege, by Dummett] |
10583 | Abstraction principles identify a common property, which is some third term with the right relation [Russell] |
10582 | The principle of Abstraction says a symmetrical, transitive relation analyses into an identity [Russell] |
10584 | A certain type of property occurs if and only if there is an equivalence relation [Russell] |
10549 | Since abstract objects cannot be picked out, we must rely on identity statements [Dummett] |
9857 | We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett] |
8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
8907 | The abstract direction of a line is the equivalence class of it and all lines parallel to it [Lewis] |
8908 | For most sets, the concept of equivalence is too artificial to explain abstraction [Lewis] |
15443 | Mathematicians abstract by equivalence classes, but that doesn't turn a many into one [Lewis] |
13898 | If we can establish directions from lines and parallelism, we were already committed to directions [Wright,C] |
10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
8786 | One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright] |
12227 | Abstractionism needs existential commitment and uniform truth-conditions [Hale/Wright] |
12228 | Equivalence abstraction refers to objects otherwise beyond our grasp [Hale/Wright] |
10802 | Frege's 'parallel' and 'direction' don't have the same content, as we grasp 'parallel' first [Yablo] |
10805 | A sentence should be recarved to reveal its content or implication relations [Yablo] |
9993 | There is no reason why abstraction by equivalence classes should be called 'logical' [Tait] |
9985 | Abstraction may concern the individuation of the set itself, not its elements [Tait] |
9142 | Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Fine,K, by Cook/Ebert] |
10135 | We can abstract from concepts (e.g. to number) and from objects (e.g. to direction) [Fine,K] |
10137 | Abstractionism can be regarded as an alternative to set theory [Fine,K] |
10138 | An object is the abstract of a concept with respect to a relation on concepts [Fine,K] |
10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |
10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
10567 | We can create objects from conditions, rather than from concepts [Fine,K] |
10231 | Abstract objects might come by abstraction over an equivalence class of base entities [Shapiro] |
9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
8306 | You can think of a direction without a line, but a direction existing with no lines is inconceivable [Lowe] |
8918 | Functional terms can pick out abstractions by asserting an equivalence relation [Rosen] |
8919 | Abstraction by equivalence relationships might prove that a train is an abstract entity [Rosen] |
18883 | Any equivalence relation among similar things allows the creation of an abstractum [Simons] |
18884 | Abstraction is usually seen as producing universals and numbers, but it can do more [Simons] |
9141 | Abstraction theories build mathematics out of second-order equivalence principles [Cook/Ebert] |