more from this thinker     |     more from this text


Single Idea 9142

[filed under theme 18. Thought / E. Abstraction / 7. Abstracta by Equivalence ]

Full Idea

Fine considers abstraction principles as instances of reconceptualization (rather than implicit definition, or using the Context Principle). This centres not on reference, but on new senses emerging from analysis of a given sense.

Gist of Idea

Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses

Source

report of Kit Fine (The Limits of Abstraction [2002], 035) by R Cook / P Ebert - Notice of Fine's 'Limits of Abstraction' 2

Book Ref

-: 'British Soc for the Philosophy of Science' [-], p.793


A Reaction

Fine develops an argument against this view, because (roughly) the procedure does not end in a unique result. Intuitively, the idea that abstraction is 'reconceptualization' sounds quite promising to me.


The 40 ideas with the same theme [defining abstraction by the principle of equivalence]:

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