more on this theme
|
more from this thinker
Single Idea 15443
[filed under theme 18. Thought / E. Abstraction / 7. Abstracta by Equivalence
]
Full Idea
When mathematicians abstract one thing from others, they take an equivalence class. ....But it is only superficially a one; underneath, a class are still many.
Gist of Idea
Mathematicians abstract by equivalence classes, but that doesn't turn a many into one
Source
David Lewis (Against Structural Universals [1986], 'The pictorial')
Book Ref
Lewis,David: 'Papers in Metaphysics and Epistemology' [CUP 1999], p.93
A Reaction
This is Frege's approach to abstraction, and it is helpful to have it spelled out that this is a mathematical technique, even when applied by Frege to obtaining 'direction' from classes of parallels. Too much philosophy borrows inappropriate techniques.
The
17 ideas
from 'Against Structural Universals'
15433
|
Tropes are particular properties, which cannot recur, but can be exact duplicates
[Lewis]
|
15448
|
The 'magical' view of structural universals says they are atoms, even though they have parts
[Lewis]
|
15449
|
If 'methane' is an atomic structural universal, it has nothing to connect it to its carbon universals
[Lewis]
|
15439
|
The 'pictorial' view of structural universals says they are wholes made of universals as parts
[Lewis]
|
15441
|
The structural universal 'methane' needs the universal 'hydrogen' four times over
[Lewis]
|
15440
|
A whole is distinct from its parts, but is not a further addition in ontology
[Lewis]
|
15443
|
Mathematicians abstract by equivalence classes, but that doesn't turn a many into one
[Lewis]
|
15450
|
Maybe abstraction is just mereological subtraction
[Lewis]
|
15451
|
I assume there could be natural properties that are not instantiated in our world
[Lewis]
|
15445
|
Butane and Isobutane have the same atoms, but different structures
[Lewis]
|
15446
|
Composition is not just making new things from old; there are too many counterexamples
[Lewis]
|
15444
|
Different things (a toy house and toy car) can be made of the same parts at different times
[Lewis]
|
15434
|
Structural universals have a necessary connection to the universals forming its parts
[Lewis]
|
15437
|
We can't get rid of structural universals if there are no simple universals
[Lewis]
|
15435
|
If you think universals are immanent, you must believe them to be sparse, and not every related predicate
[Lewis]
|
15436
|
Universals are meant to give an account of resemblance
[Lewis]
|
15438
|
We can add a primitive natural/unnatural distinction to class nominalism
[Lewis]
|