more on this theme
|
more from this thinker
Single Idea 10574
[filed under theme 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
]
Full Idea
What is the union of the singleton {0}, of zero, and the singleton {φ}, of the null set? Is it the one-element set {0}, or the two-element set {0, φ}? Unless the question of identity between 0 and φ is resolved, we cannot say.
Gist of Idea
Unless we know whether 0 is identical with the null set, we create confusions
Source
Kit Fine (Replies on 'Limits of Abstraction' [2005], 2)
Book Ref
-: 'Philosophical Studies' [-], p.388
The
14 ideas
from 'Replies on 'Limits of Abstraction''
|
10569
|
If you ask what F the second-order quantifier quantifies over, you treat it as first-order
[Fine,K]
|
|
10565
|
There is no stage at which we can take all the sets to have been generated
[Fine,K]
|
|
10564
|
We might combine the axioms of set theory with the axioms of mereology
[Fine,K]
|
|
10560
|
Set-theoretic imperialists think sets can represent every mathematical object
[Fine,K]
|
|
10563
|
A generative conception of abstracts proposes stages, based on concepts of previous 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]
|
|
10571
|
Concern for rigour can get in the way of understanding phenomena
[Fine,K]
|
|
10568
|
Logicists say mathematics can be derived from definitions, and can be known that way
[Fine,K]
|
|
10570
|
Assigning an entity to each predicate in semantics is largely a technical convenience
[Fine,K]
|
|
10573
|
Dedekind cuts lead to the bizarre idea that there are many different number 1's
[Fine,K]
|
|
10575
|
Why should a Dedekind cut correspond to a number?
[Fine,K]
|
|
10574
|
Unless we know whether 0 is identical with the null set, we create confusions
[Fine,K]
|