Ideas from 'Frege versus Cantor and Dedekind' by William W. Tait [1996], by Theme Structure
[found in 'Philosophy of Mathematics: anthology' (ed/tr Jacquette,Dale) [Blackwell 2002,0-631-21870-x]].
green numbers give full details |
back to texts
|
expand these ideas
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
9978
|
Analytic philosophy focuses too much on forms of expression, instead of what is actually said
|
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
9986
|
The null set was doubted, because numbering seemed to require 'units'
|
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
9984
|
We can have a series with identical members
|
18. Thought / E. Abstraction / 2. Abstracta by Selection
9981
|
Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete
|
9982
|
Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs
|
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
9985
|
Abstraction may concern the individuation of the set itself, not its elements
|
18. Thought / E. Abstraction / 8. Abstractionism Critique
9972
|
Why should abstraction from two equipollent sets lead to the same set of 'pure units'?
|
9980
|
If abstraction produces power sets, their identity should imply identity of the originals
|