Combining Philosophers
Ideas for Rescher,N/Oppenheim,P, John Mayberry and Jrgen Habermas
expand these ideas
|
start again
|
choose
another area for these philosophers
display all the ideas for this combination of philosophers
14 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
|
17784
|
Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry]
|
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / b. Quantity
|
17782
|
Greek quantities were concrete, and ratio and proportion were their science [Mayberry]
|
|
17781
|
Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
|
17799
|
Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry]
|
|
17797
|
Cantor extended the finite (rather than 'taming the infinite') [Mayberry]
|
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
|
17775
|
If proof and definition are central, then mathematics needs and possesses foundations [Mayberry]
|
|
17776
|
The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry]
|
|
17777
|
Foundations need concepts, definition rules, premises, and proof rules [Mayberry]
|
|
17804
|
Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry]
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
|
17792
|
1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry]
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
|
17793
|
It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry]
|
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
|
17794
|
Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry]
|
|
17802
|
We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry]
|
|
17805
|
Set theory is not just another axiomatised part of mathematics [Mayberry]
|