Combining Texts
Ideas for
'fragments/reports', 'What Required for Foundation for Maths?' and 'Lectures on the Philosophy of (World) History'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
9 ideas
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]
|