Combining Philosophers
Ideas for Ion, Harr�,R./Madden,E.H. and Kurt Gdel
expand these ideas
|
start again
|
choose
another area for these philosophers
display all the ideas for this combination of philosophers
6 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10132
|
There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
15273
|
Points can be 'dense' by unending division, but must meet a tougher criterion to be 'continuous' [Harré/Madden]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
15274
|
Points are 'continuous' if any 'cut' point participates in both halves of the cut [Harré/Madden]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10046
|
The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
|
10868
|
The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
|
13517
|
If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
|