Combining Texts
Ideas for
'On the Question of Absolute Undecidability', 'Paradoxes of the Infinite' and 'The Philosophy of Logic'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
7 ideas
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10856
|
A truly infinite quantity does not need to be a variable [Bolzano]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
18200
|
Very large sets should be studied in an 'if-then' spirit [Putnam]
|
17890
|
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887
|
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891
|
Arithmetical undecidability is always settled at the next stage up [Koellner]
|
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
18199
|
Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam]
|
8857
|
We must quantify over numbers for science; but that commits us to their existence [Putnam]
|