Combining Philosophers

Ideas for Dennis Whitcomb, Oliver,A/Smiley,T and Peter Koellner

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5 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics

14246

If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

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 / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

14247

Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]