Jane Frances McDonnell

Jane Frances McDonnell is a philosopher who focuses on the philosophy of mathematics and physics. She obtained her doctorate from Monash University in Victoria, Australia.

The Pythagorean World (2016)



 * 1. Mathematics is about the structure of Being.
 * p. 206
 * 2. Mathematics is necessary and true.
 * p. 206
 * 3. Mathematical objects do not exist in a mysterious Platonic heaven totally independent of the physical world. Rather, physical reality is a mental interpretation of a subset of mathematical structure.
 * p. 206
 * 4. Human mathematics is the cultural product of a community of rational beings.
 * p. 206
 * 5. We come to know about mathematics by abstracting structure from the world around us and focusing on the structure of Being mirrored in us.
 * p. 207
 * 6. Mathematics is applicable because it truly describes the fundamental structure of reality.
 * p. 210
 * 7. There are rational beings with mental powers surpassing those of humans who have a deeper insight into mathematics than we do.
 * p. 210
 * 8. Model theory provides the correct picture of how mathematical languages describe mathematical reality.
 * p. 211
 * 9. No mathematics is surplus.
 * p. 211
 * 10. There is one, true mathematics.
 * p. 217
 * 11. There are no absolutely undecidable propositions in mathematics.
 * p. 217
 * 12. Some human mathematics is fiction.
 * p. 217
 * 13. The universe of sets V cannot be Gödel’s L; it must be something like Woodin’s Ultimate L which contains all possible large cardinals and has the semantic resources to witness them.
 * p. 219